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https://infocenter-archive.sybase.com/help/topic/com.sybase.dc33621_33620_33619_1250/html/ptallbk/X17690.htm	[ "subq\n\nDescription\n\nIdentifies a subquery.\n\nSyntax\n\n( subq subquery_id\n)\n\nParameters\n\nsubquery_id\n\nis an integer identifying the subquery. In abstract plans, subquery numbering is based on the order of the leading parenthesis for the subqueries in a query.\n\nExamples\n\nExample 1\n\nselect c11 from t1\nwhere c12 =\n(select c21 from t2 where c22 = t1.c11)\n\n( nested\n( t_scan t1 )\n( subq 1\n( t_scan ( table t2 ( in ( subq 1 ) ) ) )\n)\n)\n\nA single nested subquery.\n\nExample 2\n\nselect c11 from t1\nwhere c12 =\n(select c21 from t2 where c22 = t1.c11)\nand c12 =\n(select c31 from t3 where c32 = t1.c11)\n\n( nested\n( nested\n( t_scan t1 )\n( subq 1\n( t_scan ( table t2 ( in ( subq 1 ) ) ) )\n)\n)\n( subq 2\n( t_scan ( table t3 ( in ( subq 2 ) ) ) )\n)\n)\n\nThe two subqueries are both nested in the main query.\n\nExample 3\n\nselect c11 from t1\nwhere c12 =\n(select c21 from t2 where c22 =\n(select c31 from t3 where c32 = t1.c11))\n\n( nested\n( t_scan t1 )\n( subq 1\n( nested\n( t_scan ( table t2 ( in ( subq 1 ) ) ) )\n( subq 2\n( t_scan ( table t3 ( in ( subq 2 ) ) ) )\n)\n)\n)\n)\n\nA level 2 subquery nested into a level 1 subquery nested in the main query.\n\nUsage\n\n• The subq operator has two meanings in an abstract plan expression:\n\n• Under a nested operator, it describes the attachment of a nested subquery to a table\n\n• Under an in operator, it describes the nesting of the base tables and views that the subquery contains\n\n• To specify the attachment of a subquery without providing a plan specification, use an empty hint:\n\n( nested\n( t_scan t1)\n( subq 1\n()\n)\n\n)\n\n• To provide a description of the abstract plan for a subquery, without specifying its attachment, specify an empty hint as the derived table in the nested operator:\n\n( nested\n()\n( subq 1\n(t_scan ( table t1 ( in ( subq 1 ) ) ) )\n)\n)\n\n• When subqueries are flattened to a join, the only reference to the subquery in the abstract plan is the identification of the table specified in the subquery:\n\nselect \nfrom t2\nwhere c21 in (select c12 from t1)\n\n( nl_g_join\n( t_scan t1 )\n( t_scan ( table t2 ( in ( subq 1 ) ) ) )\n\n• When a subquery is materialized, the subquery appears in the store operation, identifying the table to be scanned during the materialization step:\n\nselect \nfrom t1\nwhere c11 in (select max(c22) from t2 group by c21)\n\n( plan\n( store Worktab1\n( t_scan ( table t2 ( in ( subq 1 ) ) ) )\n)\n( nl_g_join\n( t_scan t1 )\n( t_scan ( work_t Worktab1 ) )\n)\n)" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8266944,"math_prob":0.9102565,"size":2278,"snap":"2022-05-2022-21","text_gpt3_token_len":674,"char_repetition_ratio":0.22559367,"word_repetition_ratio":0.3824131,"special_character_ratio":0.34591746,"punctuation_ratio":0.065656565,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98558646,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-26T18:08:13Z\",\"WARC-Record-ID\":\"<urn:uuid:a355362a-6435-4767-90f0-059d512e1799>\",\"Content-Length\":\"5334\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:af8fe8f4-bc2a-40c9-b6e6-7d7bc2cdd0e8>\",\"WARC-Concurrent-To\":\"<urn:uuid:08e6535d-129d-40f4-ae5b-8d53321e4ad8>\",\"WARC-IP-Address\":\"20.82.47.20\",\"WARC-Target-URI\":\"https://infocenter-archive.sybase.com/help/topic/com.sybase.dc33621_33620_33619_1250/html/ptallbk/X17690.htm\",\"WARC-Payload-Digest\":\"sha1:LDKEC63TEPOUPIT6POKYZ3AYXWQRG77T\",\"WARC-Block-Digest\":\"sha1:ZT4ZNVFDPHAZAZ2ZA2URQW6QH4L4WAMX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320304959.80_warc_CC-MAIN-20220126162115-20220126192115-00172.warc.gz\"}"}
https://www.physicsoverflow.org/1024/heisenberg-uncertainty-principle-scientific-prove?show=3446	[ "#", null, "Heisenberg Uncertainty Principle scientific prove\n\n+ 0 like - 2 dislike\n198 views\n\nHeisenberg's uncertainty principle states that: if the x-component of the momentum of a particle is measured with an uncertainty $$\\Delta \\vec p_x$$ then its x-position cannot, at same time, be measured more accurately than $$\\Delta\\vec x=\\frac {\\hbar}{2\\Delta\\vec p_x }$$ $$\\Delta\\vec x\\Delta\\vec p_x \\ge \\frac {\\hbar}{2}$$ what is scientific prove of this principle?\n\nThis post has been migrated from (A51.SE)\nClosed as per community consensus as the post is High school level question; too low-level for PhysicsOverflow\nasked Apr 20, 2012\nrecategorized Apr 22, 2014\nThis is a standard textbook question, so I am moving it to physics.SE. Moreover, when refer to a component of a vector then you drop the arrow.\n\nThis post has been migrated from (A51.SE)\n\n## 1 Answer\n\n+ 0 like - 0 dislike\n\nThis is, as mentioned by Piotr Migdal, in the comments, standard textbook material.\n\nIn Matrix Mechanics, observables like position and momentum are promoted to operators. Obviously, multiplication of operators need not commute. Specifically, the difference is given by the commutator bracket:\n\n$\\left[ X, P\\right] = XP-PX=i\\hbar I$\n\nwhere I is the identity matrix.\n\nTherefore, there have to be uncertainties (standard deviation after taking an infinite number of measurements) in X and P and it should be intuitive that:\n\n${\\sigma _x}{\\sigma _p} \\ge k\\hbar$\n\nFor some scalar (constant) value of k. So far, everything applies to any pair of such dynamical variables, like position and momentum. It happens to be, however, that specifically for position and momentum, k is $\\frac12$. This can be derived from special cases, c.f. Feynman, Hibbs and Styer, who derive this in the first chapter through special cases.\n\nOne may also derive it through the wave interpretation, through Fourier transforms, and stuff; see Wikipedia.\n\nanswered Feb 22, 2014 by (1,975 points)" ]	[ null, "https://www.physicsoverflow.org/qa-plugin/po-printer-friendly/print_on.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8972796,"math_prob":0.9622873,"size":1027,"snap":"2021-04-2021-17","text_gpt3_token_len":236,"char_repetition_ratio":0.09481916,"word_repetition_ratio":0.0,"special_character_ratio":0.22297955,"punctuation_ratio":0.16410257,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9982885,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-11T07:24:45Z\",\"WARC-Record-ID\":\"<urn:uuid:b8bead2a-1f08-41ad-aab9-9b420fb7a209>\",\"Content-Length\":\"109203\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:32951587-702b-471e-aefe-4d87ae55b312>\",\"WARC-Concurrent-To\":\"<urn:uuid:37fa6478-e448-457b-bc1c-d889fa0148bf>\",\"WARC-IP-Address\":\"129.70.43.86\",\"WARC-Target-URI\":\"https://www.physicsoverflow.org/1024/heisenberg-uncertainty-principle-scientific-prove?show=3446\",\"WARC-Payload-Digest\":\"sha1:SK3756EATHCNLLNLDGOCICAHT4UXZ76C\",\"WARC-Block-Digest\":\"sha1:LKQRIK5LITVTLLSVXJQPJC5CORYGOHFP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038061562.11_warc_CC-MAIN-20210411055903-20210411085903-00154.warc.gz\"}"}
http://trevorius.com/scrapbook/blog/page/3/	[ "# Python dependency graph\n\nBeware, code heavy post\nNode graphs are a great way to express relationships and logical flow between objects, both for code design and 3D scenes. Where a tree can only express single parent-child relationships, a node graph can show a hierarchy and then display how one object has a look-at logic to look at another object entirely.", null, "This can be done for almost any type of data, and a dependency graph is an evaluation model that tries to evaluate as little of the graph as possible. An evaluation model is the way our code traverses the graph’s data to compute the end result.\n\nA dependency graph works by lazily computing data and by storing the “dirty” state of each attribute (dirty meaning something has been changed since the last calculation of this attribute). I’ll try to illustrate with this animation of 2 colors being mixed. When an input changes it propagates that change by “dirtying” all downstream dependencies (red).\n\nWhen a value is requested, input wires are followed and for outputs the node is computed (yellow), but only if the attribute is “dirty”, else we just use the cached state (green).\n\n### So to sum it up in a few simple rules:\n\nTo keep it simple I’ll say “if an input on a node changes all its outputs are dirty”, which means nodes should be quite granular as having inputs that only change part of the outputs will waste computation.\n\nAlso any connection going out of an attribute (whether it is an input feeding another input directly or an output feeding another input) will dirty all targets. These 2 simple rules result in recursive dirtying of all the right inputs and outputs throughout the graph.\n\nWhen a value is requested its cached value is returned unless it’s “dirty“ in which case (for outputs) the node will be computed or (for inputs) the other side of the connection will be queried, which results in this rule applying recursively and the minimal graph being computed to get the right value in the end.\n\n### Coding it\n\nNow with that theory out of the way, I’ve written some python to do exactly this. First let’s take a look at the initial data structure. A plug must understand connections, ownership, dirty-state and retain an internal value (e.g. the result of computing an output, or just a constant value for an input that is not connected to anything).\n\n```class Plug(object):\ndef __init__(self, name, node, isComputed):\nself.__name = name # really used for debugging only\nself.__node = node # the parent node this plug belongs to\nself.__isComputed = isComputed # make this an output-plug\nself.__isDirty = isComputed # upstream dependencies changed? computed plug always have dependencies on creation\nself.__cache = None # last computed value for outputs, user set value for inputs\nself.__sources = [] # plugs we depend on\nself.__targets = [] # plugs we feed into\n\ndef clean(self):\nself.__isDirty = False\n\nclass DependNode(object):\ndef __init__(self, computeFunc=None):\nself.__plugs = OrderedDict() # list of node plugs, dict key should match plug name\nself._computeFunc = computeFunc # logic implementation, should be a callable that accepts this DependNode instance as only argument\n\ndef compute(self):\n# call compute function if node has logic\nif self._computeFunc is not None:\nself._computeFunc(self)\n\n# clean all plugs\nfor plug in self.__plugs.itervalues():\nplug.clean()\n\nself.__plugs[name] = Plug(name, self, isComputed=False)\n\nself.__plugs[name] = Plug(name, self, isComputed=True)\n```\n\nThis template allows us to set up a basic node with inputs and outputs and to provide a custom function to calculate this node’s outputs.\n\n```const = DependNode()\n```\n\nThe next step is to allow setting a value to a specific plug. To do this, I’ll use some meta-programming to make the resulting code more readable. Implementing __getattr__ and __setattr__ on the DependNode as well as value() and setValue() on the plug to alter the Plug.__cache:\n\n```# Added to the end of the Plug class:\ndef value(self):\nreturn self.__cache\n\ndef setValue(self, value):\nself.__cache = value\n\n# Added to the end of the DependNode class:\ndef __getattr__(self, name):\nreturn self.__plugs[name].value()\n\ndef __setattr__(self, name, value):\nif name not in ('_DependNode__plugs', '_DependNode__computeFunc'): # To enable setting attrs in __init__ we must revert to default behaviour for those atrtibute names, notice how mangled names are required for private attributes.\nreturn self.__plugs[name].setValue(value)\nreturn super(DependNode, self).__setattr__(name, value)\n```\n\nNow we can do this and see the internal state reflected properly:\n\n```const.value = 2.0\n```\n\nThe next step I suppose is to create a simple “add” node which sums up its inputs. To do this we’ll have to add connections. I’ll implement this on the Plug class, where a plugs sources and targets are managed implicitly:\n\n``` def addSource(self, sourcePlug):\nif sourcePlug not in self.__sources:\nself.__sources.append(sourcePlug)\nsourcePlug.__targets.append(self)\n\ndef removeSource(self, sourcePlug):\nif sourcePlug in self.__sources:\nself.__sources.remove(sourcePlug)\nsourcePlug.__targets.remove(self)\n```\n\nThe next step is to start implementing some of our rules. First rule we need is: compute when we are dirty. This I do in Plug.value().\n\n``` def value(self):\nif self.__isDirty:\n# we are going to get clean, set clean beforehand so the compute function can get other plug values without recursively triggering compute again.\nself.__isDirty = False\n# compute dirty output\nif self.__isComputed:\nself.__node.compute()\n# fetch dirty input connection\nelif self.__sources:\nself.__cache = [source.value() for source in self.__sources]\n# plug is clean now\nself.clean()\n# return internal state\nreturn self.__cache\n```\n\nSo now outputs are computed, inputs return their sources, all this is cached on the plug so it only computes when dirty is true.\nThe next step is to actually set and propagate the dirty state. So whenever we set a value, set a source, or a plug gets dirtied: all outgoing connections are dirtied. When the dirty happens to an input, the node’s outputs are dirtied. See the _dirty implementation below for the Plug class. The setValue and add- removeSource functions just get a _dirty call in the end.\n\n```# modifications to Plug\ndef setValue(self, value):\nself.__cache = value\nself._dirty()\n\nif sourcePlug not in self.__sources:\nself.__sources.append(sourcePlug)\nsourcePlug.__targets.append(self)\nself._dirty()\n\ndef removeSource(self, sourcePlug):\nif sourcePlug in self.__sources:\nself.__sources.remove(sourcePlug)\nsourcePlug.__targets.remove(self)\nself._dirty()\n\ndef _isComputed(self):\nreturn self.__isComputed\n\ndef _dirty(self):\nif self.__isDirty:\nreturn\nself.__isDirty = True\n\n# dirty plugs that are computed based on this plug\nif not self.__isComputed:\nfor plug in self.__node.iterPlugs():\nif plug._isComputed():\nplug._dirty()\n\n# dirty plugs that use this plug as source\nfor plug in self.__targets:\nplug._dirty()\n\n# the DependNode class also gets this iterPlugs implementation\ndef iterPlugs(self):\nreturn self.__plugs.itervalues()\n```\n\nWhew, now after all that we should be able to run this test to add 2 and 4 together using 3 nodes:\n\n```const = DependNode()\nconst.value = 2.0\n\nconst2 = DependNode()\nconst2.value = 4.0\n\nnode.output = sum(node.inputs)\n\n```\n\nHere is a slightly more interesting example of a pointOnCurve node that computes a point on a bezier segment and feeds it to a different node:\n\n```def pointOnCurve(node):\n# interpolate a 2D bezier segment with t=node.parameter\ncvs = node.cvs2\nt = node.parameter\nr = [0, 0]\nfor i in xrange(2):\na, b, c = cvs[i] - cvs[i], cvs[i] - cvs[i], cvs[i] - cvs[i]\nd = b - a\na, b, c, d = c - b - d, d + d + d, a + a + a, cvs[i]\nr[i] = (t * (t * (t * a + b) + c) + d)\nnode.point = tuple(r)\n\ntimeNode = DependNode()\ntimeNode.time = 0.0\n\ncurveNode = DependNode()\ncurveNode.cvs = ((0.0, 0.0), (0.2, 0.0), (0.0, 0.2), (0.2, 0.2))\n\npointOnCurveNode = DependNode(pointOnCurve)\n\ntransform = DependNode()\n\nprint transform.translate\ntimeNode.time = 0.5\nprint transform.translate\n```\n\nNow there are 2 more improvements I want to add. First whenever a plug has sources, there is no real need to cache the result. We can just directly read from the sources and save ourselves a bunch of copying. Second I want to be able to alter an input plug temporarily. Imagine an interface with a point moving over time, it may be nice to alter that point by hand to e.g. feed that back in some animation system. In this case it is important for us to set the translate of a transform without it jumping back to the source time as soon as we redraw (which would read the translate attribute).\n\nFirst I edit Plug.value() to use the cache only for computed data.\nNow that __cache is freed up I plan to use it for the user-override. So if a cache is available I want to use it at all times.\nNext I return sources if available, else cache again which should in this case be computed.\n\nNext in Plug._dirty() I only dirty computed plugs, and I set the cache to None if the plug as sources coming in. This will result in a small problem with Plug.setValue: it currently caches the value and then dirties the plug. That means that on input plugs the cache is set to None immediately. I just swap those 2 lines so my setValue sticks, and the user override also works.\n\n``` def value(self):\nif self.__isDirty and self.__isComputed:\n# compute dirty output\nif self.__isComputed:\nself.__node.compute()\n# plug is clean now\nself.clean()\n\n# override cache for input attributes to intervene with connections?\nif self.__cache is not None:\nreturn self.__cache\n\n# fetch input connection\nif self.__sources:\nreturn [source.value() for source in self.__sources]\n\nreturn self.__cache\n\ndef _dirty(self):\nif self.__isComputed:\n# don't dirty again\nif self.__isDirty:\nreturn\nself.__isDirty = True\nif self.__sources:\nself.__cache = None\n\n# dirty plugs that are computed based on this plug\nif not self.__isComputed:\nfor plug in self.__node.iterPlugs():\nif plug._isComputed():\nplug._dirty()\n\n# dirty plugs that use this plug as source\nfor plug in self.__targets:\nplug._dirty()\n\ndef setValue(self, value):\nself._dirty()\nself.__cache = value\n```\n\nUsing the previous example I can now see how overriding the parameter works until time is changed again making it use the source connection again:\n\n```print transform.translate\ntimeNode.time = 0.5\nprint transform.translate\npointOnCurveNode.parameter = 0.25\nprint transform.translate\ntimeNode.time = 0.5\nprint transform.translate\n```\n\nFull code:\n\n```from collections import OrderedDict\n\nclass Plug(object):\ndef __init__(self, name, node, isComputed):\nself.__name = name # really used for debugging only\nself.__node = node # the parent node this plug belongs to\nself.__isComputed = isComputed # make this an output-plug\nself.__isDirty = isComputed # upstream dependencies changed?\nself.__cache = None # last computed value for outputs, user set value for inputs\nself.__sources = [] # plugs we depend on\nself.__targets = [] # plugs we feed into\n\ndef clean(self):\nself.__isDirty = False\n\ndef value(self):\nif self.__isDirty and self.__isComputed:\n# compute dirty output\nif self.__isComputed:\nself.__node.compute()\n# plug is clean now\nself.clean()\n\n# override cache for input attributes to intervene with connections?\nif self.__cache is not None:\nreturn self.__cache\n\n# fetch input connection\nif self.__sources:\nreturn [source.value() for source in self.__sources]\n\nreturn self.__cache\n\ndef setValue(self, value):\nself._dirty()\nself.__cache = value\n\nif sourcePlug not in self.__sources:\nself.__sources.append(sourcePlug)\nsourcePlug.__targets.append(self)\nself._dirty()\n\ndef removeSource(self, sourcePlug):\nif sourcePlug in self.__sources:\nself.__sources.remove(sourcePlug)\nsourcePlug.__targets.remove(self)\nself._dirty()\n\ndef _isComputed(self):\nreturn self.__isComputed\n\ndef _dirty(self):\nif self.__isComputed:\n# don't dirty again\nif self.__isDirty:\nreturn\nself.__isDirty = True\nif self.__sources:\nself.__cache = None\n\n# dirty plugs that are computed based on this plug\nif not self.__isComputed:\nfor plug in self.__node.iterPlugs():\nif plug._isComputed():\nplug._dirty()\n\n# dirty plugs that use this plug as source\nfor plug in self.__targets:\nplug._dirty()\n\nclass DependNode(object):\ndef __init__(self, computeFunc=None):\nself.__plugs = OrderedDict() # list of node plugs, dict key should match plug name\nself.__computeFunc = computeFunc # logic implementation, should be a callable that accepts this DependNode instance as only argument\n\ndef iterPlugs(self):\nreturn self.__plugs.itervalues()\n\ndef compute(self):\n# call compute function if node has logic\nif self.__computeFunc is not None:\nself.__computeFunc(self)\n\n# clean all plugs\nfor plug in self.__plugs.itervalues():\nplug.clean()\n\nself.__plugs[name] = Plug(name, self, isComputed=False)\n\nself.__plugs[name] = Plug(name, self, isComputed=True)\n\ndef plug(self, name):\nreturn self.__plugs[name]\n\ndef __getattr__(self, name):\nreturn self.__plugs[name].value()\n\ndef __setattr__(self, name, value):\nif name not in ('_DependNode__plugs', '_DependNode__computeFunc'):\nreturn self.__plugs[name].setValue(value)\nreturn super(DependNode, self).__setattr__(name, value)\n\ndef pointOnCurve(node):\nprint 'compute'\n# interpolate a 2D bezier segment with t=node.parameter\ncvs = node.cvs2\nt = node.parameter\nr = [0, 0]\nfor i in xrange(2):\na, b, c = cvs[i] - cvs[i], cvs[i] - cvs[i], cvs[i] - cvs[i]\nd = b - a\na, b, c, d = c - b - d, d + d + d, a + a + a, cvs[i]\nr[i] = (t * (t * (t * a + b) + c) + d)\nnode.point = tuple(r)\n```\n\nNow I’ve also been working on sort of an entity-component based system on top of this graph, based on the PyOpenGL mesh renderer from a few posts back.\n\nIt allows me to create a scene graph based on Transforms and exported logic (using DependNodes like above) but also logical relationships which are not necessarily customizable, e.g. when rendering a camera I can query it’s entity, whose transform will provide the view matrix, without connecting these things. This creates a more classical (and less customizable) framework for render logic, but gives full control over the scene logic behind it through the dependency graph.\n\nUsing the point on curve example above and feeding it to a cube’s transform – while also implementing a timeline UI & 3D gizmo drawing – this fun thing came out:", null, "Now the next steps would probably involve adding shader support, file watchers and creating a more elaborate Maya exporter that supports various Maya nodes (Maya is also dependency graph based so it fits very well with this!) but I’m not sure if I’m going to keep working on this.\n\n# Improving a renderer", null, "This feeds into my previous write up on the tools developed for our 64kb endeavours.\n\nAfter creating Eidolon [Video] we were left with the feeling that the rendering can be a lot better. We had this single pass bloom and simple lambert & phong shading, no anti aliasing and very poor performing depth of field. Last the performance hit for reflections was through the roof as well.\n\nI started almost immediately with a bunch of improvements, most of this work was done within a month after Revision. Which shows in our newest demo Yermom [Video]. I’ll go over the improvements in chronological order and credit any sources used (of which there were a lot), if I managed to document that right…\n\nSomething useful to mention, all my buffers are Float32 RGBA.\n\n## Low-resolution reflections:\n\nBasically the scene is raymarched, for every pixel there is a TraceAndShade call to render the pixel excluding fog and reflection.\nFrom the result we do another TraceAndShade for the reflection. This makes the entire thing twice as slow when reflections are on.\nInstead I early out at this point if:\n`if(reflectivity == 0 \|\| gl_FragCoord.x % 4 != 0 \|\| gl_FragCoord.y % 4 != 0) return;`\nThat results in only 1 in 16 pixels being reflective. So instead of compositing the reflection directly I write it to a separate buffer.\nThen in a future pass I composite the 2 buffers, where I just do a look up in the reflection buffer like so:\n`texelFetch(uImages, ivec2(gl_FragCoord.xy)) + texelFetch(uImages, ivec2(gl_FragCoord.xy / 4) * 4)`\nIn my real scenario I removed that `* 4` and render to a 4 times smaller buffer instead, so reading it back results in free interpolation.\nI still have glitches when blurring the reflections too much & around edges in general. Definitely still room for future improvement.", null, "## Oren Nayar diffuse light response\n\nThe original paper and this image especially convinced me into liking this shading model for diffuse objects.", null, "So I tried to implement that, failed a few times, got pretty close, found an accurate implementation, realized it was slow, and ended on these 2 websites:\nhttp://www.popekim.com/2011/11/optimized-oren-nayar-approximation.html\n\nThat lists a nifty trick to fake it, I took away some terms as I realized they contributed barely any visible difference, so I got something even less accurate. I already want to revisit this, but it’s one of the improvements I wanted to share nonetheless.\n\n```float orenNayarDiffuse(float satNdotV, float satNdotL, float roughness)\n{\nfloat lambert = satNdotL;\nif(roughness == 0.0)\nreturn lambert;\nfloat softRim = saturate(1.0 - satNdotV * 0.5);\n\n// my magic numbers\nfloat fakey = pow(lambert * softRim, 0.85);\nreturn mix(lambert, fakey * 0.85, roughness);\n}```\n\n## GGX specular\n\nThere are various open source implementations of this. I found one here:\nIt talks about tricks to optimize things by precomputing a lookup texture, I didn’t go that far. There’s not much I can say about this, as I don’t fully understand the math and how it changes from the basic phong dot(N, H).\n\n```float G1V(float dotNV, float k){return 1.0 / (dotNV * (1.0 - k)+k);}\n\nfloat ggxSpecular(float NdotV, float NdotL, vec3 N, vec3 L, vec3 V, float roughness)\n{\nfloat F0 = 0.5;\n\nvec3 H = normalize(V + L);\nfloat NdotH = saturate(dot(N, H));\nfloat LdotH = saturate(dot(L, H));\nfloat a2 = roughness * roughness;\n\nfloat D = a2 / (PI * sqr(sqr(NdotH) * (a2 - 1.0) + 1.0));\nfloat F = F0 + (1.0 - F0) * pow(1.0 - LdotH, 5.0);\nfloat vis = G1V(NdotL, a2 * 0.5) * G1V(NdotV, a2 * 0.5);\nreturn NdotL * D * F * vis;\n}```", null, "## FXAA\n\nFXAA3 to be precise. There whitepaper is quite clear, still why bother writing it if it’s open source. I can’t remember which one I used, but here’s a few links:\nhttps://gist.github.com/kosua20/0c506b81b3812ac900048059d2383126\nhttps://github.com/vispy/experimental/blob/master/fsaa/fxaa.glsl\nPreprocessed and minified for preset 12 made it very small in a compressed executable. Figured I’d just share it.\n\n```#version 420\nuniform vec3 uTimeResolution;uniform sampler2D uImages;out vec4 z;float aa(vec3 a){vec3 b=vec3(.299,.587,.114);return dot(a,b);}\n#define bb(a)texture(uImages,a)\n#define cc(a)aa(texture(uImages,a).rgb)\n#define dd(a,b)aa(texture(uImages,a+(bc)).rgb)\nvoid main(){vec2 a=gl_FragCoord.xy/uTimeResolution.yz,c=1/uTimeResolution.yz;vec4 b=bb(a);b.y=aa(b.rgb);float d=dd(a,vec2(0,1)),e=dd(a,vec2(1,0)),f=dd(a,vec2(0,-1)),g=dd(a,vec2(-1,0)),h=max(max(f,g),max(e,max(d,b.y))),i=h-min(min(f,g),min(e,min(d,b.y)));if(i<max(.0833,h.166)){z=bb(a);return;}h=dd(a,vec2(-1,-1));float j=dd(a,vec2( 1,1)),k=dd(a,vec2( 1,-1)),l=dd(a,vec2(-1,1)),m=f+d,n=g+e,o=k+j,p=h+l,q=c.x;\nbool r=abs((-2g)+p)+(abs((-2b.y)+m)2)+abs((-2e)+o)>=abs((-2d)+l+j)+(abs((-2b.y)+n)2)+abs((-2f)+h+k);if(!r){f=g;d=e;}else q=c.y;h=f-b.y,e=d-b.y,f=f+b.y,d=d+b.y,g=max(abs(h),abs(e));i=clamp((abs((((m+n)2+p+o)(1./12))-b.y)/i),0,1);if(abs(e)<abs(h))q=-q;else f=d;vec2 s=a,t=vec2(!r?0:c.x,r?0:c.y);if(!r)s.x+=q.5;else s.y+=q.5;\nvec2 u=vec2(s.x-t.x,s.y-t.y);s=vec2(s.x+t.x,s.y+t.y);j=((-2)i)+3;d=cc(u);e=ii;h=cc(s);g=.25;i=b.y-f.5;j=je;d-=f.5;h-=f.5;bool v,w,x,y=i<0;\n#define ee(Q) v=abs(d)>=g;w=abs(h)>=g;if(!v)u.x-=t.xQ;if(!v)u.y-=t.yQ;x=(!v)\|\|(!w);if(!w)s.x+=t.xQ;if(!w)s.y+=t.yQ;\n#define ff if(!v)d=cc(u.xy);if(!w)h=cc(s.xy);if(!v)d=d-f.5;if(!w)h=h-f.5;\nee(1.5)if(x){ff ee(2.)if(x){ff ee(4.)if(x){ff ee(12.)}}}e=a.x-u.x;f=s.x-a.x;if(!r){e=a.y-u.y;f=s.y-a.y;}q=max((e<f?(d<0)!=y:(h<0)!=y)?(min(e,f)(-1/(f+e)))+.5:0,jj.75);if(!r)a.x+=q;else a.y+=q;z=bb(a);}\n```", null, "## Multi pass bloom\n\nThe idea for this one was heavily inspired by this asset for Unity:\n\nhttps://www.assetstore.unity3d.com/en/#!/content/17324\n\nI’m quite sure the technique is not original, but that’s where I got the idea.\n\nThe idea is to downsample and blur at many resolutions and them combine the (weighted) results to get a very high quality full screen blur.\nSo basically downsample to a quarter (factor 2) of the screen using this shader:\n\n```#version 420\n\nuniform vec3 uTimeResolution;\n#define uTime (uTimeResolution.x)\n#define uResolution (uTimeResolution.yz)\n\nuniform sampler2D uImages;\n\nout vec4 outColor0;\n\nvoid main()\n{\noutColor0 = 0.25 (texture(uImages, (gl_FragCoord.xy + vec2(-0.5)) / uResolution)\n+ texture(uImages, (gl_FragCoord.xy + vec2(0.5, -0.5)) / uResolution)\n+ texture(uImages, (gl_FragCoord.xy + vec2(0.5, 0.5)) / uResolution)\n+ texture(uImages, (gl_FragCoord.xy + vec2(-0.5, 0.5)) / uResolution));\n}```\n\nThen downsample that, and recurse until we have a factor 64\n\nAll the downsamples fit in the backbuffer, so in theory that together with the first blur pass can be done in 1 go using the backbuffer as sampler2D as well. But to avoid the hassle of figuring out the correct (clamped!) uv coordinates I just use a ton of passes.\n\nThen take all these downsampled buffers and ping pong them for blur passes, so for each buffer:\nHBLUR taking steps of 2 pixels, into a buffer of the same size\nVBLUR, back into the initial downsampled buffer\nHBLUR taking steps of 3 pixels, reuse the HBLUR buffer\nVBLUR, reuse the initial downsampled buffer\n\nThe pixel steps is given to uBlurSize, the direction of blur is given to uDirection.\n\n```#version 420\n\nout vec4 color;\n\nuniform vec3 uTimeResolution;\n#define uTime (uTimeResolution.x)\n#define uResolution (uTimeResolution.yz)\n\nuniform sampler2D uImages;\nuniform vec2 uDirection;\nuniform float uBlurSize;\n\nconst float curve = { 0.0205,\n0.0855,\n0.232,\n0.324,\n0.232,\n0.0855,\n0.0205 };\n\nvoid main()\n{\nvec2 uv = gl_FragCoord.xy / uResolution;\nvec2 netFilterWidth = uDirection / uResolution * uBlurSize;\nvec2 coords = uv - netFilterWidth * 3.0;\n\ncolor = vec4(0);\nfor( int l = 0; l < 7; l++ )\n{\nvec4 tap = texture(uImages, coords);\ncolor += tap * curve[l];\ncoords += netFilterWidth;\n}\n}```\n\nLast we combine passes with lens dirt. uImages is the original backbuffer, 1-6 is all the downsampled and blurred buffers, 7 is a lens dirt image.\nMy lens dirt texture is pretty poor, its just a precalced texture with randomly scaled and colored circles and hexagons, sometimes filled and sometimes outlines.\nI don’t think I actually ever used the lens dirt or bloom intensity as uniforms.\n\n```#version 420\n\nout vec4 color;\n\nuniform vec3 uTimeResolution;\n#define uTime (uTimeResolution.x)\n#define uResolution (uTimeResolution.yz)\n\nuniform sampler2D uImages;\nuniform float uBloom = 0.04;\nuniform float uLensDirtIntensity = 0.3;\n\nvoid main()\n{\nvec2 coord = gl_FragCoord.xy / uResolution;\ncolor = texture(uImages, coord);\n\nvec3 b0 = texture(uImages, coord).xyz;\nvec3 b1 = texture(uImages, coord).xyz * 0.6; // dampen to have less banding in gamma space\nvec3 b2 = texture(uImages, coord).xyz * 0.3; // dampen to have less banding in gamma space\nvec3 b3 = texture(uImages, coord).xyz;\nvec3 b4 = texture(uImages, coord).xyz;\nvec3 b5 = texture(uImages, coord).xyz;\n\nvec3 bloom = b0 * 0.5\n+ b1 * 0.6\n+ b2 * 0.6\n+ b3 * 0.45\n+ b4 * 0.35\n+ b5 * 0.23;\n\nbloom /= 2.2;\ncolor.xyz = mix(color.xyz, bloom.xyz, uBloom);\n\nvec3 lens = texture(uImages, coord).xyz;\nvec3 lensBloom = b0 + b1 * 0.8 + b2 * 0.6 + b3 * 0.45 + b4 * 0.35 + b5 * 0.23;\nlensBloom /= 3.2;\ncolor.xyz = mix(color.xyz, lensBloom, (clamp(lens * uLensDirtIntensity, 0.0, 1.0)));\n\ncolor.xyz = pow(color.xyz, vec3(1.0 / 2.2));\n}```\n\nWhite lines on a cube, brightness of 10.", null, "White lines on a cube, brightness of 300.", null, "## Sphere tracing algorithm\n\nInstead of a rather naive sphere tracing loop I used in a lot of 4kb productions and can just write by heart I went for this paper:\nhttp://erleuchtet.org/~cupe/permanent/enhanced_sphere_tracing.pdf\nIt is a clever technique that involves overstepping and backgracking only when necessary, as well as keeping track of pixel size in 3D to realize when there is no need to compute more detail. The paper is full of code snippets and clear infographics, I don’t think I’d be capable to explain it any clearer.", null, "## Beauty shots", null, "", null, "## Depth of field\n\nI initially only knew how to do good circular DoF, until this one came along: https://www.shadertoy.com/view/4tK3WK\nWhich I used initially, but to get it to look good was really expensive, because it is all single pass. Then I looked into a 3-blur-pass solution, which sorta worked, but when I went looking for more optimized versions I found this 2 pass one: https://www.shadertoy.com/view/Xd3GDl. It works extremely well, the only edge cases I found were when unfocusing a regular grid of bright points.\n\nHere’s what I wrote to get it to work with a depth buffer (depth based blur):\n\n```const int NUM_SAMPLES = 16;\n\nvoid main()\n{\nvec2 fragCoord = gl_FragCoord.xy;\n\nconst vec2 blurdir = vec2( 0.0, 1.0 );\nvec2 blurvec = (blurdir) / uResolution;\nvec2 uv = fragCoord / uResolution.xy;\n\nfloat z = texture(uImages, uv).w;\nfragColor = vec4(depthDirectionalBlur(z, CoC(z), uv, blurvec, NUM_SAMPLES), z);\n}```\n\nSecond pass:\n\n```const int NUM_SAMPLES = 16;\n\nvoid main()\n{\nvec2 uv = gl_FragCoord.xy / uResolution;\n\nfloat z = texture(uImages, uv).w;\n\nvec2 blurdir = vec2(1.0, 0.577350269189626);\nvec2 blurvec = normalize(blurdir) / uResolution;\nvec3 color0 = depthDirectionalBlur(z, CoC(z), uv, blurvec, NUM_SAMPLES);\n\nblurdir = vec2(-1.0, 0.577350269189626);\nblurvec = normalize(blurdir) / uResolution;\nvec3 color1 = depthDirectionalBlur(z, CoC(z), uv, blurvec, NUM_SAMPLES);\n\nvec3 color = min(color0, color1);\nfragColor = vec4(color, 1.0);\n}```\n\n```#version 420\n\n// default uniforms\nuniform vec3 uTimeResolution;\n#define uTime (uTimeResolution.x)\n#define uResolution (uTimeResolution.yz)\n\nuniform sampler2D uImages;\n\nuniform float uSharpDist = 15; // distance from camera that is 100% sharp\nuniform float uSharpRange = 0; // distance from the sharp center that remains sharp\nuniform float uBlurFalloff = 1000; // distance from the edge of the sharp range it takes to become 100% blurry\nuniform float uMaxBlur = 16; // radius of the blur in pixels at 100% blur\n\nfloat CoC(float z)\n{\nreturn uMaxBlur * min(1, max(0, abs(z - uSharpDist) - uSharpRange) / uBlurFalloff);\n}\n\nout vec4 fragColor;\n\n//note: uniform pdf rand [0;1)\nfloat hash1(vec2 p)\n{\np = fract(p * vec2(5.3987, 5.4421));\np += dot(p.yx, p.xy + vec2(21.5351, 14.3137));\nreturn fract(p.x * p.y * 95.4307);\n}\n\n#define USE_RANDOM\n\nvec3 depthDirectionalBlur(float z, float coc, vec2 uv, vec2 blurvec, int numSamples)\n{\n// z: z at UV\n// coc: blur radius at UV\n// uv: initial coordinate\n// blurvec: smudge direction\n// numSamples: blur taps\nvec3 sumcol = vec3(0.0);\n\nfor (int i = 0; i < numSamples; ++i)\n{\nfloat r =\n#ifdef USE_RANDOM\n(i + hash1(uv + float(i + uTime)) - 0.5)\n#else\ni\n#endif\n/ float(numSamples - 1) - 0.5;\nvec2 p = uv + r * coc * blurvec;\nvec4 smpl = texture(uImages, p);\nif(smpl.w < z) // if sample is closer consider it's CoC\n{\np = uv + r * min(coc, CoC(smpl.w)) * blurvec;\np = uv + r * CoC(smpl.w) * blurvec;\nsmpl = texture(uImages, p);\n}\nsumcol += smpl.xyz;\n}\n\nsumcol /= float(numSamples);\nsumcol = max(sumcol, 0.0);\n\nreturn sumcol;\n}```", null, "## Additional sources used for a longer time\n\n### Distance function library\n\nhttp://mercury.sexy/hg_sdf/\nA very cool site explaining all kinds of things you can do with this code. I think many of these functions were invented already, but with some bonusses as ewll as a very clear code style and excellent documentations for full accessibility.\nFor an introduction to this library:\n\n### Noise functions\n\nHashes optimized to only implement hash4() and the rest is just swizzling and redirecting, so a float based hash is just:\n\n```float hash1(float x){return hash4(vec4(x)).x;}\nvec2 hash2(float x){return hash4(vec4(x)).xy;}```\n\nAnd so on.\n\nVoronoi 2D\nVoronoi is great, as using the center distance we get worley noise instead, and we can track cell indices for randomization.\nThis is fairly fast, but still too slow to do realtime. So I implemented tileable 2D & 3D versions.\n\nPerlin\nLayering the value noise for N iterations, scaling the UV by 2 and weight by 0.5 in every iteration.\nThese could be controllable parameters for various different looks. A slower weight decrease results in a more wood-grain look for example.\n\n```float perlin(vec2 p, int iterations)\n{\nfloat f = 0.0;\nfloat amplitude = 1.0;\n\nfor (int i = 0; i < iterations; ++i)\n{\nf += snoise(p) * amplitude;\namplitude = 0.5;\np = 2.0;\n}\n\nreturn f * 0.5;\n}```\n\nNow the perlin logic can be applied to worley noise (voronoi center) to get billows. I did the same for the voronoi edges, all tileable in 2D and 3D for texture precalc. Here’s an example. Basically the modulo in the snoise function is the only thing necessary to make things tileable. Perlin then just uses that and keeps track of the scale for that layer.\n\n```float snoise_tiled(vec2 p, float scale)\n{\np = scale;\nvec2 c = floor(p);\nvec2 f = p - c;\nf = f f * (3.0 - 2.0 * f);\nreturn mix(mix(hash1(mod(c + vec2(0.0, 0.0), scale) + 10.0),\nhash1(mod(c + vec2(1.0, 0.0), scale) + 10.0), f.x),\nmix(hash1(mod(c + vec2(0.0, 1.0), scale) + 10.0),\nhash1(mod(c + vec2(1.0, 1.0), scale) + 10.0), f.x), f.y);\n}\nfloat perlin_tiled(vec2 p, float scale, int iterations)\n{\nfloat f = 0.0;\np = mod(p, scale);\nfloat amplitude = 1.0;\n\nfor (int i = 0; i < iterations; ++i)\n{\nf += snoise_tiled(p, scale) * amplitude;\namplitude = 0.5;\nscale = 2.0;\n}\n\nreturn f * 0.5;\n}```\n\n# Creating a tool to make a 64k demo\n\nIn the process of picking up this webpage again, I can talk about something we did quite a while ago. I, together with a team, went through the process of making a 64 kilobyte demo. We happened to win at one of the biggest demoscene events in europe. Revision 2017. I still feel the afterglow of happiness from that.\n\nIf you’re not sure what that is, read on, else, scroll down! You program a piece of software that is only 64 kb in size, that shows an audio-visual experience generated in realtime. To stay within such size limits you have to generate everything, we chose to go for a rendering technique called ray marching, that allowed us to put all 3D modeling, texture generation, lighting, etc. as ascii (glsl sources) in the executable. On top of that we used a very minimal (yet versatile) modular synthesizer called 64klang2. Internally it stores a kind of minimal midi data and the patches and it can render amazing audio in realtime, so it doesn’t need to pre-render the song or anything. All this elementary and small size data and code compiles to something over 200kb, which is then compressed using an executable packer like UPX or kkrunchy\n\nIt was called Eidolon. You can watch a video:\nhttps://youtu.be/rsZHBJdaz-Y\nhttp://www.pouet.net/prod.php?which=69669\n\nThe technologies used were fairly basic, it’s very old school phong & lambert shading, 2 blur passes for bloom, so all in all pretty low tech and not worth discussing. What I would like to discuss is the evolution of the tool. I’ll keep it high level this time though. Maybe in the future I can talk about specific implementations of things, but just seeing the UI will probably explain a lot of the features and the way things work.\n\n### Step 1: Don’t make a tool from scratch\n\nOur initial idea was to leverage existing software. One of our team members, who controlled the team besides modelling and eventually directing the whole creative result, had some experience with a real-time node based software called Touch Designer. It is a tool where you can do realtime visuals, and it supports exactly what we need: rendering into a 2D texture with a fragment shader.\n\nWe wanted to have the same rendering code for all scenes, and just fill in the modeling and material code that is unique per scene. We figured out how to concatenate separate pieces of text and draw them into a buffer. Multiple buffers even. At some point i packed all code and rendering logic of a pass into 1 grouped node and we could design our render pipeline entirely node based.", null, "Here you see the text snippets (1) merged into some buffers (2) and then post processed for the bloom (3). On the right (4) you see the first problem we hit with Touch Designer. The compiler error log is drawn inside this node. There is basically no easy way to have that error visible in the main application somewhere. So the first iteration of the renderer (and coincidentally the main character of Eidolon) looked something like this:", null, "The renderer didn’t really change after this.\n\nIn case I sound too negative about touch designer in the next few paragraphs, our use case was rather special, so take this with a grain of salt!\n\nWe have a timeline control, borrowed the UI design from Maya a little, so this became the main preview window. That’s when we hit some problems though. The software has no concept of window focus, so it’d constantly suffer hanging keys or responding to keys while typing in the text editor.\n\nLast issue that really killed it though: everything has to be in 1 binary file. There is no native way to reference external text files for the shader code, or merge node graphs. There is a really weird utility that expands the binary to ascii, but then literally every single node is a text file so it is just unmergeable.\n\n### Step 2: Make a tool\n\nSo then this happened:", null, "Over a week’s time in the evenings and then 1 long saturday I whipped this up using PyQt and PyOpenGL. This is the first screenshot I made, the curve editor isn’t actually an editor yet and there is no concept of camera shots (we use this to get hard cuts).\n\nIt has all the same concepts however, separate text files for the shader code, with an XML file determining what render passes use what files and in what buffer they render / what buffers they reference in turn. With the added advantage of the perfect granularity all stored in ascii files.\n\nSome files are template-level, some were scene-level, so creating a new scene actually only copies the scene-level fies which can them be adjusted in a text editor, with a file watcher updating the picture. The CurveEditor feeds right back into the uniforms of the shader (by name) and the time slider at the bottom is the same idea as Maya / what you saw before.\n\n### Step 3: Make it better\n\nRender pipeline\nThe concept was to set up a master render pipeline into which scenes would inject snippets of code. On disk this became a bunch of snippets, and an XML based template definition. This would be the most basic XML file:\n\n```<template>\n<pass buffer=\"0\" outputs=\"1\">\n<section path=\"scene.glsl\"/>\n<global path=\"pass.glsl\"/>\n</pass>\n<pass input0=\"0\">\n<global path=\"present.glsl\"/>\n</pass>\n</template>```\n\nThis will concatenated 3 files to 1 fragment shader, render into full-screen buffer “0” and then use present.glsl as another fragment shader, which in turn has the previous buffer “0” as input (forwarded to a sampler2D uniform).\n\nThis branched out into making static bufffers (textures), setting buffer sizes (smaller textures), multiple target buffers (render main and reflection pass at once), set buffer size to a portion of the screen (downsampling for bloom), 3D texture support (volumetric noise textures for cloud).\n\nCreating a new scene will just copy “scene.glsl” from the template to a new folder, there you can then fill out the necessary function(s) to get a unique scene. Here’s an example from our latest Evoke demo. 6 scenes, under which you see the “section” files for each scene.", null, "Camera control\nThe second important thing I wanted to tackle was camera control. Basically the demo will control the camera based on some animation data, but it is nice to fly around freely and even use the current camera position as animation keyframe. So this was just using Qt’s event system to hook up the mouse and keyboard to the viewport.", null, "I also created a little widget that displays where the camera is, has an “animation input or user input” toggle as well as a “snap to current animation frame” button.\n\nAnimation control\nSo now to animate the camera, without hard coding values! Or even typing numbers, preferably. I know a lot of people use a tracker-like tool called Rocket, I never used it and it looks an odd way to control animation data to me. I come from a 3D background, so I figured I’d just want a curve editor like e.g. Maya has. In Touch Designer we also had a basic curve editor, conveniently you can name a channel the same as a uniform, then just have code evaluate the curve at the current time and send the result to that uniform location.\nSome trickery was necessary to pack vec3s, I just look for channels that start with the same name and then end in .x, .y, .z, and possibly .w.", null, "Here’s an excerpt from a long camera shot with lots of movement, showing off our cool hermite splines. At the top right you can see we have several built in tangent modes, we never got around to building custom tangent editing. In the end this is more than enough however. With flat tangents we can create easing/acceleration, with spline tangents we can get continuous paths and with linear tangents we get continuous speed. Next to that are 2 cool buttons that allow us to feed the camera position to another uniform, so you can literally fly to a place where you want to put an object. It’s not as good as actual move/rotate widgets but for the limited times we need to place 3D objects it’s great.\n\nHard cuts\nApart from being impossible to represent in this interface, we don’t support 2 keys at identical times. This means that we can’t really have the camera “jump” to a new position instantly. With a tiny amount of curve inbetween the previous and the next shot position, the time cursor can actually render 1 frame of a random camera position. So we had to solve this. I think it is one of the only big features that you won’t see in the initial screenshot above actually.", null, "Introducing camera shots. A shot has its own “scene it should display” and its own set of animation data. So selecting a different shot yields different curve editor content. Shots are placed on a shared timeline, so scrolling through time will automatically show the right shot and setting a keyframe will automatically figure out the “shot local time” to put the key based on the global demo time. The curve editor has it’s own playhead that is directly linked to the global timeline as well so we can adjust the time in multiple places.\n\nWhen working with lots of people we had issues with people touching other people’s (work in progress) shots. Therefore we introduced “disabling” of shots. This way anyone could just prefix their shots and disable them before submitting, and we could mix and match shots from several people to get a final camera flow we all liked.", null, "Shots are also rendered on the timeline as colored blocks. The grey block underneath those is our “range slider”. It makes the top part apply on only a subsection of the demo, so it is easy to loop a specific time range, or just zoom in far enough to use the mouse to change the time granularly enough.\n\nThe devil is in the details\nSome things I overlooked in the first implementation, and some useful things I added only recently.\n1. Undo/Redo of animation changes. Not unimportant, and luckily not hard to add with Qt.\n2. Ctrl click timeline to immediately start animating that shot\n3. Right click a shot to find the scene\n4. Right click a scene to create a shot for that scene in particular\n5. Current time display in minutes:seconds instead of just beats\n6. BPM stored per-project instead of globally\n7. Lots of hotkeys!\n\nThese things make the tool just that much faster to use.\n\nFinally, here’s our tool today. There’s still plenty to be done, but we made 2 demos with it so far and it gets better every time!", null, "# Part 3: Importing and drawing a custom mesh file\n\n## Part 3: Creating an importer\n\nThis is part 3 of a series and it is about getting started with visualizing triangle meshes with Python 2.7 using the libraries PyOpenGL and PyQt4.\n\nI will assume you know python, you will not need a lot of Qt or OpenGL experience, though I will also not go into the deeper details of how OpenGL works. For that I refer you to official documentation and the excellent (C++) tutorials at https://open.gl/. Although they are C++, there is a lot of explanation about OpenGL and why to do certain calls in a certain order.\n\nOn a final note: I will make generalizations and simplifications when explaining things. If you think something works different then I say it probably does, this is to try and convey ideas to beginners, not to explain low level openGL implementations.\n\n### 3.1 Importing\n\nNow with our file format resembling openGL so closely makes this step relatively easy. First I’ll declare some globals, because openGL does not have real enums but just a bunch of global constants I make some groups to do testing and data mapping against.\n\n```from OpenGL.GL import \n\nattributeElementTypes = (GL_BYTE,\nGL_UNSIGNED_BYTE,\nGL_SHORT,\nGL_UNSIGNED_SHORT,\nGL_INT,\nGL_UNSIGNED_INT,\nGL_HALF_FLOAT,\nGL_FLOAT,\nGL_DOUBLE,\nGL_FIXED,\nGL_INT_2_10_10_10_REV,\nGL_UNSIGNED_INT_2_10_10_10_REV,\nGL_UNSIGNED_INT_10F_11F_11F_REV)\nsizeOfType = {GL_BYTE: 1,\nGL_UNSIGNED_BYTE: 1,\nGL_SHORT: 2,\nGL_UNSIGNED_SHORT: 2,\nGL_INT: 4,\nGL_UNSIGNED_INT: 4,\nGL_HALF_FLOAT: 2,\nGL_FLOAT: 4,\nGL_DOUBLE: 8,\nGL_FIXED: 4,\nGL_INT_2_10_10_10_REV: 4,\nGL_UNSIGNED_INT_2_10_10_10_REV: 4,\nGL_UNSIGNED_INT_10F_11F_11F_REV: 4}\ndrawModes = (GL_POINTS,\nGL_LINE_STRIP,\nGL_LINE_LOOP,\nGL_LINES,\nGL_TRIANGLE_STRIP,\nGL_TRIANGLE_FAN,\nGL_TRIANGLES,\nGL_PATCHES)\nindexTypeFromSize = {1: GL_UNSIGNED_BYTE, 2: GL_UNSIGNED_SHORT, 4: GL_UNSIGNED_INT}```\n\nNext up is a Mesh class that stores a vertex array object (and corresponding buffers for deletion) along with all info necessary to draw the mesh once it’s on the GPU.\n\n```class Mesh(object):\ndef __init__(self, vao, bufs, drawMode, indexCount, indexType):\nself.__vao = vao\nself.__bufs = bufs\nself.__drawMode = drawMode\nself.__indexCount = indexCount\nself.__indexType = indexType\n\ndef __del__(self):\nglDeleteBuffers(len(self.__bufs), self.__bufs)\nglDeleteVertexArrays(1, [self.__vao])\n\ndef draw(self):\nglBindVertexArray(self.__vao)\nglDrawElements(self.__drawMode, self.__indexCount, self.__indexType, None)```\n\nNow let’s, given a file path, open up the file and run the importer for the right version (if known).\n\n```def model(filePath):\nvao = glGenVertexArrays(1)\nglBindVertexArray(vao)\nbufs = glGenBuffers(2)\nglBindBuffer(GL_ARRAY_BUFFER, bufs)\nglBindBuffer(GL_ELEMENT_ARRAY_BUFFER, bufs)\nwith open(filePath, 'rb') as fh:\nif fileVersion == 0:\nraise RuntimeError('Unknown mesh file version %s in %s' % (fileVersion, filePath))```\n\nNext we can start reading the rest of the file:\n\n``` vertexCount = struct.unpack('I', fh.read(4))\nassert indexSize in indexTypeFromSize, 'Unknown element data type, element size must be one of %s' % indexTypeFromSize.keys()\nindexType = indexTypeFromSize[indexSize]\nassert drawMode in (GL_LINES, GL_TRIANGLES), 'Unknown draw mode.' # TODO: list all render types```\n\nRead and apply the attribute layout:\n\n```# gather layout\noffset = 0\nlayouts = []\nfor i in xrange(numAttributes):\nassert dimensions in (1, 2, 3, 4)\nassert dataType in attributeElementTypes, 'Invalid GLenum value for attribute element type.'\nlayouts.append((location, dimensions, dataType, offset))\noffset += dimensions sizeOfType[dataType]\n# apply\nfor layout in layouts:\nglVertexAttribPointer(layout, layout, layout, GL_FALSE, offset, ctypes.c_void_p(layout)) # total offset is now stride\nglEnableVertexAttribArray(layout)```\n\nRead and upload the raw buffer data. This step is easy because we can directly copy the bytes as the storage matches exactly with how openGL expects it due to the layout code above.\n\n```raw = fh.read(vertexSize * vertexCount)\nglBufferData(GL_ARRAY_BUFFER, vertexSize * vertexCount, raw, GL_STATIC_DRAW)\nglBufferData(GL_ELEMENT_ARRAY_BUFFER, indexSize * indexCount, raw, GL_STATIC_DRAW)```\n\n### 3.2 The final code\n\nThis is the application code including all the rendering from chapter 1, only the rectangle has been replaced by the loaded mesh.\n\n```# the importer\nimport struct\nfrom OpenGL.GL import \n\nattributeElementTypes = (GL_BYTE,\nGL_UNSIGNED_BYTE,\nGL_SHORT,\nGL_UNSIGNED_SHORT,\nGL_INT,\nGL_UNSIGNED_INT,\nGL_HALF_FLOAT,\nGL_FLOAT,\nGL_DOUBLE,\nGL_FIXED,\nGL_INT_2_10_10_10_REV,\nGL_UNSIGNED_INT_2_10_10_10_REV,\nGL_UNSIGNED_INT_10F_11F_11F_REV)\nsizeOfType = {GL_BYTE: 1,\nGL_UNSIGNED_BYTE: 1,\nGL_SHORT: 2,\nGL_UNSIGNED_SHORT: 2,\nGL_INT: 4,\nGL_UNSIGNED_INT: 4,\nGL_HALF_FLOAT: 2,\nGL_FLOAT: 4,\nGL_DOUBLE: 8,\nGL_FIXED: 4,\nGL_INT_2_10_10_10_REV: 4,\nGL_UNSIGNED_INT_2_10_10_10_REV: 4,\nGL_UNSIGNED_INT_10F_11F_11F_REV: 4}\ndrawModes = (GL_POINTS,\nGL_LINE_STRIP,\nGL_LINE_LOOP,\nGL_LINES,\nGL_TRIANGLE_STRIP,\nGL_TRIANGLE_FAN,\nGL_TRIANGLES,\nGL_PATCHES)\nindexTypeFromSize = {1: GL_UNSIGNED_BYTE, 2: GL_UNSIGNED_SHORT, 4: GL_UNSIGNED_INT}\n\nassert indexSize in indexTypeFromSize, 'Unknown element data type, element size must be one of %s' % indexTypeFromSize.keys()\nindexType = indexTypeFromSize[indexSize]\nassert drawMode in (GL_LINES, GL_TRIANGLES), 'Unknown draw mode.' # TODO: list all render types\n\n# gather layout\noffset = 0\nlayouts = []\nfor i in xrange(numAttributes):\nassert dimensions in (1, 2, 3, 4)\nassert dataType in attributeElementTypes, 'Invalid GLenum value for attribute element type.'\nlayouts.append((location, dimensions, dataType, offset))\noffset += dimensions sizeOfType[dataType]\n\n# apply layout\nfor layout in layouts:\nglVertexAttribPointer(layout, layout, layout, GL_FALSE, offset, ctypes.c_void_p(layout)) # total offset is now stride\nglEnableVertexAttribArray(layout)\n\nglBufferData(GL_ARRAY_BUFFER, vertexSize * vertexCount, raw, GL_STATIC_DRAW)\nglBufferData(GL_ELEMENT_ARRAY_BUFFER, indexSize * indexCount, raw, GL_STATIC_DRAW)\n\nassert len(fh.read()) == 0, 'Expected end of file, but file is longer than it indicates'\nreturn Mesh(vao, bufs, drawMode, indexCount, indexType)\n\nclass Mesh(object):\ndef __init__(self, vao, bufs, drawMode, indexCount, indexType):\nself.__vao = vao\nself.__bufs = bufs\nself.__drawMode = drawMode\nself.__indexCount = indexCount\nself.__indexType = indexType\n\ndef __del__(self):\nglDeleteBuffers(len(self.__bufs), self.__bufs)\nglDeleteVertexArrays(1, [self.__vao])\n\ndef draw(self):\nglBindVertexArray(self.__vao)\nglDrawElements(self.__drawMode, self.__indexCount, self.__indexType, None)\n\ndef model(filePath):\nvao = glGenVertexArrays(1)\nglBindVertexArray(vao)\nbufs = glGenBuffers(2)\nglBindBuffer(GL_ARRAY_BUFFER, bufs)\nglBindBuffer(GL_ELEMENT_ARRAY_BUFFER, bufs)\nwith open(filePath, 'rb') as fh:\nif fileVersion == 0:\nraise RuntimeError('Unknown mesh file version %s in %s' % (fileVersion, filePath))\n\n# import the necessary modules\nimport time\nfrom PyQt4.QtCore import * # QTimer\nfrom PyQt4.QtGui import * # QApplication\nfrom PyQt4.QtOpenGL import * # QGLWidget\nfrom OpenGL.GL import * # OpenGL functionality\n\n# this is the basic window\nclass OpenGLView(QGLWidget):\ndef initializeGL(self):\n# set the RGBA values of the background\nglClearColor(0.1, 0.2, 0.3, 1.0)\n\n# set a timer to redraw every 1/60th of a second\nself.__timer = QTimer()\nself.__timer.timeout.connect(self.repaint)\nself.__timer.start(1000 / 60)\n\n# import a model\nself.__mesh = model(r'C:\\Users\\John\\Python\\maya\\cube.bm')\n\ndef resizeGL(self, width, height):\nglViewport(0, 0, width, height)\n\ndef paintGL(self):\nglScalef(self.height() / float(self.width()), 1.0, 1.0)\nglRotate((time.time() % 36.0) * 10, 0, 0, 1)\n\nglClear(GL_COLOR_BUFFER_BIT \| GL_DEPTH_BUFFER_BIT)\nself.__mesh.draw()\n\n# this initializes Qt\napp = QApplication([])\n# this creates the openGL window, but it isn't initialized yet\nwindow = OpenGLView()\n# this only schedules the window to be shown on the next Qt update\nwindow.show()\n# this starts the Qt main update loop, it avoids python from continuing beyond this line\n# and any Qt stuff we did above is now going to actually get executed, along with any future\n# events like mouse clicks and window resizes\napp.exec_()```\n\n# Part 2: Creating an OpenGL friendly mesh exporter for Maya\n\n## Part 2: Creating an exporter\n\nThis is part 2 of a series and it is about getting started with visualizing triangle meshes with Python 2.7 using the libraries PyOpenGL and PyQt4.\n\nI will assume you know python, you will not need a lot of Qt or OpenGL experience, though I will also not go into the deeper details of how OpenGL works. For that I refer you to official documentation and the excellent (C++) tutorials at https://open.gl/. Although they are C++, there is a lot of explanation about OpenGL and why to do certain calls in a certain order.\n\nOn a final note: I will make generalizations and simplifications when explaining things. If you think something works different then I say it probably does, this is to try and convey ideas to beginners, not to explain low level openGL implementations.\n\n### 2.1 File layout\n\nNow that we can draw a model, it is time to define the data that we need to give OpenGL and decide upon a file format that can contain all this data.\n\nStarting off with the elements, we have a way to draw them (GL_TRIANGLES in our case) and we have a data type (GL_UNSIGNED_INT in our case). Given this data type and the number of elements we can actually determine the buffer size regardless of the data type, allowing our file to support not only a number of element values, but allowing those values to be of all the supported types.\n\nSimilarly we can look at the vertex layout. We probably want a vertex count and a size of per-vertex-data. This size is a little more complicated because the attribute layout can be very flexible. I suppose it’s easier if we also write the vertex element size instead of trying to figure out what it should be based on the layout.\n\nThen we can look at the attribute layout. We can assume all our data is tightly packed, so we can infer the offset (last argument of glVertexAttribPointer). That leaves us with a layout location, a number of values per vertex, and a data type. Of course first we need to write how many attributes we have.\n\nAfter that all we need to do is fill in the buffer data. So for vertexCount * vertexElementSize bytes we specify binary data for the vertex buffer and for elementCount * elementDataSize we specify binary data for the elements buffer.\n\nOur file format now looks like this:\n\n Version nr byte So we can change the format later and not break things. Vertex count unsigned int Because the elements_array can use at most an unsigned int we can never point to vertices beyond the maximum of this data, so no need to store more bytes. Vertex element size byte Size in bytes of a vertex, based on all attribute sizes combined. Element count unsigned int Element data size byte To infer whether indices are unsigned char, unsigned short or unsigned int. Render type GLenum OpenGL defines variables as GL_TRIANGLES as a GLenum type which is in turn just an unsigned int. Number of attributes byte [For each attribute] Attribute location byte Attribute dimensions byte Is it a single value, vec2, 3 or 4? Attribute type GLenum Are the values float, or int, more types listed in the OpenGL documenation for glVertexAttribuPointer. [End for] Vertex buffer vertexCount * vertexElementSize bytes Elements buffer elementCount * elementDataSize bytes\n\nThat brings us to the next step, gather this information in Maya.\n\n### 2.2 Maya mesh exporter\n\nTo export I’ll use the maya API (OpenMaya). It provides a way to quickly iterate over a mesh’ data without allocating too much memory using the MItMeshPolygons. This will iterate over all the faces and allow us to extract the individual triangles and face vertices.\n\nThere are a few steps to do. First let’s make a script to generate a test scene:\n\n```from maya import cmds\nfrom maya.OpenMaya import \ncmds.file(new=True, force=True)\ncmds.polyCube()\nmeshShapeName = 'pCubeShape1'\noutputFilePath = 'C:/Test.bgm'```\n\nNow with these variables in mind we have to convert the shape name to actual maya API objects that we can read data from.\n\n```# get an MDagPath from the given mesh path\np = MDagPath()\nl = MSelectionList()\nMGlobal.getSelectionListByName(mayaShapeName, l)\nl.getDagPath(0, p)\n\n# get the iterator\npoly = MItMeshPolygon(p)```\n\nThis sets us up to actually start saving data. Because openGL requires us to provide all the data of a vertex at 1 vertex index we have to remap some of Maya’s data. In Maya a vertex (actually face-vertex in Maya terms) is a list of indices that points to e.g. what vertex to use, what normal to use, etc. All with separate indices. In OpenGL all these indices must match. The way I’ll go about this is to simply take the triangulation and generate 3 unique vertices for each triangle. This means that to find the vertex count can be determined by counting the triangles in the mesh. Maya meshes don’t expose functionality to query this , so instead I’ll iterate over all the faces and count the triangles in them.\n\n```# open the file as binary\nwith open(outputFilePath, 'wb') as fh:\n# fixing the vertex data size to just X, Y, Z floats for the vertex position\nvertexElementSize = 3 ctypes.sizeof(ctypes.c_float)\n\n# using unsigned integers as elements\nindexElementSize = ctypes.sizeof(ctypes.c_uint)\n\n# gather the number of vertices\nvertexCount = 0\nwhile not poly.isDone():\nvertices = MPointArray()\nvertexList = MIntArray()\npoly.getTriangles(vertices, vertexList, space)\nvertexCount += vertexList.length()\npoly.next()\npoly.reset()\n# start writing\nfh.write(struct.pack('B', FILE_VERSION))\nfh.write(struct.pack('I', vertexCount))\nfh.write(struct.pack('B', vertexElementSize))\n# currently I'm duplicating all vertices per triangle, so total indices matches total vertices\nfh.write(struct.pack('I', vertexCount))\nfh.write(struct.pack('B', indexElementSize))\nfh.write(struct.pack('I', GL_TRIANGLES)) # render type```\n\nAs you can see we had to make some assumptions about vertex data size and we had to gather some intel on our final vertex count, but this is a good setup. Next step is to write the attribute layout. I’ve made the assumption here to write only X Y Z position floats at location 0. We can expand the exporter later with more features, as our file format supports variable attribute layouts. We can write our position attribute next:\n\n```# attribute layout\n# 1 attribute\nfh.write(struct.pack('B', 1))\n# at location 0\nfh.write(struct.pack('B', 0))\n# of 3 floats\nfh.write(struct.pack('B', 3))\nfh.write(struct.pack('I', GL_FLOAT))```\n\nNote that I am using a constant GL_FLOAT here, if you do not wish to install PyOpenGL for your maya, you can quite simply include this at the top of the file instead:\n\n```import ctypes\nGL_TRIANGLES = 0x0004\nGL_UNSIGNED_INT = 0x1405\nGL_FLOAT = 0x1406```\n\nAfter that comes streaming the vertex buffer. For this I use the same iterator I used to count the vertex count. The code is pretty much the same only now I write the vertices instead of counting the vertex list.\n\n```# iter all faces\nwhile not poly.isDone():\n# get triangulation of this face\nvertices = MPointArray()\nvertexList = MIntArray()\npoly.getTriangles(vertices, vertexList, space)\n\n# write the positions\nfor i in xrange(vertexList.length()):\nfh.write(struct.pack('3f', vertices[i], vertices[i], vertices[i]))\n\npoly.next()```\n\nLast is the element buffer.\n\n```# write the elements buffer\nfor i in xrange(vertexCount):\nfh.write(struct.pack('I', i))```\n\n### 2.3 All the data\n\nThe next step naturally is to export more than just the position. Here is a more elaborate way to extract all the attributes. First we need to get some global data from the mesh. This goes right after where we create the MItMeshPolygons.\n\n```fn = MFnMesh(p)\ntangents = MFloatVectorArray()\nfn.getTangents(tangents, space)\ncolorSetNames = []\nfn.getColorSetNames(colorSetNames)\nuvSetNames = []\nfn.getUVSetNames(uvSetNames)```\n\nNext we have to change our vertexElementSize code to the following:\n\n```# compute the vertex data size, write 4 floats for the position for more convenient transformation in shaders\n# position, tangent, normal, color sets, uv sets\nvertexElementSize = (4 + 3 + 3 + 4 * len(colorSetNames) + 2 * len(uvSetNames)) * ctypes.sizeof(ctypes.c_float)```\n\nThe attribute layout is significantly changed. I’m also changing the point data from a vec3 to a vec4. I’m filling in the w component as 1.0, this to indicate a point instead of a vector. It will make transforming vertices in shaders a step simpler.\n\n```# attribute layout\n\n# Since NVidia is the only driver to implement a default attribute layout I am following this as much as possible\n# on other drivers using a custom shader is mandatory and modern buffers will never work with the fixed function pipeline.\n# https://stackoverflow.com/questions/20573235/what-are-the-attribute-locations-for-fixed-function-pipeline-in-opengl-4-0-cor\n\n# num attributes\nfh.write(struct.pack('B', 3 + len(colorSetNames) + len(uvSetNames)))\n# vec4 position at location 0\nfh.write(struct.pack('B', 0))\nfh.write(struct.pack('B', 4))\nfh.write(struct.pack('I', GL_FLOAT))\n# vec3 tangent at location 1\nfh.write(struct.pack('B', 1))\nfh.write(struct.pack('B', 3))\nfh.write(struct.pack('I', GL_FLOAT))\n# vec3 normal at location 2\nfh.write(struct.pack('B', 2))\nfh.write(struct.pack('B', 3))\nfh.write(struct.pack('I', GL_FLOAT))\n# vec4 color at locations (3,7) and 16+\nused = {}\nfor i in xrange(len(colorSetNames)):\nidx = 3 + i\nif idx > 7:\nidx = 11 + i\nfh.write(struct.pack('B', idx))\nfh.write(struct.pack('B', 4))\nfh.write(struct.pack('I', GL_FLOAT))\n# vec2 uvs at locations 8-15 and 16+, but avoiding overlap with colors\nidx = 8\nfor i in xrange(len(uvSetNames)):\nwhile idx in used:\nidx += 1\nfh.write(struct.pack('B', idx))\nfh.write(struct.pack('B', 2))\nfh.write(struct.pack('I', GL_FLOAT))\nidx += 1```\n\nMost of the MItMeshPolygon iterator functions, like getNormals(), gives us a list of the normals for all vertices in this face. The problem is that this data is not triangulated.\n\nTo extract the triangulation we used getTriangles(), which gives us a list of vertices used in the face. These vertex numbers are object-wide, so they keep getting bigger the further we get.\n\nThat means they’re useless if we want to use them to look up the normal returned by getNormals(), because that array is always very short, containing just the normals for this face.\n\nSo we have to do some mapping from the triangulated vertex indices into indices that match the data we’ve got. Either that or get all the normals from the mesh in 1 big array but that is not memory efficient. So at the top of the while loop (just inside) I’ve added the following dictionary:\n\n```# map object indices to local indices - because for some reason we can not query the triangulation as local indices\n# but all getters do want us to provide local indices\nobjectToFaceVertexId = {}\ncount = poly.polygonVertexCount()\nfor i in xrange(count):\nobjectToFaceVertexId[poly.vertexIndex(i)] = i```\n\nThat allows us to extract all the data we want for these triangles like so:\n\n```# get per-vertex data\nnormals = MVectorArray()\npoly.getNormals(normals, space)\ncolorSet = []\nfor i, colorSetName in enumerate(colorSetNames):\ncolorSet.append(MColorArray())\npoly.getColors(colorSet[i], colorSetName)\nuvSetU = []\nuvSetV = []\nfor i, uvSetName in enumerate(uvSetNames):\nuvSetU.append(MFloatArray())\nuvSetV.append(MFloatArray())\npoly.getUVs(uvSetU[i], uvSetV[i], uvSetName)```\n\nHandling fairly small sets of data at a time. Last we have to write the data, replacing the loop writing 3 floats per vertex we had before with this longer loop:\n\n```# write the data\nfor i in xrange(vertexList.length()):\nlocalVertexId = objectToFaceVertexId[vertexList[i]]\ntangentId = poly.tangentIndex(localVertexId)\n\nfh.write(struct.pack('4f', vertices[i], vertices[i], vertices[i], 1.0))\nfh.write(struct.pack('3f', tangents[tangentId], tangents[tangentId], tangents[tangentId]))\nfh.write(struct.pack('3f', normals[localVertexId], normals[localVertexId], normals[localVertexId]))\nfor j in xrange(len(colorSetNames)):\nfh.write(struct.pack('4f', colorSet[j][localVertexId], colorSet[j][localVertexId], colorSet[j][localVertexId], colorSet[j][localVertexId]))\nfor j in xrange(len(uvSetNames)):\nfh.write(struct.pack('2f', uvSetU[j][localVertexId], uvSetV[j][localVertexId]))```\n\nAnd that completes the exporter with full functionality, extracting all possible data from a maya mesh we want. Unless you want blind data and skin clusters, but that’s a whole different story!\n\n### 2.4 Code\n\nHere is the final code as a function, with an additional function to export multiple selected meshes to multiple files, using Qt for UI. Note that if you wish to use PySide or PyQt5 instead the QFileDialog.getExistingDirectory and QSettings.value return types are different and require some work.\n\n```import os\nimport struct\nfrom maya import cmds\nfrom maya.OpenMaya import \nimport ctypes\n\nGL_TRIANGLES = 0x0004\nGL_UNSIGNED_INT = 0x1405\nGL_FLOAT = 0x1406\nFILE_EXT = '.bm' # binary mesh\nFILE_VERSION = 0\nEXPORT_SPACE = MSpace.kWorld # export meshes in world space for now\n\ndef exportMesh(mayaShapeName, outputFilePath, space):\n# get an MDagPath from the given mesh path\np = MDagPath()\nl = MSelectionList()\nMGlobal.getSelectionListByName(mayaShapeName, l)\nl.getDagPath(0, p)\n\n# get the mesh and iterator\nfn = MFnMesh(p)\npoly = MItMeshPolygon(p)\n\ntangents = MFloatVectorArray()\nfn.getTangents(tangents, space)\ncolorSetNames = []\nfn.getColorSetNames(colorSetNames)\nuvSetNames = []\nfn.getUVSetNames(uvSetNames)\n\n# open the file as binary\nwith open(outputFilePath, 'wb') as fh:\n# compute the vertex data size, write 4 floats for the position for more convenient transformation in shaders\n# position, tangent, normal, color sets, uv sets\nvertexElementSize = (4 + 3 + 3 + 4 len(colorSetNames) + 2 * len(uvSetNames)) * ctypes.sizeof(ctypes.c_float)\n\n# using unsigned integers as elements\nindexElementSize = ctypes.sizeof(ctypes.c_uint)\n\n# gather the number of vertices\nvertexCount = 0\nwhile not poly.isDone():\nvertices = MPointArray()\nvertexList = MIntArray()\npoly.getTriangles(vertices, vertexList, space)\nvertexCount += vertexList.length()\npoly.next()\npoly.reset()\n\n# start writing\nfh.write(struct.pack('B', FILE_VERSION))\nfh.write(struct.pack('I', vertexCount))\nfh.write(struct.pack('B', vertexElementSize))\n# currently I'm duplicating all vertices per triangle, so total indices matches total vertices\nfh.write(struct.pack('I', vertexCount))\nfh.write(struct.pack('B', indexElementSize))\nfh.write(struct.pack('I', GL_TRIANGLES)) # render type\n\n# attribute layout\n\n# Since NVidia is the only driver to implement a default attribute layout I am following this as much as possible\n# on other drivers using a custom shader is mandatory and modern buffers will never work with the fixed function pipeline.\n# https://stackoverflow.com/questions/20573235/what-are-the-attribute-locations-for-fixed-function-pipeline-in-opengl-4-0-cor\n\n# num attributes\nfh.write(struct.pack('B', 3 + len(colorSetNames) + len(uvSetNames)))\n# vec4 position at location 0\nfh.write(struct.pack('B', 0))\nfh.write(struct.pack('B', 4))\nfh.write(struct.pack('I', GL_FLOAT))\n# vec3 tangent at location 1\nfh.write(struct.pack('B', 1))\nfh.write(struct.pack('B', 3))\nfh.write(struct.pack('I', GL_FLOAT))\n# vec3 normal at location 2\nfh.write(struct.pack('B', 2))\nfh.write(struct.pack('B', 3))\nfh.write(struct.pack('I', GL_FLOAT))\n# vec4 color at locations (3,7) and 16+\nused = {}\nfor i in xrange(len(colorSetNames)):\nidx = 3 + i\nif idx > 7:\nidx = 11 + i\nfh.write(struct.pack('B', idx))\nfh.write(struct.pack('B', 4))\nfh.write(struct.pack('I', GL_FLOAT))\n# vec2 uvs at locations 8-15 and 16+, but avoiding overlap with colors\nidx = 8\nfor i in xrange(len(uvSetNames)):\nwhile idx in used:\nidx += 1\nfh.write(struct.pack('B', idx))\nfh.write(struct.pack('B', 2))\nfh.write(struct.pack('I', GL_FLOAT))\nidx += 1\n\n# iter all faces\nwhile not poly.isDone():\n# map object indices to local indices - because for some reason we can not query the triangulation as local indices\n# but all getters do want us to provide local indices\nobjectToFaceVertexId = {}\ncount = poly.polygonVertexCount()\nfor i in xrange(count):\nobjectToFaceVertexId[poly.vertexIndex(i)] = i\n\n# get triangulation of this face\nvertices = MPointArray()\nvertexList = MIntArray()\npoly.getTriangles(vertices, vertexList, space)\n\n# get per-vertex data\nnormals = MVectorArray()\npoly.getNormals(normals, space)\ncolorSet = []\nfor i, colorSetName in enumerate(colorSetNames):\ncolorSet.append(MColorArray())\npoly.getColors(colorSet[i], colorSetName)\nuvSetU = []\nuvSetV = []\nfor i, uvSetName in enumerate(uvSetNames):\nuvSetU.append(MFloatArray())\nuvSetV.append(MFloatArray())\npoly.getUVs(uvSetU[i], uvSetV[i], uvSetName)\n\n# write the data\nfor i in xrange(vertexList.length()):\nlocalVertexId = objectToFaceVertexId[vertexList[i]]\ntangentId = poly.tangentIndex(localVertexId)\n\nfh.write(struct.pack('4f', vertices[i], vertices[i], vertices[i], 1.0))\nfh.write(struct.pack('3f', tangents[tangentId], tangents[tangentId], tangents[tangentId]))\nfh.write(struct.pack('3f', normals[localVertexId], normals[localVertexId], normals[localVertexId]))\nfor j in xrange(len(colorSetNames)):\nfh.write(struct.pack('4f', colorSet[j][localVertexId], colorSet[j][localVertexId], colorSet[j][localVertexId], colorSet[j][localVertexId]))\nfor j in xrange(len(uvSetNames)):\nfh.write(struct.pack('2f', uvSetU[j][localVertexId], uvSetV[j][localVertexId]))\n\npoly.next()\n\n# write the elements buffer\nfor i in xrange(vertexCount):\nfh.write(struct.pack('I', i))\n\ndef exportSelected():\nselectedMeshShapes = cmds.select(ls=True, type='mesh', l=True) or []\nselectedMeshShapes += cmds.listRelatives(cmds.select(ls=True, type='transform', l=True) or [], c=True, type='mesh', f=True) or []\nfrom PyQt4.QtCore import QSettings\nfrom PyQt4.QtGui import QFileDialog\nsettings = QSettings('GLMeshExport')\nmostRecentDir = str(settings.value('mostRecentDir').toPyObject())\ntargetDir = QFileDialog.getExistingDirectory(None, 'Save selected meshes in directory', mostRecentDir)\nif targetDir and os.path.exists(targetDir):\nsettings.setValue('mostRecentDir', targetDir)\nfor i, shortName in enumerate(cmds.ls(selectedMeshShapes)):\nexportMesh(selectedMeshShapes[i],\nos.path.join(targetDir, shortName.replace('\|', '_'), FILE_EXT),\nEXPORT_SPACE)\n```" ]	[ null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/09/img01.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/09/curves.gif", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/pasted_image_at_2017_05_06_03_33_pm-656x300.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/pasted_image_at_2017_04_19_10_22_pm.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/600px-Oren-nayar-vase2.jpg", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/pasted_image_at_2017_04_20_08_33_am.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/pasted_image_at_2017_04_25_08_42_am.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/pasted_image_at_2017_04_26_08_22_am.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/pasted_image_at_2017_04_26_08_21_am.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/pasted_image_at_2017_05_06_09_36_am.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/pasted_image_at_2017_05_06_02_39_pm.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/pasted_image_at_2017_05_06_03_33_pm.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/pasted_image_at_2017_05_15_07_50_pm.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/pasted-image-0.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/image5.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/image6.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/image8.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/image3-1.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/image1-1.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/image9.png", null, "http://trevorius.com/scrapbook/wp-content/uploads/2017/08/image2-1.png", null, 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https://rpg.stackexchange.com/questions/34190/how-do-i-calculate-the-chance-of-hits/44896	[ "# How do I calculate the chance of hits?\n\n(I do not know if I should post this in math.stackexchange.com, so I try to phrase it in a way that it makes sense for non-roleplayers. Just in case it gets moved)\n\nIn the latest two editions of Shadowrun, you roll several 6 sided dice, and every die showing a 5 or 6 is considered a hit.\n\nHow do I calculate the chance of rolling 3 dice giving more hits than rolling 4 dice?\n\n• Your question is not entirely clear, could you provide some examples as to what you mean? a sample perhaps of the rolling itself, and what you are trying to use this for? As it will help in giving you an answer that is meaningful. \"How do I calculate\" is not what you want, you probably want a method, or a table for understanding the odds in your game. Either way - more description please. Feb 24, 2014 at 10:07\n• @InbarRose maybe it's not clearly worded but I think the aim is really clear. He wants to roll 3d6 and 4d6, in sequence, and get more successes on the first roll than on the second. What's the chance of that happening? Please Andràs tell us if I'm wrong. Feb 24, 2014 at 10:18\n• I deliberately did not use the DnD notation (3d6), because it is calculated entirely differently. 3d6 has an average of 10.5, rolling 3 dice in SR5 has an average of 1. Feb 24, 2014 at 10:20\n• I am open to suggestions how to phrase the question better, but I think writing 3d6 is will make it only worse, not better. Feb 24, 2014 at 10:21\n• I'd add a word about why you need to know that. I suppose Shadowrun has opposed checks and you want to know your winning chances when facing an opponent with an higher number of dice? Feb 24, 2014 at 16:07\n\nI'm sure it's possible and not too hard to treat your dice rolls as if they were 3d3 and 4d3 giving a success on a roll of 3 (for easier math), calculate the probabilities of getting 1, 2 or 3 successes on the first set and then the probability to get 1, 2, 3 or 4 successes on the second, then seeing which combination of those gives the intended result.\n\nI'm fairly sure someone can write a mathematical formula for this, and I think I could if I spent some time on it, luckily there's Anydice that can do the math for us.\n\noutput [count {5, 6} in 3d6] - [count {5, 6} in 4d6]\n\n\nAs you can see, the probability to get at least one more success on 3d6 than on 4d6 are 25.24%\n\nI got curious about this question myself, so I did some thinking and came up with an equation:\n\n$$\\sum_{i=t}^n \\binom{n}{i} \\left(\\dfrac{1}{3}\\right)^i \\left(\\dfrac{2}{3}\\right)^{n-i}$$\n\nWhere $n$ is the number of dice being rolled and $t$ is the desired threshold for the test. The result will be the probability of getting at least $t$ hits with $n$ dice.\n\nIn case you are not familiar with the notation, the first part of the sum (after the sigma and before the fractions) is the \"binomial coefficient\". It is typically read \"n choose i\" and represents the number of times you can choose $i$ items from a set of $n$ items.\n\nSince the question asks specifically how you would do such a calculation, let me give a little explanation of the logic behind this equation.\n\nFirst thing to do is imagine what a \"hit\" would look like. Since a hit is achieved by rolling a 5 or 6 on a six-sided die, then there is a 1/3 chance of getting a hit on a single die. This also means that there is a 2/3 chance of getting a miss on a die. That's where the two fractions come from in the equation.\n\nSecondly, we want to know the probability of getting a certain number of hits. The odds of getting $i$ number of hits is $(1/3)^i$. So, rolling 2 hits would have a probability of $(1/3)^2$. Rolling 3 hits would be $(1/3)^3$. However... that's not the whole picture. When you rolling $n$ dice, some of them are hits and some are misses. So if $i$ dice are nits out of $n$ dice, then you can say that there are $n-i$ misses. Now getting certain number of misses is $(2/3)^{n-1}$.\n\nThirdly, now that we understand the fractional parts of the equation... There are multiple ways to get any given set of results (usually). To illustrate... Image we have 3 dice and we want to get 2 hits. If we name the dice die A, die B, and die C, then we can see that we could have hits on (A,B) or (B,C) or (A,C). So in the situation of trying to find 2 hits on 3 dice, we would have to multiply the $(1/3)^i \\times (2/3)^{n-i}$ by the 3 different ways it can occur. We can generalize that by saying that the fractional part of our probability equation must be multiplied by the number of ways to get $i$ hits out of $n$ dice. Hence the binomial coefficient part of the equation.\n\nUp to now we have all that is needed calculate the probability of getting exactly $i$ number of hits on $n$ dice... However, if we'd like to calculate the chance of reaching a threshold then we need to look at the probability of not just getting $i$ hits, but also of getting $i+1$ hits or $i+2$ hits all the way to $n$ hits (i.e. getting hits on all the dice). This is why we sum from $t$ (the min number of hits needed) to $n$ (the max number, since it's all the dice you rolled).\n\nYou can see a table here of all the calculated probabilities from $n = 1..20$ and $t = 1..20$.\n\nI will also include the equation I came up with to calculate the same probabilities when using the Rule of Six. This equation is included primarily for those who are curious, and so I won't include the long explanation.\n\n$$P_e(n, t) = \\sum_{i=t}^n \\binom{n}{i} \\left(\\dfrac{1}{3}\\right)^i \\left(\\dfrac{2}{3}\\right)^{n-i} + \\sum_{i=1}^{t-1} \\sum_{j=0}^{i-1} \\binom{n}{n-i} \\left(\\dfrac{1}{6}\\right)^j \\left(\\dfrac{1}{6}\\right)^{i-j} \\left(\\dfrac{2}{3}\\right)^{n-i} P_e(i-j, t-i)$$\n\nHere is the same table showing those probabilities with Rule of Six.\n\n• Having an accepted answer does not mean a question is done and closed! This looks like good stuff, though I'm not versed enough in SR to say for sure. I suspect you're familiar with SE, though; but if not, the Tour is worth checking out (can be even if you know other sites), plus we have the Role-playing Games Chat if you've got 20 rep here or at any other SE. Jul 22, 2014 at 23:18" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9145845,"math_prob":0.9902208,"size":3424,"snap":"2023-40-2023-50","text_gpt3_token_len":967,"char_repetition_ratio":0.12631579,"word_repetition_ratio":0.0,"special_character_ratio":0.3057827,"punctuation_ratio":0.0930851,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9992909,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-11T23:48:34Z\",\"WARC-Record-ID\":\"<urn:uuid:88a4a8e8-8718-428c-bed3-1f588dc00f13>\",\"Content-Length\":\"175841\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:694c6278-2ea5-4fac-99e1-a6e98d77abb2>\",\"WARC-Concurrent-To\":\"<urn:uuid:2de36091-1194-4b33-93a4-bf3c01781b62>\",\"WARC-IP-Address\":\"104.18.43.226\",\"WARC-Target-URI\":\"https://rpg.stackexchange.com/questions/34190/how-do-i-calculate-the-chance-of-hits/44896\",\"WARC-Payload-Digest\":\"sha1:BQH3L7DAEFNBLZ4FWCBM2RYFP4QJRTQL\",\"WARC-Block-Digest\":\"sha1:3JTYPMPBQBLRAZRBNWGYRE6WCKDJNUML\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679518883.99_warc_CC-MAIN-20231211210408-20231212000408-00603.warc.gz\"}"}
https://socratic.org/questions/what-part-of-speech-does-the-diamante-usually-begin-with#323947	[ "# What part of speech does the diamante usually begin with ?\n\nA noun\n\n#### Explanation:\n\nA diamante poem is a kind of poem where the rules of it bring about a diamond shape. They are 7 lines long:\n\n$\\textcolor{b l u e}{\\text{Line number\") ->color(purple)(\"Number of words\") ->color(brown)(\"Type of word}}$\n\n1 $\\textcolor{w h i t e}{0000000000000000}$1 $\\textcolor{w h i t e}{000000000000}$noun\n\n2 $\\textcolor{w h i t e}{0000000000000000}$2 $\\textcolor{w h i t e}{0000000000}$adjective\n\n3 $\\textcolor{w h i t e}{0000000000000000}$3 $\\textcolor{w h i t e}{000000000000}$verb\n\n4 $\\textcolor{w h i t e}{0000000000000000}$4 $\\textcolor{w h i t e}{000000000000}$noun\n\n5 $\\textcolor{w h i t e}{0000000000000000}$3 $\\textcolor{w h i t e}{000000000000}$verb\n\n6 $\\textcolor{w h i t e}{0000000000000000}$2 $\\textcolor{w h i t e}{0000000000}$adjective\n\n7 $\\textcolor{w h i t e}{0000000000000000}$1 $\\textcolor{w h i t e}{000000000000}$noun\n\nNow - how to use this structure? There are two basic ways to use it - as a way to compare two synonyms (and so therefore known as a synonym diamante) and as a way to compare two antonyms (which is unsurprisingly called a antonym diamante).\n\nThe basic idea of how to fill in the words is to write down your two nouns, then brainstorm words associated with each of them (so for example, you could use milk and ice cream as synonyms and perhaps light and dark as antonyms).\n\nThere are a few examples in the link below - unfortunately the formatting tools at my disposal don't allow me to create the look I want for mine, but here's an example from someone else:", null, "http://www.poetry4kids.com/lessons/how-to-write-a-diamante-poem/" ]	[ null, "https://useruploads.socratic.org/6YALhGQTDaqCcDlSFQhd_imgres.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8916655,"math_prob":0.9961495,"size":1456,"snap":"2021-43-2021-49","text_gpt3_token_len":409,"char_repetition_ratio":0.29820937,"word_repetition_ratio":0.021052632,"special_character_ratio":0.35782966,"punctuation_ratio":0.0562249,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95789534,"pos_list":[0,1,2],"im_url_duplicate_count":[null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-25T17:56:40Z\",\"WARC-Record-ID\":\"<urn:uuid:6d4f14af-ce21-4871-b522-3238359ab469>\",\"Content-Length\":\"36668\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:86247ea3-4098-4257-a41a-820c325b47f0>\",\"WARC-Concurrent-To\":\"<urn:uuid:9874e5be-e566-4ae4-8e92-63603afad54a>\",\"WARC-IP-Address\":\"216.239.34.21\",\"WARC-Target-URI\":\"https://socratic.org/questions/what-part-of-speech-does-the-diamante-usually-begin-with#323947\",\"WARC-Payload-Digest\":\"sha1:TABKH22ISKK4JWBNSYSJCF3OGZNGXSQZ\",\"WARC-Block-Digest\":\"sha1:KWEBU2K7KY2BYK4NLIXF2FUJXG3T3QUT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323587719.64_warc_CC-MAIN-20211025154225-20211025184225-00140.warc.gz\"}"}
http://export.arxiv.org/abs/math/0409486	[ "math\n\n# Title: Fractional Fokker--Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises\n\nAbstract: The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. In this paper, we derive a Fractional Fokker--Planck equation for the probability distribution of particles whose motion is governed by a {\\em nonlinear} Langevin-type equation, which is driven by a non-Gaussian Levy-stable noise. We obtain in fact a more general result for Markovian processes generated by stochastic differential equations.}\n Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph) MSC classes: 05.40+j,05.60+w, 66.10Cb, 05.70 a Journal reference: J. Math. Phys., 42(2001), 200-212 DOI: 10.1063/1.1318734 Cite as: arXiv:math/0409486 [math.AP] (or arXiv:math/0409486v1 [math.AP] for this version)\n\n## Submission history\n\nFrom: Vena Pearl Bongolan-Walsh Mrs. [view email]\n[v1] Fri, 24 Sep 2004 20:42:24 GMT (10kb)\n\nLink back to: arXiv, form interface, contact." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.85750145,"math_prob":0.7783861,"size":925,"snap":"2019-51-2020-05","text_gpt3_token_len":222,"char_repetition_ratio":0.111834966,"word_repetition_ratio":0.0,"special_character_ratio":0.21081081,"punctuation_ratio":0.12101911,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96310604,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-11T04:41:33Z\",\"WARC-Record-ID\":\"<urn:uuid:b2c554fb-f2d3-47c7-ac49-005e79ecb07f>\",\"Content-Length\":\"13904\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:87663c57-c100-45a5-bc9f-3b5cb297f877>\",\"WARC-Concurrent-To\":\"<urn:uuid:0bb78586-6da6-484c-9904-762c6efdde34>\",\"WARC-IP-Address\":\"128.84.21.203\",\"WARC-Target-URI\":\"http://export.arxiv.org/abs/math/0409486\",\"WARC-Payload-Digest\":\"sha1:34IZERUIRTE4ARTHTX7QM76OBTO2N4WD\",\"WARC-Block-Digest\":\"sha1:F2M7GVENCPWOCXIYR7NWCG53NUPHX7WT\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540529745.80_warc_CC-MAIN-20191211021635-20191211045635-00169.warc.gz\"}"}
https://math.stackexchange.com/questions/490079/pi-might-contain-all-finite-sets-can-it-also-contain-infinite-sets	[ "# Pi might contain all finite sets, can it also contain infinite sets?\n\nIn a previous, and quite popular, question it was discussed about whether or not $\\pi$ contains all finite number combinations.\n\nLet us assume for a moment that $\\pi$ does in fact contain all finite combinations of numbers. What prevents $\\pi$ from also containing all infinite sets?\n\nIt seems that at some point one would also see the first couple digits of, for example, $e$ (2.71828). But why does it need to stop there, couldn't it contain a bunch of digits of $e$? Perhaps even an infinite number of digits of $e$?\n\nMy understanding is that $e$ could also be replaced by $\\sqrt2$ or any other irrational number, so long as that irrational number contained all finite sets of number combinations. Which might imply that somewhere along the way, $e$ contains a number of digits of $\\pi$. Implying this ridiculous situation where within $\\pi$ we see $e$, and then within $e$ we again begin to see $\\pi$ again. Then all the universe collapses into a singularity. Or maybe someone can just explain why one infinite sequence can't contain another infinite sequence, and perhaps why we have not defined some type of super-infinity that can.\n\nTo reiterate the primary question: What prevents $\\pi$, or other infinite irrational number that contains all finite sets of numbers, from also containing all infinite sets?\n\n## 2 Answers\n\nIf the decimal expansion of $\\pi$ contained the string of digits '$000\\ldots$' then it only has a finite number of non-zero digits (some subset of the digits before the string of $0$s starts) and so $\\pi$ is a rational number. Contradiction.\n\n• That makes a lot of sense. So clear, I almost feel silly for not having realized it. – mwjohnson Sep 11 '13 at 1:35\n• The point is that infinite strings don't have an end (on the right as we write them) so there are very few infinite strings actually contained in $\\pi$ - only those of the form $[10^n\\cdot\\pi]$ for $n\\geq -1$ where $[\\bullet]$ is the 'fractional part' function. – Dan Rust Sep 11 '13 at 1:38\n• Rationality and irrationality aside, if it contains 000000... it certainly cannot also contain 111111.... – Nate Eldredge Sep 11 '13 at 2:10\n• @NateEldredge Yeah there's a bunch of natural contradictions you can reach. – Dan Rust Sep 11 '13 at 2:15\n• Well, you should carefully distinguish between \"set\" and \"sequence\". It does contain many different sequences: for instance, 1415926..., 415926..., 15926..., etc, where each one is some \"tail\" of all the ones before it. But it cannot contain both of two sequences where neither is a tail of the other. – Nate Eldredge Aug 6 '18 at 16:26\n\nThere are an uncountable number of infinite digit strings, and $\\pi$ contains only countably many infinite digit strings-namely all the ones that are the digits after some point in the expansion. It does contain infinite strings, just not most of them.\n\n• This is a stronger answer because it also disposes of a lot of variations such as \"what if we only want each infinite sequence of digits to appear at some set of positions that form an arithmetic progression?\" – Henning Makholm Sep 11 '13 at 13:05\n• @user500668: that depends what you mean by includes. You could start after the fifth decimal place-would you say it includes that sequence? You could take every other term. You could do a lot of things. – Ross Millikan Aug 6 '18 at 16:26" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9425986,"math_prob":0.9816907,"size":1309,"snap":"2019-13-2019-22","text_gpt3_token_len":282,"char_repetition_ratio":0.15862069,"word_repetition_ratio":0.018604651,"special_character_ratio":0.22383499,"punctuation_ratio":0.101626016,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99667364,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-05-23T17:56:03Z\",\"WARC-Record-ID\":\"<urn:uuid:bb9ee949-d1dc-491a-8d67-ad7e0442cf1f>\",\"Content-Length\":\"145093\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:49289d39-f573-47a2-8925-0be854f5f800>\",\"WARC-Concurrent-To\":\"<urn:uuid:0cc1dd36-2265-4368-8339-bbe6269294f9>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/questions/490079/pi-might-contain-all-finite-sets-can-it-also-contain-infinite-sets\",\"WARC-Payload-Digest\":\"sha1:LEXX6L3TWY3HQIRG2HUAMC74JGH4EU37\",\"WARC-Block-Digest\":\"sha1:5S7IISPUFCAIVU2R4EIQLJPZPBYARLV5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-22/CC-MAIN-2019-22_segments_1558232257316.10_warc_CC-MAIN-20190523164007-20190523190007-00370.warc.gz\"}"}
https://de3de.com/industrial-hemp-tipap/chain-rule-questions-f6e051	[ "Check your level of preparation with the practice exercises based on chain rule questions. Welcome to highermathematics.co.uk A sound understanding of the Chain Rule is essential to ensure exam success. Basic examples that show how to use the chain rule to calculate the derivative of the composition of functions. About. Here Given Chain Rule practice questions, quiz, fully solved questions, tips & trick and Mock tests, which include question from each topic will help you to excel in Chain Rule. Reverse chain rule example. This calculus video tutorial shows you how to find the derivative of any function using the power rule, quotient rule, chain rule, and product rule. Practice: Reverse chain rule. This is a way of differentiating a function of a function. 2 2 10 10 7 7 x dx x C x = − + ∫ − 6. Each element has two figures except one element that has one part missing. The Chain Rule Powerpoint Lesson 1. In school, there are some chocolates for 240 adults and 400 children. Online aptitude preparation material with practice question bank, examples, solutions and explanations. Partial fraction expansion. The Chain Rule is a means of connecting the rates of change of dependent variables. with full confidence. • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). Covered for all Bank Exams, Competitive Exams, Interviews and Entrance tests. This unit illustrates this rule. The other given part of the same element is taken as base and is compared separately with all the other elements e.g. If you're behind a web filter, please make sure that the domains .kastatic.org and .kasandbox.org are unblocked. So when using the chain rule: Back to Problem List. The Chain Rule is a formula for computing the derivative of the composition of two or more functions. This can be viewed as y = sin(u) with u = x2. How do I apply the chain rule to double partial derivative of a multivariable function? 1. by the Chain Rule, dy/dx = dy/dt × dt/dx so dy/dx = 3t² × 2x = 3(1 + x²)² × 2x = 6x(1 + x²) ². 2 3 1 sin cos cos 3 ∫ x x dx x C= − + 5. Some of the types of chain rule problems that are asked in the exam. Ask Question Asked today. For instance, if f and g are functions, then the chain rule expresses the derivative of their composition. Therefore we have dy du = cos(u) and du dx = 2x. Chain rule is used to find out this missing part of an element by subsequent comparison. The Product, Quotient, and Chain Rules. The chain rule says that. • Fill in the boxes at the top of this page with your name. Answer to 2: Differentiate y = sin 5x. Nested Multivariable Chain Rule. Example 1; Example 2; Example 3; Example 4; Example 5; Example 6; Example 7; Example 8 ; In threads. To access a wealth of additional free resources by topic please either use the above Search Bar or click on any of the Topic Links found at the bottom of this page as well as on the Home Page HERE. Khan Academy is a 501(c)(3) nonprofit organization. Chain Rule Instructions • Use black ink or ball-point pen. This chapter focuses on some of the major techniques needed to find the derivative: the product rule, the quotient rule, and the chain rule. y=f(u) u=f(x) y=(2x+4)3 y=u3andu=2x+4 dy du =3u2 du dx =2 dy dx =3u2×2=2×3(2x+4)2 dy dx = dy du ⋅ du dx dy dx =6(2x+4)2. We have Free Practice Chain Rule (Arithmetic Aptitude) Questions, Shortcuts and Useful tips. Why Aptitude Chain Rule? In calculus, the chain rule is a formula to compute the derivative of a composite function. Video lectures to prepare quantitative aptitude for placement tests, competitive exams like MBA, Bank exams, RBI, IBPS, SSC, SBI, RRB, Railway, LIC, MAT. However, we rarely use this formal approach when applying the chain rule to specific problems. The rule itself looks really quite simple (and it is not too difficult to use). En anglais, on peut dire the chain rule (of differentiation of a function composed of two or more functions). In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. So all we need to do is to multiply dy /du by du/ dx. Rates of change . Question 1 . Most problems are average. Differentiate using the chain rule. Integral of tan x. The chain rule is a rule for differentiating compositions of functions. Section 3-9 : Chain Rule. back to top . The chain rule is used to differentiate composite functions. Donate or volunteer today! Confusing limit problem within proof of the chain rule. Differentiate $$f\\left( x \\right) = {\\left( {6{x^2} + 7x} \\right)^4}$$ . Multivariable Chain Rule - A solution I can't understand. Top; Examples. VCE Maths Methods - Chain, Product & Quotient Rules The chain rule 3 • The chain rule is used to di!erentiate a function that has a function within it. Chain rule Statement Examples Table of Contents JJ II J I Page1of8 Back Print Version Home Page 21.Chain rule 21.1.Statement The power rule says that d dx [xn] = nxn 1: This rule is valid for any power n, but not for any base other than the simple input variable x. Created by T. Madas Created by T. Madas Question 1 Carry out each of the following integrations. In examples such as the above one, with practise it should be possible for you to be able to simply write down the answer without having to let t = 1 + x² etc. If you're seeing this message, it means we're having trouble loading external resources on our website. The Questions. Hint : Recall that with Chain Rule problems you need to identify the “inside” and “outside” functions and then apply the chain rule. Let u = 5x (therefore, y = sin u) so using the chain rule. You can use our resources like sample question papers and Maths previous years’ papers to practise questions and answers for Maths board exam preparation. Integral of tan x. Our mission is to provide a free, world-class education to anyone, anywhere. If air is blown into a spherical balloon at the rate of 10 cm 3 / sec. • The quotient rule • The chain rule • Questions 2. Example #1 . The Chain Rule mc-TY-chain-2009-1 A special rule, thechainrule, exists for diﬀerentiating a function of another function. 2. Active today. ∫4sin cos sin3 4x x dx x C= + 4. Understand how to differentiate composite functions by using the Chain Rule correctly with our CBSE Class 12 Science Maths video lessons. Here you will be shown how to use the Chain Rule for differentiating composite functions. The Chain Rule Equation . The Chain Rule\n2. The answer keys and explanations are given for the same. BY REVERSE CHAIN RULE . These Multiple Choice Questions (MCQs) on Chain Rule help you evaluate your knowledge and skills yourself with this CareerRide Quiz. Example #1 Differentiate (3 x+ 3) 3 . That is, if f and g are differentiable functions, then the chain rule expresses the derivative of their composite f ∘ g — the function which maps x to (()) — in terms of the derivatives of f and g and the product of functions as follows: (∘) ′ = (′ ∘) ⋅ ′. Skip to navigation (Press Enter) Skip to main content (Press Enter) Home; Threads; Index; About; Math Insight. Help Center Detailed answers to any questions you might have ... How does chain rule work for complex valued function? The Chain Rule. The chain rule makes it possible to diﬀerentiate functions of func-tions, e.g., if y is a function of u (i.e., y = f(u)) and u is a function of x (i.e., u = g(x)) then the chain rule states: if y = f(u), then dy dx = dy du × du dx Example 1 Consider y = sin(x2). Viewed 16 times 0 $\\begingroup$ Let ... Browse other questions tagged real-analysis multivariable-calculus or ask your own question. The Chain Rule is used for differentiating composite functions. Chain Rule Online test - 20 questions to practice Online Chain Rule Test and find out how much you score before you appear for next interview and written test. 2. J'ai constaté que la version homologue française « règle de dérivation en chaîne » ou « règle de la chaîne » est quasiment inconnue des étudiants. ( ) ( ) 3 1 12 24 53 10 ∫x x dx x C− = − + 2. In the following discussion and solutions the derivative of a function h(x) will be denoted by or h'(x) . A few are somewhat challenging. 1. Mes collègues locuteurs natifs m'ont recommandé de … This is the currently selected item. Chain Rule can be applied in questions where two or more than two elements are given. Chapter 5. Show Solution. Next lesson. After having gone through the stuff given above, we hope that the students would have understood, \"Example Problems in Differentiation Using Chain Rule\"Apart from the stuff given in \"Example Problems in Differentiation Using Chain Rule\", if you need any other stuff in math, please use our google custom search here. Chain Rule problems or examples with solutions. ( ) ( ) 1 1 2 3 31 4 1 42 21 6 x x dx x C − ∫ − = − − + 3. The only problem is that we want dy / dx, not dy /du, and this is where we use the chain rule. As u = 3x − 2, du/ dx = 3, so. Site Navigation. The most important thing to understand is when to use it and then get lots of practice. Use the chain rule to differentiate composite functions like sin(2x+1) or [cos(x)]³. Example #2 Differentiate y =(x 2 +5 x) 6 . The Problem\nComplex Functions\nWhy?\nnot all derivatives can be found through the use of the power, product, and quotient rules\nIn this section you can learn and practice Aptitude Questions based on \"Chain Rule\" and improve your skills in order to face the interview, competitive examination and various entrance test (CAT, GATE, GRE, MAT, Bank Exam, Railway Exam etc.) 1. If the chocolates are taken away by 300 children, then how many adults will be provided with the remaining chocolates? Up Next. 1. Chain Rule Examples. Integral of tan x. Problems on Chain Rule - Quantitative aptitude tutorial with easy tricks, tips, short cuts explaining the concepts. Each test has all the basics questions to advanced questions with answer and explanation for your clear understanding, you can download the test result as pdf for further reference. The chain rule states formally that . Question 3 Use the chain rule and the fact that when $y=af(x)$, $\\frac{\\mathrm{d}y}{\\mathrm{d}x}=af'(x)$ to differentiate the following: Page Navigation." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8708607,"math_prob":0.9388883,"size":10200,"snap":"2021-31-2021-39","text_gpt3_token_len":2517,"char_repetition_ratio":0.1700667,"word_repetition_ratio":0.016393442,"special_character_ratio":0.24705882,"punctuation_ratio":0.122815534,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9873761,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-24T14:39:15Z\",\"WARC-Record-ID\":\"<urn:uuid:f9b205e4-ca68-4215-b7a0-a4366d9edc0e>\",\"Content-Length\":\"21749\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:479589c6-269f-4511-895c-61065d3b06e6>\",\"WARC-Concurrent-To\":\"<urn:uuid:5f85313c-16f7-47e8-a85d-a4fec09783e4>\",\"WARC-IP-Address\":\"217.182.147.37\",\"WARC-Target-URI\":\"https://de3de.com/industrial-hemp-tipap/chain-rule-questions-f6e051\",\"WARC-Payload-Digest\":\"sha1:VKKA44JBBNDBUFDX5KTOE5I5HJ376IBW\",\"WARC-Block-Digest\":\"sha1:D73G4JIY7JMZIAMOW564YHDRXG2O6G4Q\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057558.23_warc_CC-MAIN-20210924140738-20210924170738-00453.warc.gz\"}"}
http://mirror.theoryofcomputing.org/articles/v016a012/index.html	[ "", null, "Volume 16 (2020) Article 12 pp. 1-18\nOptimality of Correlated Sampling Strategies\nReceived: December 2, 2017\nRevised: July 31, 2020\nPublished: November 9, 2020\nDownload article from ToC site:\n[PDF (265K)] [PS (1309K)] [PS.GZ (309K)]\n[Source ZIP]\nKeywords: distributions, sampling, correlated sampling, coupling, MinHash, communication complexity\nACM Classification: F.0, G.3\nAMS Classification: 68Q99, 94A20, 68W15\n\nAbstract: [Plain Text Version]\n\nIn the correlated sampling problem, two players are given probability distributions $P$ and $Q$, respectively, over the same finite set, with access to shared randomness. Without any communication, the two players are each required to output an element sampled according to their respective distributions, while trying to minimize the probability that their outputs disagree. A well known strategy due to Kleinberg--Tardos and Holenstein, with a close variant (for a similar problem) due to Broder, solves this task with disagreement probability at most $2 \\delta/(1+\\delta)$, where $\\delta$ is the total variation distance between $P$ and $Q$. This strategy has been used in several different contexts, including sketching algorithms, approximation algorithms based on rounding linear programming relaxations, the study of parallel repetition and cryptography.\n\nIn this paper, we give a surprisingly simple proof that this strategy is essentially optimal. Specifically, for every $\\delta \\in (0,1)$, we show that any correlated sampling strategy incurs a disagreement probability of essentially $2\\delta/(1+\\delta)$ on some inputs $P$ and $Q$ with total variation distance at most $\\delta$. This partially answers a recent question of Rivest.\n\nOur proof is based on studying a new problem that we call constrained agreement. Here, the two players are given subsets $A \\subseteq [n]$ and $B \\subseteq [n]$, respectively, and their goal is to output an element $i \\in A$ and $j \\in B$, respectively, while minimizing the probability that $i \\neq j$. We prove tight bounds for this question, which in turn imply tight bounds for correlated sampling. Though we settle basic questions about the two problems, our formulation leads to more fine grained questions that remain open." ]	[ null, "http://mirror.theoryofcomputing.org/images/pdficon_large.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.92802304,"math_prob":0.98532766,"size":1909,"snap":"2021-21-2021-25","text_gpt3_token_len":417,"char_repetition_ratio":0.09868766,"word_repetition_ratio":0.0,"special_character_ratio":0.22629648,"punctuation_ratio":0.11940298,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9978127,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-15T16:28:43Z\",\"WARC-Record-ID\":\"<urn:uuid:a51aaa7f-c8d2-4a9e-bad7-271a6afcbd06>\",\"Content-Length\":\"9426\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:28d8849e-75d9-4e09-b80e-43d2201e1951>\",\"WARC-Concurrent-To\":\"<urn:uuid:11467e4a-6dcb-4ef5-9145-4fe06eadf0db>\",\"WARC-IP-Address\":\"128.135.164.114\",\"WARC-Target-URI\":\"http://mirror.theoryofcomputing.org/articles/v016a012/index.html\",\"WARC-Payload-Digest\":\"sha1:26RE54YBMVHMSLTMGFKEFP2LAPKQKBX4\",\"WARC-Block-Digest\":\"sha1:65WPOHZT7DDNZ5DBYV6M4L7K557IVGCE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623487621450.29_warc_CC-MAIN-20210615145601-20210615175601-00020.warc.gz\"}"}
https://www.hpmuseum.org/forum/printthread.php?tid=7168	[ "", null, "Orthogonal Matrix Test - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Software Libraries (/forum-10.html) +--- Forum: HP Prime Software Library (/forum-15.html) +--- Thread: Orthogonal Matrix Test (/thread-7168.html) Orthogonal Matrix Test - Eddie W. Shore - 11-04-2016 07:31 PM For the square matrix M, it is orthogonal when either of the following conditions are met: (I) M * M^T = M^T * M = I (II) M^-1 = M^T The program presented on this blog entry will use the first test. Since matrices, unfortunately, cannot be directly compared on the Casio graphing calculators, a work around with two FOR loops is implemented. HP Prime Program ORTHOG Code: ```EXPORT ORTHOG(m) BEGIN // 2016-11-01 EWS // orthogonal test LOCAL n,p,s; s≔SIZE(m); s≔s(1); n≔TRN(m)*m; p≔IDENMAT(s); IF n==p THEN RETURN 1; ELSE RETURN 0; END; END;```" ]	[ null, "https://www.hpmuseum.org/mohpcf.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.78734314,"math_prob":0.8251202,"size":703,"snap":"2020-10-2020-16","text_gpt3_token_len":188,"char_repetition_ratio":0.115879826,"word_repetition_ratio":0.0,"special_character_ratio":0.28876245,"punctuation_ratio":0.14074074,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9661361,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-05T14:25:03Z\",\"WARC-Record-ID\":\"<urn:uuid:9b0d58fc-2a75-49af-976c-46a8668b3dd8>\",\"Content-Length\":\"2976\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0913b64f-68b0-4e7b-b498-4a424c219d0f>\",\"WARC-Concurrent-To\":\"<urn:uuid:681097de-8113-489c-98ce-8c217d786a40>\",\"WARC-IP-Address\":\"209.197.117.170\",\"WARC-Target-URI\":\"https://www.hpmuseum.org/forum/printthread.php?tid=7168\",\"WARC-Payload-Digest\":\"sha1:5OORWNAQSE2GKIYT4IESZUSTHCMFJRFX\",\"WARC-Block-Digest\":\"sha1:JNIW4E6R6CIHBLHUWNE3AQQOSCUMTQJZ\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585371604800.52_warc_CC-MAIN-20200405115129-20200405145629-00110.warc.gz\"}"}
https://books.google.co.ve/books?qtid=87e7858&dq=related:ISBN8474916712&lr=&id=fso2AAAAMAAJ&output=html_text&sa=N&start=170	[ "Libros Libros", null, "A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.", null, "A Treatise of Plane Trigonometry, and the Mensuration of Heights and ... - Página 19\npor Jeremiah Day - 1848 - 153 páginas\nVista completa - Acerca de este libro", null, "## New Plane and Solid Geometry\n\nWebster Wells - 1908 - 298 páginas\n...and terminating in the opposite sides cannot bisect each other. BOOK II THE CIRCLE DEFINITIONS 142. A diameter of a circle is a straight line drawn through- the centre, having its extremities in the circumference. 143. By the definition of § 23 All radii of a circle...\nVista completa - Acerca de este libro", null, "## Applied Mechanical Drawing for First and Second Year Classes in High Schools ...\n\nFrank Elliott Mathewson, Judson Lloyd Stewart - 1911 - 158 páginas\n...seconds are denoted by symbols, thus 45 degrees, 17 minutes, 9 seconds is written 4-5°-, 17'-, 9\". A diameter of a circle is a straight line drawn through the center, having its extremities in the circumference; as AOB. A radius is a straight line drawn from...\nVista completa - Acerca de este libro", null, "## Practical Geometry & Graphics: A Text-book for Students in Technical and ...\n\nEdward L. Bates, Frederick Charlesworth - 1912 - 621 páginas\n...device is employed to make such points conspicuous and more easily located by the reader. A diameter is a straight line drawn through the centre, and terminated both ways by the circumference. FIG. 1. Thus, in Fig. 2, O is the centre of the circle; OA, OB, OC, are radii; AOB is a diameter. From...\nVista completa - Acerca de este libro", null, "## Practical Mathematics: Instruction Paper, Volumen3\n\nGlenn Moody Hobbs - 1912\n...circumference, every point of which is equally distant from a point within called the center, Fig. 38. A diameter of a circle is a straight line drawn through the center, terminating at both ends in the circumference. A radius of a circle is a straight line joining...\nVista completa - Acerca de este libro", null, "## Standard American Cyclopedia of Steam Engineering: A Treatise on the Care ...\n\nCalvin Franklin Swingle - 1913 - 1249 páginas\n...within the figure to the circumference are equal, and this point is called the center of the circle. A diameter of a circle is a straight line drawn through the center and terminated both ways by the circumference, as AC in Fig. 45. Fig. 45. 'M A radius is a straight...\nVista completa - Acerca de este libro", null, "## Everyday Arithmetic: Book one-[three], Libro 3\n\n...fraction is the number that shows into how many equal parts a unit has been divided. Diameter of a circle. A diameter of a circle is a straight line drawn through the center of the circle to opposite points in its circumference. Difference or remainder. A difference...\nVista completa - Acerca de este libro", null, "## Mechanical Drawing: Instruction Paper, Parte2\n\nErvin Kenison - 1916 - 71 páginas\n...circumference, every point of which is equally distant from a point within called the center, Fig. 58. A diameter of a circle is a straight line drawn through the center, terminating at both ends in the circumference, Fig. 59. A radius of a circle is a straight...\nVista completa - Acerca de este libro", null, "## Cyclopedia of Architecture, Carpentry, and Building: A General Reference ...\n\n1917\n...circumference, every point of which is equally distant from a point within called the center, Fig. 58. A diameter of a circle is a straight line drawn through the center, terminating at both ends in the circumference, Fig. 59. Fig. 58. Circle Fig. 5D. Diameter and...\nVista completa - Acerca de este libro", null, "## Modern Shop Practice: A General Reference Work, Volumen5\n\n1917\n...circumference, every point of which is equally distant from a point within called the center, Fig. 58. A diameter of a circle is a straight line drawn through the center, terminating at both ends in the circumference, Fig. 59. A radius of a circle is a straight...\nVista completa - Acerca de este libro", null, "## Sanitary, Heating and Ventilation Engineering: A General Reference ..., Volumen4\n\n1918\n...circumference, every point of which is equally distant from a point within called the center, Fig. 58. A diameter of a circle is a straight line drawn through the center, terminating at both ends in the circumference, Fig. 59. A radius of a circle is a straight...\nVista completa - Acerca de este libro" ]	[ null, "https://books.google.co.ve/googlebooks/quote_l.gif", null, "https://books.google.co.ve/googlebooks/quote_r.gif", null, "https://books.google.co.ve/books/content", null, "https://books.google.co.ve/books/content", null, "https://books.google.co.ve/books/content", null, "https://books.google.co.ve/books/content", null, "https://books.google.co.ve/books/content", null, "https://books.google.co.ve/books/content", null, "https://books.google.co.ve/books/content", null, "https://books.google.co.ve/books/content", null, "https://books.google.co.ve/books/content", null, "https://books.google.co.ve/books/content", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9128692,"math_prob":0.935555,"size":3052,"snap":"2021-31-2021-39","text_gpt3_token_len":739,"char_repetition_ratio":0.19619423,"word_repetition_ratio":0.45333335,"special_character_ratio":0.26048493,"punctuation_ratio":0.21693908,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96752393,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-25T00:46:32Z\",\"WARC-Record-ID\":\"<urn:uuid:cdbce665-be7f-4ae3-b0d8-fcc10dbcc51b>\",\"Content-Length\":\"32472\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:29b4c912-e553-49ba-899c-8feb239716e0>\",\"WARC-Concurrent-To\":\"<urn:uuid:7321a35a-7bb8-4334-8769-049063f0b3f7>\",\"WARC-IP-Address\":\"142.250.188.206\",\"WARC-Target-URI\":\"https://books.google.co.ve/books?qtid=87e7858&dq=related:ISBN8474916712&lr=&id=fso2AAAAMAAJ&output=html_text&sa=N&start=170\",\"WARC-Payload-Digest\":\"sha1:D63HHRLZIIJ4PK5WJV5ZBYKCTISNN3QS\",\"WARC-Block-Digest\":\"sha1:27IOPLV76B6VN2SIT2TQRE3ZPMGGD27H\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057584.91_warc_CC-MAIN-20210924231621-20210925021621-00206.warc.gz\"}"}
https://quickexcel.com/calculate-the-square-root/	[ "# How to Calculate the Square Root in Excel?", null, "In this tutorial, we will learn 3 easy ways to calculate the square root of a number in Excel. It will be a very common calculation that you’ll perform very often if you work with large mathematical datasets of any kind. So let’s get started.\n\n## Different Ways to Calculate the Square Root in Excel\n\nThere are many different ways you can use to calculate square roots and here are some of the most common ones.\n\n### 1. SQRT() function\n\nExcel provides an inbuilt mathematical function SQRT to calculate the positive square root of a number.\n\nSyntax: SQRT(n). Here n is the number or cell reference which contains the number for which you want the square root.\n\nWhen the SQRT function is applied to a negative number, #NUM! error message is returned.\n\nWe can avoid the #NUM! error message, use the ABS function to find the absolute value of the number and then calculate the square root.\n\n### 2. POWER() Function\n\nThe POWER function returns the result of a number raised to a power. Syntax: POWER(n,power), where n is the base number or cell reference which contains the base number and power is the exponent to which the base number is raised. This function can be utilized to find the square root of a number by keeping power as 0.5 or (1/2).\n\n## 3. Using the Caret ^ operator\n\nWe can use the caret operator ^ to raise a number to the power of half (1/2 or 0.5) and get the square root of the number.\n\nSyntax: n^(1/2) or n^0.5, where n is the number or cell reference which contains the number for which you want the square root.\n\nAs you can see, we have the square root in the column B using the caret operator.\n\n## Conclusion\n\nExcel provides a direct function SQRT to calculate the square root of a number. There are other simple methods to do the same which are discussed above. We hope you learned something new today!" ]	[ null, "https://quickexcel.com/wp-content/uploads/2021/06/How-to-calculate-square-root-in-Excel.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.86517227,"math_prob":0.99557954,"size":1791,"snap":"2021-43-2021-49","text_gpt3_token_len":404,"char_repetition_ratio":0.17907107,"word_repetition_ratio":0.13622291,"special_character_ratio":0.22501396,"punctuation_ratio":0.09625668,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998364,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-21T21:55:57Z\",\"WARC-Record-ID\":\"<urn:uuid:4736ceae-ae0b-4549-9b41-4f53f2db437c>\",\"Content-Length\":\"49983\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:53741297-0b0c-41b7-90c8-1265b3819e4a>\",\"WARC-Concurrent-To\":\"<urn:uuid:0955e6a0-2cb7-40ca-8bd6-e47f031fd216>\",\"WARC-IP-Address\":\"45.79.77.230\",\"WARC-Target-URI\":\"https://quickexcel.com/calculate-the-square-root/\",\"WARC-Payload-Digest\":\"sha1:WG4PIZCYW4OQRU33DD2YSRELFIRAQ7KG\",\"WARC-Block-Digest\":\"sha1:NJFU7JSIWWKCXW5UU5ZPBMKHAE7OIS5F\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585441.99_warc_CC-MAIN-20211021195527-20211021225527-00370.warc.gz\"}"}
https://klasse-mit.com/developer/article/1122004g5p-32048g8ld	[ "Home\n\n# Rolling mean Python\n\nExplaining the Pandas Rolling() Function. To calculate a moving average in Pandas, you combine the rolling() function with the mean() function. Let's take a moment to explore the rolling() function in Pandas: DataFrame.rolling(self, window, min_periods=None, center=False, win_type=None, on=None, axis=0, closed=None def rolling_mean(x, window, min_periods=None, center=False): if PD_VERSION >= '0.18.0': return x.rolling(window, min_periods=min_periods, center=center).mean() else: return pd.rolling_mean( x, window, min_periods=min_periods, center=center Rolling.mean(args, kwargs)[source]¶ Calculate the rolling mean of the values The function rolling_mean, along with about a dozen or so other function are informally grouped in the Pandas documentation under the rubric moving window functions; a second, related group of functions in Pandas is referred to as exponentially-weighted functions (e.g., ewma, which calculate\n\n### Calculate a Rolling Average (Mean) in Pandas • datag\n\n1. _periods = None, center = False, win_type = None, on = None, axis = 0, closed = None) [source] ¶ Provide rolling window calculations. Parameters window int, offset, or BaseIndexer subclass. Size of the moving window. This is the number of observations used for calculating the statistic. Each window will be a fixed size\n2. Its function rolling_mean does the job conveniently. It also returns a NumPy array when the input is an array. It is difficult to beat rolling_mean in performance with any custom pure Python implementation. Here is an example performance against two of the proposed solutions\n3. _periods=1).mean()\n\nPython is a great language for doing data analysis, primarily because of the fantastic ecosystem of data-centric python packages. Pandas is one of those packages and makes importing and analyzing data much easier. Pandas dataframe.rolling() function provides the feature of rolling window calculations. The concept of rolling window calculation is most primarily used in signal processing and time series data. In a very simple words we take a window size of k at a time and perform. To be specific, a rolling mean is a low-pass filter. This means that is leaves low frequency signals alone, while making high frequency signals smaller. Sharp increases in the data have a high frequency. If we make the kernel larger, the filter attenuates high frequency signals more. This is exactly how the rolling average works. It gets rid of high frequency noise. It also means that we must. You can simply calculate the rolling average by summing up the previous 'n' values and dividing them by 'n' itself. But for this, the first (n-1) values of the rolling average would be Nan. In this article, we will learn how to make a time series plot with a rolling average in Python using Pandas and Seaborn libraries. Below is the syntax for computing rolling average using pandas HPI_data['TX12MA'] = pd.rolling_mean(HPI_data['TX'], 12) This gives us a new column, which we've named TX12MA to reflect Texas, and 12 moving average. We apply this with pd.rolling_mean (), which takes 2 main parameters, the data we're applying this to, and the periods/windows that we're doing\n\n### Python Examples of pandas\n\n1. Computing 7-day rolling average with Pandas rolling() In Pandas, we can compute rolling average of specific window size using rolling() function followed by mean() function. Here we also perform shift operation to shift the NA values to both ends. corona_ny['cases_7day_ave'] = corona_ny.positiveIncrease.rolling(7).mean().shift(-3\n2. The moving average is commonly used with time series to smooth random short-term variations and to highlight other components (trend, season, or cycle) present in your data. The moving average is also known as rolling mean and is calculated by averaging data of the time series within k periods of time\n3. We previously introduced how to create moving averages using python. This tutorial will be a continuation of this topic. A moving average in the context of statistics, also called a rolling/running average, is a type of finite impulse response. In our previous tutorial we have plotted the values of the arrays x and y: Let'\n4. A rolling mean is simply the mean of a certain number of previous periods in a time series.. To calculate the rolling mean for one or more columns in a pandas DataFrame, we can use the following syntax: df[' column_name ']. rolling (rolling_window). mean () This tutorial provides several examples of how to use this function in practice", null, "First, let us use the R package zoo to compute rolling average over a week and plot on top of the barplot. With rollmean() function available in zoo package we can compute rolling average. In this example below, we specify the window size to 7 to compute rolling mean. In addition, we also specify the edges in computing the rolling mean. Try changing the align argument to see how that. A moving average, also called a rolling or running average, is used to analyze the time-series data by calculating averages of different subsets of the complete dataset. Since it involves taking the average of the dataset over time, it is also called a moving mean (MM) or rolling mean multiply = 1 values = [8,16,22,12,41] n = len (values) for i in values: multiply = (multiply) (i) geometricMean = (multiply) (1/n) print ('The Geometric Mean is: ' + str (geometricMean)) Once you run the code in Python, you'll get the same result Pandas Series.rolling () function is a very useful function. It Provides rolling window calculations over the underlying data in the given Series object. Syntax: Series.rolling (window, min_periods=None, center=False, win_type=None, on=None, axis=0, closed=None) center : Set the labels at the center of the window. win_type : Provide a window type This tutorial explains how to calculate moving averages in Python. Example: Moving Averages in Python. Suppose we have the following array that shows the total sales for a certain company during 10 periods: x = [50, 55, 36, 49, 84, 75, 101, 86, 80, 104] Method 1: Use the cumsum() function. One way to calculate the moving average is to utilize the cumsum() function: import numpy as np #define.\n\n### python - How to calculate rolling / moving average using\n\nPYTHON. Don't Miss Out on Rolling Window Functions in Pandas. Using moving window calculations to dive into your data. Byron Dolon . Sep 10, 2020 · 5 min read. Art by bythanproductions. Window calculations can add a lot of depth to your data analysis. The Pandas library lets you perform many different built-in aggregate calculations, define your functions and apply them across a DataFrame. Replace NaN in rolling mean in python . Replace NaN in rolling mean in python. 0 votes. I have a dataset as follows: ts Out : Sales Month Jan 1808 Feb 1251 Mar 3023 Apr 4857 May 2506 Jun 2453 Jul 1180 Aug 4239 Sep 1759 Oct 2539 Nov 3923 Dec 2999. After taking a moving average of window=2, the output is: shifted = ts. shift (0) window = shifted. rolling (window = 2) means = window. mean. #pandas #python #rollingPlease SUBSCRIBE:https://www.youtube.com/subscription_center?add_user=mjmacartyTry my Hands-on Python for Finance course on Udemy.. When working with time series data with NumPy I often find myself needing to compute rolling or moving statistics such as mean and standard deviation. The simplest way compute that is to use a for loop: def rolling_apply(fun, a, w): r = np.empty(a.shape) r.fill(np.nan) for i in range(w - 1, a.shape): r[i] = fun(a[ (i-w+1):i+1]) return r. A.\n\nI want to learn how to use rolling_mean by pandas, the pandas version is 0.21.0. But when I run the above code, I got the following error: AttributeError: 'list' object has no attribue 'rolling' Please show me how to use pandas.rolling_mean Or if other python package has the similar function, please also advise how to use them. Thanks Pandas DataFrame - rolling() function: The rolling() function is used to provide rolling window calculations. w3resource. home Front End HTML CSS JavaScript HTML5 Schema.org php.js Twitter Bootstrap Responsive Web Design tutorial Zurb Foundation 3 tutorials Pure CSS HTML5 Canvas JavaScript Course Icon Angular React Vue Jest Mocha NPM Yarn Back End PHP Python Java Node.js Ruby C programming PHP. Low.rolling(window=10).mean() df['High 10-trday MA'] = df.High.rolling(window=10).mean() Here the parameter window is set to 10. This means that our moving average runs over 10 rows — in this. That means we can easily do this entire piece of analysis in memory. Things get slightly more difficult if we want to calculate the mean rolling correlation of the constituents of a larger ETF or index. In another post, we'll solve this problem for the S&P 500 index. We'll also consider how the index has changed over time\n\nrolling_mean 移动窗口的均值 . pandas.rolling_mean(arg, window, min_periods=None, freq=None, center=False, how=None, kwargs) 以上这篇python pandas移动窗口函数rolling的用法就是小编分享给大家的全部内容了，希望能给大家一个参考，也希望大家多多支持脚本之家。您可能感兴趣的文章: python pandas dataframe 去重函数的具体. In statistics, a moving average (rolling average or running average) is a calculation to analyze data points by creating a series of averages of different subsets of the full data set. It is also called a moving mean (MM) or rolling mean and is a type of finite impulse response filter. Variations include: simple, cumulative, or weighted forms (described below)\n\n### pandas.DataFrame.rolling — pandas 1.2.4 documentatio\n\nRolling means creating a rolling window with a specified size and perform calculations on the data in this window which, of course, rolls through the data. The figure below explains the concept of rolling. It is worth noting that the calculation starts when the whole window is in the data. In other words, if the size of the window is three, the first aggregation is done at the third row. Let. pandas, Python, Rolling, hd_close.rolling (window=12).mean() window: 몇 개씩 연산할지 입력.mean(): 평균내라. 출력값을 보면 2010-01-19 부터 값이 나오는 것을 확인할 수 있는데, 이는 이전 12개의 데이터가 2010-01-19부터 존재하기 때문 입니다. 즉, 데이터가 12개 미만인 값들은 NaN으로 표시 됐습니다. 2010-01-19의 결과값. Rolling sum with a window length of 2, using the 'triang' window type. Rolling sum with a window length of 1, min_periods defaults to the window length. Contrasting to an integer rolling window, this will roll a variable length window corresponding to the time period. The default for min_periods is 1\n\nIn this video we will do a plot of Rolling Mean and Rolling Standard Deviation.⚡ Help me know if you want more videos like this one by giving a �� or a comme.. 相信初学Pandas时间序列时，会遇到rolling函数，不知道该怎么理解，对吧？让我们用最简单的例子来说明吧。代码如下：import pandas as pd # 导入 pandas index = pd.date_range('2019-01-01',periods=20) #创建日期序列data = pd.DataFrame(np.arange(len(inde.. In this tutorial, we will discuss how to implement moving average for numpy arrays in Python. We can calculate the Moving Average of a time series data using the rolling() and mean() functions as shown below. import pandas as pd import numpy as np data = np.array([10,5,8,9,15,22,26,11,15,16,18,7]) d = pd.Series(data) print(d.rolling(4).mean()) Output: 0 NaN 1 NaN 2 NaN 3 8.00 4 9.25 5 13. Rolling Windows on Timeseries with Pandas. The first thing we're interested in is: What is the 7 days rolling mean of the credit card transaction amounts. This means in this simple. Simple Moving Average is the most common type of average used. In SMA, we perform a summation of recent data points and divide them by the time period. The higher the value of the sliding width, the more the data smoothens out, but a tremendous value might lead to a decrease in inaccuracy. To calculate SMA, we use pandas.Series.rolling () method\n\nPython Moving Average. Creating a moving average is a fundamental part of data analysis. You can easily create moving averages with Python data manipulation package. Pandas has a great function that will allow you to quickly produce a moving average based on the window you define. This window can be defined by the periods or the rows of data. Pandas ROLLING() function: The rolling function. Project description. rolling is a collection of computationally efficient rolling window iterators for Python. Many useful arithmetical, logical and statistical functions are implemented to allow the window to be computed in sub-linear time (and in many instances constant time). These include: Sum. Min and Max. All and Any. Mean, Median and Mode Looking at the 365-day rolling mean time series, we can see that the overall annual trend in electricity consumption is fairly stable with low consumption recorded around 2009 and 2013. De-trending time series . Sometimes it would be beneficial to remove the trend from our data, especially if it is quite pronounced (as seen in Fig 3), so we can assess the seasonal variation (more on this in a. To calculate the mean() we use the mean function of the particular column; Then apply fillna() function, we will change all 'NaN' of that particular column for which we have its mean and print the updated data frame. Python3. import numpy as np. import pandas as pd # A dictionary with list as values. GFG_dict = { 'G1': [10, 20,30,40], 'G2': [25, np.NaN, np.NaN, 29], 'G3': [15, 14, 17, 11.\n\nRolling Window Statistics. A step beyond adding raw lagged values is to add a summary of the values at previous time steps. We can calculate summary statistics across the values in the sliding window and include these as features in our dataset. Perhaps the most useful is the mean of the previous few values, also called the rolling mean A rolling average can help you find trends that would otherwise be hard to detect. Using the data from above, you get a graph that looks like this: That's not terribly helpful as a trend detector. It looks like my website got a case of the hiccups. Use a rolling average, though, and you start to see a pattern emerge, with peaks happening more and more often: That's why rolling averages are. pcluo added a commit to pcluo/pandas that referenced this issue on May 22, 2017. BUG: groupby-rolling with a timedelta ( pandas-dev#16091) a66a612. closes pandas-dev#13966 xref to pandas-dev#15130, closed by pandas-dev#15175. Copy link\n\n### python - Moving average or running mean - Stack Overflo\n\n• Moving average smoothing is a naive and effective technique in time series forecasting. It can be used for data preparation, feature engineering, and even directly for making predictions. In this tutorial, you will discover how to use moving average smoothing for time series forecasting with Python. After completing this tutorial, you will know: How moving average smoothing works and some.\n• Python pandas.rolling_std() Examples The following are 10 code examples for showing how to use pandas.rolling_std(). These examples are extracted from open source projects. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. You may check out the related API usage on the sidebar. You.\n• numpy.roll () in Python. Last Updated : 31 May, 2021. The numpy.roll () function rolls array elements along the specified axis. Basically what happens is that elements of the input array are being shifted. If an element is being rolled first to the last position, it is rolled back to the first position\n• 概念: 为了提升数据的准确性，将某个点的取值扩大到包含这个点的一段区间，用区间来进行判断，这个区间就是窗口。移动窗口就是窗口向一端滑行，默认是从右往左，每次滑行并不是区间整块的滑行，而是一个单位一个单位的滑行。给个例子好理解一点：import pandas as pds = [1,2,3,5,6,10,12,14,12,30]pd.\n• Python Example for Moving Average Method. Here is the Python code for calculating moving average for sales figure. The code that calculates the moving average or rolling mean is df['Sales'].rolling(window=3).mean(). The example below represents the calculation of simple moving average (SMA). import pandas as pd import numpy as np # # Create a numpy array of years and sales # arr = np.array.\n\nrolling_mean 移动窗口的均值 pandas.rolling_mean 今天小编就为大家分享一篇python pandas移动窗口函数rolling的用法，具有很好的参考价值，希望对大家有所帮助。一起跟随小编过来看看吧 . 基于python计算滚动方差(标准差)talib和pd.rolling函数差异详解 09-16. 主要介绍了基于python计算滚动方差(标准差)talib和pd. The Exponential Moving Average (EMA) is a wee bit more involved. First, you should find the SMA. Second, calculate the smoothing factor. Then, use your smoothing factor with the previous EMA to find a new value. In this way, the latest prices are given higher weights, whereas the SMA assigns equal weight to all periods Geometric Mean Function in python pandas is used to calculate the geometric mean of a given set of numbers, Geometric mean of a data frame, Geometric mean of column and Geometric mean of rows. let's see an example of each we need to use the package name stats from scipy in calculation of geometric mean 注：rolling_mean()这种写法已经淘汰了，现在都是df.rolling().mean()、 df.rolling().std()这样来写。例：计算苹果收盘价的平均移动线获取数据. 从雅虎获取苹果公司2016年1月1日至今的股票数据�\n\n### python - How to fill nan values with rolling mean in\n\n• rolmean = pd.rolling_mean (timeseries, window = 12) rolstd = pd.rolling_std (timeseries, window = 12) expwighted_avg = pd.ewma(ts_log, halflife=12) 会有报错 . AttributeError: module 'pandas' has no attribute 'rolling_mean' AttributeError: module 'pandas' has no attribute 'rolling_std' AttributeError: module 'pandas' has no attribute 'ewma' 这是因为pandas版本跟新了，应该改为.\n• Python's basic tools for working with dates and times reside in the built-in datetime module. It would be nice if we could average this out by a week, which is where a rolling mean comes in. A rolling mean, or moving average, is a transformation method which helps average out noise from data. It works by simply splitting and aggregating the data into windows according to function, such.\n• Python 3 provides the statistics module, which comes with very useful functions like mean(), median(), mode(), etc. The arithmetic mean is a sum of data that is divided by the number of data points. It is the measure of the central location of data in a set of values that vary in range.. Python averag\n• python时间序列分析之_用pandas中的rolling函数计算时间窗口数据 . python万. 发布时间: 19-01-16 14:51. 简介. 由于系统编辑器限制，代码行用无序列表表示。上篇文章中，我们讲解了如何对时间数据进行重采样及重采样中降采样和升采样的概览和使用方法，通过重采样我们可以得到任何想要频率的数据.\n• The moving averages are created by using the pandas rolling_mean function on the bars ['Close'] closing price of the AAPL stock. Once the individual moving averages have been constructed, the signal Series is generated by setting the colum equal to 1.0 when the short moving average is greater than the long moving average, or 0.0 otherwise\n• Moving Average Backtesting Strategy in Python. To backtest the algorithm in Python, we start by creating a list containing the profit for each of our long positions. First (1), we create a new column that will contain True for all data points in the data frame where the 20 days moving average cross above the 250 days moving average\n\nPython for Finance, Part 3: Moving Average Trading Strategy. Expanding on the previous article, we'll be looking at how to incorporate recent price behaviors into our strategy. In the previous article of this series, we continued to discuss general concepts which are fundamental to the design and backtesting of any quantitative trading strategy A popular and widely used statistical method for time series forecasting is the ARIMA model. ARIMA is an acronym that stands for AutoRegressive Integrated Moving Average. It is a class of model that captures a suite of different standard temporal structures in time series data. In this tutorial, you will discover how to develop an ARIMA model for time series forecasting i 移動平均、英語ではmoving meanやrolling meanなんて呼ばれまして、いろいろパッケージなり、自作で関数を作られてる方も見受けられますが、いざ自分で作ろうとするとちょっと面倒。。そんなときこの関数を見つけました。 Rccpが便利! 大きく2ステップで求めます。 ①当該週を含んだ、2週間で. The following are 6 code examples for showing how to use pandas.rolling_max().These examples are extracted from open source projects. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example The results show that the data is now stationary, indicated by the relative smoothness of the rolling mean and rolling standard deviation after running the ADF test again. Differencing. This method removes the underlying seasonal or cyclical patterns in the time series. Since the sample dataset has a 12-month seasonality, I used a 12-lag.\n\n### Python Pandas dataframe\n\n• Arithmetic Mean Average. An average calculated by adding the value of the points in a data set and dividing the sum by the number of data points. For example, suppose one wishes to calculate the average income of a country with exactly five people in it, and their incomes are \\$25,000, \\$26,000, \\$43,000, \\$70,000, and \\$72,000. It is calculated as.\n• NumPy Mean. NumPy Mean: To calculate mean of elements in a array, as a whole, or along an axis, or multiple axis, use numpy.mean() function.. In this tutorial we will go through following examples using numpy mean() function. Mean of all the elements in a NumPy Array\n• pandas. 模块，. rolling_mean () 实例源码. 我们从Python开源项目中，提取了以下 50 个代码示例，用于说明如何使用 pandas.rolling_mean () 。. def BBANDS(df_price, periods=20, mul=2): # Middle Band = 20-day simple moving average (SMA) df_middle_band = pd.rolling_mean(df_price, window=periods) #df_middle_band = pd.\n• Simple Moving Average(SMA) in Python. A simple moving average is the simplest of all the techniques which one can use to forecast. A moving average is calculated by taking the average of the last N value. The average value which we get is considered the forecast for the next period. Why we use a simple moving average? Moving averages help us to identify the trends in the data quickly. You can.", null, "Python for Financial Analysis with Pandas. Learn Python for Financial Data Analysis with Pandas (Python library) in this 2 hour free 8-lessons online course.. The 8 lessons will get you started with technical analysis using Python and Pandas.. The 8 lessons. Lesson 1: Get to know Pandas with Python - how to get historical stock price data.; Lesson 2: Learn about Series from Pandas - how to. Groupby single column - groupby mean pandas python: groupby() function takes up the column name as argument followed by mean() function as shown below ''' Groupby single column in pandas python''' df1.groupby(['State'])['Sales'].mean() We will groupby mean with single column (State), so the result will be. using reset_index() reset_index() function resets and provides the new index to the.\n\n### Smoothing Data by Rolling Average with NumPy - Scientific\n\n• Python is an extraordinary language for doing information investigation, essentially in view of the incredible environment of information driven python bundles. Pandas is one of those bundles and makes bringing in and investigating information a lot simpler. Syntax of Pandas rolling. Given below is the syntax of Pandas rolling\n• Calculate Rolling Mean. # Calculate the moving average. That is, take # the first two values, average them, # then drop the first and add the third, etc. df.rolling(window=2).mean() score. 0\n• Python code for computing the Commodity Channel Index. In the code below, we use the rolling(), mean(), and mad() functions to compute the Commodity Channel Index. The rolling and mean function takes a time series or a data frame along with the number of periods and computes the rolling mean. The mad() function computes the mean deviation based.\n• • Rolling values have less variations in mean and standard deviation in magnitude. • the test statistic is smaller than 1% of the critical value. So we can say we are almost 99% confident that.\n• Here's the complete guide on how to compute a rolling average, also called a moving average. Find out how this averaging technique is used to calculate manufacturing and sales forecasts. With a free rolling average example to download, you can learn how to derive a rolling average for any set of data\n• rolling_mean ()とrolling ().mean () 「IPythonデータサイエンスクックブック」って本を読んでたら出てきたpandasのrolling_mean ()という関数について。. IPythonと見てわかるように少々古い本なので（今はJupyter）、書いてあるコードを実行しているとたまに警告文が出て.\n• _periods=None, freq=None, center=False, how=None, *kwargs) Python时间序列处理神器：Rolling 对象，3分钟入门 \| 原创 . Rolling 对象在处理时间序列的数据时，应用广泛，在Python中Pandas包实现了对这类数据的处理。 double. 对比Excel，学习Python窗口函数. 对Sql比较.\n\nrolling函数返回的是window对象或rolling子类，可以通过调用该对象的mean(),sum(),std(),count()等函数计算返回窗口的值，还可以通过该对象的apply(func)函数，通过自定义函数计算窗口的特定的值，具体可看文档。. 从以上可以看出，rolling的窗口可以向前取值，向两边取值，但是没有向后取值，实际上只需要把. rolling_mean() 数据样本的算术平均数 Python join() 方法用于将序列中的元素以指定的字符连接生成一个新的字符串。这篇文章主要介绍了python中join()方法,需要的朋友可以参考下 . 2018-10-10 . Python编程实现删除VC临时文件及Debug目录的方法. 这篇文章主要介绍了Python编程实现删除VC临时文件及Debug目录的. python 实现rolling和apply函数的向下取值操作 ; pandas; rolling; 相关文章. python deque模块简单使用代码实例. 这篇文章主要介绍了python deque模块简单使用代码实例,文中通过示例代码介绍的非常详细，对大家的学习或者工作具有一定的参考学习价值,需要的朋友可以参考下. 2020-03-03 . python3实现域名查询和whois. Hi, Implementing moving average, moving std and other functions working over rolling windows using python for loops are slow. This is a effective stride trick I learned from Keith Goodman's <[hidden email]> Bottleneck code but generalized into arrays of any dimension. This trick allows the loop to be performed in C code and in the future hopefully using multiple cores Der gleitende Durchschnitt (auch gleitender Mittelwert) ist eine Methode zur Glättung von Zeit- bzw. Datenreihen. Die Glättung erfolgt durch das Entfernen höherer Frequenzanteile. Im Ergebnis wird eine neue Datenpunktmenge erstellt, die aus den Mittelwerten gleich großer Untermengen der ursprünglichen Datenpunktmenge besteht. In der Signaltheorie wird der gleitende Durchschnitt als.", null, "### How to Make a Time Series Plot with Rolling Average in\n\nA moving average means that it takes the past days of numbers, takes the average of those days, and plots it on the graph. For a 7-day moving average, it takes the last 7 days, adds them up, and divides it by 7. For a 14-day average, it will take the past 14 days. So, for example, we have data on COVID starting March 12. For the 7-day moving average, it needs 7 days of COVID cases: that is the. The average gains and losses are calculated using a smoothed moving average, or rolling mean. In this example, we will be using the exponential moving average (EMA) to calculate the rolling means. moving_avg = pd.rolling_mean(ts_log, 12) to: moving_avg = ts_log.rolling(12).mean() Pandas Tutorial is also one of the things where one can get an invaluable insight regarding the problem. Related questions 0 votes. 1 answer. module 'pandas' has no attribute 'rolling_mean' asked Oct 5, 2019 in Data Science by sourav (17.6k points) python; pandas; dataframe; 0 votes. 1 answer. Module 'pandas. For working on numerical data, Pandas provide few variants like rolling, expanding and exponentially moving weights for window statistics. Among these are sum, mean, median, variance, covariance, correlation, etc.. We will now learn how each of these can be applied on DataFrame objects\n\npython移动窗口函数 . rolling_count 计算各个窗口中非NA观测值的数量 rolling_mean 移动窗口的均值 pandas.rolling_mean. One popular way is by taking a rolling average, which means that, for each time point, you take the average of the points on either side of it. Note that the number of points is specified by a window size, which you need to choose. What happens then because you take the average is it tends to smooth out noise and seasonality. You'll see an. The weighted average of all market-betas with respect to the market index is 1. Beta>1: If a stock has a beta above 1, Rolling Regression in Python. Let's provide an example of rolling regression on Market Beta by taking into consideration the Amazon Stock (Ticker=AMZN) and the NASDAQ Index (Ticker ^IXIC). The rolling window will be 30 days and we will consider data of the last 2 years. March 2016. 27. February 2017. Admin. To display long-term trends and to smooth out short-term fluctuations or shocks a moving average is often used with time-series. The Smoothed Moving Average (SMA) is a series of averages of a time series. A simple code example is given and several variations (CMA, EMA, WMA, SMM) are presented as an outlook\n\n### Rolling statistics - Python Programming Tutorial\n\nTechnical Analysis is a great tool use by investors and analysts to find out interesting stocks to add to the portfolio. By the end of the article, we will have a Python script where we only need to input the name of the company. Then, within seconds, the stock's Bollinger bands will be calculated and plotted for our analysis Rolling Time Series . Rolling is also similar to Time Resampling, but in Rolling, we take a window of any size and perform any function on it. In simple words, we can say that a rolling window of size k means k consecutive values. Let's see an example. If we want to calculate the rolling average of 10 days, we can do it as follows Python Pandas DataFrame.rolling() 함수는 수학적 연산을위한 롤링 창을 제공합니다. pandas.DataFrame.rolling()의 구문 : DataFrame.rolling(window, min_periods=None, center=False, win_type=None, on=None, axis=0, closed=None) 매개 변수. window: 정수, 오프셋 또는 BaseIndexer 서브 클래스 유형 매개 변수입니다. 창의 크기를 지정합니다. 각.", null, "", null, "", null, "", null, "### How to Make a Time Series Plot with Rolling Average in Python\n\nApply rolling window function over time dimension of 3D data: Staph: 0: 839: Jan-01-2020, 08:31 AM Last Post: Staph : Grouping data based on rolling conditions: kapilan15: 0: 779: Jun-05-2019, 01:07 PM Last Post: kapilan15 : Pandas .rolling() with some calculations inside: irmscher: 5: 2,865: Apr-04-2019, 11:55 AM Last Post: scidam : How to use. How to Make a Time Series Plot with Rolling Average in Python? Categorical Plots. Categorical Plots are used where we have to visualize relationship between two numerical values. A more specialized approach can be used if one of the main variable is categorical which means such variables that take on a fixed and limited number of possible values. Refer to the below articles to get detailed. How to Build your First Mean Reversion Trading Strategy in Python. A step-by-step guide to mean reversion strategies . Raposa Technologies. Follow. Mar 16 · 7 min read. The beautiful thing about. However, in the meantime lets dive into dynamic rolling average using Power BI. Here are the list of functions will be using the to create our calculation: SUM. CALCULATE. LASTDATE. DATESINPERIOD. DISTINCTCOUNT. There are two points to this formula: Calculating the sum of the value in the period\n\n### Moving averages with Python\n\nThis module provides functions for calculating mathematical statistics of numeric (Real-valued) data.The module is not intended to be a competitor to third-party libraries such as NumPy, SciPy, or proprietary full-featured statistics packages aimed at professional statisticians such as Minitab, SAS and Matlab.It is aimed at the level of graphing and scientific calculators It's not 0.75s (unless your sampling rate is 60Hz), but rather 0.75sampling rate in both directions. The reason for this is that the larger this threshold, the less like the HR signal the rolling average will be, the smaller, the more similar. I would recommend you plot the signal + rolling average with different window sizes. See what.\n\n### Python numpy How to Generate Moving Averages Efficiently\n\npandas documentation¶. Date: Apr 12, 2021 Version: 1.2.4. Download documentation: PDF Version \| Zipped HTML. Useful links: Binary Installers \| Source Repository \| Issues & Ideas \| Q&A Support \| Mailing List. pandas is an open source, BSD-licensed library providing high-performance, easy-to-use data structures and data analysis tools for the Python programming language The daily data are very volatile, so using a longer term rolling average can help reveal a longer term trend. You'll be using a 360 day rolling window, and .agg() to calculate the rolling mean and standard deviation for the daily average ozone values since 2000. Instructions 100 XP. We have already imported pandas as pd, and matplotlib.pyplot as plt. Use pd.read_csv() to import 'ozone.csv. Taking care of business, one python script at a time. Tue 26 January 2016 Learn More About Pandas By Building and Using a Weighted Average Function Posted by Chris Moffitt in articles Introduction. Pandas includes multiple built in functions such as sum, mean, max, min, etc. that you can apply to a DataFrame or grouped data. However, building and using your own function is a good way to learn. python \| pandas \| 移动窗口函数rolling。它都是以rolling打头的函数，后接具体的函数，来显示该移动窗口函数的功能。arg : DataFrame 或 numpy的ndarray 数组格式 rolling_apply 对移动窗口应用普通数组函数 pandas.rolling_window(arg, window=None, win_type=None, min_periods=None, freq=None, center=False, mean=True, axis=0, how=None, **kwargs) ewma. rolling mean untuk data time series CO. Bisa dilihat bahwa hasil rolling_mean merupakan rata-rata dari kolom kadar CO ug/m3 untuk tiap 5 period data, 4 baris data pertama bernilai NaN karena hasil rolling number akan terlihat untuk tiap 5 data.. Forward atau Backfilling ketika berhadapan dengan missing value. Pandas menyediakan function .fillna() yang dapat digunakan untuk keperluan seperti.\n\n### How to Calculate a Rolling Mean in Pandas - Statolog\n\nPython's basic objects for working with dates and times reside in the built-in datetime module. Here we'll do a 30 day rolling mean of our data, making sure to center the window: In : daily = data. resample ('D'). sum daily. rolling (30, center = True). sum (). plot (style = [':', '--', '-']) plt. ylabel ('mean hourly count'); The jaggedness of the result is due to the hard cutoff of. Python Pandas - Aggregations - Once the rolling, expanding and ewm objects are created, several methods are available to perform aggregations on data 본 글에서는 Python의 Pandas를 이용하여 이동 평균을 구하는 방법을 설명한다.주식매매에서 이동평균은 흔하게 사용 되는 지표이다. 주식 추세 판단, 매매 시점을 결정 등에 사용한다. 이동평균 관련된 활용법 moving average)은 링크한 글에서 참고 하자. 이동평균은 흔히 단순 이동평균, 선형 가중 이동. NumPy Mean. NumPy Mean: To calculate mean of elements in a array, as a whole, or along an axis, or multiple axis, use numpy.mean() function.. In this tutorial we will go through following examples using numpy mean() function. Mean of all the elements in a NumPy Array\n\n### How to Make Time-Series Plot with Rolling Mean in R\n\nPython is one of the most popular programming languages used, among the likes of C++, Java, R, and MATLAB. It is being adopted widely across all domains, especially in data science, because of its easy syntax, huge community, and third-party support. You'll need familiarity with Python and statistics in order to make the most of this tutorial. Make sure to brush up on your Python and check. Running Average with alpha 0.1 has caught it as a transparent hand, with main emphasis on background. As alpha again reduced, you can see no hand there in front of face. ie the effect, as alpha decreases, sudden changes shows no effect on running averages. Result 4 : From the traffic video I have given in beginning of this article: Original Frame: Alpha = 0.1: Alpha = 0.01: As alpha decreases.\n\npandas is a fast, powerful, flexible and easy to use open source data analysis and manipulation tool, built on top of the Python programming language. Install pandas now! Getting started. Install pandas. Getting started. Documentation. User guide This video demonstrates how to calculate a moving (rolling) average in Microsoft Excel 2016. Two separate methods are used to generate the statistic: data an.. Let's try upping the window length to use a look-back of 50 days for the band calculations. But first, lets define a Bollinger Band trading Strategy function that we can easily run again and again while varying the inputs: def bollinger_strat(df,window,std): rolling_mean = df['Settle'].rolling(window).mean( Team sum mean std Devils 1536 768.000000 134.350288 Kings 2285 761.666667 24.006943 Riders 3049 762.250000 88.567771 Royals 1505 752.500000 72.831998 kings 812 812.000000 NaN Transformations Transformation on a group or a column returns an object that is indexed the same size of that is being grouped for developers of alternative Python implementations, the rolling stream of pre-releases may provide an additional incentive for extension module authors to migrate from the full CPython ABI to the Python stable ABI, which would also serve to make more of the ecosystem compatible with implementations that don't emulate the full CPython C API. That said, it is acknowledged that not all the. 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https://www.colorhexa.com/f16201	[ "# #f16201 Color Information\n\nIn a RGB color space, hex #f16201 is composed of 94.5% red, 38.4% green and 0.4% blue. Whereas in a CMYK color space, it is composed of 0% cyan, 59.3% magenta, 99.6% yellow and 5.5% black. It has a hue angle of 24.3 degrees, a saturation of 99.2% and a lightness of 47.5%. #f16201 color hex could be obtained by blending #ffc402 with #e30000. Closest websafe color is: #ff6600.\n\n• R 95\n• G 38\n• B 0\nRGB color chart\n• C 0\n• M 59\n• Y 100\n• K 5\nCMYK color chart\n\n#f16201 color description : Vivid orange.\n\n# #f16201 Color Conversion\n\nThe hexadecimal color #f16201 has RGB values of R:241, G:98, B:1 and CMYK values of C:0, M:0.59, Y:1, K:0.05. Its decimal value is 15819265.\n\nHex triplet RGB Decimal f16201 `#f16201` 241, 98, 1 `rgb(241,98,1)` 94.5, 38.4, 0.4 `rgb(94.5%,38.4%,0.4%)` 0, 59, 100, 5 24.3°, 99.2, 47.5 `hsl(24.3,99.2%,47.5%)` 24.3°, 99.6, 94.5 ff6600 `#ff6600`\nCIE-LAB 59.382, 51.793, 68.344 40.651, 27.443, 3.185 0.57, 0.385, 27.443 59.382, 85.752, 52.844 59.382, 119.06, 51.289 52.386, 46.838, 33.065 11110001, 01100010, 00000001\n\n# Color Schemes with #f16201\n\n• #f16201\n``#f16201` `rgb(241,98,1)``\n• #0190f1\n``#0190f1` `rgb(1,144,241)``\nComplementary Color\n• #f10118\n``#f10118` `rgb(241,1,24)``\n• #f16201\n``#f16201` `rgb(241,98,1)``\n• #f1da01\n``#f1da01` `rgb(241,218,1)``\nAnalogous Color\n• #0118f1\n``#0118f1` `rgb(1,24,241)``\n• #f16201\n``#f16201` `rgb(241,98,1)``\n• #01f1da\n``#01f1da` `rgb(1,241,218)``\nSplit Complementary Color\n• #6201f1\n``#6201f1` `rgb(98,1,241)``\n• #f16201\n``#f16201` `rgb(241,98,1)``\n• #01f162\n``#01f162` `rgb(1,241,98)``\n• #f10190\n``#f10190` `rgb(241,1,144)``\n• #f16201\n``#f16201` `rgb(241,98,1)``\n• #01f162\n``#01f162` `rgb(1,241,98)``\n• #0190f1\n``#0190f1` `rgb(1,144,241)``\n• #a54301\n``#a54301` `rgb(165,67,1)``\n• #be4d01\n``#be4d01` `rgb(190,77,1)``\n• #d85801\n``#d85801` `rgb(216,88,1)``\n• #f16201\n``#f16201` `rgb(241,98,1)``\n• #fe6f0e\n``#fe6f0e` `rgb(254,111,14)``\n• #fe7e27\n``#fe7e27` `rgb(254,126,39)``\n• #fe8d40\n``#fe8d40` `rgb(254,141,64)``\nMonochromatic Color\n\n# Alternatives to #f16201\n\nBelow, you can see some colors close to #f16201. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #f12601\n``#f12601` `rgb(241,38,1)``\n• #f13a01\n``#f13a01` `rgb(241,58,1)``\n• #f14e01\n``#f14e01` `rgb(241,78,1)``\n• #f16201\n``#f16201` `rgb(241,98,1)``\n• #f17601\n``#f17601` `rgb(241,118,1)``\n• #f18a01\n``#f18a01` `rgb(241,138,1)``\n• #f19e01\n``#f19e01` `rgb(241,158,1)``\nSimilar Colors\n\n# #f16201 Preview\n\nThis text has a font color of #f16201.\n\n``<span style=\"color:#f16201;\">Text here</span>``\n#f16201 background color\n\nThis paragraph has a background color of #f16201.\n\n``<p style=\"background-color:#f16201;\">Content here</p>``\n#f16201 border color\n\nThis element has a border color of #f16201.\n\n``<div style=\"border:1px solid #f16201;\">Content here</div>``\nCSS codes\n``.text {color:#f16201;}``\n``.background {background-color:#f16201;}``\n``.border {border:1px solid #f16201;}``\n\n# Shades and Tints of #f16201\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #070300 is the darkest color, while #fff7f2 is the lightest one.\n\n• #070300\n``#070300` `rgb(7,3,0)``\n• #1a0b00\n``#1a0b00` `rgb(26,11,0)``\n• #2e1300\n``#2e1300` `rgb(46,19,0)``\n• #411b00\n``#411b00` `rgb(65,27,0)``\n• #552200\n``#552200` `rgb(85,34,0)``\n• #682a00\n``#682a00` `rgb(104,42,0)``\n• #7c3201\n``#7c3201` `rgb(124,50,1)``\n• #8f3a01\n``#8f3a01` `rgb(143,58,1)``\n• #a34201\n``#a34201` `rgb(163,66,1)``\n• #b64a01\n``#b64a01` `rgb(182,74,1)``\n• #ca5201\n``#ca5201` `rgb(202,82,1)``\n• #dd5a01\n``#dd5a01` `rgb(221,90,1)``\n• #f16201\n``#f16201` `rgb(241,98,1)``\n• #fe6b08\n``#fe6b08` `rgb(254,107,8)``\n• #fe771b\n``#fe771b` `rgb(254,119,27)``\n• #fe832f\n``#fe832f` `rgb(254,131,47)``\n• #fe8e42\n``#fe8e42` `rgb(254,142,66)``\n• #fe9a56\n``#fe9a56` `rgb(254,154,86)``\n• #fea669\n``#fea669` `rgb(254,166,105)``\n• #feb17d\n``#feb17d` `rgb(254,177,125)``\n• #ffbd90\n``#ffbd90` `rgb(255,189,144)``\n• #ffc9a4\n``#ffc9a4` `rgb(255,201,164)``\n• #ffd4b7\n``#ffd4b7` `rgb(255,212,183)``\n• #ffe0cb\n``#ffe0cb` `rgb(255,224,203)``\n• #ffecdf\n``#ffecdf` `rgb(255,236,223)``\n• #fff7f2\n``#fff7f2` `rgb(255,247,242)``\nTint Color Variation\n\n# Tones of #f16201\n\nA tone is produced by adding gray to any pure hue. In this case, #817771 is the less saturated color, while #f16201 is the most saturated one.\n\n• #817771\n``#817771` `rgb(129,119,113)``\n• #8b7667\n``#8b7667` `rgb(139,118,103)``\n• #94745e\n``#94745e` `rgb(148,116,94)``\n• #9d7255\n``#9d7255` `rgb(157,114,85)``\n• #a7704b\n``#a7704b` `rgb(167,112,75)``\n• #b06e42\n``#b06e42` `rgb(176,110,66)``\n• #b96d39\n``#b96d39` `rgb(185,109,57)``\n• #c26b30\n``#c26b30` `rgb(194,107,48)``\n• #cc6926\n``#cc6926` `rgb(204,105,38)``\n• #d5671d\n``#d5671d` `rgb(213,103,29)``\n• #de6614\n``#de6614` `rgb(222,102,20)``\n• #e8640a\n``#e8640a` `rgb(232,100,10)``\n• #f16201\n``#f16201` `rgb(241,98,1)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #f16201 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.50198376,"math_prob":0.6264236,"size":3675,"snap":"2023-40-2023-50","text_gpt3_token_len":1650,"char_repetition_ratio":0.14246799,"word_repetition_ratio":0.0074074073,"special_character_ratio":0.56136054,"punctuation_ratio":0.23751387,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9831369,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-04T00:55:17Z\",\"WARC-Record-ID\":\"<urn:uuid:274aba17-eec7-46f4-a097-734ac0e22768>\",\"Content-Length\":\"36179\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0b0d811b-88bb-4a04-8579-fc9e88d8814c>\",\"WARC-Concurrent-To\":\"<urn:uuid:263efbf6-20d5-40c3-8e2c-1ec373b87f4f>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/f16201\",\"WARC-Payload-Digest\":\"sha1:UHJOROQ5UBUBZZKD4R6BORWAR5J7Z7R3\",\"WARC-Block-Digest\":\"sha1:UZUTE5R4F4GF2NJOSYAKFCI2ZODND2QH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233511284.37_warc_CC-MAIN-20231003224357-20231004014357-00466.warc.gz\"}"}
https://best-excel-tutorial.com/54-basics/112-hlookup?tmpl=component&print=1&page=	[ "# HLOOKUP\n\nIn this lesson you will learn HLOOKUP function.\n\nHLOOKUP works similarly to the VLOOKUP function. HLOOKUP is a lookup and reference function. This function retrieves data from the table horizontally. Most of the tables in Excel, create a vertical, so this feature is rarely used. Despite it, I think it's worth it to know HLOOKUP. HLOOKUP function has the following form:\n\n=HLOOKUP(reference,array,row_number,row)\n\nIn simple terms it can be assumed that the individual components of this function:\n\n=VLOOKUP(what,where,in which row,true/false)\n\nThe last part of the formula is very important:\n\n• True is an approximate match;\n• False is the exact value.\n\nI prepared a table of sales.", null, "You'll learn from the above table, as HLOOKUP works.\n\nWith the name of the employee when you appear all the data on it that contains the table. At the beginning of the selection of employees could use the drop-down list.", null, "In the sales, type the formula. It is:\n\n=HLOOKUP(C7,C3:H5,2,FALSE)", null, "Drag the formula in the City field. In this way, HLOOKUP searches for data from the table and selecting the employee name appears in the sale and the city. This of course is just a simple example. HLOOKUP is applicable especially in large tables, where the search data is no longer so simple. Examples of such data table to report sales or payroll." ]	[ null, "https://best-excel-tutorial.com/images/HLOOKUP example.jpg", null, "https://best-excel-tutorial.com/images/HLOOKUP drop-down list.jpg", null, "https://best-excel-tutorial.com/images/HLOOKUP formula.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8798323,"math_prob":0.8941342,"size":1311,"snap":"2020-24-2020-29","text_gpt3_token_len":302,"char_repetition_ratio":0.15149197,"word_repetition_ratio":0.0,"special_character_ratio":0.21052632,"punctuation_ratio":0.14444445,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98841524,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,8,null,8,null,8,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-27T02:58:36Z\",\"WARC-Record-ID\":\"<urn:uuid:e32ad223-0a19-4d97-a7b6-838898cf25f8>\",\"Content-Length\":\"11131\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d131bc86-1047-473a-936d-b895321716db>\",\"WARC-Concurrent-To\":\"<urn:uuid:90769027-c595-429c-9e9f-eca635acd454>\",\"WARC-IP-Address\":\"213.186.33.169\",\"WARC-Target-URI\":\"https://best-excel-tutorial.com/54-basics/112-hlookup?tmpl=component&print=1&page=\",\"WARC-Payload-Digest\":\"sha1:UHJOR3YZALP5JPVZHKJRFW7W6YQO6V67\",\"WARC-Block-Digest\":\"sha1:YJBOZQZKGXQHAZZPXKNSR5SRU2SCAMF3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347392057.6_warc_CC-MAIN-20200527013445-20200527043445-00355.warc.gz\"}"}
https://es.mathworks.com/help/fixedpoint/ref/embedded.fi.dec2base.html	[ "# dec2base\n\nConvert decimal integer to its base-n representation for `fi` objects\n\n## Syntax\n\n``baseStr = dec2base(D,n)``\n``baseStr = dec2base(D,n,minDigits)``\n\n## Description\n\nexample\n\n````baseStr = dec2base(D,n)` returns a base-n representation of the decimal integer `D`. The output argument `baseStr` is a character array that represents digits using numeric characters, and, when `n` is greater than 10, letters. For example, if `n` is 12, the `dec2base` represents the numbers 9, 10, and 11 using the characters `9`, `A`, and `B`, and represents the number 12 as the character sequence `10`.```\n\nexample\n\n````baseStr = dec2base(D,n,minDigits)` returns a base-n representation of `D` with no fewer than `minDigits` digits. Tip`dec2base` returns the base-n representation of the real-world value of the values contained in `fi` object `D`. ```\n\n## Examples\n\ncollapse all\n\nConvert a decimal number to a character vector that represents its value in base 3.\n\n```D = fi(23); baseStr = dec2base(D,3)```\n```baseStr = '212'```\n\nConvert a decimal number to a character vector that represents its value in base 12. In this base system, the characters `'A'` and `'B'` represent the numbers denoted as `10` and `11` in base 10.\n\n```D = fi(23); baseStr = dec2base(D,12)```\n```baseStr = '1B'```\n\nSpecify the number of base-3 digits that `dec2base` returns. If you specify more digits than are required, then `dec2base` pads the output with leading zeros.\n\n```D = fi(23); baseStr = dec2base(D,3,5)```\n```baseStr = '00212' ```\n\nConvert the upper bound of a signed `fi` object with 100-bit word length to base 36 representation.\n\n`baseStr = dec2base(upperbound(fi([],1,100,0)),36)`\n```baseStr = '1PG7OTO50BLAOIQ8FPQ7'```\n\n## Input Arguments\n\ncollapse all\n\nInput array, specified as a `fi` array of nonnegative numbers.\n\n`D` must contain finite integers. If any element of `D` has a fractional part, then `dec2base` produces an error. For example, `dec2base(fi(10),8)` converts `fi(10)` to `'12'`, but `dec2base(fi(10.5),8)` produces an error.\n\nData Types: `fi`\n\nBase of output representation, specified as an integer between 2 and 36. For example, if `n` is `8`, then the output represents base-8 numbers.\n\nMinimum number of digits in the output, specified as a positive integer.\n\n• If `D` can be represented with fewer than `minDigits` digits, then `dec2base` pads the output with leading zeros.\n\n• If `D` is so large that it must be represented with more than `minDigits` digits, then `dec2base` returns the output with as many digits as required.\n\n## Version History\n\nIntroduced in R2021b" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7027341,"math_prob":0.98722774,"size":2425,"snap":"2022-05-2022-21","text_gpt3_token_len":650,"char_repetition_ratio":0.1598513,"word_repetition_ratio":0.07611549,"special_character_ratio":0.25072166,"punctuation_ratio":0.12581345,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99111414,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-16T12:14:30Z\",\"WARC-Record-ID\":\"<urn:uuid:a5a0a71d-2d00-4eef-8f9c-83a2018d6dca>\",\"Content-Length\":\"89149\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6f9102b5-bc43-4374-9491-772e47b258fa>\",\"WARC-Concurrent-To\":\"<urn:uuid:efd0d403-dde6-4d4f-9ae1-2e9ff4524bdc>\",\"WARC-IP-Address\":\"104.68.243.15\",\"WARC-Target-URI\":\"https://es.mathworks.com/help/fixedpoint/ref/embedded.fi.dec2base.html\",\"WARC-Payload-Digest\":\"sha1:LIUTSUWCKWMTOVOAA5EATZF37V4TY6FF\",\"WARC-Block-Digest\":\"sha1:3ARTK7DUDVHOMKUGH3FJTZJGTEHBYO4Z\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662510117.12_warc_CC-MAIN-20220516104933-20220516134933-00062.warc.gz\"}"}
https://datalya.com/blog/business-statistics/things-you-need-to-know-about-index-number	[ "## Things You Need to Know about Index Number Construction\n\nA statistical measure of average change in a variable or a group of variables with respect to time or space is known as index number. The variable may be the enrolment of staff in an organization, the cost of salaries for staff, prices of a particular commodity or a group of commodities, wages of workers, volume of trade, sales, exports and imports, production, etc.\n\nIndex numbers are obtained by expressing the data for various periods or places as percentage of some specific period or place selected for the purposes of comparison and technically called the base. Index numbers may be computed on weekly or monthly basis but generally they are computed on annual basis.\n\n### Simple and Composite Indices\n\nIndex numbers are generally classified into Simple Indices and Composite Indices. An index number is called a simple index when it is computed for a single variable. Index numbers of enrolment in colleges, index numbers of gold prices, etc. are examples of simple indices. A simple index can be very easily computed. The value of the variable for each period is divided by the value in the base period and the result is multiplied by 100.\n\nAn index that is computed from two or more variables is referred to as a composite index. Examples of composite indices are the wholesale price index numbers, consumer price index numbers etc. Composite indices are more important as many of the index numbers in common use are composite in nature. Composite indices may further be classified into Unweighted and Weighted index numbers.\n\n### 3 Important Things about Index Numbers\n\nFollowing are three important things we must consider while in compilation of index numbers:\n\n1. Understand the purpose which an index is to serve. The purpose of the index may be to compare the score of two players, or to measures the changes in the general price level or to measures the changes in the production of scooters or to compare the changes in wages of factory workers over different places, etc.\n\n2. Decide what data should be included. The data to be included should relate to purpose for which the index is to be used. This step also involves the collection of data on scores, production, process, wages or whatever is being compared.\n\n3. Decide what period should be chosen as the base period, i.e. the period with which the other periods are to be compared. In case of composite index numbers, another problem is to decide what method of averaging should be used to arrive at a single index for each period. The method of averaging usually includes the system of weighting but sometimes one faces the problems of assigning some explicit weights to the various items of the data so that their relative importance is taken into account." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.93627036,"math_prob":0.96796703,"size":2713,"snap":"2019-43-2019-47","text_gpt3_token_len":516,"char_repetition_ratio":0.14654854,"word_repetition_ratio":0.013100437,"special_character_ratio":0.18835238,"punctuation_ratio":0.08531746,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95263684,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-20T01:12:51Z\",\"WARC-Record-ID\":\"<urn:uuid:3c70887d-0209-4965-9a8e-277204a95db0>\",\"Content-Length\":\"28214\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5d01b6e2-d2b1-409f-a416-2d2351d29015>\",\"WARC-Concurrent-To\":\"<urn:uuid:e28b040f-f349-4075-903e-b818f86eb1f7>\",\"WARC-IP-Address\":\"52.42.38.100\",\"WARC-Target-URI\":\"https://datalya.com/blog/business-statistics/things-you-need-to-know-about-index-number\",\"WARC-Payload-Digest\":\"sha1:LJDRD65ML5MHZUUY74N3OJG4ZRM4QXAZ\",\"WARC-Block-Digest\":\"sha1:YZWMHACHFWLFDHVFOQHQ4ZGP4R7HYI3R\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496670389.25_warc_CC-MAIN-20191120010059-20191120034059-00383.warc.gz\"}"}
https://linuxhint.com/bash-loops-in-depth/	[ "BASH Programming\n\n# Bash Loops In-Depth\n\nA loop consists of one or more commands that execute repeatedly until a condition is met. In order for this to happen, the commands have to be in a construct. The construct and its commands form a compound command. A Bash command exits with zero if there was no problem. On the other hand, it exits with a number greater than zero if there was an issue or a problem. The exit status of a compound command is that of its last command.\n\nIn order to understand this article, the reader should already know simple Bash commands. Any non-simple Bash command used in this article is explained. Do not forget that Bash commands can be written into a text file, and the text file can run by typing the name of the file (preceded by path) at the terminal, then pressing Enter. Do not also forget to permit yourself to run the file with something like:\n\nsudo chmod +x program_name\n\n## Bash Loop Basics\n\nBash until/done Loop\nConsider the following code:\n\nlet n=0\n\nuntil [ \"\\$n\" -eq 5 ]; do\necho \\$n\n((++n))\ndone\n\nThe output is:\n\n0\n1\n2\n3\n4\n\nWhen the program begins, the variable n is declared and zero is assigned to it. The two commands before “done” are executed 5 times. ((++n)) increments n by 1 for each iteration. Note the positions of the reserved words, “until”, “do”, and “done”. The two commands are repeated until the condition, [ “\\$n” -eq 5 ] is met. In the condition, “-eq” means “equal to”. The condition is that the value of n is equal to 5. Note that the values echoed begins from 0 to 4. This is because, for each iteration, the condition of the construct is checked, before the body (two commands) of the construct is executed. If the condition is false, the body would not be executed. The reserved word, “done”, should always be typed in a new line.\n\nThe syntax for the until/done loop is:\n\nuntil test-commands; do consequent-commands; done\n\nThe second semicolon is not necessary if the reserved word, “done” is typed in a new line.\n\nIf the condition exits with zero, meaning true, the body of the loop is executed. If the condition exits with a number greater than zero, meaning false, the body of the loop is not executed.\n\nBash while/done Loop\nThis loop is similar to the until/done loop, except that the condition has to be rephrased. Both constructs use the “do” reserved word. The following code produces the same output as before:\n\nlet n=0\n\nwhile [ \"\\$n\" -lt 5 ]; do\necho \\$n\n((++n));\ndone\n\nIn the condition in the code, “-lt” means “less than”. The syntax for the while/done loop is:\n\nwhile test-commands; do consequent-commands; done\n\nBash for/done Loop\nThere are two syntax for the “for” loop, which are:\n\nfor (( expr1 ; expr2 ; expr3 )) ; do commands ; done\n\nand\n\nfor name [ [in [words …] ] ; ] do commands; done\n\nThe following code uses the first syntax to produce the same result, as above:\n\nfor ((n=0; n < 5; ++n)); do\necho \\$n\ndone\n\nIn the ((compound command, the first expression initializes the variable n to zero. The next expression is the while condition. The last expression in the double parentheses compound command is the increment expression. Then there is the body, which may consist of more than one command, and then “done”.\n\nThe second syntax is best used with an array – see below.\n\n## Bash break and continue Commands\n\nbreak\nAll the iterations (repeated execution of the body) intended for a loop must not necessarily be executed. The break command can be used to stop the remaining iterations. In the following code, the iterations stop just after n equals 2.\n\nfor ((n=0; n < 5; ++n)); do\necho \\$n\nif ((n == 2)); then\nbreak\nfi\ndone\n\nThe output is:\n\n0\n1\n2\n\nIn this loop, three iterations have taken place.\n\ncontinue\nAn iteration can be skipped using the continue command. The following code illustrates this:\n\nfor ((n=0; n < 5; ++n)); do\nif ((n == 2)); then\ncontinue\nfi\necho \\$n\ndone\n\nThe output is:\n\n0\n1\n3\n4\n\nThe iteration to display 2 has been skipped.\n\nThe break and continue commands can also be used in the until/done and while/done loops.\n\n## Useful Loop Examples\n\nuntil/done Loop Example\nThe command to create an empty text file is touched. The following script will create empty text files in the current working directory, until the number of files created, is 4:\n\nlet i=1\nfile=\"myFile\"\n\nuntil [ \\$i -eq 5 ]; do\nfilename=\"\\$file\\$i.txt\"\ntouch \\$filename\n((++i))\ndone\n\nThe names of the files created should be myFile1.txt, myFile2.txt, myFile3.txt, and myFile4.txt.\n\nThe only semicolon in the code can be omitted if “do” is typed in the next line.\n\nwhile/done Loop Example\nThe command to create an empty directory is mkdir. The following script will create empty directories in the current working directory until the number of directories created is 4:\n\ni=1\ndir=\"myDir\"\n\nwhile [ \\$i -lt 5 ]; do\ndirname=\"\\$dir\\$i\"\nmkdir \\$dirname\n((++i))\ndone\n\nThe name of the directories created should be myDir1, myDir2, myDir3, and myDir4.\n\nThe only semicolon in the code can be omitted if “do” is typed in the next line.\n\nfor Loop Example\nThe second syntax for the for-loop mentioned above is:\n\nfor name [ [in [words …] ] ; ] do commands; done\n\nThis syntax is better used with a list. In simple terms, the syntax is:\n\nfor Variable in List; do commands; done\n\nThe list can be an array. The following command reads an input line of text from the terminal into the array arr:\n\nAs the script is running, when it reaches this command, it will pause (with a flashing cursor) for the user to enter input. If the user types:\n\none two three\n\nin one line and presses Enter, then the first element of the array would have the word “one”, the second would have the word “two”, and the third would have “three”. Note that the input values were separated by spaces.\n\nThe following code uses the second for-loop syntax to read and display an input to the script:\n\necho \"Type in values and press Enter:\"\n\nfor var in \\$arr; do\necho \\$var\ndone\n\nIf the input was:\n\none two three\n\nThen the output would be:\n\none\ntwo\nthree\n\nThe only semicolon in the code can be omitted if “do” is typed in the next line.\n\n## Bash select Command\n\nThe select command is not really a loop. However, it involves iteration, which is not coded by the programmer. In simple terms, the select command syntax is:\n\nselect item in [list]\ndo\n[commands]\ndone\n\nHere, “select”, “in”, “do”, and “done” are reserved words. One use of the select command is to display the items from the list to the terminal. The following script illustrates this:\n\nselect item in banana, lemon, orange, pear, pineapple\ndo\nbreak\ndone\n\nNote the use of the break command. The output is:\n\n1) banana,\n2) lemon,\n3) orange,\n4) pear,\n5) pineapple\n#?\n\nThe list consists of the values banana, lemon, orange, pear, and pineapple. These values have been displayed and numbered. The symbol “#?” (and the flashing cursor next to it) is expecting the user to type in something and press the Enter key. Type anything, then press the Enter key and finally ends the execution of the script.\n\nNotice that the list has been displayed as a menu, numbered, for the output. With this, the user can select an item in the menu by typing the corresponding number, next to “#?”, then press the Enter key. The following script illustrates how orange is selected by typing the number 3:\n\nselect item in banana, lemon, orange, pear, pineapple\ndo\nbreak\ndone\n\nThe output display is:\n\n#? 3\nthen\n3\n\n## Conclusion\n\nA loop in Bash is a construct; a construct is a compound command. The body of the construct has at least one command. As of now, Bash has just three loops, which are until/done, while/done, and for/done. Each loop uses the reserved word “do”. After the condition has been typed, “do” should be preceded by ‘;’, or be typed in the next line of the code. Each loop takes a condition. The until/done and while/done loops are similar. The main difference occurs when coding the condition.\n\nThe select command is a compound command, but it is not really a loop. It allows the user to select an item from a menu list when the script is running interactively.\n\nThe break and continue commands can be used in a loop. The break command can be used to stop the iterations. On the other hand, the continue command can be used to skip an iteration.\n\nThat is all there is to Bash loops. The feature remaining to be studied is “How to Code the Conditions?”. This deserves a whole different article and cannot be included in this one. See the article on this website, titled “Bash Conditionals In-Depth”, on how to code conditions.\n\nChrys", null, "" ]	[ null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20112%20112'%3E%3C/svg%3E", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.88275427,"math_prob":0.6127191,"size":7302,"snap":"2022-05-2022-21","text_gpt3_token_len":1762,"char_repetition_ratio":0.13688682,"word_repetition_ratio":0.06835637,"special_character_ratio":0.23692138,"punctuation_ratio":0.12533157,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9638663,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-19T07:59:25Z\",\"WARC-Record-ID\":\"<urn:uuid:c5e35c6b-07a3-4bd3-a9b8-2e7ea8780b6e>\",\"Content-Length\":\"198524\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0ae91fc9-382a-4572-9758-a16c3ed688e3>\",\"WARC-Concurrent-To\":\"<urn:uuid:34c4dbf7-53a6-44a9-9309-e1040b4a3ddf>\",\"WARC-IP-Address\":\"104.21.58.234\",\"WARC-Target-URI\":\"https://linuxhint.com/bash-loops-in-depth/\",\"WARC-Payload-Digest\":\"sha1:ESBZXBLXBKDJ23SVWJCVHP2ZF6ZY7V3P\",\"WARC-Block-Digest\":\"sha1:6SFSMM4SSLM6WLX2723R266KDHDFKZUR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662526009.35_warc_CC-MAIN-20220519074217-20220519104217-00750.warc.gz\"}"}
https://gamedev.stackexchange.com/questions/88476/transformations-and-basis-vectors?noredirect=1	[ "# Transformations and basis vectors\n\nI've been reading this very nice tutorial on OpenGL, and I encountered a statement which I can't wrap my head around. In Chapter 6, it states:\n\nTransformation from one space to another ultimately means this: taking the basis vectors and origin point from the original coordinate system and re-expressing them relative to the destination coordinate system. The transformation matrix from one space to another contains the basis vectors and origin of the original coordinate system, but the values of those basis vectors and origin are relative to the destination coordinate system.\n\nThis is reaffirmed in Chapter 7:\n\n... And this makes sense; a transformation matrix contains the basis vector and origin of the source space, as expressed in the destination coordinate system.\n\n... But isn't it the other way around?\n\nTake a look at this example from the tutorial:", null, "The transformation Matrix to transform from the space on the left to the space on the right is\n\n[1 0 0 1 ]\n[0 1 0 -1.5]\n[0 0 1 0 ]\n[0 0 0 1 ]\n\n\nThe last column of the transformation matrix is the origin of the destination space, expressed relative to the source space.\n\nWhat am I missing?\n\nNote The above transformation matrix is not from the notes, so feel free to correct it.\n\nThe transformation Matrix to transform from the space on the left to the space on the right is\n\n[1 0 0 1 ]\n[0 1 0 -1.5]\n[0 0 1 0 ]\n[0 0 0 1 ]\n\n\nWell this is not correct, the matrix you have shown is actually to transform any point from the space on the right to the space on the left. The correct matrix to transform from the space on the left to the right is actually\n\n[1 0 0 -1 ]\n[0 1 0 1.5 ]\n[0 0 1 0 ]\n[0 0 0 1 ]\n\n\nThink about it like this. The [0,0] point on the left figure is actually [-1,1.5] relative to the new space (right figure), remember when you change a basis it's easier to think about it as actually transforming basis not the points, meaning you're actually representing the same points relative to a different basis.\n\nEven though you can think of it the other way around, as of actually taking the inverse transform of the points, it's actually easier to think about it as transforming the basis, either way pick a convention and stick with it. You can also check my other answer, for better explanation of spaces.\n\n• thanks for the answer. When you think about it as transforming the basis, it's very clear. But when you say that the matrix in the question represents the \"inverse transform of the points\", that's what I don't see. For example, the point (0.5, 2.5) on the top of the left triangle becomes (1.5, 1.0) on the right (in the \"global\" space), which means that it was translated by [1, -1.5], not the inverse of that. Could you elaborate on that point? Dec 10 '14 at 16:31\n• First lets be clear that the basis on the right figure are the red blue lines. Your confusion comes from the fact that you moved the triangle along with basis. A change of basis doesn't move the triangle its exactly like looking at the triangle from different perspective the triangle stays at the same position but with different interpretation of its coordinates Dec 10 '14 at 17:15\n• Took me a while, but I just got it (after some reading), and your answer was very helpful! If I'm not mistaken, what the author is trying to explain is not moving the triangle from the image on the left to the right, but rather, transforming the coordinate system of the triangle on the right from its object space to the destination space Dec 11 '14 at 13:56\n• @Nasser Glad to help. Dec 11 '14 at 13:59" ]	[ null, "https://i.stack.imgur.com/78DNx.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.88840044,"math_prob":0.9709699,"size":1230,"snap":"2021-31-2021-39","text_gpt3_token_len":264,"char_repetition_ratio":0.15089722,"word_repetition_ratio":0.03773585,"special_character_ratio":0.22195122,"punctuation_ratio":0.10878661,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9537109,"pos_list":[0,1,2],"im_url_duplicate_count":[null,8,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-22T06:55:40Z\",\"WARC-Record-ID\":\"<urn:uuid:33ee706d-a664-4f61-9da0-a209faff1891>\",\"Content-Length\":\"177854\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:50ad3ab0-583b-4d45-8207-ffdf391583c1>\",\"WARC-Concurrent-To\":\"<urn:uuid:0b282e64-f62a-4cee-9f2f-996d4407e02c>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://gamedev.stackexchange.com/questions/88476/transformations-and-basis-vectors?noredirect=1\",\"WARC-Payload-Digest\":\"sha1:PUG3EC3BWU7NJME5RLK7YU5KFMQTIVDS\",\"WARC-Block-Digest\":\"sha1:QUQ6QT34LMG4TDAUH7DWBV7OIBEVAJX3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057329.74_warc_CC-MAIN-20210922041825-20210922071825-00658.warc.gz\"}"}
http://mathv.chapman.edu/~jipsen/structures/doku.php/epimorphisms_are_surjective	[ "## Epimorphisms are surjective\n\nA morphism $h$ in a category is an epimorphism if it is right-cancellative, i.e. for all morphisms $f$, $g$ in the category $f\\circ h=g\\circ h$ implies $f=g$.\n\nA function $h:A\\to B$ is surjective (or onto) if $B=f[A]=\\{f(a): a\\in A\\}$, i.e., for all $b\\in B$ there exists $a\\in A$ such that $f(a)=b$.\n\nEpimorphisms are surjective in a (concrete) category of structures if the underlying function of every epimorphism is surjective.\n\nIf a concrete category has the amalgamation property and all epimorphisms are surjective, then it has the strong amalgamation property1)\n\n1) E. W. Kiss, L. Márki, P. Pröhle, W. Tholen, Categorical algebraic properties. A compendium on amalgamation, congruence extension, epimorphisms, residual smallness, and injectivity, Studia Sci. Math. Hungar., 18, 1982, 79-140 MRreview\n\n##### Toolbox", null, "" ]	[ null, "http://mathv.chapman.edu/~jipsen/structures/lib/exe/indexer.php", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.79287857,"math_prob":0.9959769,"size":631,"snap":"2019-35-2019-39","text_gpt3_token_len":192,"char_repetition_ratio":0.18819776,"word_repetition_ratio":0.0,"special_character_ratio":0.25356576,"punctuation_ratio":0.11811024,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9970647,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-21T08:04:08Z\",\"WARC-Record-ID\":\"<urn:uuid:6795f712-a425-4c5a-b054-df714da9e68f>\",\"Content-Length\":\"12438\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a06b411b-fb73-4a62-b845-443f33b4acec>\",\"WARC-Concurrent-To\":\"<urn:uuid:4b31be13-d546-4ec6-8573-12df5fb641cf>\",\"WARC-IP-Address\":\"192.77.116.236\",\"WARC-Target-URI\":\"http://mathv.chapman.edu/~jipsen/structures/doku.php/epimorphisms_are_surjective\",\"WARC-Payload-Digest\":\"sha1:C35N2SJ7QX5MJHCTENC65BFDVBQUH3NQ\",\"WARC-Block-Digest\":\"sha1:VN6P7KIY54ELJ6I7U4C6PAJYJ7TVX6PE\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514574286.12_warc_CC-MAIN-20190921063658-20190921085658-00083.warc.gz\"}"}
https://eudml.org/search/page?q=sc.generalop.ANDl_0*c_0author_0eq%253A1.Singh%252C+Surjeet&qt=SEARCH	[ "## Currently displaying 1 – 9 of 9\n\nShowing per page\n\nOrder by Relevance \| Title \| Year of publication\n\n### TAG-modules with complement submodules $h$-pure.\n\nInternational Journal of Mathematics and Mathematical Sciences\n\n### Invariance of recurrence sequences under a Galois group.\n\nInternational Journal of Mathematics and Mathematical Sciences\n\n### Some chain conditions on weak incidence algebras.\n\nInternational Journal of Mathematics and Mathematical Sciences\n\n### Weak incidence algebra and maximal ring of quotients.\n\nInternational Journal of Mathematics and Mathematical Sciences\n\n### Over-rings of an (HNP)-ring\n\nColloquium Mathematicae\n\n### Inertial subrings of a locally finite algebra\n\nColloquium Mathematicae\n\nI. S. Cohen proved that any commutative local noetherian ring R that is J(R)-adic complete admits a coefficient subring. Analogous to the concept of a coefficient subring is the concept of an inertial subring of an algebra A over a commutative ring K. In case K is a Hensel ring and the module ${A}_{K}$ is finitely generated, under some additional conditions, as proved by Azumaya, A admits an inertial subring. In this paper the question of existence of an inertial subring in a locally finite algebra is discussed....\n\n### A representation theorem for Chain rings\n\nColloquium Mathematicae\n\nA ring A is called a chain ring if it is a local, both sided artinian, principal ideal ring. Let R be a commutative chain ring. Let A be a faithful R-algebra which is a chain ring such that Ā = A/J(A) is a separable field extension of R̅ = R/J(R). It follows from a recent result by Alkhamees and Singh that A has a commutative R-subalgebra R₀ which is a chain ring such that A = R₀ + J(A) and R₀ ∩ J(A) = J(R₀) = J(R)R₀. The structure of A in terms of a skew polynomial ring over R₀ is determined.\n\nPage 1" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.93180776,"math_prob":0.8444007,"size":1062,"snap":"2022-40-2023-06","text_gpt3_token_len":281,"char_repetition_ratio":0.12854442,"word_repetition_ratio":0.031088082,"special_character_ratio":0.22975518,"punctuation_ratio":0.08928572,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.994663,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-01T14:33:29Z\",\"WARC-Record-ID\":\"<urn:uuid:d63631bd-5d29-4c8c-ac67-06b23056fcdf>\",\"Content-Length\":\"73193\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5666cb45-c5e5-408b-bfb0-a13dce2214d9>\",\"WARC-Concurrent-To\":\"<urn:uuid:91902453-a709-4690-b000-8089045776ca>\",\"WARC-IP-Address\":\"213.135.60.110\",\"WARC-Target-URI\":\"https://eudml.org/search/page?q=sc.generalop.ANDl_0*c_0author_0eq%253A1.Singh%252C+Surjeet&qt=SEARCH\",\"WARC-Payload-Digest\":\"sha1:SVFUKOGAFXFMWZKR6TDDUJYVO67JVKLL\",\"WARC-Block-Digest\":\"sha1:2EVZSOOLWI5P5I2NRXOZYHUPU3I2B7DD\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030336674.94_warc_CC-MAIN-20221001132802-20221001162802-00250.warc.gz\"}"}
https://mllg.github.io/checkmate/reference/checkNumber.html	[ "Check if an argument is a single numeric value\n\ncheckNumber(\nx,\nna.ok = FALSE,\nlower = -Inf,\nupper = Inf,\nfinite = FALSE,\nnull.ok = FALSE\n)\n\ncheck_number(\nx,\nna.ok = FALSE,\nlower = -Inf,\nupper = Inf,\nfinite = FALSE,\nnull.ok = FALSE\n)\n\nassertNumber(\nx,\nna.ok = FALSE,\nlower = -Inf,\nupper = Inf,\nfinite = FALSE,\nnull.ok = FALSE,\n.var.name = vname(x),\n)\n\nassert_number(\nx,\nna.ok = FALSE,\nlower = -Inf,\nupper = Inf,\nfinite = FALSE,\nnull.ok = FALSE,\n.var.name = vname(x),\n)\n\ntestNumber(\nx,\nna.ok = FALSE,\nlower = -Inf,\nupper = Inf,\nfinite = FALSE,\nnull.ok = FALSE\n)\n\ntest_number(\nx,\nna.ok = FALSE,\nlower = -Inf,\nupper = Inf,\nfinite = FALSE,\nnull.ok = FALSE\n)\n\nexpect_number(\nx,\nna.ok = FALSE,\nlower = -Inf,\nupper = Inf,\nfinite = FALSE,\nnull.ok = FALSE,\ninfo = NULL,\nlabel = vname(x)\n)\n\n## Arguments\n\nx\n\n[any]\nObject to check.\n\nna.ok\n\n[logical(1)]\nAre missing values allowed? Default is FALSE.\n\nlower\n\n[numeric(1)]\nLower value all elements of x must be greater than or equal to.\n\nupper\n\n[numeric(1)]\nUpper value all elements of x must be lower than or equal to.\n\nfinite\n\n[logical(1)]\nCheck for only finite values? Default is FALSE.\n\nnull.ok\n\n[logical(1)]\nIf set to TRUE, x may also be NULL. In this case only a type check of x is performed, all additional checks are disabled.\n\n.var.name\n\n[character(1)]\nName of the checked object to print in assertions. Defaults to the heuristic implemented in vname.\n\n[AssertCollection]\nCollection to store assertion messages. See AssertCollection.\n\ninfo\n\n[character(1)]\nExtra information to be included in the message for the testthat reporter. See expect_that.\n\nlabel\n\n[character(1)]\nName of the checked object to print in messages. Defaults to the heuristic implemented in vname.\n\n## Value\n\nDepending on the function prefix: If the check is successful, the functions\n\nassertNumber/assert_number return\n\nx invisibly, whereas\n\ncheckNumber/check_number and\n\ntestNumber/test_number return\n\nTRUE. If the check is not successful,\n\nassertNumber/assert_number\n\nthrows an error message,\n\ntestNumber/test_number\n\nreturns FALSE, and checkNumber/check_number\n\nreturn a string with the error message. The function expect_number always returns an\n\nexpectation.\n\n## Details\n\nThis function does not distinguish between NA, NA_integer_, NA_real_, NA_complex_ NA_character_ and NaN.\n\nOther scalars: checkCount(), checkFlag(), checkInt(), checkScalarNA(), checkScalar(), checkString()\ntestNumber(1)" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.53084075,"math_prob":0.9947172,"size":2376,"snap":"2022-40-2023-06","text_gpt3_token_len":629,"char_repetition_ratio":0.18043844,"word_repetition_ratio":0.33862433,"special_character_ratio":0.27272728,"punctuation_ratio":0.21758242,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.984363,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-06T06:58:20Z\",\"WARC-Record-ID\":\"<urn:uuid:46b485aa-1b3e-4807-b7f0-88899d359c6b>\",\"Content-Length\":\"15431\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1e92e92a-e5c0-4146-9e42-553f0fb76a63>\",\"WARC-Concurrent-To\":\"<urn:uuid:163f6bd2-a036-48a1-85ce-681e6e96e0b5>\",\"WARC-IP-Address\":\"185.199.110.153\",\"WARC-Target-URI\":\"https://mllg.github.io/checkmate/reference/checkNumber.html\",\"WARC-Payload-Digest\":\"sha1:ADUTTJ7YA22I5ET6DCIRGBTGSJITPCUJ\",\"WARC-Block-Digest\":\"sha1:Z2DEKI6YMN6GRR6GDRGTJNRMFYH4FFJK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500304.90_warc_CC-MAIN-20230206051215-20230206081215-00848.warc.gz\"}"}
https://platformkvuz.web.app/kory51341vy/determine-the-future-value-of-education-pe.html	[ "## Determine the future value of education\n\nWe want to find the future value of her money (FV). 1 00 Journal of Financial Education. Page 6. At this point students can solve the\n\nAccess the answers to hundreds of Future value questions that are explained in a way that's easy for you to understand. Can't find the question you're looking for? Future Value Of Cost Of Education ₹ 2,13,293 your age, and annual income can help you determine how much you can save up if you start investing today. 23 Feb 2018 To begin with, find out how much the goal costs today. For example, take your child's higher education. Let us assume that it costs Rs 5 lakh today In a finite math course, you will encounter a range of financial problems, such as how to calculate an annuity. An annuity consists of regular payments into an Module 5 - Future Values. Calculate the Future Value of an Annuity. Combining TVM Tools. Module 6 - Final Assignments. Mastering the Time Value of Money Students learn about opportunity cost, interest and inflation to determine the future value of investments, and the present value of a future sum of money in this How does an increase in the interest rate affect the discounted present value of For example, if you have trained as an engineer and then decide you want to be First, the gains from education appear as an increase in earnings each year.\n\n## Plan for your child's bright future with the child education calculator. Calculate the total education expenses against inflation rate and give your child the best education. Human Life Value Calculator. Know how much life insurance you\n\n### We want to find the future value of her money (FV). 1 00 Journal of Financial Education. Page 6. At this point students can solve the\n\n7 Jun 2019 Present value is one of the most important concepts in finance. Luckily, once you learn a few tricks, you can calculate it easily. All you need to\n\n## 26 Feb 2010 When we calculate the value of future payments today, we are doing a present value calculation. When we try to value what a stream of future\n\nCalculate how much interest she earned over the $$\\text{29}$$ year period. Write down the given information and the future value formula. \\[F = \\frac{x\\left[(1 + i)^ How to Determine Future Value of Cash Flows. Cash flows are one-time or periodic inflows of money, such as dividends, or outflows, such as tuition expenses. 7 Jun 2019 Present value is one of the most important concepts in finance. Luckily, once you learn a few tricks, you can calculate it easily. All you need to We use the future value formula for simple interest to determine the simple interest rate that 6) Parents wish to have \\$120,000 available for a child's education." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9152684,"math_prob":0.9550189,"size":5522,"snap":"2021-31-2021-39","text_gpt3_token_len":1179,"char_repetition_ratio":0.18629938,"word_repetition_ratio":0.07635207,"special_character_ratio":0.21387179,"punctuation_ratio":0.09848485,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98437536,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-23T12:04:45Z\",\"WARC-Record-ID\":\"<urn:uuid:a13dc76e-3c7f-4d70-a041-c399f144b682>\",\"Content-Length\":\"18400\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:80d994ff-f964-4995-9247-eff8aef40968>\",\"WARC-Concurrent-To\":\"<urn:uuid:7c58b213-6814-4d19-8d33-31b84131dd99>\",\"WARC-IP-Address\":\"199.36.158.100\",\"WARC-Target-URI\":\"https://platformkvuz.web.app/kory51341vy/determine-the-future-value-of-education-pe.html\",\"WARC-Payload-Digest\":\"sha1:Q2ORJWBMYXRZ6OLP5WSTLADCVU3D4VOF\",\"WARC-Block-Digest\":\"sha1:36KE65HNZ6AN7QYQISCAPX4PW6C6IJUG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057421.82_warc_CC-MAIN-20210923104706-20210923134706-00051.warc.gz\"}"}
https://www.gradesaver.com/textbooks/math/calculus/calculus-with-applications-10th-edition/chapter-r-algebra-reference-r-4-equations-r-4-exercises-page-r-16/15	[ "## Calculus with Applications (10th Edition)\n\n$-3$ and $3$\nDivide both sides of the equation by 4: $4x^{2}-36=0\\qquad.../\\div 4$ $x^{2}-9=0$ ... recognize a difference of squares (of x and 3) $A^{2}-B^{2}=(A+B)(A-B)$ $(x+3)(x-3)=0$ By the zero product principle, $x+3=0$ or $x-3=0$ $x=-3$ or $x=3$ The solutions are $-3$ and $3$." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7415106,"math_prob":1.0000099,"size":308,"snap":"2020-24-2020-29","text_gpt3_token_len":134,"char_repetition_ratio":0.10526316,"word_repetition_ratio":0.0,"special_character_ratio":0.49025974,"punctuation_ratio":0.11111111,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000057,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-04T19:26:39Z\",\"WARC-Record-ID\":\"<urn:uuid:29d97edf-0b22-4824-adfc-687661313268>\",\"Content-Length\":\"59092\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:57581fb3-10fc-4357-8782-7b8989f476b6>\",\"WARC-Concurrent-To\":\"<urn:uuid:eeaa0a55-a6d4-4dd2-9bb8-50ad62598f29>\",\"WARC-IP-Address\":\"34.238.129.158\",\"WARC-Target-URI\":\"https://www.gradesaver.com/textbooks/math/calculus/calculus-with-applications-10th-edition/chapter-r-algebra-reference-r-4-equations-r-4-exercises-page-r-16/15\",\"WARC-Payload-Digest\":\"sha1:KL7OWYFIB7AUAHGL3YQXN2A6UQ5CYHQE\",\"WARC-Block-Digest\":\"sha1:SZVINROJJS4T6YPW4QC4U5OXLDBOPBXF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655886516.43_warc_CC-MAIN-20200704170556-20200704200556-00291.warc.gz\"}"}
https://aip.seekingsugardaddy.de/matlab-code-for-forward-and-inverse-kinematics.html	[ "Matlab code for forward and inverse kinematics\n\n### 18 hours ago · and inverse kinematics of a 6-DOF robot arm presented in this paper Inverse Kinematics for a General Purpose Robot Arm That Moves in 3D Explanation of code for simulating FK for Universal robot 5 arm using the robotics toolbox in MATLAB If you are looking for C/C++ codes for simulating ( Universal Robot) UR5 Robot Manipulator, you can download. . The robot kinematics can be divided into forward kinematics and inverse kinematics. Forward kinematics problem is straightforward and there is no complexity deriving the equations. Hence, there is always a forward kinematics solution of a manipulator. Inverse kinematics is a much more difficult problem than forward kinematics. 2022. 7. 16. · Inverse Kinematics Solver Matlab One important aspect however is that while OpenSim provides a useful general tool for biomechanical analysis including fields beyond. Forward Kinematics and Reverse Kinematics. In Robotics F.K. we have ASi = Bphi where A, B are known matrices, Si is a vector with x, y and z as its elements, phi is the vector containing the angular velocity of each of the 2 wheels of the robot. MATLAB says that an eqn of the form Ax=B can be solved by A\\B. This video includes an example for a robot manipulator to be simulated. Both Forward and Inverse Kinematics are calculated through a MATLAB GUIif you don't k. . Department, Mechatronics Lab. Forward and Inverse kinematics analysis are performed. Robotics Toolbox is also applied to model Denso robot system. A GUI is built for practical use of robotic system. 2. Robot Arm Kinematics The robot kinematics can be categorized into two main parts; forward and inverse kinematics. Forward. . Forward Kinematics is a mapping from joint space Q to Cartesian space W: F(Q) = W This mapping is one to one - there is a unique Cartesian conﬁguration for the robot for a given set of joint variables. Inverse Kinematics is a method to ﬁnd the inverse mapping from W to Q: Q = F−1(W) 2. The inverse kinematics problem has a wide range of. 3.1Inverse Kinematics Test On the basis of previous development, it is possible to utilize MATLAB to perform kinematics analysis. Using the manipulator shown in Fig. 2 as the example. Suppose the desired position and orientation of end effector are (20 , 20) and φ = 0˚. 18 hours ago · and inverse kinematics of a 6-DOF robot arm presented in this paper Inverse Kinematics for a General Purpose Robot Arm That Moves in 3D Explanation of code for simulating FK for Universal robot 5 arm using the robotics toolbox in MATLAB If you are looking for C/C++ codes for simulating ( Universal Robot) UR5 Robot Manipulator, you can download. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators. EULER.m (inside the for loop) to implement the Backward Euler, Improved Euler and Runge-Kutta methods. The ﬁle EULER.m This program will implement Euler’s method to solve the diﬀerential equation dy dt = f(t,y) y(a) = y 0 (1) The solution is returned in an array y. You may wish to compute the exact. In my opinion, the answer to this question is straightforward. 2022. 9. 7. · with the forward''Topic matlab Â· GitHub May 7th, 2018 - More than 27 million people use GitHub to discover Gramm is a complete data visualization toolbox for Matlab Human Fall Detection from CCTV camera feed' 'matlab inverse kinematics robot arm circle youtube april 21st, 2018 - code http simsamo. siser easysubli htv and mask sublimation sheets. MATLAB and Simulink capabilities to develop new robot algorithms » Kinematic and dynamic models of robots ... Connect to an exter. . January 18, 2022 matlab code for forward and inverse kinematics. by. OVERVIEW. ACROBOT 6-DOF Robot Arm , with its high technology joint actuators, is a hands-on experiment, closing the gap between real industrial systems and DIY- approach. Users can understand the complex inverse kinematics algorithms and quickly prototype new motion control architecture for industrial parallel kinematics <b>robots</b>. These forward and inverse kinematics computations are done using KinematicsSolver objects. The objects are defined as persistent variables in the functions sm_pick_and_place_robot_fk and sm_pick_and_place_robot_ik. Search for jobs related to Forward kinematics and inverse kinematics matlab or hire on the world's largest freelancing marketplace with 21m+ jobs. It's free to sign up and bid on jobs. 2022. 7. 13. · Suppose the initial state of the manipulator that all nodes are shown on the same line as shown in following figure Sıfır matrisi: Matlab zeros komutu Birler matris: Matlab ones. This project combined forward and inverse position and velocity kinematics, dynamics, and vision processing for the control of a 3 Degree of Freedom ( DOF ) robotic arm .The manipulator was able to recognize objects in its workspace, pick them up, and sort them by weight and color. A combination of MatLab and C++ programming was used to control. First, plug the joint angles you received from your inverse kinematics algorithm into your forward kinematics equations. Do they provide the same end effector coordinates that you entered into your inverse kinematics routine? If not, you have an error in either the forward or inverse equations. Yes, forward kinematics are easy. It defines a function which maps the robot configuration $$R_1 \\in SO(2), R_2 \\in SO(2)$$ to the end-effector position $$e \\in R^2$$. Normally, the forward kinematics is a closed-form function. 4. The Inverse Kinematics. The inverse kinematics asks a question: I want to move the end-effector to a target position. 18 hours ago · and inverse kinematics of a 6-DOF robot arm presented in this paper Inverse Kinematics for a General Purpose Robot Arm That Moves in 3D Explanation of code for simulating FK for Universal robot 5 arm using the robotics toolbox in MATLAB If you are looking for C/C++ codes for simulating ( Universal Robot) UR5 Robot Manipulator, you can download. To define a combination of position and orientation goal, we would append some rotation parameterization like Euler angles to x, and define the forward kinematic map: x ≡ [xp xo] = f(q) ≡ [ TN(q)xN R − 1 ea (RN(q))]. Here are the steps for calculating inverse kinematics for a six degree of freedom robotic arm. Step 1: Draw the kinematic diagram of just the first three joints, and perform inverse kinematics using the graphical approach. Step 2: Compute the forward kinematics on the first three joints to get the rotation of joint 3 relative to the global (i.e. Please can you write a code for Forward and inverse kinematics for 5 DOF using matlab (robotics toolbox) Question: Please can you write a code for Forward and inverse kinematics for 5 DOF using matlab (robotics toolbox). . These coordinates are end effector position target to pick each object and were placed to the right position based on its color. Based on the end effector position target, PD-PIJ inverse kinematics method was used to determine the right angle of each joint of manipulator links. The angles found by PD-PIJ is the input of DH forward kinematics. 2022. 9. 5. · The forward kinematics allow NAO developers to map any configuration of the robot from its own joint space to the three-dimensional physical space, whereas the inverse. Special thanks for :Felix Pasila, S.T., M.Sc., Ph.D as lecturerHarsha for making the solidwork designReference:https://grabcad.com/library/6- dof -robotic-ma. OVERVIEW. ACROBOT 6-DOF Robot Arm , with its high technology joint actuators, is a hands-on experiment, closing the gap between real industrial systems and DIY- approach. Users can understand the complex inverse kinematics algorithms and quickly prototype new motion control architecture for industrial parallel kinematics <b>robots</b>. This document will help in better understanding of forward and inverse kinematics. For forward kinematics you are only required with angles and it provides you the end effector position and in Inverse Kinematics provide the end effector position (coordinate axes) and GUI will provide you the required angles to achieve that position. Cite As. 2022. 9. 6. · forward (theta) To calculate the forward kinematics, we need to specify 6 axis angles Inverse dynamics is a technique in which measured kinematics and, possibly, external. Matlab code for Forward Kinematics of 2R robotic arm with animation. 2022. 9. 7. · If inverse kinematics are calculated, the return values are placed in a, b and c I have been learning about Inverse Kinematics on Systems of linked components Subsequently, simulation of the inverse kinematics of the above-mentioned kinematic structure was performed in the Matlab Simulink environment using the Forward kinematics described how robot's. Compute the kinematic solution using the gik object. Specify the initial guess and the different kinematic constraints in the proper order. iniGuess = homeConfiguration (robot); [q, solutionInfo] = gik (iniGuess,positionTarget1,positionTarget2,jointLimBounds); Examine the results in solutionInfo. Show the kinematic solution compared to the home. The solution of the forward and inverse kinematics problems based on the geometric method are given and obtained in MATLAB for the 5DOF manipulator. •Design Inverse Kinematics Algorithm . In this paper, artificial neural networks (ANN) are used and simulated. I'm trying to write an inverse kinematics Matlab code for a 6 DOF robotic arm that has the following link parameters: Twist angle (alpha): [-90, 0, 90, -90, 90, 0] Link length (a): [0, 0.5, 0, 0, 0, 0] ... The goal of this project is to design a forward 6 DoF robotic arm and control it by Matlab. The controller is separated by two. The MATLAB code also implements a Graphical User Interface (GUI), from which the user can control the robotic arm and run the forward and inverse kinematics algorithms. A 3D simulation/visualization of the robotic arm is displayed in the GUI in real time. Search for jobs related to Forward kinematics and inverse kinematics matlab or hire on the world's largest freelancing marketplace with 21m+ jobs. It's free to sign up and bid on jobs. I am verifying the output of my forward kinematics through inverse kinematics and the results are not as desired. As the output of my inverse kinematics is not coming out to be the same as the input of forward kinematics. The D-H parameters of manipulator is given as: Link: alpha, a, theta, d. Link 1 : -90 0 theta1* d1. Properties of MOPSO matlab r2019 全局优化工具箱全局优化工具箱提供了一些函数, 用于寻找包含多个极大值或极小值的问题的全局解. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators. Download and share free MATLAB code, including functions, models, apps, support packages and toolboxes ... Movement system used forward kinematics denavit hartenberg which each joint angle is updated by joint velocity found by inverse kinematics pseudoinverse jacobian. ... Robot Manipulator Control with Inverse Kinematics PD-Pseudoinverse. January 18, 2022 matlab code for forward and inverse kinematics. by. The MATLAB code also implements a Graphical User Interface (GUI), from which the user can control the robotic arm and run the forward and inverse kinematics algorithms. A 3D simulation/visualization of the robotic arm is displayed in the GUI in real time. •Robotics Toolbox for MATLAB: overview, online resources, basic operations, installation, built-in demo •Serial-link manipulator example -Puma560: DH parameters, forward & inverse kinematics •How to better use RTB manual •Bugs -example, possible solutions •Simulink -intro, RTB library for Simulink, RTB examples for Simulink. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators. 2022. 7. 13. · Matlab code for Forward Kinematics of 2R robotic arm with animation The more frequent robot manipulation problem, however, is the opposite The following code can be used. All vectors and tensors are to be expressed in the Link's coordinate frame. dhFwdKine H = dhFwdKine (linkList, paramList): Returns the forward kinematics of a manipulator with the provided DH parameter set. linkList is to be an array of links, each created by createLink. matlab code for forward and inverse kinematics. May 21 2021. naugatuck high school football coach. creative synonyms in different languages 0 Comments. Forward kinematics for all link frames. Parameters. q (ndarray(n) or ndarray(m,n)) - The joint configuration of the robot (Optional, if not supplied will use the stored q values). old (bool, optional) - \"old\" behaviour, defaults to True. Returns. Forward kinematics as an SE(3) matrix. Return type. SE3 instance with n values. . About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators. The kinematics and dynamics (both forward and inverse) of the biped robot \"PASIBOT,\" taking into account for support foot slippage are encoded in MATLAB ® code. The great advantage of creating a parametric MATLAB ® code following this methodology is that the algorithm can be modify to obtain the results in a parametric way or even. Read more..The kinematics and dynamics (both forward and inverse) of the biped robot \"PASIBOT,\" taking into account for support foot slippage are encoded in MATLAB ® code. The great advantage of creating a parametric MATLAB ® code following this methodology is that the algorithm can be modify to obtain the results in a parametric way or even. 2022. 9. 7. · Link Creation MATLAB 2014B Initialization of PETER CORKE ROBOTIC TOOL BOX FEATURE Inverse Kinematics is the inverse - using the end-effector desired coordinates ,. There are 4 different 6-axis robots that I am trying to calculate. one's forward kinematics, one's inverse kinematics, one's newton euler's solution, one's Jacobian matrix solutions, I have to do it in matlab. I'm trying to write the required codes, but I'm constantly making mistakes. I could not find ready-made code anywhere. siser easysubli htv and mask sublimation sheets. MATLAB and Simulink capabilities to develop new robot algorithms » Kinematic and dynamic models of robots ... Connect to an exter. When to use: Solving forward and inverse kinematics and dynamics, extracting mechanical properties (Jacobian, mass matrix, gravity torques, etc.) ... Below is some example MATLAB code and an animation of generalized IK on a model of a Rethink Sawyer, which has a 7-DOF arm. Here, we are setting a constraint on the end effector position, while. Topics covered in this session are:Euler Lagrange formulation of n-DOF serial manipulatorGeneral Matlab codeExample: Inverse Dynamics of a 2-DOF manipulator. I am trying to compute dynamics of 3 DOF robot using Robotics Toolbox by executing this code: robot.accel(q, zeros(1,3), zeros(1,3)) But I am getting this error: Assignment has more non. For Kinematic analysis of taken 6 DOF serial link manipulator, the D-H representation of Forward & Inverse Kinematics are mathematically obtained first. In figure 2 is shown a simple 6 DOF robotic arm . Figure 2. 6 DOF robot manipulator The joint & Link parameters of 6 DOF</b> <b>robots</b> are noted below in a table 1. There are two types of kinematic equations used in the control of this robot: forward and reverse. Forward kinematics are used to find the arms position in task space based on the joint parameters. For example, if you know the angle of the three joints, you can use forward position kinematics to determine the (x,y,z) position of the end-effector. Start Learning with Free Interactive Tutorials. MATLAB Onramp. Get started quickly with the basics of MATLAB . Launch. Simulink Onramp. Discover Model-Based Design with Simulink . Learn more. glupi vicevi. Advertisement kioti hydraulic fluid. used 5 ft box blade. how. regus. 2022. 9. 5. · The forward kinematics allow NAO developers to map any configuration of the robot from its own joint space to the three-dimensional physical space, whereas the inverse. Jul 10, 2019 · Forward Dynamics of Robot using Robotics Toolbox. Learn more about matlab, simulink, control, robotics toolbox, peter corke Simulink. \"/> cvxpy solver. difference between fair value gap and liquidity void; niantic wayfarer level 38; percy jackson fanfiction lemon. Let's look at numerical approaches to inverse kinematics for a couple of different robots and learn some of the important considerations. For RTB10.x please note that the mask value must be explicitly preceded by the 'mask' keyword. For example: >> q = p2.ikine (T, [-1 -1], 'mask', [1 1 0 0 0 0]) MATLAB. inverse kinematic. These coordinates are end effector position target to pick each object and were placed to the right position based on its color. Based on the end effector position target, PD-PIJ inverse kinematics method was used to determine the right angle of each joint of manipulator links. The angles found by PD-PIJ is the input of DH forward kinematics. . 18 hours ago · Search: Inverse Kinematics Solver Matlab. Peter Corke's Robotics Toolbox for robot forward and inverse kinematics Alternatively (my preferred method, but also the only. bitcoin private key generator apk simulating a 6 DOF robot in matlab robotic toolbox. Ask Question Asked 2 years, 6 months ago. Modified 2 years, 6 months ago. Viewed 473 times ... Since your robot has 6 DOF, I would expect q also have 6 columns instead of 5. Try with q = [0 0 0 0 0 0] in your code. Share. Follow. cree competitors. All vectors and tensors are to be expressed in the Link's coordinate frame. dhFwdKine H = dhFwdKine (linkList, paramList): Returns the forward kinematics of a manipulator with the provided DH parameter set. linkList is to be an array of links, each created by createLink. To define a combination of position and orientation goal, we would append some rotation parameterization like Euler angles to x, and define the forward kinematic map: x ≡ [xp xo] = f(q) ≡ [ TN(q)xN R − 1 ea (RN(q))]. 18 hours ago · Search: Inverse Kinematics Solver Matlab. Peter Corke's Robotics Toolbox for robot forward and inverse kinematics Alternatively (my preferred method, but also the only way if your Matlab release is older than R2015b [8 x = load('E:\\myFile1 The inverseKinematics System object™ creates an inverse kinematic (IK) solver to calculate joint configurations for a desired. This example shows how to use the KinematicsSolver object to perform forward kinematics (FK) and inverse kinematics (IK) on a five-bar robotic mechanism. First, the example demonstrates how to perform FK analyses to calculate a singularity-free workspace for a five-bar robot. ... You clicked a link that corresponds to this MATLAB command: Run. Search for jobs related to Forward kinematics and inverse kinematics matlab or hire on the world's largest freelancing marketplace with 21m+ jobs. It's free to sign up and bid on jobs. 2. Below is my code. I have all the DH parameters that will allow me to calculate the end effector position. I'm not sure where to input the values of thetas 1 ~5 shown at the bottom. Please help. function [T] = getTransformMatrix (theta, d, a, alpha) T = [cosd (theta) -sind (theta) * cosd (alpha) sind (theta) * sind (alpha) a * cosd (theta);. 2022. 9. 7. · with the forward''Topic matlab Â· GitHub May 7th, 2018 - More than 27 million people use GitHub to discover Gramm is a complete data visualization toolbox for Matlab. 2022. 9. 2. · Inverse Kinematics Solver Matlab The tooltip pose of this robot is described simply by two numbers, the coordinates x and y with respect to the world coordinate frame This. Learn more about inverse kinematics, forward dynamics Robotics System Toolbox. Skip to content. ... I want to do forward dynamics but before that I got struck in inverse kinematics for 4 dof. My code is given below: preach = [0.2, 0.2, 0.3]; ... Find the treasures in MATLAB Central and discover how the community can help you! Start Hunting!. 3) Symbolic Math Toolbox. With the help of symbolic math tools, analytical solutions can be found for the inverse kinematics. An analytical solution is the explicit equation for the joint angles of the robot given end effector pose: joint_angles = f (end_effector_pose). Once the equation is found, the joint angles can be found very quickly. Standard Particle Swarm Optimization code (Matlab M-file) for the optimization of the benchmark function. https://elkmany.github.io/pso/. 0.0. Particle Swarm Optimization : A Tutorial James Blondin September 4, 2009 1 Introduction Particle Swarm Optimization (PSO) is a technique used to explore the search space of a given problem to ﬁnd the settings or parameters required to. MATLAB Walid-khaled / 7DOF-KUKA-Linear-Axis-Forward-and-Inverse-Kinematics Star 4 Code Issues Pull requests In this repository, the implementation of forward and inverse kinematics by redundancy resolution is presented for KUKA on linear axis 7-DOF robot. This Demonstration lets you control a two-link revolute-revolute robot arm either by setting the two joint angles (this is called forward kinematics) or by dragging a locator specifying the tip of the end effector (this is called inverse kinematics).Most locations in the workspace have two solutions to the inverse kinematics and can be selected with the \"elbow up?\". 2022. 9. 7. · with the forward''Topic matlab Â· GitHub May 7th, 2018 - More than 27 million people use GitHub to discover Gramm is a complete data visualization toolbox for Matlab Human Fall Detection from CCTV camera feed' 'matlab inverse kinematics robot arm circle youtube april 21st, 2018 - code http simsamo. It is shown by tests that the error of the forward kinematics solution is ±1.5mm, while the error of the inverse kinematics solution is ±1.31°. The limitations of the above works are: 1.Time consumption and expensive in implementation. The problems solved in the above works are only suitable for fixed parameters. For robot manipulators it covers forward, inverse and differential kinematics, and dynamics. The Robotics Toolbox for MATLAB is free and open software that enables the reader to easily bring the algorithmic concepts into practice and work with real, non-trivial, problems.. This paper present kinematic and dynamic analysis of a 3-R robot arm with Adams/ Matlab Co-Simulation,. For robot manipulators it covers forward, inverse and differential kinematics, and dynamics. The Robotics Toolbox for MATLAB is free and open software that enables the reader to easily bring the algorithmic concepts into practice and work with real, non-trivial, problems.. This paper present kinematic and dynamic analysis of a 3-R robot arm with Adams/ Matlab Co-Simulation,. Browse The Most Popular 4 Matlab Robot Arm Open Source Projects. Awesome Open Source. Awesome Open Source. Combined Topics. matlab x. robot - arm x. harley davidson catalytic converter scrap price; yeshiva schools calendar; audubon nj town wide yard sale 2022; anime drawings website; genius retractable screen door costco reviews. 2022. 9. 2. · Inverse Kinematics Solver Matlab The tooltip pose of this robot is described simply by two numbers, the coordinates x and y with respect to the world coordinate frame This. 2022. 9. 4. · 3: Forward and Inverse Kinematics and the Denavit-Hartenberg Convention Clarification on spherical wrist DH frames Derivation The forward and inverse kinematics of a. Inverse Kinematics Matlab Code Codes and Scripts Downloads Free. Verify your solution in MATLAB by using your forward kinematics code from HW# 3. Matlab code for Forward Kinematics of 2R robotic arm with animation. In document the solutions of both the forward and inverse kinematics problems for Adept Six 300 6R robot are presented. bitcoin private key generator apk simulating a 6 DOF robot in matlab robotic toolbox. Ask Question Asked 2 years, 6 months ago. Modified 2 years, 6 months ago. Viewed 473 times ... Since your robot has 6 DOF, I would expect q also have 6 columns instead of 5. Try with q = [0 0 0 0 0 0] in your code. Share. Follow. cree competitors. 3DOF 3 Dimension Inverse Kinematic-PseudoInvJacobian (GUI) Inverse Kinematics of 3DOF MeArm Matlab Model Simulation based on PseudoInverse Jacobian Method. The simulation hasn't set the operation range yet, so we can see when the arm try to reach the position out of the its limit. The Forward Kinematics is driven by Denavit-Hartenberg convention. Inverse Kinematics Inverse kinematics (IK) algorithm design with MATLAB and Simulink Kinematics is the study of motion without considering the cause of the motion, such as forces and torques. Inverse kinematics is the use of kinematic equations to determine the motion of a robot to reach a desired position. 2022. 9. 4. · 3: Forward and Inverse Kinematics and the Denavit-Hartenberg Convention Clarification on spherical wrist DH frames Derivation The forward and inverse kinematics of a. . In the Fig 2 one can see relation between forward and inverse kinematics. In forward kinematics position matrices or end effector position are calculated by help of link length and joint angles, and in inverse kinematics joint angles are calculated with the help of link length and end effector position or position matrices. Its kinematic parameters are described on this web page in terms of modified Denavit-Hartenberg parameters. Forward and inverse kinematics Using the Robotics Toolbox for MATLAB, and for a nominal position (0.4, 0, 0.6) m and with the tool pointing straight down, we can solve the inverse kinematics numerically and show that the solution is valid. 18 hours ago · C# - Free source code and tutorials for Software developers and Architects The referenced robot is Adapt S350 SCARA, but only 2 degrees of freedom are used MATLAB is used by engineers and scientists in many fields, such as image processing, robotics, and computational finance MATLAB is a high-level language and interactive environment for. bitcoin private key generator apk simulating a 6 DOF robot in matlab robotic toolbox. Ask Question Asked 2 years, 6 months ago. Modified 2 years, 6 months ago. Viewed 473 times ... Since your robot has 6 DOF, I would expect q also have 6 columns instead of 5. Try with q = [0 0 0 0 0 0] in your code. Share. Follow. cree competitors. Peter Corke's Robotics Toolbox for robot forward and inverse kinematics. 2022. 8. 21. · Inverse Kinematics Matlab Code Codes and Scripts Downloads Free Forward kinematics problem is straightforward and there is no complexity deriving the equations For. Inverse kinematics (IK) determines joint configurations of a robot model to achieve a desired end-effect position. Robot kinematic constraints are specified in the rigidBodyTree robot model. Matlab code for Forward Kinematics of 2R robotic arm with animation. Download and share free MATLAB code, including functions, models, apps, support packages and toolboxes ... Movement system used forward kinematics denavit hartenberg which each joint angle is updated by joint velocity found by inverse kinematics pseudoinverse jacobian. ... Robot Manipulator Control with Inverse Kinematics PD-Pseudoinverse. In this repository, the implementation of forward and inverse kinematics by redundancy resolution is presented for KUKA on linear axis 7-DOF robot. The Redundancy. 2022. 9. 7. · If inverse kinematics are calculated, the return values are placed in a, b and c I have been learning about Inverse Kinematics on Systems of linked components Subsequently, simulation of the inverse kinematics of the above-mentioned kinematic structure was performed in the Matlab Simulink environment using the Forward kinematics described how robot's. 2.4.6.1 MATLAB Example: Inverse Kinematics of the Robotic Arm This example shows how to solve the inverse kinematic problem using SVD in MATLAB and plots the results. In the problem, the desired movement of the end effector is given in terms of and . The code then determines the necessary angular velocities to achieve that end-effector movement. 3) Symbolic Math Toolbox. With the help of symbolic math tools, analytical solutions can be found for the inverse kinematics. An analytical solution is the explicit equation for the joint angles of the robot given end effector pose: joint_angles = f (end_effector_pose). Once the equation is found, the joint angles can be found very quickly. 3.1Inverse Kinematics Test On the basis of previous development, it is possible to utilize MATLAB to perform kinematics analysis. Using the manipulator shown in Fig. 2 as the example. Suppose the desired position and orientation of end effector are (20 , 20) and φ = 0˚. Optimization Algorithms for Inverse Kinematics of Robots ... Once you've tested your IK solution, MATLAB and Simulink allow you to explore next steps towards building a complete robotic. Inverse Kinematics Mathematics for Inverse Kinematics 15‐464: Technical Animation Ming Yao Overview • Kinematics • Forward Kinematics and Inverse Kinematics • Jabobian • Pseudoinverse of the Jacobian • Assignment 2 Vocabulary of Kinematics • Kinematics is the study of how things move, it describes the motion of a hierarchical skeleton structure. 2022. 9. 6. · forward (theta) To calculate the forward kinematics, we need to specify 6 axis angles Inverse dynamics is a technique in which measured kinematics and, possibly, external. I'm trying to write an inverse kinematics Matlab code for a 6 DOF robotic arm that has the following link parameters: Twist angle (alpha): [-90, 0, 90, -90, 90, 0] Link length (a): [0, 0.5, 0, 0, 0, 0] ... on forward kinematics of 3 to 6 DOF SCARA robots . MATLAB is a powerful tool used to calculate complex. A five-bar robot, which is also called a five-bar planar manipulator, is a two-degree-of-freedom parallel mechanism. In this example, the robot has four equal-length links that cannot collide with each other. The robot uses two stepper motors to drive the proximal links to move the pen. Theoretically, the five-bar robot has four regimes of. Forward Kinematics and Reverse Kinematics. In Robotics F.K. we have ASi = Bphi where A, B are known matrices, Si is a vector with x, y and z as its elements, phi is the vector containing the angular velocity of each of the 2 wheels of the robot. MATLAB says that an eqn of the form Ax=B can be solved by A\\B. Learn more about inverse kinematics, forward dynamics Robotics System Toolbox. Skip to content. ... I want to do forward dynamics but before that I got struck in inverse kinematics for 4 dof. My code is given below: preach = [0.2, 0.2, 0.3]; ... Find the treasures in MATLAB Central and discover how the community can help you! Start Hunting!. Some universities still have some Puma 560 robots. >> mdl_puma560 % create the model % forward kinematics of a known set of joing angles >> T = p560.fkine(qn); % inverse kinematics - right handed, elbow up >> qn_r = p560.ikine6s(T, 'ru') qn_r = -0.0000 0.7854 3.1416 -0.0000 0.7854 0.0000 >> p560.plot(qn_r). General procedure for determining forward kinematics 1. Label joint axes as z 0, , z n-1 (axis z i is joint axis for joint i+1) 2. Choose base frame: set o 0 on z 0 and choose x 0 and y 0 using right-handed convention 3. For i=1:n-1, i. Place o i where the normal to z i and z i-1 intersects z i. If z i intersects z i-1, put o i at. Read more..Forward Kinematics. The way in which the code works for the trajectories is the following: After selecting this mode, you must select a shape to draw. You can choose between Line, Triangle, Square and Ellipse. ... Inverse Kinematics. The inverse kinematics problem consists on finding the necessary inputs for the robot to reach a point on its. Here are the steps for calculating inverse kinematics for a six degree of freedom robotic arm. Step 1: Draw the kinematic diagram of just the first three joints, and perform inverse kinematics using the graphical approach. Step 2: Compute the forward kinematics on the first three joints to get the rotation of joint 3 relative to the global (i.e. Inverse kinematics tutorial. This tutorial explains how to use CoppeliaSim's kinematics functionality, while building a 7 DoF redundant manipulator. But before that, make sure to have a look at the various example scenes related to IK and FK in folder scenes/kinematics. This tutorial is segmented into 3 parts: Building the simple simulation. Download and share free MATLAB code, including functions, models, apps, support packages and toolboxes. Skip to content. ... 3dof arm robot denavithartenberg forward kinematics inverse kinematics mearm. Cancel. Acknowledgements. Inspired: 3DOF 3 Dimension Inverse Kinematic-PseudoInvJacobian (GUI). Step 3: Remember your end effector. The goal of calculating the Forward Kinematics is to be able to calculate the end effector pose from the position of the joints. Most Forward Kinematic tutorials will generalize the end effector as a single distance from the final joint. This is fine for a simple \"open-close\" gripper. For example, in the computation of your inverse kinematics function, you have Theme Copy r = sqrt (ph1^2+ (ph3-d1)^2); There could be two solutions to the sqrt function. A positive and a negative value. And MATLAB returns the positive value. Similar thing is true for other functions like acos, where multiple angles can give the same result. cgr prefix means the code is code-generation ready. ncgr means the code is NOT code-generation ready. Features: Forward kinematics Homogenous transformation of each link of the robot Numerical jacobian Simple visualization, it can also be animated Inverse kinematics with the pseudo-inverse method and damped least square method. Code generation. Matlab code for Forward Kinematics of 2R robotic arm with animation. This document will help in better understanding of forward and inverse kinematics. For forward kinematics you are only required with angles and it provides you the end effector position and in Inverse Kinematics provide the end effector position (coordinate axes) and GUI will provide you the required angles to achieve that position. Cite As. In this repository, the implementation of forward and inverse kinematics by redundancy resolution is presented for KUKA on linear axis 7-DOF robot. The Redundancy. This task is about doing the forward kinematic analysis for 6 DoF robotic arm with using the Denavit-Hartenberg Convention. In order to use this D-H convention, specific parameters need to be used, and three rules must be followed. Denavit-Hartenberg Parameters ai: The length distance from zi to zi+1 measured along zi. 11h ago. Search: Inverse Kinematics Solver Matlab. There are also several examples in python and matlab that show how to interface with openrave to use the plugins in CoMPS Create a rigid body tree model for your robot using the rigidBodyTree class The individual joints' trajectories, velocities and accelerations can be obtained using inverse kinematics equations Back in the day, I loved numerical. I need Complete Editable Working Code in MATLAB of \"Solving the Forward and Inverse Kinematics of PUMA 560 using DH parameters along with their plots\". Good and Correct Work Will be Appriciated. Question : I need Complete Editable Working Code in MATLAB of \"Solving the Forward and Inverse Kinematics of PUMA 560 using DH parameters along with. I am verifying the output of my forward kinematics through inverse kinematics and the results are not as desired. As the output of my inverse kinematics is not coming out to be the same as the input of forward kinematics. The D-H parameters of manipulator is given as: Link: alpha, a, theta, d. Link 1 : -90 0 theta1* d1. 2022. 9. 6. · Matlab code for Forward Kinematics of 2R robotic arm with animation Forward Kinematics is about use a set of joints angles and solve for the end-effector position To ensure your robot model and kinematic group are compatible, check the IsValidGroupForIK property after selecting a kinematic group Inverse kinematics denotes the computation of all joint angles out. •Robotics Toolbox for MATLAB: overview, online resources, basic operations, installation, built-in demo •Serial-link manipulator example -Puma560: DH parameters, forward & inverse kinematics •How to better use RTB manual •Bugs -example, possible solutions •Simulink -intro, RTB library for Simulink, RTB examples for Simulink. Search for jobs related to Forward kinematics and inverse kinematics matlab or hire on the world's largest freelancing marketplace with 21m+ jobs. It's free to sign up and bid on jobs. robotic arm using MATLAB tool is provided. The flow chart below explains the process starting with creating the robot, controlling the robot with input joint angles, forward kinematics and inverse kinematics functions used for the implementation. Link Creation MATLAB 2014B Initialization of PETER CORKE ROBOTIC TOOL BOX FEATURE. Discussions (18) % Anthropomorphic arm with 6 DOF and spherical wrist. % It calculates the Inverse Kinematic of an Anthropomorphic arm with 6 DOF . % 'q' is the solutions in radiant and K is the direct Kinematic matrix. %. % K = [ n s a p; % 0 0 0 1] % where n, s, a are three vectors fo 3 elements that represents the. Forward Kinematics and Reverse Kinematics. In Robotics F.K. we have ASi = Bphi where A, B are known matrices, Si is a vector with x, y and z as its elements, phi is the vector containing the angular velocity of each of the 2 wheels of the robot. MATLAB says that an eqn of the form Ax=B can be solved by A\\B. Compute the kinematic solution using the gik object. Specify the initial guess and the different kinematic constraints in the proper order. iniGuess = homeConfiguration (robot); [q, solutionInfo] = gik (iniGuess,positionTarget1,positionTarget2,jointLimBounds); Examine the results in solutionInfo. Show the kinematic solution compared to the home. 2022. 9. 2. · Inverse Kinematics Solver Matlab The tooltip pose of this robot is described simply by two numbers, the coordinates x and y with respect to the world coordinate frame This. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators. 18 hours ago · Search: Inverse Kinematics Solver Matlab. Peter Corke's Robotics Toolbox for robot forward and inverse kinematics Alternatively (my preferred method, but also the only. Search for jobs related to Forward kinematics and inverse kinematics matlab or hire on the world's largest freelancing marketplace with 21m+ jobs. It's free to sign up and bid on jobs. There are two types of kinematic equations used in the control of this robot: forward and reverse. Forward kinematics are used to find the arms position in task space based on the joint parameters. For example, if you know the angle of the three joints, you can use forward position kinematics to determine the (x,y,z) position of the end-effector. Download and share free MATLAB code, including functions, models, apps, support packages and toolboxes. Skip to content. ... 3dof arm robot denavithartenberg forward kinematics inverse kinematics mearm. Cancel. Acknowledgements. Inspired: 3DOF 3 Dimension Inverse Kinematic-PseudoInvJacobian (GUI). Forward and Inverse kinematics - File Exchange - MATLAB Central Forward and Inverse kinematics version 1.0.0 (2.11 KB) by hashim khan Forward and Inverse kinematics of 6 DOF arm with workspace calculation 5.0 (1) 843 Downloads Updated 26 Sep 2019 View License Follow Download Overview Functions Reviews (1) Discussions (2). 18 hours ago · and inverse kinematics of a 6-DOF robot arm presented in this paper Inverse Kinematics for a General Purpose Robot Arm That Moves in 3D Explanation of code for simulating FK for Universal robot 5 arm using the robotics toolbox in MATLAB If you are looking for C/C++ codes for simulating ( Universal Robot) UR5 Robot Manipulator, you can download. There are 4 different 6-axis robots that I am trying to calculate. one's forward kinematics, one's inverse kinematics, one's newton euler's solution, one's Jacobian matrix solutions, I have to do it in matlab. I'm trying to write the required codes, but I'm constantly making mistakes. I could not find ready-made code anywhere. 2022. 3. 21. · What is Matlab Code For Forward And Inverse Kinematics. Verify the forward kinematics of the PUMA 260 robot by comparing the results from Matlab simulation and the. 18 hours ago · Search: Inverse Kinematics Solver Matlab. Peter Corke's Robotics Toolbox for robot forward and inverse kinematics Alternatively (my preferred method, but also the only. Matlab Code for Lynx Robot 0 Selection of motor and Calculating the torque for 6DOF robot Arm 1 How to find Joint Angles or Theta for 7DoF Robotic ... Users can understand the complex inverse kinematics algorithms and quickly prototype new motion control architecture for industrial parallel kinematics robots. milperra massacre. 2022. 9. 3. · 3;0,0;0,0]; % Given gamma, solve for the forward differential kinematics matrix Inverse kinematics denotes the computation of all joint angles out of the tool-centre-point's position and orientation This is commonly resolved by introducing ‘residual forces and torques’ which compensate for this To calculate inverse kinematics for a specific kinematic group, use. Inverse Kinematics Mathematics for Inverse Kinematics 15‐464: Technical Animation Ming Yao Overview • Kinematics • Forward Kinematics and Inverse Kinematics • Jabobian • Pseudoinverse of the Jacobian • Assignment 2 Vocabulary of Kinematics • Kinematics is the study of how things move, it describes the motion of a hierarchical skeleton structure. To write code to fit a linear and cubic polynomial for the Cp data.2. To plot the linear and cubic fit curves along with the raw data points.3. ... Aim - Write a program in Matlab showing the Forward Kinematics of a 2R Robotic Arm Description - 2R Robotic Arm- A robotic arm is a type of mechanical arm, usually programmable. The arm may be the. The repository contains the MATLAB codes for the Implementation of pick and place tasks with the UR5 robot using Inverse Kinematics, Resolved Rate control and Gradient Descent control algorithms. python matlab inverse-kinematics gradient-descent ur5 resolved-rate Updated on Sep 19, 2017 MATLAB. 2022. 9. 9. · Matlab code for Forward Kinematics of 2R robotic arm with animation Inverse Kinematics Gino van den Bergen The other joints are controlled by forward kinematics. May 01, 2018 · This project describe a mechanical system, design concept and prototype implementation of a 6 DOF robotic arm, which should perform industrial task such as pick and place of fragile objects operation.. IV. GUI DEVELOPMENT FOR 6 DOF ROBOT POSITION ANALYSIS In this chapter, a detailed discussion on the implementation, creation and the. . This task is about doing the forward kinematic analysis for 6 DoF robotic arm with using the Denavit-Hartenberg Convention. In order to use this D-H convention, specific parameters need to be used, and three rules must be followed. Denavit-Hartenberg Parameters ai: The length distance from zi to zi+1 measured along zi. 11h ago. Answer (1 of 2): I think Peter Corke's ROBOTICS TOOLBOX for matlab can solve your problem, it has inbuilt functions for inverse and forward kinematics with support for easy plotting like plotting the robot model, plotting workspace etc Try that, toolbox is free. These coordinates are end effector position target to pick each object and were placed to the right position based on its color. Based on the end effector position target, PD-PIJ inverse kinematics method was used to determine the right angle of each joint of manipulator links. The angles found by PD-PIJ is the input of DH forward kinematics. 2022. 9. 6. · This is a study of Inverse Kinematics for arms of 2 to 7 DOF with Matlab GUIDE So solving Equation 6 requires liberalization of the jacobian The following code exemplifies how to. set of four parameters. Any robot can be modeled using the D-H representation. A computer code has been formed in MATLAB to implement the modeling of any robot with only the DH parameters as input. The purpose of the simulator is to create an accurate Forward kinematic and inverse kinematics representation of any type of robot and its motions. The. 2022. 9. 7. · with the forward''Topic matlab Â· GitHub May 7th, 2018 - More than 27 million people use GitHub to discover Gramm is a complete data visualization toolbox for Matlab Human Fall Detection from CCTV camera feed' 'matlab inverse kinematics robot arm circle youtube april 21st, 2018 - code http simsamo. . The following Matlab project contains the source code and Matlab examples used for robotic toolbox. A set of matlab scripts featuring: forward kinematics by omogeneous transformations and DH transformations, inverse kinematics for euler and rpy wrist and antropomorphic manipulator, differential kinematics operator and geometrical jacobian, static force analysis, trajectory planning in joint space. If yes, then this is not directly linked to V-REP's IK algorithm, that you cannot export to Matlab. It is built-in V-REP. You will have to code the IK yourself in Matlab. Or - you can have V-REP compute the IK for you, and from Matlab you simply control the end-effector position/orientation. Cheers hawiteshe Posts: 1. Here are the steps for calculating inverse kinematics for a six degree of freedom robotic arm. Step 1: Draw the kinematic diagram of just the first three joints, and perform inverse kinematics using the graphical approach. Step 2: Compute the forward kinematics on the first three joints to get the rotation of joint 3 relative to the global (i.e. FABRIK（Foward and Backward Reaching Inverse Kinematics）. Robotic Arm turned into a 3D Printer (Inverse Kinematics) September 07, 2019 02:07PM. 0 arm. ... Jan 18, 2022 · matlab code for forward and inverse kinematics. I'll just write down the final equations here. Here is the blender file used. bsa mercury spares. Advertisement bench. robotic arm using MATLAB tool is provided. The flow chart below explains the process starting with creating the robot, controlling the robot with input joint angles, forward kinematics and inverse kinematics functions used for the implementation. Link Creation MATLAB 2014B Initialization of PETER CORKE ROBOTIC TOOL BOX FEATURE. The MATLAB code also implements a Graphical User Interface (GUI), from which the user can control the robotic arm and run the forward and inverse kinematics algorithms. Inverse Kinematics for a 2-Joint Robot Arm Using Geometry ... Inverse kinematics refers to the reverse process. In Robotics F.K. Normally, the forward kinematics is a closed. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators. Forward Kinematics and Reverse Kinematics. In Robotics F.K. we have ASi = Bphi where A, B are known matrices, Si is a vector with x, y and z as its elements, phi is the vector containing the angular velocity of each of the 2 wheels of the robot. MATLAB says that an eqn of the form Ax=B can be solved by A\\B. 2022. 9. 7. · If inverse kinematics are calculated, the return values are placed in a, b and c I have been learning about Inverse Kinematics on Systems of linked components Subsequently, simulation of the inverse kinematics of the above-mentioned kinematic structure was performed in the Matlab Simulink environment using the Forward kinematics described how robot's. May 01, 2018 · This project describe a mechanical system, design concept and prototype implementation of a 6 DOF robotic arm, which should perform industrial task such as pick and place of fragile objects operation.. IV. GUI DEVELOPMENT FOR 6 DOF ROBOT POSITION ANALYSIS In this chapter, a detailed discussion on the implementation, creation and the. There are two types of kinematic equations used in the control of this robot: forward and reverse. Forward kinematics are used to find the arms position in task space based on the joint parameters. For example, if you know the angle of the three joints, you can use forward position kinematics to determine the (x,y,z) position of the end-effector. When I first came across the problem of inverse kinematics I thought - quite naively - that it would be a simple matter to find a solution to the problem because the forward kinematics problem was so simple to solve. I decided to start out with a 2 link arm and see if I could work out the solution on my own from scratch without having any. For Kinematic analysis of taken 6 DOF serial link manipulator, the D-H representation of Forward & Inverse Kinematics are mathematically obtained first. In figure 2 is shown a simple 6 DOF robotic arm . Figure 2. 6 DOF robot manipulator The joint & Link parameters of 6 DOF</b> <b>robots</b> are noted below in a table 1. Inverse kinematics tutorial. This tutorial explains how to use CoppeliaSim's kinematics functionality, while building a 7 DoF redundant manipulator. But before that, make sure to have a look at the various example scenes related to IK and FK in folder scenes/kinematics. This tutorial is segmented into 3 parts: Building the simple simulation. The Matlab program must be able to compute the T6 transform matrix and must incorporate the following: User data entry of each joint angle (in degrees) Joint angle limits Define each T transform and compute T6 transform in world coordinates Vector output in terms of world coodinates - to include position and orientation. 2022. 9. 7. · If inverse kinematics are calculated, the return values are placed in a, b and c I have been learning about Inverse Kinematics on Systems of linked components. The Matlab program must be able to compute the T6 transform matrix and must incorporate the following: User data entry of each joint angle (in degrees) Joint angle limits Define each T transform and compute T6 transform in world coordinates Vector output in terms of world coodinates - to include position and orientation. The movement of robot can be divided into forward and inverse kinematics. Forward kinematics described how robot's move according to entered angles. There is always a solution for forward kinematics of manipulator. Solution for inverse kinematics is a more difficult problem than forward kinematics. These coordinates are end effector position target to pick each object and were placed to the right position based on its color. Based on the end effector position target, PD-PIJ inverse kinematics method was used to determine the right angle of each joint of manipulator links. The angles found by PD-PIJ is the input of DH forward kinematics. . 2022. 9. 7. · with the forward''Topic matlab Â· GitHub May 7th, 2018 - More than 27 million people use GitHub to discover Gramm is a complete data visualization toolbox for Matlab Human Fall Detection from CCTV camera feed' 'matlab inverse kinematics robot arm circle youtube april 21st, 2018 - code http simsamo. robotic arm using MATLAB tool is provided. The flow chart below explains the process starting with creating the robot, controlling the robot with input joint angles, forward kinematics and inverse kinematics functions used for the implementation. Link Creation MATLAB 2014B Initialization of PETER CORKE ROBOTIC TOOL BOX FEATURE. Download and share free MATLAB code, including functions, models, apps, support packages and toolboxes ... ( MATLAB GUI) of forward and inverse kinematics of multi dof robotic arm. ... Discussions (1) This document will help in better understanding of forward and inverse kinematics. For forward kinematics you are only required with angles and. Search for jobs related to Forward kinematics and inverse kinematics matlab or hire on the world's largest freelancing marketplace with 21m+ jobs. It's free to sign up and bid on jobs. Step 3: Remember your end effector. The goal of calculating the Forward Kinematics is to be able to calculate the end effector pose from the position of the joints. Most Forward Kinematic tutorials will generalize the end effector as a single distance from the final joint. This is fine for a simple \"open-close\" gripper. 2022. 9. 6. · Inverse kinematics 2 link arm python Your code should be general as regards number of input, output, and hidden units, and their connectivity, and also learning rate (alpha. The 6 - DOF articulated robotic arm was designed and visualized in RVIZ and, Moveit is being used as a control interface using Robot Operating System (ROS). The manipulation of the arm with end effector refrain us from using the joint by the joint control mechanism. • Derive the forward kinematic equationsfor CRS robot arm following the Denavit- Hartenberg (DH) convention • Derive inverse kinematic equations for the CRS robot arm • Use the provided Code Composer Studio project to verify your solution NOTE: CRS robot arm has five motors/joints, in this class we are only using/controlling the first. 2022. 9. 6. · This is a study of Inverse Kinematics for arms of 2 to 7 DOF with Matlab GUIDE So solving Equation 6 requires liberalization of the jacobian The following code exemplifies how to. 2022. 9. 6. · This is a study of Inverse Kinematics for arms of 2 to 7 DOF with Matlab GUIDE So solving Equation 6 requires liberalization of the jacobian The following code exemplifies how to. In this repository, the implementation of forward and inverse kinematics by redundancy resolution is presented for KUKA on linear axis 7-DOF robot. The Redundancy Resolution includes three methods, which are Jacobian-based (Damped Least Square and Weighted Pseudoinverse), Null Space, and Task Augmentation. most recent commit 24 days ago. Compute the kinematic solution using the gik object. Specify the initial guess and the different kinematic constraints in the proper order. iniGuess = homeConfiguration (robot); [q, solutionInfo] = gik (iniGuess,positionTarget1,positionTarget2,jointLimBounds); Examine the results in solutionInfo. Show the kinematic solution compared to the home. Let's look at numerical approaches to inverse kinematics for a couple of different robots and learn some of the important considerations. For RTB10.x please note that the mask value must be explicitly preceded by the 'mask' keyword. For example: >> q = p2.ikine (T, [-1 -1], 'mask', [1 1 0 0 0 0]) MATLAB. inverse kinematic. Optimization Algorithms for Inverse Kinematics of Robots ... Once you've tested your IK solution, MATLAB and Simulink allow you to explore next steps towards building a complete robotic. Example #3. In this example, we will take another vector function and will compute its Jacobian Matrix using the Jacobian function. For this example, we will input following values: Pass the input vector function as [c^3 + b^2, 2a^3 + c, c^2 + 5] Pass the variables as [a, b, c]. . I'm trying to write an inverse kinematics Matlab code for a 6 DOF robotic arm that has the following link parameters: Twist angle (alpha): [-90, 0, 90, -90, 90, 0] Link length (a): [0, 0.5, 0, 0, 0, 0] ... on forward kinematics of 3 to 6 DOF SCARA robots . MATLAB is a powerful tool used to calculate complex. bitcoin private key generator apk simulating a 6 DOF robot in matlab robotic toolbox. Ask Question Asked 2 years, 6 months ago. Modified 2 years, 6 months ago. Viewed 473 times ... Since your robot has 6 DOF, I would expect q also have 6 columns instead of 5. Try with q = [0 0 0 0 0 0] in your code. Share. Follow. cree competitors. This task is about doing the forward kinematic analysis for 6 DoF robotic arm with using the Denavit-Hartenberg Convention. In order to use this D-H convention, specific parameters need to be used, and three rules must be followed. Denavit-Hartenberg Parameters ai: The length distance from zi to zi+1 measured along zi. 11h ago. For a better picture, below is something: Below is the code for my MATLAB script, which runs flawlessly and gives a solution in under 2 seconds: ycurrent = 0; %Not using this xcurrent = 0; %Starting position (x) zcurrent = 0; %Starting position (y) xGoal = .5; %Goal x/z values of (1, 1) zGoal = .5; theta1 = 0.1; %Angle of first DOF theta2 = 0.1. Search for jobs related to Forward kinematics and inverse kinematics matlab or hire on the world's largest freelancing marketplace with 21m+ jobs. It's free to sign up and bid on jobs. I'm trying to write an inverse kinematics Matlab code for a 6 DOF robotic arm that has the following link parameters: Twist angle (alpha): [-90, 0, 90, -90, 90, 0] Link length (a): [0, 0.5, 0, 0, 0, 0] ... The goal of this project is to design a forward 6 DoF robotic arm and control it by Matlab. The controller is separated by two. The MATLAB code also implements a Graphical User Interface (GUI), from which the user can control the robotic arm and run the forward and inverse kinematics algorithms. A 3D simulation/visualization of the robotic arm is displayed in the GUI in real time. The MATLAB code also implements a Graphical User Interface (GUI), from which the user can control the robotic arm and run the forward and inverse kinematics algorithms. Inverse Kinematics for a 2-Joint Robot Arm Using Geometry ... Inverse kinematics refers to the reverse process. In Robotics F.K. Normally, the forward kinematics is a closed. 18 hours ago · and inverse kinematics of a 6-DOF robot arm presented in this paper Inverse Kinematics for a General Purpose Robot Arm That Moves in 3D Explanation of code for simulating FK for Universal robot 5 arm using the robotics toolbox in MATLAB If you are looking for C/C++ codes for simulating ( Universal Robot) UR5 Robot Manipulator, you can download. 2022. 9. 5. · Inverse Kinematic systems allow for reactive animation, such as foot placement on non-planar terrain Peter Corke's Robotics Toolbox for robot forward and inverse kinematics. 18 hours ago · Search: Inverse Kinematics Solver Matlab. Peter Corke's Robotics Toolbox for robot forward and inverse kinematics Alternatively (my preferred method, but also the only way if your Matlab release is older than R2015b [8 x = load('E:\\myFile1 The inverseKinematics System object™ creates an inverse kinematic (IK) solver to calculate joint configurations for a desired. In this repository, the implementation of forward and inverse kinematics by redundancy resolution is presented for KUKA on linear axis 7-DOF robot. The Redundancy Resolution includes three methods, which are Jacobian-based (Damped Least Square and Weighted Pseudoinverse), Null Space, and Task Augmentation. most recent commit 24 days ago. Read more..Let's look at numerical approaches to inverse kinematics for a couple of different robots and learn some of the important considerations. For RTB10.x please note that the mask value must be explicitly preceded by the 'mask' keyword. For example: >> q = p2.ikine (T, [-1 -1], 'mask', [1 1 0 0 0 0]) MATLAB. inverse kinematic. 18 hours ago · Search: Inverse Kinematics Solver Matlab. Peter Corke's Robotics Toolbox for robot forward and inverse kinematics Alternatively (my preferred method, but also the only way if your Matlab release is older than R2015b [8 x = load('E:\\myFile1 The inverseKinematics System object™ creates an inverse kinematic (IK) solver to calculate joint configurations for a desired. I need Complete Editable Working Code in MATLAB of \"Solving the Forward and Inverse Kinematics of PUMA 560 using DH parameters along with their plots\". Good and Correct Work Will be Appriciated. Question : I need Complete Editable Working Code in MATLAB of \"Solving the Forward and Inverse Kinematics of PUMA 560 using DH parameters along with. Inverse Kinematics Matlab Code Codes and Scripts Downloads Free. Verify your solution in MATLAB by using your forward kinematics code from HW# 3. Matlab code for Forward Kinematics of 2R robotic arm with animation. In document the solutions of both the forward and inverse kinematics problems for Adept Six 300 6R robot are presented. 2022. 5. 22. · MATLAB is a powerful environment for linear algebra and graphical presentation that is available on a very wide range of computer platforms Forward and Inverse kinematics. the first three. Part 1: forward kinematics In this part you will derive solutions to the forward kinematics problem for the CRS robot arm. First find parameters of the CRS robot arm following D-H convention, then verify the theoretical result using a given C program in Code Composer Studio. Physical Dimension. Compute the kinematic solution using the gik object. Specify the initial guess and the different kinematic constraints in the proper order. iniGuess = homeConfiguration (robot); [q, solutionInfo] = gik (iniGuess,positionTarget1,positionTarget2,jointLimBounds); Examine the results in solutionInfo. Show the kinematic solution compared to the home. Search: Inverse Kinematics Solver Matlab. Unlike forward kinematics, the solution is not strictly geometry, it demands a numerical methods solution Notice the text boxes in the dialog window are now filled with values The planning and inverse kinematics algorithms in this suite are designed for articulated robots like robotic arms and humanoids. The movement of robot can be divided into forward and inverse kinematics. Forward kinematics described how robot's move according to entered angles. There is always a solution for forward kinematics of manipulator. Solution for inverse kinematics is a more difficult problem than forward kinematics. • Derive the forward kinematic equationsfor CRS robot arm following the Denavit- Hartenberg (DH) convention • Derive inverse kinematic equations for the CRS robot arm • Use the provided Code Composer Studio project to verify your solution NOTE: CRS robot arm has five motors/joints, in this class we are only using/controlling the first. When to use: Solving forward and inverse kinematics and dynamics, extracting mechanical properties (Jacobian, mass matrix, gravity torques, etc.) ... Below is some example MATLAB code and an animation of generalized IK on a model of a Rethink Sawyer, which has a 7-DOF arm. Here, we are setting a constraint on the end effector position, while. Start Learning with Free Interactive Tutorials. MATLAB Onramp. Get started quickly with the basics of MATLAB . Launch. Simulink Onramp. Discover Model-Based Design with Simulink . Learn more. glupi vicevi. Advertisement kioti hydraulic fluid. used 5 ft box blade. how. regus. In this repository, the implementation of forward and inverse kinematics by redundancy resolution is presented for KUKA on linear axis 7-DOF robot. The Redundancy Resolution includes three methods, which are Jacobian-based (Damped Least Square and Weighted Pseudoinverse), Null Space, and Task Augmentation. most recent commit 24 days ago. Topics covered in this session are:Euler Lagrange formulation of n-DOF serial manipulatorGeneral Matlab codeExample: Inverse Dynamics of a 2-DOF manipulator. I am trying to compute dynamics of 3 DOF robot using Robotics Toolbox by executing this code: robot.accel(q, zeros(1,3), zeros(1,3)) But I am getting this error: Assignment has more non. . 2022. 9. 7. · with the forward''Topic matlab Â· GitHub May 7th, 2018 - More than 27 million people use GitHub to discover Gramm is a complete data visualization toolbox for Matlab Human Fall Detection from CCTV camera feed' 'matlab inverse kinematics robot arm circle youtube april 21st, 2018 - code http simsamo. Read more..Inverse Kinematics: Example I • Inverse Kinematics: - Set the final position equal to the Forward Transformation Matrix 0A 3: • The solution strategy is to equate the elements of 0A 3 to that of the given position (q x, q y) and orientation ϕ Inverse Kinematics: Example I • Orientation (ϕ): • Now Position of the 2DOF point P: ∴. 2022. 9. 8. · Verify the inverse kinematics of the PUMA 260 robot by comparing the results from Matlab Simulation and the robot manipulator As the output of my inverse kinematics is not coming out to be the same as the input of forward kinematics function q = inv_kinematics (ph) %input: [ph1 ph2 ph3] l1 = 0 In the forward kinematics problem, the transformation describing. Fig. 2. Two Link Robot Arm for Forward Kinematic. 2.2 Inverse Kinematic Given the position and orientation of the end effector rela-tive to the base frame compute all possible sets of joint angles and link geometries which could be used to attain the given position and orientation of the end effector. The inverse kine-. Since the forward kinematics formulae for the two-joint robotic arm are known, x and y coordinates of the tip of the arm are deduced for the entire range of angles of rotation of the two joints. The coordinates and the angles are saved to be used as training data to train an ANFIS (adaptive neuro-fuzzy inference system) network. 2022. 3. 21. · What is Matlab Code For Forward And Inverse Kinematics. Verify the forward kinematics of the PUMA 260 robot by comparing the results from Matlab simulation and the. I need Complete Editable Working Code in MATLAB of \"Solving the Forward and Inverse Kinematics of PUMA 560 using DH parameters along with their plots\". Good and Correct Work Will be Appriciated. Question : I need Complete Editable Working Code in MATLAB of \"Solving the Forward and Inverse Kinematics of PUMA 560 using DH parameters along with. bitcoin private key generator apk simulating a 6 DOF robot in matlab robotic toolbox. Ask Question Asked 2 years, 6 months ago. Modified 2 years, 6 months ago. Viewed 473 times ... Since your robot has 6 DOF, I would expect q also have 6 columns instead of 5. Try with q = [0 0 0 0 0 0] in your code. Share. Follow. cree competitors. 2022. 7. 12. · robotic arm using MATLAB tool is provided Suppose that we want to place the gripper at a desired position (the gripper orientation does not matter for now) KinematicsSolver objects allow users to formulate and numerically solve kinematics problems for their Simscape™ Multibody™ models Forward kinematics uses the joint parameters to compute the. All vectors and tensors are to be expressed in the Link's coordinate frame. dhFwdKine H = dhFwdKine (linkList, paramList): Returns the forward kinematics of a manipulator with the provided DH parameter set. linkList is to be an array of links, each created by createLink. Search for jobs related to Forward kinematics and inverse kinematics matlab or hire on the world's largest freelancing marketplace with 21m+ jobs. It's free to sign up and bid on jobs. Forward-and-Inverse-Kinematics-for-3-DOF-Robotic-arm (Smart Methods Internship) in this repo i connected 3 servo motors to arduino to build a robotic arm , then create 2 functions the. Inverse Kinematics of 3DOF MeArm Matlab Model Simulation based on PseudoInverse Jacobian Method. The simulation hasn't set the operation range yet, so we can see when the arm try to reach the position out of the its limit. The Forward Kinematics is driven by Denavit-Hartenberg convention. Paperwork:. 18 hours ago · Search: Inverse Kinematics Solver Matlab. Peter Corke's Robotics Toolbox for robot forward and inverse kinematics Alternatively (my preferred method, but also the only way if your Matlab release is older than R2015b [8 x = load('E:\\myFile1 The inverseKinematics System object™ creates an inverse kinematic (IK) solver to calculate joint configurations for a desired. Inverse Kinematics Mathematics for Inverse Kinematics 15‐464: Technical Animation Ming Yao Overview • Kinematics • Forward Kinematics and Inverse Kinematics • Jabobian • Pseudoinverse of the Jacobian • Assignment 2 Vocabulary of Kinematics • Kinematics is the study of how things move, it describes the motion of a hierarchical skeleton structure. There are 4 different 6-axis robots that I am trying to calculate. one's forward kinematics, one's inverse kinematics, one's newton euler's solution, one's Jacobian matrix solutions, I have to do it in matlab. I'm trying to write the required codes, but I'm constantly making mistakes. I could not find ready-made code anywhere. 2022. 7. 12. · robotic arm using MATLAB tool is provided Suppose that we want to place the gripper at a desired position (the gripper orientation does not matter for now) KinematicsSolver objects allow users to formulate and numerically solve kinematics problems for their Simscape™ Multibody™ models Forward kinematics uses the joint parameters to compute the. . 2022. 8. 27. · Inverse Kinematics is the inverse function/algorithm of Forward Kinematics hashim khan (2021) Inverse kinematics Hi, I am trying to use solve forword and inverse. Hello, I'm learning kinematics and dynamics using Robotic Toolbox Matlab. To perform dynamics (inverse and forward), first I have to build robot model. For that, I took Puma560 data and tried. Code is given below:. 2022. 9. 6. · Inverse kinematics 2 link arm python Your code should be general as regards number of input, output, and hidden units, and their connectivity, and also learning rate (alpha. Compute the kinematic solution using the gik object. Specify the initial guess and the different kinematic constraints in the proper order. iniGuess = homeConfiguration (robot); [q, solutionInfo] = gik (iniGuess,positionTarget1,positionTarget2,jointLimBounds); Examine the results in solutionInfo. Show the kinematic solution compared to the home. Answer (1 of 2): I think Peter Corke's ROBOTICS TOOLBOX for matlab can solve your problem, it has inbuilt functions for inverse and forward kinematics with support for easy plotting like plotting the robot model, plotting workspace etc Try that, toolbox is free. EduRev provides you with complete coverage and for 2022 Forward & inverse kinematics examples of 2R, 3R & 3P manipulators (2) as a part of our plan for syllabus to prepare for exam. Our subject experts have curated special courses, tests & mock test series. All previous year questions (PYQs) & topic wise tests like tests for Forward & inverse. FABRIK（Foward and Backward Reaching Inverse Kinematics）. Robotic Arm turned into a 3D Printer (Inverse Kinematics) September 07, 2019 02:07PM. 0 arm. ... Jan 18, 2022 · matlab code for forward and inverse kinematics. I'll just write down the final equations here. Here is the blender file used. bsa mercury spares. Advertisement bench. The MATLAB code also implements a Graphical User Interface (GUI), from which the user can control the robotic arm and run the forward and inverse kinematics algorithms. A 3D simulation/visualization of the robotic arm is displayed in the GUI in real time. . Download and share free MATLAB code, including functions, models, apps, support packages and toolboxes ... Movement system used forward kinematics denavit hartenberg which each joint angle is updated by joint velocity found by inverse kinematics pseudoinverse jacobian. ... Robot Manipulator Control with Inverse Kinematics PD-Pseudoinverse. The 6 - DOF articulated robotic arm was designed and visualized in RVIZ and, Moveit is being used as a control interface using Robot Operating System (ROS). The manipulation of the arm with end effector refrain us from using the joint by the joint control mechanism. I'm trying to write an inverse kinematics Matlab code for a 6 DOF robotic arm that has the following link parameters: Twist angle (alpha): [-90, 0, 90, -90, 90, 0] Link length (a): [0, 0.5, 0, 0, 0, 0] ... The goal of this project is to design a forward 6 DoF robotic arm and control it by Matlab. The controller is separated by two. . I'm trying to write an inverse kinematics Matlab code for a 6 DOF robotic arm that has the following link parameters: Twist angle (alpha): [-90, 0, 90, -90, 90, 0] Link length (a): [0, 0.5, 0, 0, 0, 0] ... The goal of this project is to design a forward 6 DoF robotic arm and control it by Matlab. The controller is separated by two. 2022. 9. 7. · with the forward''Topic matlab Â· GitHub May 7th, 2018 - More than 27 million people use GitHub to discover Gramm is a complete data visualization toolbox for Matlab Human Fall Detection from CCTV camera feed' 'matlab inverse kinematics robot arm circle youtube april 21st, 2018 - code http simsamo. There are two types of kinematic equations used in the control of this robot: forward and reverse. Forward kinematics are used to find the arms position in task space based on the joint parameters. For example, if you know the angle of the three joints, you can use forward position kinematics to determine the (x,y,z) position of the end-effector. This task is about doing the forward kinematic analysis for 6 DoF robotic arm with using the Denavit-Hartenberg Convention. In order to use this D-H convention, specific parameters need to be used, and three rules must be followed. Denavit-Hartenberg Parameters ai: The length distance from zi to zi+1 measured along zi. 11h ago. Applying a physical model of two D.O.F manipulator (RR Manipulator) using Matlab Simulink- SimMechanics. Applied Inverse kinematics for this Manipulator. You can compare the reading of position sensor and inverse kinematics equations. It's supposed to be the same. Cite As Wesam Rezk (2022). tools for computing the forward and inverse kinematics in using symbolic and numerical computations in MATLAB. A separate MATLAB script will be provided for the 3D visualization of the robot arm. 1 Introduction The following exercise is based on an ABB IRB 120 depicted in gure 2. It is a 6-link robotic manipulator with a xed base. 18 hours ago · Search: Inverse Kinematics Solver Matlab. Peter Corke's Robotics Toolbox for robot forward and inverse kinematics Alternatively (my preferred method, but also the only way if your Matlab release is older than R2015b [8 x = load('E:\\myFile1 The inverseKinematics System object™ creates an inverse kinematic (IK) solver to calculate joint configurations for a desired. Properties of MOPSO matlab r2019 全局优化工具箱全局优化工具箱提供了一些函数, 用于寻找包含多个极大值或极小值的问题的全局解. Download and share free MATLAB code, including functions, models, apps, support packages and toolboxes ... ( MATLAB GUI) of forward and inverse kinematics of multi dof robotic arm. ... Discussions (1) This document will help in better understanding of forward and inverse kinematics. For forward kinematics you are only required with angles and. This video includes an example for a robot manipulator to be simulated. Both Forward and Inverse Kinematics are calculated through a MATLAB GUIif you don't k. Simulation of a Puma 762 manipulator capable of solving the Forward and Inverse Kinematics problems demo robotics simulation matlab draw inverse-kinematics puma matlab-gui robotics-simulation inverse-kinematics-problem It turns out that the reason that the inverse kinematics weren't being calculated is because of the collapsed shoulder joing as defined in the D-H table in the \"4 DOF arm\" VI. . Derivation The forward kinematics x=f(θ) is a mapping ℜnm, e.g., from a n-dimensional joint space to a m-dimensional Cartesian space. The singular value decomposition of the Jacobian of this mapping is: J(θ)=USVT The rows [V] i whose corresponding entry in the diagonal matrix S is zero are the vectors which span the Null space of J(θ. 2019. 6. 28. · I am verifying the output of my forward kinematics through inverse kinematics and the results are not as desired. As the output of my inverse kinematics is not coming out. 18 hours ago · Search: Inverse Kinematics Solver Matlab. Peter Corke's Robotics Toolbox for robot forward and inverse kinematics Alternatively (my preferred method, but also the only way if your Matlab release is older than R2015b [8 x = load('E:\\myFile1 The inverseKinematics System object™ creates an inverse kinematic (IK) solver to calculate joint configurations for a desired. Simulink Coder™ MATLAB Coder™ Embedded Coder ® Compilation and programming of the code generated with this blockset requires the latest MPLAB XC compiler and. Fig. 7. . Multi-agent. Search: Inverse Kinematics Solver Matlab. 2022. 9. 8. · Verify the inverse kinematics of the PUMA 260 robot by comparing the results from Matlab Simulation and the robot manipulator As the output of my inverse kinematics is not coming out to be the same as the input of forward kinematics function q = inv_kinematics (ph) %input: [ph1 ph2 ph3] l1 = 0 In the forward kinematics problem, the transformation describing. Its kinematic parameters are described on this web page in terms of modified Denavit-Hartenberg parameters. Forward and inverse kinematics Using the Robotics Toolbox for MATLAB, and for a nominal position (0.4, 0, 0.6) m and with the tool pointing straight down, we can solve the inverse kinematics numerically and show that the solution is valid. mathematical formulation using the MATLAB for the forward kinematic and dynamic analysis of two link planar robot manipulator . Then, forward and inverse kinematics experiments are tested in realistic 2 DOF manipulator. Figure 1: (a) 2 R Robot using V-rep (b) Modify the Rigid Body Dynamics Properties. Mechanical Design. 18 hours ago · and inverse kinematics of a 6-DOF robot arm presented in this paper Inverse Kinematics for a General Purpose Robot Arm That Moves in 3D Explanation of code for simulating FK for Universal robot 5 arm using the robotics toolbox in MATLAB If you are looking for C/C++ codes for simulating ( Universal Robot) UR5 Robot Manipulator, you can download. In this repository, the implementation of forward and inverse kinematics by redundancy resolution is presented for KUKA on linear axis 7-DOF robot. The Redundancy. Search for jobs related to Forward kinematics and inverse kinematics matlab or hire on the world's largest freelancing marketplace with 21m+ jobs. It's free to sign up and bid on jobs. Compute the kinematic solution using the gik object. Specify the initial guess and the different kinematic constraints in the proper order. iniGuess = homeConfiguration (robot); [q, solutionInfo] = gik (iniGuess,positionTarget1,positionTarget2,jointLimBounds); Examine the results in solutionInfo. Show the kinematic solution compared to the home. January 18, 2022 matlab code for forward and inverse kinematics. by. Read more..18 hours ago · and inverse kinematics of a 6-DOF robot arm presented in this paper Inverse Kinematics for a General Purpose Robot Arm That Moves in 3D Explanation of code for simulating FK for Universal robot 5 arm using the robotics toolbox in MATLAB If you are looking for C/C++ codes for simulating ( Universal Robot) UR5 Robot Manipulator, you can download. Robotics 1 U1 Kinematics S6 Inverse Kinematics P1 Inverse Kinematics. Matlab code for Forward Kinematics of 2R robotic arm with animation. The variables of the end-effector in a given Cartesian space are to be. Inverse Kinematics - If the hand is moved, the rotation and bending of the arm is calculated, in accordance with the length and joint. 2022. 8. 27. · Atranslation trans- formationhasX=I3(the identity matrix) and the desired offset asy¯ in Eq The inversion of Jacobian matrix was used for numerical solution of the inverse kinematics task matlab code for image restoration using inverse filter, May 03, 2016 · Q4) In Fig Multiple solutions are possible for the same desired conﬁguration Singularities Forward and. I'm trying to write an inverse kinematics Matlab code for a 6 DOF robotic arm that has the following link parameters: Twist angle (alpha): [-90, 0, 90, -90, 90, 0] Link length (a): [0, 0.5, 0, 0, 0, 0] ... on forward kinematics of 3 to 6 DOF SCARA robots . MATLAB is a powerful tool used to calculate complex. Matlab code for Forward Kinematics of 2R robotic arm with animation. While, to develop the kinematics that calculates the required joint angles (𝜃1− 𝜃6), both geometrical and analytical approaches are used to solve the inverse kinematic problem. After introducing the forward and inverse kinematic models, a MATLAB code is written to obtain the solutions of these models. Search for jobs related to Forward kinematics and inverse kinematics matlab or hire on the world's largest freelancing marketplace with 21m+ jobs. It's free to sign up and bid on jobs. In this repository, the implementation of forward and inverse kinematics by redundancy resolution is presented for KUKA on linear axis 7-DOF robot. The Redundancy. Search: Inverse Kinematics Solver Matlab. Unlike forward kinematics, the solution is not strictly geometry, it demands a numerical methods solution Notice the text boxes in the dialog window are now filled with values The planning and inverse kinematics algorithms in this suite are designed for articulated robots like robotic arms and humanoids. These functions are called by the MATLAB function blocks Planning and Control/Forward Kinematics and Planning and Control/Inverse Kinematics highlighted below. To speed up computation and help ensure the KinematicsSolver object for the inverse kinematics problem finds the desired solutions, the previous solution is used as the initial guess for. 2022. 9. 5. · Inverse Kinematic systems allow for reactive animation, such as foot placement on non-planar terrain Peter Corke's Robotics Toolbox for robot forward and inverse kinematics. The forward model is a fully connected neural network with four inputs, one hidden layer of 16 neuron and three output. The input to the model is the four cables' actuations, and the output is the position of the tip of the arm. The mean absolute error of the output is (3.0876, 3.4107, 3.2158) in cm with standard deviation (2.7049, 2.3013, 2.2238). This document will help in better understanding of forward and inverse kinematics. For forward kinematics you are only required with angles and it provides you the end effector position and in Inverse Kinematics provide the end effector position (coordinate axes) and GUI will provide you the required angles to achieve that position. Cite As. For example, in the computation of your inverse kinematics function, you have r = sqrt (ph1^2+ (ph3-d1)^2); There could be two solutions to the sqrt function. A positive and a negative value. And MATLAB returns the positive value. Similar thing is true for other functions like acos, where multiple angles can give the same result. Search for jobs related to Forward kinematics and inverse kinematics matlab or hire on the world's largest freelancing marketplace with 21m+ jobs. It's free to sign up and bid on jobs. Answer (1 of 2): I think Peter Corke's ROBOTICS TOOLBOX for matlab can solve your problem, it has inbuilt functions for inverse and forward kinematics with support for easy plotting like plotting the robot model, plotting workspace etc Try that, toolbox is free. 2022. 9. 6. · forward (theta) To calculate the forward kinematics, we need to specify 6 axis angles Inverse dynamics is a technique in which measured kinematics and, possibly, external. 2022. 8. 27. · Inverse Kinematics is the inverse function/algorithm of Forward Kinematics hashim khan (2021) Inverse kinematics Hi, I am trying to use solve forword and inverse. bitcoin private key generator apk simulating a 6 DOF robot in matlab robotic toolbox. Ask Question Asked 2 years, 6 months ago. Modified 2 years, 6 months ago. Viewed 473 times ... Since your robot has 6 DOF, I would expect q also have 6 columns instead of 5. Try with q = [0 0 0 0 0 0] in your code. Share. Follow. cree competitors. The robot kinematics can be divided into forward kinematics and inverse kinematics. Forward kinematics problem is straightforward and there is no complexity deriving the equations. Hence, there is always a forward kinematics solution of a manipulator. Inverse kinematics is a much more difficult problem than forward kinematics. Let's look at numerical approaches to inverse kinematics for a couple of different robots and learn some of the important considerations. For RTB10.x please note that the mask value must be explicitly preceded by the 'mask' keyword. For example: >> q = p2.ikine (T, [-1 -1], 'mask', [1 1 0 0 0 0]) MATLAB. inverse kinematic. 2022. 9. 7. · Link Creation MATLAB 2014B Initialization of PETER CORKE ROBOTIC TOOL BOX FEATURE Inverse Kinematics is the inverse - using the end-effector desired coordinates ,. Inverse Kinematics (1) So using forward kinematics we can determine x, y and z, given the angles φ and θ. But forward kinematics is not enough. Generally with a robot, we know where we want the robot to be (x,y), and need to find the angles. This process is called inverse kinematics. Search: Inverse Kinematics Solver Matlab. There are also several examples in python and matlab that show how to interface with openrave to use the plugins in CoMPS Create a rigid body tree model for your robot using the rigidBodyTree class The individual joints' trajectories, velocities and accelerations can be obtained using inverse kinematics equations Back in the day, I loved numerical. bitcoin private key generator apk simulating a 6 DOF robot in matlab robotic toolbox. Ask Question Asked 2 years, 6 months ago. Modified 2 years, 6 months ago. Viewed 473 times ... Since your robot has 6 DOF, I would expect q also have 6 columns instead of 5. Try with q = [0 0 0 0 0 0] in your code. Share. Follow. cree competitors. Inverse Kinematics (1) So using forward kinematics we can determine x, y and z, given the angles φ and θ. But forward kinematics is not enough. Generally with a robot, we know where we want the robot to be (x,y), and need to find the angles. This process is called inverse kinematics. Inverse Kinematics: Example I • Inverse Kinematics: - Set the final position equal to the Forward Transformation Matrix 0A 3: • The solution strategy is to equate the elements of 0A 3 to that of the given position (q x, q y) and orientation ϕ Inverse Kinematics: Example I • Orientation (ϕ): • Now Position of the 2DOF point P: ∴. Example. Solving analytically, the solution is y = ex and y (1) = 2.71828. (Note: This analytic solution is just for comparing the accuracy.) Using Euler's method , considering h = 0.2, 0.1, 0.01, you can see the results in the diagram below. You can notice, how accuracy improves when steps are small. If this article was helpful,. This project combined forward and inverse position and velocity kinematics, dynamics, and vision processing for the control of a 3 Degree of Freedom ( DOF ) robotic arm .The manipulator was able to recognize objects in its workspace, pick them up, and sort them by weight and color. A combination of MatLab and C++ programming was used to control. 3DOF 3 Dimension Inverse Kinematic-PseudoInvJacobian (GUI) Inverse Kinematics of 3DOF MeArm Matlab Model Simulation based on PseudoInverse Jacobian Method. The simulation hasn't set the operation range yet, so we can see when the arm try to reach the position out of the its limit. The Forward Kinematics is driven by Denavit-Hartenberg convention. 2022. 9. 7. · with the forward''Topic matlab Â· GitHub May 7th, 2018 - More than 27 million people use GitHub to discover Gramm is a complete data visualization toolbox for Matlab Human Fall Detection from CCTV camera feed' 'matlab inverse kinematics robot arm circle youtube april 21st, 2018 - code http simsamo. Inverse Kinematics of 3DOF MeArm Matlab Model Simulation based on PseudoInverse Jacobian Method. The simulation hasn't set the operation range yet, so we can see when the arm try to reach the position out of the its limit. The Forward Kinematics is driven by Denavit-Hartenberg convention. Paperwork:. 2022. 8. 21. · Inverse Kinematics Matlab Code Codes and Scripts Downloads Free Forward kinematics problem is straightforward and there is no complexity deriving the equations For. Robotics 1 U1 Kinematics S6 Inverse Kinematics P1 Inverse Kinematics. Matlab Code-Forward kinematic model. The complete Toolbox and documentation is freely available via anonymous ftp. In inverse-kinematics mode, the model only moves when the user clicks-and-drags on the object to adjust the joint angles. 2022. 9. 7. · with the forward''Topic matlab Â· GitHub May 7th, 2018 - More than 27 million people use GitHub to discover Gramm is a complete data visualization toolbox for Matlab Human Fall Detection from CCTV camera feed' 'matlab inverse kinematics robot arm circle youtube april 21st, 2018 - code http simsamo. Step 3: Remember your end effector. The goal of calculating the Forward Kinematics is to be able to calculate the end effector pose from the position of the joints. Most Forward Kinematic tutorials will generalize the end effector as a single distance from the final joint. This is fine for a simple \"open-close\" gripper. Discussions (18) % Anthropomorphic arm with 6 DOF and spherical wrist. % It calculates the Inverse Kinematic of an Anthropomorphic arm with 6 DOF . % 'q' is the solutions in radiant and K is the direct Kinematic matrix. %. % K = [ n s a p; % 0 0 0 1] % where n, s, a are three vectors fo 3 elements that represents the. Properties of MOPSO matlab r2019 全局优化工具箱全局优化工具箱提供了一些函数, 用于寻找包含多个极大值或极小值的问题的全局解. matlab code for forward and inverse kinematics. May 21 2021. naugatuck high school football coach. creative synonyms in different languages 0 Comments. 2022. 7. 13. · Matlab code for Forward Kinematics of 2R robotic arm with animation The more frequent robot manipulation problem, however, is the opposite The following code can be used. Discussions (18) % Anthropomorphic arm with 6 DOF and spherical wrist. % It calculates the Inverse Kinematic of an Anthropomorphic arm with 6 DOF . % 'q' is the solutions in radiant and K is the direct Kinematic matrix. %. % K = [ n s a p; % 0 0 0 1] % where n, s, a are three vectors fo 3 elements that represents the. Peter Corke's Robotics Toolbox for robot forward and inverse kinematics Alternatively (my preferred method, but also the only way if your Matlab release is older than R2015b [8 x = load('E:\\myFile1 The inverseKinematics System object™ creates an inverse kinematic (IK) solver to calculate joint configurations for a desired end-effector pose based on a specified rigid body tree model However. Inverse kinematics (IK) determines joint configurations of a robot model to achieve a desired end-effect position. Robot kinematic constraints are specified in the rigidBodyTree robot model. I'm trying to write an inverse kinematics Matlab code for a 6 DOF robotic arm that has the following link parameters: Twist angle (alpha): [-90, 0, 90, -90, 90, 0] Link length (a): [0, 0.5, 0, 0, 0, 0] ... sevcon mos90 fault codes; kama sutra a position a; rpgbot sorcerer metamagic; circuitpython string functions; nextbot chase. This document will help in better understanding of forward and inverse kinematics. For forward kinematics you are only required with angles and it provides you the end effector position and in Inverse Kinematics provide the end effector position (coordinate axes) and GUI will provide you the required angles to achieve that position. Cite As. 3.1Inverse Kinematics Test On the basis of previous development, it is possible to utilize MATLAB to perform kinematics analysis. Using the manipulator shown in Fig. 2 as the example. Suppose the desired position and orientation of end effector are (20 , 20) and φ = 0˚. 2022. 3. 21. · What is Matlab Code For Forward And Inverse Kinematics. Verify the forward kinematics of the PUMA 260 robot by comparing the results from Matlab simulation and the. Discussions (18) % Anthropomorphic arm with 6 DOF and spherical wrist. % It calculates the Inverse Kinematic of an Anthropomorphic arm with 6 DOF . % 'q' is the solutions in radiant and K is the direct Kinematic matrix. %. % K = [ n s a p; % 0 0 0 1] % where n, s, a are three vectors fo 3 elements that represents the. 3) Symbolic Math Toolbox. With the help of symbolic math tools, analytical solutions can be found for the inverse kinematics. An analytical solution is the explicit equation for the joint angles of the robot given end effector pose: joint_angles = f (end_effector_pose). Once the equation is found, the joint angles can be found very quickly. In this repository, the implementation of forward and inverse kinematics by redundancy resolution is presented for KUKA on linear axis 7-DOF robot. The Redundancy Resolution includes three methods, which are Jacobian-based (Damped Least Square and Weighted Pseudoinverse), Null Space, and Task Augmentation. Peter Corke's Robotics Toolbox for robot forward and inverse kinematics. Figure 2: Illustration showing all possible theta1 and theta2 values. Now, for every combination of theta1 and theta2 values the x and y coordinates are deduced using forward kinematics formulae.. The following code snippet shows how data is generated for all combination of theta1 and theta2 values and saved into a matrix to be used as training data. The reason for saving the data in two. robotic arm using MATLAB tool is provided. The flow chart below explains the process starting with creating the robot, controlling the robot with input joint angles, forward kinematics and inverse kinematics functions used for the implementation. Link Creation MATLAB 2014B Initialization of PETER CORKE ROBOTIC TOOL BOX FEATURE. 18 hours ago · and inverse kinematics of a 6-DOF robot arm presented in this paper Inverse Kinematics for a General Purpose Robot Arm That Moves in 3D Explanation of code for simulating FK for Universal robot 5 arm using the robotics toolbox in MATLAB If you are looking for C/C++ codes for simulating ( Universal Robot) UR5 Robot Manipulator, you can download. Search: Inverse Kinematics Solver Matlab. Unlike forward kinematics, the solution is not strictly geometry, it demands a numerical methods solution Notice the text boxes in the dialog window are now filled with values The planning and inverse kinematics algorithms in this suite are designed for articulated robots like robotic arms and humanoids. Jul 10, 2019 · Forward Dynamics of Robot using Robotics Toolbox. Learn more about matlab, simulink, control, robotics toolbox, peter corke Simulink. \"/> cvxpy solver. difference between fair value gap and liquidity void; niantic wayfarer level 38; percy jackson fanfiction lemon. Peter Corke's Robotics Toolbox for robot forward and inverse kinematics. In this repository, the implementation of forward and inverse kinematics by redundancy resolution is presented for KUKA on linear axis 7-DOF robot. The Redundancy Resolution includes three methods, which are Jacobian-based (Damped Least Square and Weighted Pseudoinverse), Null Space, and Task Augmentation. For example, in the computation of your inverse kinematics function, you have Theme Copy r = sqrt (ph1^2+ (ph3-d1)^2); There could be two solutions to the sqrt function. A positive and a negative value. And MATLAB returns the positive value. Similar thing is true for other functions like acos, where multiple angles can give the same result. Search: Inverse Kinematics Solver Matlab. Unlike forward kinematics, the solution is not strictly geometry, it demands a numerical methods solution Notice the text boxes in the dialog window are now filled with values The planning and inverse kinematics algorithms in this suite are designed for articulated robots like robotic arms and humanoids. 2022. 9. 5. · The variables of the end-effector in a given Cartesian space are to be Inverse Kinematics is the opposite The Robotics Toolbox is a software package that allows a. Search for jobs related to Matlab code for forward and inverse kinematics or hire on the world's largest freelancing marketplace with 21m+ jobs. It's free to sign up and bid on jobs. . Download and share free MATLAB code, including functions, models, apps, support packages and toolboxes. Skip to content. ... 3dof arm robot denavithartenberg forward kinematics inverse kinematics mearm. Cancel. Acknowledgements. Inspired: 3DOF 3 Dimension Inverse Kinematic-PseudoInvJacobian (GUI). This paper presents the inverse kinematics solution using the neural network for a robotic arm in 3-dimension. This paper creates neural networks to represent x, y and z position of the end-effector in the forward kinematics equations. The structure of the network has 4 layers; input layer, 2 hidden layers, and output layer. The input and output layers are defined as robotic arm angle and. the Inverse-Kinematics Problem of a {6R} Robot Manipulator}, journal = {The International Journal of Robotics Research}, year = {1986}, volume = {5}, number = {4}, pages = {69--88} } Maybe Corke's code is based on that. Anyway, my code is only for position and velocity, not dynamics. Forward and Inverse kinematics - File Exchange - MATLAB Central Forward and Inverse kinematics version 1.0.0 (2.11 KB) by hashim khan Forward and Inverse kinematics of 6 DOF arm with workspace calculation 5.0 (1) 843 Downloads Updated 26 Sep 2019 View License Follow Download Overview Functions Reviews (1) Discussions (2). Department, Mechatronics Lab. Forward and Inverse kinematics analysis are performed. Robotics Toolbox is also applied to model Denso robot system. A GUI is built for practical use of robotic system. 2. Robot Arm Kinematics The robot kinematics can be categorized into two main parts; forward and inverse kinematics. Forward. To write code to fit a linear and cubic polynomial for the Cp data.2. To plot the linear and cubic fit curves along with the raw data points.3. ... Aim - Write a program in Matlab showing the Forward Kinematics of a 2R Robotic Arm Description - 2R Robotic Arm- A robotic arm is a type of mechanical arm, usually programmable. The arm may be the. 2022. 8. 27. · Inverse Kinematics is the inverse function/algorithm of Forward Kinematics hashim khan (2021) Inverse kinematics Hi, I am trying to use solve forword and inverse kinematics for my robot arm For example, if our end effector is a full joint with orientation, e would contain 6 DOFs: 3 translations and 3 rotations For example, if our end effector is a full joint with. 18 hours ago · Search: Inverse Kinematics Solver Matlab. Peter Corke's Robotics Toolbox for robot forward and inverse kinematics Alternatively (my preferred method, but also the only. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators. Free source code and tutorials for Software developers and Architects.; Updated: 14 May 2018. ... I am currently coding a Forward and Inverse Kinematics solver for a PUMA 560 robot. ... The matrix multiplications of my Python code are correct since I double checked them with Matlab. Any advice is appreciated. Posted 21-Feb-17 21:40pm. Yes, forward kinematics are easy. It defines a function which maps the robot configuration $$R_1 \\in SO(2), R_2 \\in SO(2)$$ to the end-effector position $$e \\in R^2$$. Normally, the forward kinematics is a closed-form function. 4. The Inverse Kinematics. The inverse kinematics asks a question: I want to move the end-effector to a target position. 2022. 9. 5. · The forward kinematics allow NAO developers to map any configuration of the robot from its own joint space to the three-dimensional physical space, whereas the inverse. In this repository, the implementation of forward and inverse kinematics by redundancy resolution is presented for KUKA on linear axis 7-DOF robot. The Redundancy. Inverse kinematics (IK) determines joint configurations of a robot model to achieve a desired end-effect position. Robot kinematic constraints are specified in the rigidBodyTree robot model. MATLAB Walid-khaled / 7DOF-KUKA-Linear-Axis-Forward-and-Inverse-Kinematics Star 4 Code Issues Pull requests In this repository, the implementation of forward and inverse kinematics by redundancy resolution is presented for KUKA on linear axis 7-DOF robot. Forward kinematics refers to the use of the kinematic equations of a The pause commad which pauses the code and records accordingly MATLAB Assignment #1 focuses on the forward and inverse pose kinematics (FPK and IPK) of the human arm The forward kinematics allow NAO developers to map any configuration of the robot from its own joint space to. I'm trying to write an inverse kinematics Matlab code for a 6 DOF robotic arm that has the following link parameters: Twist angle (alpha): [-90, 0, 90, -90, 90, 0] Link length (a): [0, 0.5, 0, 0, 0, 0] ... sevcon mos90 fault codes; kama sutra a position a; rpgbot sorcerer metamagic; circuitpython string functions; nextbot chase. The 6 - DOF articulated robotic arm was designed and visualized in RVIZ and, Moveit is being used as a control interface using Robot Operating System (ROS). The manipulation of the arm with end effector refrain us from using the joint by the joint control mechanism. Here's some quick MATLAB code for LU decomposition: function [L,U] = lucrout(A) [~,n] = size(A); L This method is quick because only back- and forward-substitution is required to solve for the In short, make sure you really need the matrix inverse and never use the matrix inverse to solve a. Are there. Read more..2022. 9. 5. · The variables of the end-effector in a given Cartesian space are to be Inverse Kinematics is the opposite The Robotics Toolbox is a software package that allows a. • Derive the forward kinematic equationsfor CRS robot arm following the Denavit- Hartenberg (DH) convention • Derive inverse kinematic equations for the CRS robot arm • Use the provided Code Composer Studio project to verify your solution NOTE: CRS robot arm has five motors/joints, in this class we are only using/controlling the first. For example, in the computation of your inverse kinematics function, you have Theme Copy r = sqrt (ph1^2+ (ph3-d1)^2); There could be two solutions to the sqrt function. A positive and a negative value. And MATLAB returns the positive value. Similar thing is true for other functions like acos, where multiple angles can give the same result. Special thanks for :Felix Pasila, S.T., M.Sc., Ph.D as lecturerHarsha for making the solidwork designReference:https://grabcad.com/library/6- dof -robotic-ma. 2022. 8. 27. · Inverse Kinematics is the inverse function/algorithm of Forward Kinematics hashim khan (2021) Inverse kinematics Hi, I am trying to use solve forword and inverse. FABRIK（Foward and Backward Reaching Inverse Kinematics）. Robotic Arm turned into a 3D Printer (Inverse Kinematics) September 07, 2019 02:07PM. 0 arm. ... Jan 18, 2022 · matlab code for forward and inverse kinematics. I'll just write down the final equations here. Here is the blender file used. bsa mercury spares. Advertisement bench. 2022. 5. 22. · MATLAB is a powerful environment for linear algebra and graphical presentation that is available on a very wide range of computer platforms Forward and Inverse kinematics. This document will help in better understanding of forward and inverse kinematics. For forward kinematics you are only required with angles and it provides you the end effector position and in Inverse Kinematics provide the end effector position (coordinate axes) and GUI will provide you the required angles to achieve that position. Cite As. Search for jobs related to Forward kinematics and inverse kinematics matlab or hire on the world's largest freelancing marketplace with 21m+ jobs. It's free to sign up and bid on jobs. Topics covered in this session are:Euler Lagrange formulation of n-DOF serial manipulatorGeneral Matlab codeExample: Inverse Dynamics of a 2-DOF manipulator. I am trying to compute dynamics of 3 DOF robot using Robotics Toolbox by executing this code: robot.accel(q, zeros(1,3), zeros(1,3)) But I am getting this error: Assignment has more non. For example, in the computation of your inverse kinematics function, you have r = sqrt (ph1^2+ (ph3-d1)^2); There could be two solutions to the sqrt function. A positive and a negative value. And MATLAB returns the positive value. Similar thing is true for other functions like acos, where multiple angles can give the same result. In the Fig 2 one can see relation between forward and inverse kinematics. In forward kinematics position matrices or end effector position are calculated by help of link length and joint angles, and in inverse kinematics joint angles are calculated with the help of link length and end effector position or position matrices. The kinematics and dynamics (both forward and inverse) of the biped robot \"PASIBOT,\" taking into account for support foot slippage are encoded in MATLAB ® code. The great advantage of creating a parametric MATLAB ® code following this methodology is that the algorithm can be modify to obtain the results in a parametric way or even. I'm trying to write an inverse kinematics Matlab code for a 6 DOF robotic arm that has the following link parameters: Twist angle (alpha): [-90, 0, 90, -90, 90, 0] Link length (a): [0, 0.5, 0, 0, 0, 0] ... The goal of this project is to design a forward 6 DoF robotic arm and control it by Matlab. The controller is separated by two. Example #3. In this example, we will take another vector function and will compute its Jacobian Matrix using the Jacobian function. For this example, we will input following values: Pass the input vector function as [c^3 + b^2, 2a^3 + c, c^2 + 5] Pass the variables as [a, b, c]. Please can you write a code for Forward and inverse kinematics for 5 DOF using matlab (robotics toolbox) Question: Please can you write a code for Forward and inverse kinematics for 5 DOF using matlab (robotics toolbox). The 6 - DOF articulated robotic arm was designed and visualized in RVIZ and, Moveit is being used as a control interface using Robot Operating System (ROS). The manipulation of the arm with end effector refrain us from using the joint by the joint control mechanism. 2022. 9. 3. · Forward and Inverse Kinematics – FK & IK For manipulators and humanoid robots, the toolbox includes algorithms for collision checking, trajectory generation, forward and. First, plug the joint angles you received from your inverse kinematics algorithm into your forward kinematics equations. Do they provide the same end effector coordinates that you entered into your inverse kinematics routine? If not, you have an error in either the forward or inverse equations. Matlab Code-Forward kinematic model. Inverse Kinematics is the opposite. The example defines the joint parameters and end-effector locations symbolically, calculates and visualizes the forward and inverse kinematics solutions, and finds the system Jacobian, which is useful for simulating the motion of the robot arm.. Answer (1 of 2): I think Peter Corke's ROBOTICS TOOLBOX for matlab can solve your problem, it has inbuilt functions for inverse and forward kinematics with support for easy plotting like plotting the robot model, plotting workspace etc Try that, toolbox is free. The movement of robot can be divided into forward and inverse kinematics. Forward kinematics described how robot's move according to entered angles. There is always a solution for forward kinematics of manipulator. Solution for inverse kinematics is a more difficult problem than forward kinematics. 18 hours ago · Search: Inverse Kinematics Solver Matlab. Peter Corke's Robotics Toolbox for robot forward and inverse kinematics Alternatively (my preferred method, but also the only way if your Matlab release is older than R2015b [8 x = load('E:\\myFile1 The inverseKinematics System object™ creates an inverse kinematic (IK) solver to calculate joint configurations for a desired. 2022. 1. 21. · About Kinematics Inverse Code Forward For Matlab And . FABRIK avoids the use of rotational angles or matri-ces, and instead ﬁnds each joint position via locating a point. Its kinematic parameters are described on this web page in terms of modified Denavit-Hartenberg parameters. Forward and inverse kinematics Using the Robotics Toolbox for MATLAB, and for a nominal position (0.4, 0, 0.6) m and with the tool pointing straight down, we can solve the inverse kinematics numerically and show that the solution is valid. Download and share free MATLAB code, including functions, models, apps, support packages and toolboxes ... Movement system used forward kinematics denavit hartenberg which each joint angle is updated by joint velocity found by inverse kinematics pseudoinverse jacobian. ... Robot Manipulator Control with Inverse Kinematics PD-Pseudoinverse. The robot kinematics can be divided into forward kinematics and inverse kinematics. Forward kinematics problem is straightforward and there is no complexity deriving the equations. Hence, there is always a forward kinematics solution of a manipulator. Inverse kinematics is a much more difficult problem than forward kinematics. 18 hours ago · Search: Inverse Kinematics Solver Matlab. Peter Corke's Robotics Toolbox for robot forward and inverse kinematics Alternatively (my preferred method, but also the only way if your Matlab release is older than R2015b [8 x = load('E:\\myFile1 The inverseKinematics System object™ creates an inverse kinematic (IK) solver to calculate joint configurations for a desired. Discussions (18) % Anthropomorphic arm with 6 DOF and spherical wrist. % It calculates the Inverse Kinematic of an Anthropomorphic arm with 6 DOF . % 'q' is the solutions in radiant and K is the direct Kinematic matrix. %. % K = [ n s a p; % 0 0 0 1] % where n, s, a are three vectors fo 3 elements that represents the. These functions are called by the MATLAB function blocks Planning and Control/Forward Kinematics and Planning and Control/Inverse Kinematics highlighted below. To speed up computation and help ensure the KinematicsSolver object for the inverse kinematics problem finds the desired solutions, the previous solution is used as the initial guess for. In this repository, the implementation of forward and inverse kinematics by redundancy resolution is presented for KUKA on linear axis 7-DOF robot. The Redundancy Resolution includes three methods, which are Jacobian-based (Damped Least Square and Weighted Pseudoinverse), Null Space, and Task Augmentation. most recent commit 24 days ago. Figure 2: Illustration showing all possible theta1 and theta2 values. Now, for every combination of theta1 and theta2 values the x and y coordinates are deduced using forward kinematics formulae.. The following code snippet shows how data is generated for all combination of theta1 and theta2 values and saved into a matrix to be used as training data. The reason for saving the data in two. 2022. 9. 3. · Forward and Inverse Kinematics – FK & IK For manipulators and humanoid robots, the toolbox includes algorithms for collision checking, trajectory generation, forward and. Standard Particle Swarm Optimization code (Matlab M-file) for the optimization of the benchmark function. https://elkmany.github.io/pso/. 0.0. Particle Swarm Optimization : A Tutorial James Blondin September 4, 2009 1 Introduction Particle Swarm Optimization (PSO) is a technique used to explore the search space of a given problem to ﬁnd the settings or parameters required to. This video includes an example for a robot manipulator to be simulated. Both Forward and Inverse Kinematics are calculated through a MATLAB GUIif you don't k. I am verifying the output of my forward kinematics through inverse kinematics and the results are not as desired. As the output of my inverse kinematics is not coming out to be the same as the input of forward kinematics. The D-H parameters of manipulator is given as: Link: alpha, a, theta, d. Link 1 : -90 0 theta1* d1. 2022. 7. 13. · Matlab code for Forward Kinematics of 2R robotic arm with animation The more frequent robot manipulation problem, however, is the opposite The following code can be used. 2022. 7. 13. · Matlab code for Forward Kinematics of 2R robotic arm with animation The more frequent robot manipulation problem, however, is the opposite The following code can be used. Inverse Kinematics (1) So using forward kinematics we can determine x, y and z, given the angles φ and θ. But forward kinematics is not enough. Generally with a robot, we know where we want the robot to be (x,y), and need to find the angles. This process is called inverse kinematics. This example shows how to use the KinematicsSolver object to perform forward kinematics (FK) and inverse kinematics (IK) on a five-bar robotic mechanism. First, the example demonstrates how to perform FK analyses to calculate a singularity-free workspace for a five-bar robot. ... You clicked a link that corresponds to this MATLAB command: Run. Download and share free MATLAB code, including functions, models, apps, support packages and toolboxes ... ( MATLAB GUI) of forward and inverse kinematics of multi dof robotic arm. ... Discussions (1) This document will help in better understanding of forward and inverse kinematics. For forward kinematics you are only required with angles and. May 01, 2018 · This project describe a mechanical system, design concept and prototype implementation of a 6 DOF robotic arm, which should perform industrial task such as pick and place of fragile objects operation.. IV. GUI DEVELOPMENT FOR 6 DOF ROBOT POSITION ANALYSIS In this chapter, a detailed discussion on the implementation, creation and the. In the Fig 2 one can see relation between forward and inverse kinematics. In forward kinematics position matrices or end effector position are calculated by help of link length and joint angles, and in inverse kinematics joint angles are calculated with the help of link length and end effector position or position matrices. MATLAB Walid-khaled / 7DOF-KUKA-Linear-Axis-Forward-and-Inverse-Kinematics Star 4 Code Issues Pull requests In this repository, the implementation of forward and inverse kinematics by redundancy resolution is presented for KUKA on linear axis 7-DOF robot. Download and share free MATLAB code, including functions, models, apps, support packages and toolboxes. Skip to content. ... 3dof arm robot denavithartenberg forward kinematics inverse kinematics mearm. Cancel. Acknowledgements. Inspired: 3DOF 3 Dimension Inverse Kinematic-PseudoInvJacobian (GUI). Search for jobs related to Matlab code for forward and inverse kinematics or hire on the world's largest freelancing marketplace with 21m+ jobs. It's free to sign up and bid on jobs. 2022. 9. 7. · with the forward''Topic matlab Â· GitHub May 7th, 2018 - More than 27 million people use GitHub to discover Gramm is a complete data visualization toolbox for Matlab. This video includes an example for a robot manipulator to be simulated. Both Forward and Inverse Kinematics are calculated through a MATLAB GUIif you don't k. Inverse Kinematics Inverse kinematics (IK) algorithm design with MATLAB and Simulink Kinematics is the study of motion without considering the cause of the motion, such as forces and torques. Inverse kinematics is the use of kinematic equations to determine the motion of a robot to reach a desired position. The robot kinematics can be divided into forward kinematics and inverse kinematics. Forward kinematics problem is straightforward and there is no complexity deriving the equations. Hence, there is always a forward kinematics solution of a manipulator. Inverse kinematics is a much more difficult problem than forward kinematics. Inverse Kinematics Matlab Code Codes and Scripts Downloads Free. Verify your solution in MATLAB by using your forward kinematics code from HW# 3. Matlab code for Forward Kinematics of 2R robotic arm with animation. In document the solutions of both the forward and inverse kinematics problems for Adept Six 300 6R robot are presented. 2022. 9. 7. · with the forward''Topic matlab Â· GitHub May 7th, 2018 - More than 27 million people use GitHub to discover Gramm is a complete data visualization toolbox for Matlab Human Fall Detection from CCTV camera feed' 'matlab inverse kinematics robot arm circle youtube april 21st, 2018 - code http simsamo. 2022. 9. 4. · 3: Forward and Inverse Kinematics and the Denavit-Hartenberg Convention Clarification on spherical wrist DH frames Derivation The forward and inverse kinematics of a. For example, in the computation of your inverse kinematics function, you have r = sqrt (ph1^2+ (ph3-d1)^2); There could be two solutions to the sqrt function. A positive and a negative value. And MATLAB returns the positive value. Similar thing is true for other functions like acos, where multiple angles can give the same result. Please can you write a code for Forward and inverse kinematics for 5 DOF using matlab (robotics toolbox) Question: Please can you write a code for Forward and inverse kinematics for 5 DOF using matlab (robotics toolbox). This video includes an example for a robot manipulator to be simulated. Both Forward and Inverse Kinematics are calculated through a MATLAB GUIif you don't k. For example, in the computation of your inverse kinematics function, you have Theme Copy r = sqrt (ph1^2+ (ph3-d1)^2); There could be two solutions to the sqrt function. A positive and a negative value. And MATLAB returns the positive value. Similar thing is true for other functions like acos, where multiple angles can give the same result. 18 hours ago · and inverse kinematics of a 6-DOF robot arm presented in this paper Inverse Kinematics for a General Purpose Robot Arm That Moves in 3D Explanation of code for simulating FK for Universal robot 5 arm using the robotics toolbox in MATLAB If you are looking for C/C++ codes for simulating ( Universal Robot) UR5 Robot Manipulator, you can download. 18 hours ago · and inverse kinematics of a 6-DOF robot arm presented in this paper Inverse Kinematics for a General Purpose Robot Arm That Moves in 3D Explanation of code for simulating FK for Universal robot 5 arm using the robotics toolbox in MATLAB If you are looking for C/C++ codes for simulating ( Universal Robot) UR5 Robot Manipulator, you can download. 2022. 9. 5. · The Mathematics of Forward Kinematics; Part 3 (20 points) Find the forward kinematics and inverse kinematics solution for problem 3 The next step for the leg (pardon. 18 hours ago · and inverse kinematics of a 6-DOF robot arm presented in this paper Inverse Kinematics for a General Purpose Robot Arm That Moves in 3D Explanation of code for simulating FK for Universal robot 5 arm using the robotics toolbox in MATLAB If you are looking for C/C++ codes for simulating ( Universal Robot) UR5 Robot Manipulator, you can download. Since the forward kinematics formulae for the two-joint robotic arm are known, x and y coordinates of the tip of the arm are deduced for the entire range of angles of rotation of the two joints. The coordinates and the angles are saved to be used as training data to train an ANFIS (adaptive neuro-fuzzy inference system) network. Read more..This example shows how to use the KinematicsSolver object to perform forward kinematics (FK) and inverse kinematics (IK) on a five-bar robotic mechanism. First, the example demonstrates how to perform FK analyses to calculate a singularity-free workspace for a five-bar robot. ... You clicked a link that corresponds to this MATLAB command: Run. Robotics 1 U1 Kinematics S6 Inverse Kinematics P1 Inverse Kinematics. Matlab Code-Forward kinematic model. The complete Toolbox and documentation is freely available via anonymous ftp. In inverse-kinematics mode, the model only moves when the user clicks-and-drags on the object to adjust the joint angles. 3DOF 3 Dimension Inverse Kinematic-PseudoInvJacobian (GUI) Inverse Kinematics of 3DOF MeArm Matlab Model Simulation based on PseudoInverse Jacobian Method. The simulation hasn't set the operation range yet, so we can see when the arm try to reach the position out of the its limit. The Forward Kinematics is driven by Denavit-Hartenberg convention. A GUI was created in MATLAB for studying the forward and inverse kinematics of the robot. It gave results with precision of 0.2 cm. the load analysis also gave the maximum load it can withstand 200 KN without permanent deformation. The approach presented in this work can also be applicable to solve the kinematics problem of other similar. EduRev provides you with complete coverage and for 2022 Forward & inverse kinematics examples of 2R, 3R & 3P manipulators (2) as a part of our plan for syllabus to prepare for exam. Our subject experts have curated special courses, tests & mock test series. All previous year questions (PYQs) & topic wise tests like tests for Forward & inverse. The forward model is a fully connected neural network with four inputs, one hidden layer of 16 neuron and three output. The input to the model is the four cables' actuations, and the output is the position of the tip of the arm. The mean absolute error of the output is (3.0876, 3.4107, 3.2158) in cm with standard deviation (2.7049, 2.3013, 2.2238). While, to develop the kinematics that calculates the required joint angles (𝜃1− 𝜃6), both geometrical and analytical approaches are used to solve the inverse kinematic problem. After introducing the forward and inverse kinematic models, a MATLAB code is written to obtain the solutions of these models. The MATLAB code also implements a Graphical User Interface (GUI), from which the user can control the robotic arm and run the forward and inverse kinematics algorithms. A 3D simulation/visualization of the robotic arm is displayed in the GUI in real time. Forward kinematics for all link frames. Parameters. q (ndarray(n) or ndarray(m,n)) - The joint configuration of the robot (Optional, if not supplied will use the stored q values). old (bool, optional) - \"old\" behaviour, defaults to True. Returns. Forward kinematics as an SE(3) matrix. Return type. SE3 instance with n values. Search: Inverse Kinematics Solver Matlab. There are also several examples in python and matlab that show how to interface with openrave to use the plugins in CoMPS Create a rigid body tree model for your robot using the rigidBodyTree class The individual joints' trajectories, velocities and accelerations can be obtained using inverse kinematics equations Back in the day, I loved numerical. For robot manipulators it covers forward, inverse and differential kinematics, and dynamics. The Robotics Toolbox for MATLAB is free and open software that enables the reader to easily bring the algorithmic concepts into practice and work with real, non-trivial, problems.. This paper present kinematic and dynamic analysis of a 3-R robot arm with Adams/ Matlab Co-Simulation,. This video includes an example for a robot manipulator to be simulated. Both Forward and Inverse Kinematics are calculated through a MATLAB GUIif you don't k. 2022. 1. 29. · What is Matlab Code For Forward And Inverse Kinematics. Inverse kinematics denotes the computation of all joint angles out of the tool-centre-point's position and. Optimization Algorithms for Inverse Kinematics of Robots ... Once you've tested your IK solution, MATLAB and Simulink allow you to explore next steps towards building a complete robotic. Search for jobs related to Forward kinematics and inverse kinematics matlab or hire on the world's largest freelancing marketplace with 21m+ jobs. It's free to sign up and bid on jobs. Search for jobs related to Forward kinematics and inverse kinematics matlab or hire on the world's largest freelancing marketplace with 21m+ jobs. It's free to sign up and bid on jobs. 2022. 7. 16. · Inverse Kinematics Solver Matlab One important aspect however is that while OpenSim provides a useful general tool for biomechanical analysis including fields beyond. 18 hours ago · C# - Free source code and tutorials for Software developers and Architects The referenced robot is Adapt S350 SCARA, but only 2 degrees of freedom are used MATLAB is used by engineers and scientists in many fields, such as image processing, robotics, and computational finance MATLAB is a high-level language and interactive environment for. The Matlab program must be able to compute the T6 transform matrix and must incorporate the following: User data entry of each joint angle (in degrees) Joint angle limits Define each T transform and compute T6 transform in world coordinates Vector output in terms of world coodinates - to include position and orientation. I'm trying to write an inverse kinematics Matlab code for a 6 DOF robotic arm that has the following link parameters: Twist angle (alpha): [-90, 0, 90, -90, 90, 0] Link length (a): [0, 0.5, 0, 0, 0, 0] ... The goal of this project is to design a forward 6 DoF robotic arm and control it by Matlab. The controller is separated by two. Matlab code for Forward Kinematics of 2R robotic arm with animation. 2022. 1. 29. · What is Matlab Code For Forward And Inverse Kinematics. Inverse kinematics denotes the computation of all joint angles out of the tool-centre-point's position and. Free source code and tutorials for Software developers and Architects.; Updated: 14 May 2018. ... I am currently coding a Forward and Inverse Kinematics solver for a PUMA 560 robot. ... The matrix multiplications of my Python code are correct since I double checked them with Matlab. Any advice is appreciated. Posted 21-Feb-17 21:40pm. This example shows how to use the KinematicsSolver object to perform forward kinematics (FK) and inverse kinematics (IK) on a five-bar robotic mechanism. First, the example demonstrates how to perform FK analyses to calculate a singularity-free workspace for a five-bar robot. ... You clicked a link that corresponds to this MATLAB command: Run. 2022. 9. 3. · Forward and Inverse Kinematics – FK & IK For manipulators and humanoid robots, the toolbox includes algorithms for collision checking, trajectory generation, forward and. About Kinematics Inverse Code Forward For Matlab And . FABRIK avoids the use of rotational angles or matri-ces, and instead ﬁnds each joint position via locating a point on a line. These representational tools will be applied to compute the workspace, the forward and inverse kinematics, the forward and inverse instantaneous kinematics, and.. 2022. 9. 6. · Inverse kinematics 2 link arm python Your code should be general as regards number of input, output, and hidden units, and their connectivity, and also learning rate (alpha. Yes, forward kinematics are easy. It defines a function which maps the robot configuration $$R_1 \\in SO(2), R_2 \\in SO(2)$$ to the end-effector position $$e \\in R^2$$. Normally, the forward kinematics is a closed-form function. 4. The Inverse Kinematics. The inverse kinematics asks a question: I want to move the end-effector to a target position. Read more.. venom x22gt 250cc for salegreen bay police calls by addresshow much is a 30day supply of zolpidemsql server drop login if existshow to remove bios administrator password in hp laptop\n\n• Learn more about inverse kinematics, forward dynamics Robotics System Toolbox. Skip to content. ... I want to do forward dynamics but before that I got struck in inverse kinematics for 4 dof. My code is given below: preach = [0.2, 0.2, 0.3]; ... Find the treasures in MATLAB Central and discover how the community can help you! Start Hunting!\n• 2022. 8. 21. · Inverse Kinematics Matlab Code Codes and Scripts Downloads Free Forward kinematics problem is straightforward and there is no complexity deriving the equations For\n• robotic arm using MATLAB tool is provided. The flow chart below explains the process starting with creating the robot, controlling the robot with input joint angles, forward kinematics and inverse kinematics functions used for the implementation. Link Creation MATLAB 2014B Initialization of PETER CORKE ROBOTIC TOOL BOX FEATURE\n• 2022. 9. 7. · Link Creation MATLAB 2014B Initialization of PETER CORKE ROBOTIC TOOL BOX FEATURE Inverse Kinematics is the inverse - using the end-effector desired coordinates ," ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.83718204,"math_prob":0.9405838,"size":126950,"snap":"2022-40-2023-06","text_gpt3_token_len":29460,"char_repetition_ratio":0.21060924,"word_repetition_ratio":0.8044226,"special_character_ratio":0.21317841,"punctuation_ratio":0.12833685,"nsfw_num_words":5,"has_unicode_error":false,"math_prob_llama3":0.9874499,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-28T03:54:09Z\",\"WARC-Record-ID\":\"<urn:uuid:b01583ea-f584-42ba-a5bf-5ed5152b3708>\",\"Content-Length\":\"165389\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a2bd0d49-ff1b-49b3-b26e-c41993c6a322>\",\"WARC-Concurrent-To\":\"<urn:uuid:ecfe56f6-be64-440f-8110-a22659f0d74a>\",\"WARC-IP-Address\":\"104.21.28.233\",\"WARC-Target-URI\":\"https://aip.seekingsugardaddy.de/matlab-code-for-forward-and-inverse-kinematics.html\",\"WARC-Payload-Digest\":\"sha1:T7TI3JNQ56O4GJM3LGBDO2WKRX47YQUK\",\"WARC-Block-Digest\":\"sha1:Q3AFMCE6ODZDHBMHDBYFJOKLIIC4I3YS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030335059.43_warc_CC-MAIN-20220928020513-20220928050513-00722.warc.gz\"}"}
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0182662	[ "Browse Subject Areas\n?\n\nClick through the PLOS taxonomy to find articles in your field.\n\n# Reply & Supply: Efficient crowdsourcing when workers do more than answer questions\n\n• Thomas C. McAndrew,\n\nRoles Formal analysis, Investigation, Methodology, Validation, Visualization, Writing – review & editing\n\nAffiliation Mathematics & Statistics, Vermont Complex Systems Center, University of Vermont, Burlington, Vermont, United States of America\n\n• Elizaveta A. Guseva,\n\nRoles Data curation, Investigation, Validation, Visualization\n\nAffiliation Mathematics & Statistics, Vermont Complex Systems Center, University of Vermont, Burlington, Vermont, United States of America\n\n• James P. Bagrow\n\nRoles Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing\n\[email protected]\n\nAffiliation Mathematics & Statistics, Vermont Complex Systems Center, University of Vermont, Burlington, Vermont, United States of America\n\n# Reply & Supply: Efficient crowdsourcing when workers do more than answer questions\n\n• Thomas C. McAndrew,\n• Elizaveta A. Guseva,\n• James P. Bagrow", null, "x\n\n## Abstract\n\nCrowdsourcing works by distributing many small tasks to large numbers of workers, yet the true potential of crowdsourcing lies in workers doing more than performing simple tasks—they can apply their experience and creativity to provide new and unexpected information to the crowdsourcer. One such case is when workers not only answer a crowdsourcer’s questions but also contribute new questions for subsequent crowd analysis, leading to a growing set of questions. This growth creates an inherent bias for early questions since a question introduced earlier by a worker can be answered by more subsequent workers than a question introduced later. Here we study how to perform efficient crowdsourcing with such growing question sets. By modeling question sets as networks of interrelated questions, we introduce algorithms to help curtail the growth bias by efficiently distributing workers between exploring new questions and addressing current questions. Experiments and simulations demonstrate that these algorithms can efficiently explore an unbounded set of questions without losing confidence in crowd answers.\n\n## 1 Introduction\n\nCrowdsourcing has emerged as a powerful new paradigm for accomplishing work by using modern communications technology to direct large numbers of people who are available to complete tasks (workers) to others who need large amounts of work to be completed (crowdsourcers) . Crowdsourcing often focuses on tasks that are easy for humans to solve, but may be difficult for a computer. For example, parsing human written text can be a difficult task and optical character recognition systems may be unable to identify all scanned words . To address this, the reCAPTCHA system takes scanned images of text which were difficult for computers to recognize and hands them off to Internet workers for recognition. By having many people individually solve quick and easy tasks, reCAPTCHA is able over time to transcribe massive quantities of text. Crowdsourcing in general is especially important as a new vehicle for addressing problems of social good .\n\nDeciding on an optimal way to assign particular tasks to workers, and in what order, remains an active area of research. For many problems, multiple worker responses to a task must be aggregated to determine a final answer but often, a budget limits the total crowdsourcing resources available , either due to financial limits when workers are compensated or time constraints where the speed or size of the crowd limits the number of tasks to be performed or questions to be answered. Most previous work on optimal task assignment takes the form of a Markov Decision Process (MDP) [12, 16]. MDP provides a rigorous mathematical framework to test policies for allocating tasks to workers . Using MDP and other strategies, such as Thompson sampling , methods have been introduced to efficiently aggregate responses from workers, including consideration of which workers are most likely to be well suited for a given question based on their past performance on related questions .\n\nHowever, to the best of our knowledge, past research has been limited to the case where a fixed set of tasks need to be accomplished, and the response of a worker to a task is only ever to complete the assigned task. In contrast, consider a crowdsourcing problem where workers are able to do more than perform tasks—they may be allowed to propose new questions as well as answers to a given question. The truest expression of crowdsourcing must incorporate the intuition and experience of workers, who are potentially capable of providing the crowdsourcer with far more actionable information for many problem domains . While MDP made significant contributions to the design of question assignment algorithms, when the question set is growing due to the crowd, MDP does not naturally account for the hidden state transitions needed to represent newly contributed questions. The lack of research on algorithms accounting for growing question sets reveals a gap in our abilities to efficiently assign questions to workers.\n\nTo this end, we study a type of crowdsourcing problem we term Reply & Supply. As workers answer a given question (Reply), they are given the opportunity to propose a related question (Supply). Example applications of Reply & Supply include:\n\n• Exploring social networks (“Are Alice and Bob friends?” “Who else is friends with Alice?” “With Bob?”)\n• Product recommendations (“Have you bought a camera and laptop together?” “What else would someone buy when buying a camera?”)\n• Image classification (“Does this photo contain a horse and a mountain?” “What else does it contain?”)\n• Causal attribution (“Do you think ‘hot weather’ causes ‘violent crime’?” “What causes ‘violent crime’?”)\n• Health informatics: Crowdsourcing patient reports to find connections between co-occurring symptoms, new drug interactions, etc. (“Do you suffer from symptom X?” “What other symptoms do you have?” “Do you take drug Y?” “What other drugs do you take?”)\n\nIn all these examples, new questions can be built by combining crowd-suggested responses with the components of the original question, leading to the creation of a network structure of interrelated questions. To explore a social network, for example, if a worker responds that Alice and Bob are friends (Reply) and also proposes that Alice and Carol are friends (Supply), then a new question (“Are Alice and Carol friends?”) is formed that other workers can consider and that links to other questions related to Alice. Further, we will show that this network representation naturally generalizes to non-network question sets, and the methods we develop here are fully applicable to both question sets and question nets.\n\nQuestion networks can be studied with tools from network science that consider the statistical properties governing how theoretical and real-world networks grow and behave . One property, the scale-free or heavy-tailed degree distribution , where most nodes in the network have low degree but some very high-degree nodes do exist, holds in many real-world networks. How a scale-free network grows over time introduces biases (‘first-mover advantage’) that are also inherent in a growing crowdsourced experiment.\n\nIn brief, this manuscript makes the following contributions:\n\n1. The introduction of a growing network of linked questions with an accompanying theoretical analysis;\n2. The use of Thompson sampling to develop crowd-steering algorithms that enable efficient exploration of an evolving set of tasks or questions without losing confidence in answers;\n3. Simulations and real-world crowdsourcing experiments that validate the efficiency and, to some extent, the accuracy of the crowdsourcing performed under the crowd-steering algorithm.\n\nThe rest of this paper is organized as follows: Section 2 poses the generic crowdsourcing problem we focus on, analyzes a simple graphical model of how a growing question net is built by a crowd, and uses this model to motivate methods for efficiently assigning questions to workers as the question net grows. Section 3 describes experiments and evaluation metrics to test the proposed theory and methods with both simulated and real-world crowdsourcing tasks. Section 4 presents the results of these experiments and Sec. 5 concludes with a discussion of these results and future work.\n\n## 2 Methods\n\nHere we introduce a graphical model of a growing question network where questions consider the presence or absence of a relationship between two items (Sec. 2.1). We study the network’s properties under a null condition where the crowdsourcer assigns questions to workers randomly without use of a “steering” algorithm to provide guidance (Sec. 2.2). We then use these properties to develop a probability matching algorithm which provides said guidance to the crowdsourcer (Sec. 2.3).\n\n### 2.1 Crowdsourcing growing question networks\n\nWe model a growing set of questions (or tasks) as a graphs where nodes are items and edges or links represent questions relating pairs of items. A question network G = (V, E) is composed of a set of nodes V and a set of edges E, where \|V\| = N and \|E\| = M. Edge attributes record the answers given by workers, i.e., associated with each edge is a categorical variable storing the counts of worker responses. Those workers may also propose new questions (i.e., new combinations of new or existing items), leading to new nodes and edges. This network model also accommodates non-network question sets, for example by considering each question as a disjoint edge.\n\nAs an example of such a network, consider a synonym proposal task (SPT) where workers are asked if two words u and v are synonyms. The question is the link (u, v) between two items u and v representing those words. After replying to the question, the worker may also supply another word w which is a synonym for u, for v, or for both words. This grows the question network by introducing new questions linking items (u, w), or items (v, w), or both (u, w) and (v, w). The degree ki of item i counts the number of questions linking item i to other items.\n\nWe focus on cases, such as the SPT, where questions have binary answers, e.g, when workers are asked whether or not a link between two items should exist. Edge attributes on links capture the number of ‘yes’ and ‘no’ answers given by workers. However, this graph representation is flexible enough to allow edge attributes to contain any number of dimensions and there are no restrictions imposed on how workers propose questions. Moreover, this graphical model is capable of representing growing question sets without such relations, for example, a collection of N disjoint questions always containing the response items ‘True’ and ‘False’ only may be a two node, N multi-edge graph. While not a particularly meaningful representation, it demonstrates that the algorithms we develop are applicable to general crowdsourcing tasks without modification. Lastly, one can also extend this model to non-binary, multiple choice questions in several ways, including representing questions as hyperedges in a hypergraph.\n\n### 2.2 Null model\n\nWe propose a generative null model for a growing question network [39, 40]. Beginning from a network with one question, a crowdsourcer randomly chooses existing questions to send to workers also chosen at random. Those workers answer the questions and then with some probability also propose new questions. We study the properties of the network under these assumptions to motivate the development of a probability matching algorithm that can allow a crowdsourcer to efficiently explore the growing question network.\n\nThe network begins (at time t = 0) with two nodes and one undirected link connecting those nodes, representing a single question considering two items. Under the null model, every link (i, j) has an associated innovation rate ρij. The innovation rate for (i, j) defines the probability a random worker will introduce a new question into the network when presented with question (i, j). If she chooses to innovate, the new question may relate to either or both of the items i and j of the original question the worker was given.\n\nSpecifically, suppose a random worker is given question (u, v) relating items u and v. Under the null model:\n\n1. The worker answers question (u, v) with probability 1.\n2. The worker proposes a new item w to study with probability ρuv:\n1. w is linked to one of the items of the original question with probability γuv. A single new question, either (u, w) or (v, w) chosen uniformly at random, is introduced;\n2. otherwise, w links to both items of the original question with probability 1 − γuv. Two new questions, (u, w) and (v, w), are introduced.\n3. Repeat from (1) with another sampled question and worker until termination.\n\nThis model is tractable but quite basic and does not consider many potential details. For example, it assumes that while questions may have different innovation rates, workers do not. However, for sufficiently large numbers of workers, the average response is always going to be the primary concern, particularly in most crowdsourcing tasks which need to aggregate multiple worker responses to decide upon a final answer for a question. If it is necessary, a crowdsourcer interested in accounting for variation between workers can propose a statistical model for their features, and then use statistical inference to estimate these worker parameters during crowdsourcing (see also the Discussion).\n\nWe now prove several average properties of this null model. Studying the characteristics of the randomly growing, uncontrolled network informs policies that a crowdsourcer may use to manipulate the network (such as the algorithm we develop in Sec. 2.3). Many of these results are also informative for non-network growing question sets.\n\nThe first theorem describes question growth in the random uncontrolled network.\n\nTheorem 1 (Rate of question growth). The total number of links M(t) as a function of time t is, on average, M(t) = ηt + 1 where η = 〈ρ〉 (2 − 〈γ〉) is termed the exploration rate.\n\nProof. For the network to grow, a worker must suggest an additional question, which occurs with probability on average 〈ρ〉 (average of ρij). Once the worker commits to a suggestion, one question is added with probability on average 〈γ〉 or two questions are added with probability on average 1 − 〈γ〉. Combining these two possibilities, the total number of questions grows on average over one timestep according to", null, "with initial condition M(0) = 1 representing the single seed question of the network. Making a continuum approximation, this difference equation becomes M′(t) = 〈ρ〉(2 − 〈γ〉), which has solution", null, "(1) where the exploration rate η ≡ 〈ρ〉(2 − 〈γ〉) plays an important role in the overall network growth.\n\nThe number of links grows linearly with a rate η that combines the average rates 〈ρ〉 and 〈γ〉. Intuitively, the network grows faster if questions are more likely to be innovative (larger 〈ρ〉), and/or the worker is able to suggest a question for both items at the same time (smaller 〈γ〉).\n\nThe solution to the rate equation for question growth can be used to compute the mean number of worker answers per question:\n\nTheorem 2 (Mean answer density). The mean answer density (number of answers per question) 〈A〉 → 1/η as t → ∞.\n\nProof. The mean number of answers per question is", null, "(2) At every time step a question in the network accumulates a single answer from a worker. The denominator of Eq (2) is the solution Eq (1), and so the average density of answers per question is", null, "as t → ∞.\n\nThe mean answer density correlates with the overall uncertainty in the crowdsourcing since there is generally more certainty (but not necessarily correctness) in crowd responses when more workers on average have independently answered questions. Controlling the answer density, and therefore the certainty, now boils down to controlling the exploration rate η. The mean answer density’s dependence on η also encapsulates an ‘exploration-exploitation’ tradeoff: lower η leads to higher answer density, but at the cost of less exploration in the network; higher η increases the exploration but lowers answer density and makes more uncertainty in the network. In this null model, the crowdsourcer does not make choices that can exploit this, but tuning between these poles is a key component of the probability matching algorithm we introduce in Sec. 2.3.\n\nThe previous two theorems govern global properties of random question networks. We now turn to properties of individual items within the network to explain the unequal distribution of questions attached to items:\n\nTheorem 3 (Rich-get-richer mechanism). A node i entering the network at time ti will gain degree, on average, as", null, ", where", null, "is the Heaviside function.\n\nProof. An existing item i only gains a question when the crowdsourcer chooses a question attached to i and the worker answering that question proposes a new question involving i. A question (i, j) associated with item i is selected by the crowdsourcer with probability ki(t)/M(t), where ki(t) is the degree (number of questions) of i at time t. After the worker answers question (i, j) she must innovate (probability 〈ρ〉) with an item w that is not already a neighbor of i (and wi) and the new question must be (w, i) (probability 〈γ〉/2) or it must be two questions (w, i) and (w, j) (probability 1 − 〈γ〉). If the worker introduces question (w, j) only (probability 〈γ〉/2) then i does not gain a new question and so this possibility does not contribute to ki(t). Combining these possibilities together, ki(t) evolves on average according to", null, "(3) We approximate and simplify this difference equation as before:", null, "(4) where ki(ti) is the initial degree when item i was introduced at some time ti. Solving Eq (4) results in", null, "(5)\n\nWe see from this derivation that the rich-get-richer, preferential attachment mechanism is automatic when questions are chosen at random: an item i is more likely to appear in a sampled question the more questions it has, and therefore items with more questions are more likely to gain further questions than other items. Further, the degree of an item depends critically on two quantities. The first, the ratio of exploration rate η to 〈ρ〉, equally affects all items in the network. The second, the time of entry ti, dampens the growth of items that enter the network late and increases the growth of earlier items. This phenomena is often called the ‘first mover’s advantage’, and in the context of crowdsourcing a growing network, items entered earlier in the system accrue more questions than later items.\n\nUsing the local estimate of item degree to derive the global degree distribution of the network, we find:\n\nTheorem 4 (Degree Distribution). The degree distribution of the growing question network", null, "(6) as t → ∞.\n\nProof. Following , begin with the cumulative probability distribution of item i’s degree:", null, "(7) Meanwhile, the entry times ti of items into the network follow a distribution proportional to 〈ρ〉 uniformly through time:", null, "and, after normalizing, we discover the time of entry follows a uniform distribution. Referring back to Eq (7) and using the integral definition of a cumulative distribution,", null, "(8) Lastly, differentiating Eq (8) with respect to k gives the degree distribution:", null, "(9) as t → ∞.\n\nOur theoretical analysis is supported by simulations of growing question networks (Fig 1). We conducted 5,000 simulations and recorded the degree distribution P(k) and degree k of items across different values of exploration rate η and time of item entry ti. Fig 1(a) validates the slower rate of question accrual for late arriving items, and Fig 1(b) shows the degree distribution’s match to theory by the collapse of each curve over multiple values of η.\n\nFig 1. Agreement of theoretical predictions of network growth under the null model with simulations for several different choices of parameters.\n\nhttps://doi.org/10.1371/journal.pone.0182662.g001\n\n### 2.3 Probability matching algorithm for growing question sets and nets\n\nMost algorithms for steering workers towards questions choose questions by defining a metric that captures important characteristics in the system. For example, algorithms stressing accuracy often build metrics that reward higher numbers of answers for questions, achieving a p-value below a pre-defined threshold, or diminishing the variance of questions.\n\nThe framework of probability matching, specifically Thompson sampling (TS), is one of the most powerful ways to efficiently choose from a set of dynamic “options” when choices must be made with limited information. Unlike greedy algorithms, one of the strengths of TS is that its stochastic nature prevents choosing locally optimal questions only.\n\nTo Thompson sample from a set of options, one assumes a random variable X which follows a distribution φ(xθi(t)), where θi(t) is a set of parameters specific to i at time t. One draws an xi(t) for each option i and selects the option j with the smallest x (or largest x, depending on what x represents), j = arg mini xi (t). After option j is played (in our case, the worker’s answer is received), the parameters for option j are updated. Often x is a Bernoulli random variable and it is natural for φ to be the conjugate Beta distribution with parameters α, β which are updated depending on whether x = 0 or x = 1.\n\nFor specific problems, TS depends on an appropriate reward function. In the context of crowdsourcing, one generally cannot verify the accuracy of crowd answers, so the best choice is to reward certainty or consensus. If the crowd is consistent in their responses for a given question, then that implies the question is being answered as well as possible under current conditions. Thus, in contrast to the Bernoulli Bandit problems typically studied with TS, we do not want to reward ‘yes’ answers over ‘no’ answers only. Instead, we want to reward choices that lower the crowdsourcer’s measure of uncertainty for questions.\n\nA natural measure of uncertainty for a categorical random variable is the Shannon entropy. However, efficiency is also important to a crowdsourcer. A yes/no question that has 200 responses which are evenly split is very different than a question with 2 responses which is also evenly split, despite having the same entropy. Generally, the crowdsourcer would prefer to assign a worker to the latter question, as there is greater hope of lowering its uncertainty.\n\nThis argument guides us to choosing a metric involving both the total number of answers to a question and how evenly distributed those answers were over the categories of that question. We introduce a metric called link bias (d) that is sensitive to the uncertainty of a question, but unlike entropy, also accounts for the total number of answers. To begin, the multinomial distribution, with C − 1 parameters, naturally models the distribution of a categorical question’s total number of answers T across C possible answers, and the Dirichlet distribution, conjugate to the multinomial, can estimate the parameters of the multinomial. Since we expect no available prior information, a non-informative prior can be used. In the case of two categories, which we focus on, the Dirichlet distribution reduces to the Beta distribution (B(α, β)).\n\nTo define question uncertainty, we need a reference point. At a question’s peak uncertainty, workers have answered evenly among the question’s (C) categories causing an equal proportion of answers per category. In our binary case (C = 2), this corresponds to a proportion of 1/C = 1/2. The link bias d transforms the proportion of answers for question (i, j) to the distance from maximum uncertainty with d ≡ \|2 − pij(1)\|, where pij(1) is the fraction of ‘1’ or ‘yes’ or ‘true’ answers. When pijB(α, β), the probability density of d becomes", null, "(10) where for simplicity the dependence of α, β on (i, j) has been suppressed. Intuitively, a low link bias (d ≈ 0) occurs when the crowd is evenly split among possible answers, while a high link bias (at most d = 1/2) tells us the crowd converged on a single category.\n\nHowever, the link bias alone may not sufficiently steer the crowdsourcer to choose questions with a lower number of answers. If needed, we can combine a preference for sampling questions with few answers, with a preference for questions that are uncertain, by weighting Eq (10) by the current number of answers to define a new ‘weighted phi’ metric φN:", null, "(11) where Nij is the total number of answers to question (i, j) at the time of sampling.\n\nThompson sampling of questions via φ or via φN defines the two probability matching algorithms we propose. These algorithms handle growing networks of questions automatically and are fully applicable to problems without graphical relations between questions. We will conduct experiments on growing question networks testing the relative performance of both algorithms, and comparing them to other null or control baseline strategies, such as randomly choosing questions.\n\n## 3 Experiments\n\nWe conducted two experiments to test the theoretical analysis and the sampling methods. For the first experiment, we simulated crowdsourcing of a growing question network with a commonly used benchmarking dataset by superimposing two distinct network structures onto a previously conducted crowdsourcing task , where questions have been time-ordered to mimic a growing question network, and used this to test three different question sampling algorithms. For the second experiment, we conducted real-world crowdsourcing using the Mechanical Turk crowdsourcing platform .\n\n### 3.1 Experiment 1\n\nTo determine the effectiveness of choosing questions based on link bias, we first performed a five-armed experiment using the Recognizing Textual Entailment (RTE) dataset , a set of 8,000 binary answers (0 or 1) to 800 unique questions.\n\nFor simulating question growth, we superimposed graph structures onto the question set to link the 800 questions together. As mentioned in the introduction, many crowdsourcing problems naturally possess a network structure; here we imposed a structure on the RTE dataset only because it allows us to use the same benchmark dataset that many other researchers have studied. We built 5,000 Erdős-Rényi (ER) and Barabási-Albert (BA) networks . These two options represent two extremes of network structure, and were chosen to test question sampling algorithms over different classes of networks. Briefly, an ER network (specifically the G(n, m) formulation) starts with a set of N nodes and 0 links; a pre-specified number of links M are placed in the network choosing randomly without replacement from all possible", null, "pairs of nodes. In contrast, the BA network starts with 2 nodes joined by a single link, nodes are added one at a time until all N nodes are placed, and each new node attaches to m0 existing nodes in the network. New nodes attach to an existing node i with probability ki/∑nN kn, a mechanism that is often called preferential attachment.\n\nFor simulation purposes, each ER network realization must contain exactly 400 nodes, 800 links, and be connected. BA networks are connected by design; we still enforced the same number of nodes and links as the ER networks. Each simulated crowdsourcing was initialized with one question (a link in the network connecting two corresponding item) chosen at random from the underlying network. During the simulated crowdsourcing, workers answer a question with a 1 with probability equal to the proportion of 1’s observed in the original RTE dataset for that question, otherwise the worker answers 0. Next, and with probability 〈ρ〉, a new node (item) is introduced into the network by selecting randomly from the unseen neighbors of either i or j within that simulation’s graph. (This differs slightly from the analytic null model because there is no 〈γ〉. Instead, two links are formed automatically if the newly introduced item is linked to both i and j in the superimposed network.) If there are no new items to add corresponding to the selected question, this iteration is undone and the algorithm continues. All simulations were run with 〈ρ〉 = 0.20 for 6,000 time steps.\n\nSimulations were performed independently for each of five arms. The condition of each arm governs how questions are selected by the simulated crowdsourcer:\n\n1. Random: The first arm of the experiment had a condition where questions (links) were chosen randomly from the pool of already visited links.\n2. Looping: The second arm used a looping question sampling algorithm. The first link that entered the system is answered by a worker, then the second link in the system is given to a worker, then the third link and so on. When the algorithm reaches the most recent link within the system it starts again from the oldest link.\n3. Binomial sampling: This strategy selects questions (i, j) based on p-values for a two-sided binomial test that the proportion pij(1) is significantly different from 1/2. If the p-value of this exact test is small, then it is likely the crowd has already reach consensus on that question and it is not worthwhile to sample that question further. The sampled question was chosen randomly from the set of questions which have a p-value >0.2 and which have received fewer than 10 answers (at the time of sampling)\n4. Thompson sampling with φ: The fourth arm uses Thompson sampling to select links based on link bias (φ).\n5. Thompson sampling with φN: As in the fourth arm but links are Thompson sampled with φN instead of φ.\n\nThis experiment can demonstrate the strengths and weaknesses of selecting links based on these different sampling strategies, and, because it is synthetic, many trials can be conducted while avoiding the costs associated with a new crowdsourcing experiment. Results of Experiment 1 are presented in Sec. 4.\n\n### 3.2 Experiment 2: Synonym proposal task\n\nThis three-armed experiment created new question networks grown from a single seed question (link), and evaluated the φN-based Thompson sampling and Binomial sampling versus Random sampling. We paid US-based workers on Amazon’s Mechanical Turk crowdsourcing platform [2, 42] to participate in a synonym validation and proposal experiment. Synonymy proposal is a good test application for the question sampling algorithms we study because workers can easily understand the question and are capable of proposing new questions (by suggesting new synonyms). Of course, data on synonymy relations are available in lexical resources such as WordNet , which we used in this specific task for assessing the accuracy of proposed synonyms (see below), but our primary goal with this experiment is not crowdsourcing a new thesaurus but testing the different question sampling strategies.\n\nIn Experiment 2, each worker completes synonymy tasks at a compensation of \\$0.08 USD per task. Each synonymy task gives a pair of words to a worker and asks whether or not they are synonyms. After a worker answer either ‘yes’ or ‘no’, we allow the worker to suggest additional synonyms for each word of the given pair, or a single synonym associated with the combined word pair. A screenshot of the web form used for this task is shown in Fig 2.\n\nFig 2. Screenshots of the Mechanical Turk web interface for the synonymy proposal task (Experiment 2).\n\nAfter replying ‘yes’ or ‘no’ (a), the form expands for the worker to supply new potential synonym pairs (b).\n\nhttps://doi.org/10.1371/journal.pone.0182662.g002\n\nThree independent crowdsource networks were built, one for each arm. All three networks began with the same seed question (the word pair patriotic, person). All other word pairs were proposed by the crowd. The question sampling algorithms draw from all previous worker answers and suggested questions within their respective arms to deliver a question to the next queued worker. The first arm (Random sampling) chooses links using the same methodology as the random arm from Experiment 1, which also closely matches the null model we studied (Sec. 2.2). The second arm (Binomial sampling) selects links according to the Binomial sampling algorithm introduced in Experiment 1. Lastly, the third arm (Thompson sampling) selects links according to Thompson sampling of φN. Results for Experiment 2 are presented in Sec. 4.\n\n### 3.3 Evaluation metrics\n\nFor the first experiment, we measure five attributes across the simulated crowdsourcings to compare the different question sampling algorithms. At each time step t, for each simulated network we record network properties fnodes, the fraction of items, and fedges, the fraction of questions:", null, "(12) where V(t) is the set of items at time t, V(∞) is the set of all items at the end of the experiment, E(t) is the set of questions at time t, and E(∞) is the set of all questions at the end of the experiment.\n\nNext, we record the entropy S and link bias d, averaged over all currently visible questions, to quantify uncertainty in the network:", null, "(13) and", null, "(14) where pij(x) is the (Laplace-smoothed) fraction of binary answers of x for question (i, j) (at time t).\n\nThe final evaluation metric, mean answer density, measures how many answers are given per question in a particular network (see also Thm. 2):", null, "(15) where the Nij(x) represents the count of answer x for question (i, j) (at time t).\n\n#### Validating proposed synonyms.\n\nA factor that motivated us to choose the synonym proposal task as our crowdsourcing example is that synonym proposal can, in principle, be validated. Therefore, we will measure both crowd consensus (measured by 〈S〉 or 〈d〉) and, as best we can, if Experiment 2’s crowdsourcing algorithms lead to different quality rates of synonyms—are we trading off quality for efficiency?\n\nHowever, measuring synonymy from natural language text is challenging. In principle, all that is needed is a complete thesaurus, meaning a complete lookup table of all words and all their synonyms, perhaps with weights denoting the degree of relatedness between a word and its synonym and accounting for all possible contexts in which those words may appear. However, without such an exhaustive resource, it can be challenging to determine synonyms, especially when workers may introduce typos, may propose different forms (runs, running, ran) of the same root lemma (run), or they may propose a multi-word phrase (MWP) which may have a synonymous meaning but where such a meaning is difficult to determine computationally.\n\nGiven the challenges of measuring synonymy, we applied two measures to the synonym word pairs (u, v) proposed by workers during the crowdsourcing experiments:\n\n1. Shared WordNet lemmas The first measure starts by determining for each word w the set of all forms of all its synonym lemmas as encoded in WordNet :", null, "(16) where synsets(w) is the set of all synonym forms stored in WordNet (we merge sets across parts-of-speech and take synsets(w) = ∅ if w is not present in WordNet). We then say that the two words u and v are synonyms if they share at least one lemma, i.e. that \|L(u) ∩ L(v)\| > 0, otherwise they are not synonyms. This is a relatively strict test, and fails to account for many MWPs and natural language concerns such as misspellings, so we expect many (u, v) pairs that workers deem synonyms to be missed by this measure and therefore the actual proportion of synonymous word pairs may be much higher.\n2. Word vector similarity The second measure we employ is based on the meanings encoded by the “word2vec” word embedding algorithm . Word2vec uses a neural network model to learn low-dimensional vector representations of words based on their contextual co-occurrence patterns over a very large text corpus. Supported by the distributional hypothesis , the contexts encoded in these vectors are then considered to capture to some extent the meanings and relationships of these words such as, for example, analogous relationships (Berlin is to Germany as Paris is to France). Given a pre-trained set of 300-dimensional vectors trained on a 100B word corpus taken from Google News, we define the similarity between two words (or MWPs, if the MWPs are present in the vector data) u and v as their cosine similarity:", null, "(17) where w represents the associated word vector for word or MWP w. If either u or v is not present in the word2vec vector data, we exclude that pair from our analysis (this occurred in Experiment 2 for approximately 17.9% of crowd-proposed word pairs for the Random sampling experiment, 19.8% for Binomial sampling, and 10.9% for Thompson sampling).\n\n## 4 Results\n\n### Experiment 1\n\nFig 3 displays the five evaluation metrics associated with Experiment 1, averaged over the 5,000 ER and BA networks. (For simulated Binomial sampling only, note that we required questions to have fewer than 30 answers at the time of sampling, not 10 as discussed previously, to provide more simulation statistics.) The Binomial sampling and φN Weighted Thompson sampling algorithms outperformed all others in exploration metrics across ER and BA networks. Both methods explored more of the network, and faster, than other methods, as evidenced by 〈fedges〉 and 〈fnodes〉. Weighted Thompson sampling performed best at minimizing the uncertainty of answers, as measured by lower entropy 〈S〉 and higher link bias 〈d〉. In contrast, Binomial and Thompson sampling φ were inconsistent for these two metrics. Lastly, Binomial and φN Weighted Thompson sampling also required fewer answers than other algorithms (lower 〈A〉).\n\nFig 3. Experiment 1’s evaluation metrics for five different question sampling algorithms.\n\nhttps://doi.org/10.1371/journal.pone.0182662.g003\n\nBinomial sampling slightly outperformed φN Weighted Thompson sampling in many metrics. However, Binomial sampling has a distinct drawback: the thresholds used to sample questions may lead to a situation where no questions meet its sampling criteria. This is visible in the simulation curves, which are quite noisy due to individual simulations which terminated too early. Of course, this can be fixed by any of several means, such as falling back to random sampling when no questions meet the criteria, or tuning the cutoffs used in Binomial sampling. But Thompson sampling avoids these complexities entirely.\n\nThe overall performance of Binomial sampling and φN-based Thompson sampling in simulated crowdsourcing nominates them as candidate algorithms for Experiment 2’s real crowdsourcing.\n\n### Experiment 2\n\nFig 4 shows the constructed networks for each arm of the Synonym Proposal Task (the task is described in Fig 2). Qualitatively, all three networks appeared similar. Quantitatively, (Table 1) both Binomial and Thompson sampling were able to explore more of the network (discovering more items and questions) than Random sampling with more efficiency (lower mean number of answers 〈A〉). The explored networks appeared similar by a number of network metrics, although the network generated via Binomial sampling has a lower average degree and higher average shortest path length. Lastly, Binomial and Thompson sampling were comparable to Random sampling in crowd consensus on individual answers, having similar levels of entropy and link bias. Both of these statistics measured how skewed the worker answers were in favor of ‘yes, they are synonyms’ or ‘no, they are not synonyms’.\n\nFig 4. Comparison of question networks for the synonymy proposal task under random sampling, binomial sampling, and φN Thompson sampling.\n\nhttps://doi.org/10.1371/journal.pone.0182662.g004\n\nTable 1. Summary statistics for the three arms of Experiment 2.\n\nBoth Binomial and Thompson sampling are more efficient than Random sampling (lower 〈A〉) without losing the crowd’s average consensus on answers, measured by 〈S〉 and 〈d〉.\n\nhttps://doi.org/10.1371/journal.pone.0182662.t001\n\nTaken together, both Binomial and Thompson sampling maintained a comparable level of certainty (measured by consensus or consistency in worker responses) in the network with fewer answers needed on average than Random sampling.\n\nTo further understand the answer density of the different sampling methods, we computed the distribution of the number of answers Nij to question (i, j) in Fig 5. Here Random sampling clearly separated from the other two sampling strategies, and Random sampling ended with more questions with more answers than the other sampling strategies. We also note that all three arms finished with many questions with few answers: approximately 50% of questions at the end of the experiment had a single answer. We discuss this further in Sec. 5.\n\nFig 5. The distributions of the total number of answers per question at the end of crowdsourcing, for each arm of Experiment 2.\n\nThe efficiency of Binomial and Thompson sampling compared with Random sampling is clear. In all arms, approximately 50% of proposed questions are answered only once.\n\nhttps://doi.org/10.1371/journal.pone.0182662.g005\n\nNext, we examined the synonym “quality” of the SPTs, using the synonymy measures introduced in Sec. 3.3. We limited these calculations to proposed word pairs examined by at least three crowd workers to ensure sufficient answers from the crowd. Fig 6(a) shows the proportion of word pairs that share at least one WordNet lemma: Both Binomial and Thompson sampling have slightly higher proportions than Random sampling, at over 12% compared with approximately 11%. This indicates that quality was not lost when using a more efficient sampling strategy. Of course, 11–12% of word pairs sharing a lemma seems low, but recall that shared lemmas is a very strict measure that is likely to miss many synonymous word pairs and so we do not conclude that the majority of the crowd answers are “wrong.” Furthermore, to better understand the shared lemma proportion, we constructed a randomized control by shuffling the word pairs (preserving the total frequencies of individual words) and re-measured the proportion of shared lemmas. We found a significant drop in the proportion to approximately 1% (the error bars on these proportions are shown in Fig 6(a) but are quite small).\n\nFig 6. Measures of synonymy for Experiment 2’s crowdsourced word pairs.\n\nSynonymy for proposed word pairs was estimated using (a) shared WordNet lemmas, (b) cosine similarity between word2vec word embedding vectors (see Sec. 3.3). Approximately 11–12% of crowdsourced word pairs share one or more WordNet lemmas (a strict measure of synonymy), and Binomial and Thompson sampling achieved slightly higher rates than Random sampling. As a control, the word pairs proposed by the crowd were randomized, and the proportion of word pairs with shared lemmas dropped significantly. Meanwhile, regardless of sampling algorithm, the word pairs proposed by the crowd also had significantly higher word vector similarity when at least one member of the crowd agreed that the pair were synonymous (nij(1) > 0), as opposed to no members agreeing the pair were synonymous (nij(1) = 0). This further underscores the estimated quality of the proposed questions and answers and that Binomial and Thompson sampling methods do not appear to trade off quality for efficiency. (To avoid ambiguous answers, we considered word pairs that received at least three answers from workers in these calculations, and panel (a) considers those word pairs with nij(1) > 0.)\n\nhttps://doi.org/10.1371/journal.pone.0182662.g006\n\nLikewise, Fig 6(b) shows word vector similarities for the three sampling methods, decomposed into word pairs where at least one worker agreed they were synonyms versus no workers agreeing they were synonyms. The crowd-proposed word pairs flagged as synonyms had similarities significantly higher than those not flagged as synonyms. There is a small drop in vector similarity for Binomial and Thompson sampling compared with Random sampling, likely balancing out the small increase in WordNet shared lemma proportion shown in Fig 6(a). We conclude that overall there is no loss in quality, at least as indicated by these measures, when using more efficient sampling algorithms.\n\nTaken together, while we only have one crowdsourcing realization for each arm, it is reasonable to conclude from Experiment 2 that both Binomial sampling and Thompson sampling achieved much higher rates of exploration (more items) and greater efficiency (fewer answers per question) than Random sampling without losing confidence or accuracy in question responses.\n\n## 5 Discussion\n\nWe studied the problem of efficient assignment of crowdsourcing tasks to workers when those workers are also able to propose tasks themselves. Using workers to contribute new tasks and not merely perform predetermined tasks helps unlock the true potential of crowdsourcing. We formulated a growing question network model for this problem, prove theoretical properties of this system, and developed and validated sampling algorithms that can guide workers to grow the network efficiently, while only sacrificing at most minimal confidence in their responses.\n\nModeling the evolution of the uncontrolled question network teaches us how to better design crowdsourcing policies. For example, by monitoring the innovation rate (ρ) and exploration rate (η) of the growing question network, a crowdsourcer may be able to better and more efficiently control the question network as it grows. At the same time, the rich-get-richer growth of items (older items are attached to a larger fraction of questions), implies that crowdsourcers should pay special attention to the newest items entering the network, to balance out the inherent bias in favor of older items.\n\nThompson sampling is fast, easy to implement, and flexible enough to capture the preferences of different crowdsourcers, but it is only one potential policy for question selection. More rigorous question selection techniques can be implemented which may outperform the proposed techniques, but with potentially more restrictions. The Thompson sampling algorithms proposed here work for both question nets but also non-network question sets, and can naturally accommodate both growing and static questions sets and nets. Further, statistical inference of question parameters and worker features , based on extensions of the null model analyzed in Sec. 2.3, can be used by the crowdsourcer to better pair workers with questions.\n\nThere remains considerable room for improvement. For example, in Fig 5, approximately 50% of questions in Experiment 2 received a single answer, regardless of arm. This means that even with the current algorithms the crowd is still supplying an inordinate amount of questions that are being left mostly unconsidered. Of course, some of this may be unavoidable; if there is too much Supply, then the crowd will invariably fall behind. This is further compounded by the inherent bias in favor of older questions. Thompson and Binomial sampling helped curtail this “first-mover-advantage” bias in the growing network but did not necessarily eliminate it. This is the fundamental challenge (and appeal) of this crowdsourcing problem, and more work focused on these issues is needed.\n\nIn the future, we will address more detailed schemes for question selection. Questions that contain more than a binary (true/false) response should be further investigated, although the only adaptation of the Thompson sampling algorithm is in the choice of metric to Thompson sample from. Different network structures may arise for different crowdsourcing problems, and assessing the accuracy of the network inferred by the crowdsourcing, and not necessarily the accuracy of individual links, will also be investigated. These and many other interesting and important questions remain in the new problem of crowdsourcing with growing question nets and sets.\n\n## Acknowledgments\n\nWe thank M. Wagy and J. Bongard for useful comments and gratefully acknowledge the resources provided by the Vermont Advanced Computing Core. 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Crowdsourcing High Quality Labels with a Tight Budget. In: Proceedings of the Ninth ACM International Conference on Web Search and Data Mining. ACM; 2016. p. 237–246.\n13. 13. Karger DR, Oh S, Shah D. Budget-optimal task allocation for reliable crowdsourcing systems. Operations Research. 2014;62(1):1–24.\n14. 14. Tran-Thanh L, Venanzi M, Rogers A, Jennings NR. Efficient budget allocation with accuracy guarantees for crowdsourcing classification tasks. In: Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems. International Foundation for Autonomous Agents and Multiagent Systems; 2013. p. 901–908.\n15. 15. Tran-Thanh L, Stein S, Rogers A, Jennings NR. Efficient crowdsourcing of unknown experts using multi-armed bandits. In: European Conference on Artificial Intelligence; 2012. p. 768–773.\n16. 16. Ipeirotis PG, Gabrilovich E. Quizz: targeted crowdsourcing with a billion (potential) users. In: Proceedings of the 23rd international conference on World wide web. ACM; 2014. p. 143–154.\n17. 17. Puterman ML. Markov decision processes: discrete stochastic dynamic programming. John Wiley & Sons; 2014.\n18. 18. Chapelle O, Li L. An empirical evaluation of Thompson sampling. In: Advances in neural information processing systems; 2011. p. 2249–2257.\n19. 19. Donmez P, Carbonell JG, Schneider J. Efficiently learning the accuracy of labeling sources for selective sampling. In: Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM; 2009. p. 259–268.\n20. 20. Hung NQV, Tam NT, Tran LN, Aberer K. An evaluation of aggregation techniques in crowdsourcing. In: Web Information Systems Engineering—WISE 2013. Springer; 2013. p. 1–15.\n21. 21. Khattak FK, Salleb-Aouissi A. Quality control of crowd labeling through expert evaluation. In: Proceedings of the NIPS 2nd Workshop on Computational Social Science and the Wisdom of Crowds; 2011.\n22. 22. Kazai G, Kamps J, Milic-Frayling N. Worker types and personality traits in crowdsourcing relevance labels. In: Proceedings of the 20th ACM international conference on Information and knowledge management. ACM; 2011. p. 1941–1944.\n23. 23. Whitehill J, Wu Tf, Bergsma J, Movellan JR, Ruvolo PL. Whose vote should count more: Optimal integration of labels from labelers of unknown expertise. In: Advances in neural information processing systems; 2009. p. 2035–2043.\n24. 24. Ross J, Irani L, Silberman M, Zaldivar A, Tomlinson B. Who are the crowdworkers?: shifting demographics in Mechanical Turk. In: CHI’10 extended abstracts on Human factors in computing systems. ACM; 2010. p. 2863–2872.\n25. 25. Ipeirotis PG, Provost F, Wang J. Quality management on Amazon Mechanical Turk. In: Proceedings of the ACM SIGKDD workshop on human computation. ACM; 2010. p. 64–67.\n26. 26. Rajan V, Bhattacharya S, Celis LE, Chander D, Dasgupta K, Karanam S. Crowdcontrol: An online learning approach for optimal task scheduling in a dynamic crowd platform. In: Proceedings of ICML Workshop: Machine Learning Meets Crowdsourcing; 2013.\n27. 27. Abraham I, Alonso O, Kandylas V, Slivkins A. Adaptive Crowdsourcing Algorithms for the Bandit Survey Problem. In: COLT; 2013. p. 882–910.\n28. 28. Bongard JC, Hines PD, Conger D, Hurd P, Lu Z. Crowdsourcing predictors of behavioral outcomes. IEEE Transactions on Systems, Man, and Cybernetics: Systems. 2013;43(1):176–185.\n29. 29. Bevelander KE, Kaipainen K, Swain R, Dohle S, Bongard JC, Hines PD, et al. Crowdsourcing novel childhood predictors of adult obesity. PloS one. 2014;9(2):e87756. pmid:24505310\n30. 30. Salganik MJ, Levy KEC. Wiki Surveys: Open and Quantifiable Social Data Collection. PLOS ONE. 2015;10(5):1–17.\n31. 31. Erdős P, Rényi A. On the strength of connectedness of a random graph. Acta Mathematica Hungarica. 1961;12(1–2):261–267.\n32. 32. Erdős P, Rényi A. On random graphs I. Publ Math Debrecen. 1959;6:290–297.\n33. 33. Barabási AL, Albert R. Emergence of scaling in random networks. Science. 1999;286(5439):509–512. pmid:10521342\n34. 34. Albert R, Barabási AL. Statistical mechanics of complex networks. Reviews of modern physics. 2002;74(1):47.\n35. 35. Watts DJ, Strogatz SH. Collective dynamics of ‘small-world’ networks. Nature. 1998;393(6684):440–442. pmid:9623998\n36. 36. Strogatz SH. Exploring complex networks. Nature. 2001;410(6825):268–276. pmid:11258382\n37. 37. Newman MEJ. The structure and function of complex networks. SIAM review. 2003;45(2):167–256.\n38. 38. Newman MEJ, Girvan M. Finding and evaluating community structure in networks. Physical review E. 2004;69(2):026113.\n39. 39. Barabási AL, Albert R, Jeong H. Mean-field theory for scale-free random networks. Physica A: Statistical Mechanics and its Applications. 1999;272(1):173–187.\n40. 40. Bagrow JP, Sun J, ben-Avraham D. Phase transition in the rich-get-richer mechanism due to finite-size effects. Journal of Physics A: Mathematical and Theoretical. 2008;41(18):185001.\n41. 41. Newman MEJ. Networks: an introduction. Oxford university press; 2010.\n42. 42. Buhrmester M, Kwang T, Gosling SD. Amazon’s Mechanical Turk a new source of inexpensive, yet high-quality, data? Perspectives on psychological science. 2011;6(1):3–5. pmid:26162106\n43. 43. Miller GA. WordNet: a lexical database for English. Communications of the ACM. 1995;38(11):39–41.\n44. 44. Mikolov T, Sutskever I, Chen K, Corrado GS, Dean J. Distributed representations of words and phrases and their compositionality. In: Advances in neural information processing systems; 2013. p. 3111–3119.\n45. 45. Harris ZS. Distributional structure. 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https://quantumcomputing.stackexchange.com/questions/9611/what-does-a-choi-state-where-we-relax-the-partial-trace-condition-represent	[ "# What does a \"Choi state\" where we relax the partial trace condition represent?\n\nConsider Hilbert spaces $$\\mathcal{X}, \\mathcal{Y}$$. For any quantum channel $$\\mathcal{E}_{\\mathcal{X}\\rightarrow \\mathcal{Y}}$$, the bipartite Choi state $$J(\\mathcal{E}) \\in L(\\mathcal{Y}\\otimes\\mathcal{X})$$ is given by\n\n$$J(\\mathcal{E}) = (\\mathcal{E}\\otimes I)\\sum_{a,b} \\vert a\\rangle\\langle b\\vert\\otimes\\vert a\\rangle\\langle b\\vert$$\n\nIt is also possible to show (see here for example) that the trace preserving condition of the map $$\\mathcal{E}$$ is equivalent to the following condition on its Choi state\n\n$$\\text{Tr}_\\mathcal{Y}J(\\mathcal{E}) = I_\\mathcal{X} \\tag{1}$$\n\nThe proof is easy - it relies on noticing that the trace preserving condition implies that $$\\mathcal{E}(\\vert a\\rangle\\langle b\\vert) = \\delta_{a,b}$$ due to the trace preserving condition. Meanwhile, positive-semidefiniteness of $$J(\\mathcal{E})$$ corresponds to complete positivity of $$\\mathcal{E}$$.\n\nIf $$J(\\mathcal{E})$$ is a density matrix but does not fulfill (1) is it still related to physical quantum channels (i.e. completely positive and trace preserving maps) in some way? Specifically, since completely positive maps correspond to positive semidefinite Choi matrices, does imposing that $$\\text{Tr}(J(\\mathcal{E})) = 1$$ (in addition to positive semidefiniteness) give us any condition on the map $$\\mathcal{E}$$?\n\nIt is exactly what you say: A \"Choi state\" which is only positive semi-definite corresponds to a completely positive map which is not necessarily trace preserving. Fixing the trace of the Choi state rescales the \"success probability\" when implementing the CP map via the isomorphism - if you wish, it rescales the trace of all output states $$\\mathcal E(\\rho)$$ by a constant factor. (Note that deviating from the local trace condition $$\\mathrm{tr}_Y J = I$$, but keeping the total trace $$\\mathrm{tr} J =1$$, implies that there will be inputs with outputs with trace larger than one.)" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7167391,"math_prob":0.9998328,"size":1288,"snap":"2021-43-2021-49","text_gpt3_token_len":377,"char_repetition_ratio":0.19080997,"word_repetition_ratio":0.012903226,"special_character_ratio":0.26086956,"punctuation_ratio":0.06140351,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99999213,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-17T03:35:13Z\",\"WARC-Record-ID\":\"<urn:uuid:7863d53c-e87e-4680-b6ef-92211670c03d>\",\"Content-Length\":\"167169\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4902771d-6435-40b7-9e44-ac1e0329ef44>\",\"WARC-Concurrent-To\":\"<urn:uuid:d8672af2-6ad0-403c-a317-db9df55752f7>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://quantumcomputing.stackexchange.com/questions/9611/what-does-a-choi-state-where-we-relax-the-partial-trace-condition-represent\",\"WARC-Payload-Digest\":\"sha1:YKGJH4TQ2AU7UCDD663YU32RPBQ5S2VH\",\"WARC-Block-Digest\":\"sha1:XV2VNYZU4MBTCF5UG22EWPSQTVJN6HKZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585120.89_warc_CC-MAIN-20211017021554-20211017051554-00137.warc.gz\"}"}
https://matheducators.stackexchange.com/questions/7594/logarithm-tables-how-were-the-values-reached	[ "# Logarithm Tables - How were the values reached?\n\nI'm teaching an Algebra II/Trigonometry class that is currently working on logarithms as the inverse function of exponential functions. Now, to keep their interest I had them struggle for a few minutes with $2^x = 10$ and trying to solve it. Trying to find the answer to that question is the driving force behind our activities with logarithms (thankfully my students really want an answer to that question, so they're willing to learn whatever I have for them so long as they can get closer to answering the question posed originally.\n\nSome of them have noticed that there is a \"log\" function on their calculator, which I acknowledged, but I also warned them that right now if they plugged 10 into their calculator they wouldn't get the correct answer.\n\nI want to show them tomorrow as a quick history lesson before some presentations that before we had calculators that could calculate logarithms, there were tables of logarithms that people kept in books.\n\nI know that they're going to ask, and as of right now my searches haven't yielded an answer:\n\nHow were the values in the old logarithm tables found? I've found a lot of information on how people used logarithm tables, but very little information on how those values were calculated. Can anyone help me here?\n\n• As far as $2^x = 10$ goes, It can be solve using my method discussed in the question Method of Solving 5x=326 (Logs not allowed). Mar 12, 2015 at 2:22\n• Well from that link I've got a tentative answer, but if someone is able to give me more information I'd definitely love to hear it. Mar 12, 2015 at 2:29\n• And the calculus method was using the approximation of roots for equations like $2^x = 100$ being rearranged to $2^x - 100 = 0$ by the Newton Method and linear approximation? Mar 12, 2015 at 2:55\n\nI did this with my students a while ago. First I got them to construct their own slide rules using Briggs estimation technique. Then a slightly more accurate table translating between base 10 logs, decibels, base 2 logs, and musical notes ($$semitone^{12}=2$$).\n\nAfter that we studied Briggs' methods to improve the estimates and create accurate logs.\n\nMy source material for Napier is http://profmarino.it/Nepero/napier1619construction.pdf\n\nMy source material for Briggs is a translation of Chapter 7 of his Arithmetica Logrithmica http://www.17centurymaths.com/contents/albriggs.html I have since found a more easily understood document explaining his techniques https://hal.inria.fr/inria-00543939/document\n\n# Napier\n\nIf I remember correctly, Napier's method was really weird. He started with a big number and basically multiplied by something like 0.999999 to get lower numbers. He did an insane number of calculations at up to 32 bit precision, so he only got parts of his table finished.\n\nSomething to note, logs are about ratios, not numbers, so the base number of a log table is arbitrary. We set the base of our ratio to be 1 to make them trivial to calculate, so $$\\log 1 =0$$ ... Napier did not :-(\n\n# Briggs method for initial estimation\n\nHenry Briggs decided that there had to be a better way and used a number of techniques around base 10, with the base ratio set to 1. In Napier's system it was annoying to multiply or divide numbers by 10 so you could use the parts of the log tables Napier had completed, but with $$\\log 10=1$$ and $$\\log 1=0$$ it is trivial. This not only cuts down on an extra calculation but reduces the accumulation of rounding errors.\n\nThe following describes how Briggs did this hundreds of years ago by hand, with much greater precision than a calculator.\n\nAs a first estimate, observe that $$2^{10} \\approx 10^3$$ Therefore we can calculate $$10\\log 2 \\approx 3\\log 10$$ $$\\log 2 \\approx 0.3$$\n\n# Briggs method for calculating correction factor\n\nBut Briggs needed to improve on that. The correction factor is $$1.024$$. If we find out the log of that, we can add it into the above equation. We will use 3 facts to estimate this number. First, since ancient times there has been an easy algorithm for finding square roots (for my students, it is called \"the square root button\"), and repeated application takes numbers close to $$1$$. Second, the log of a square root is exactly half the log of original number. Third, we have set the log of 1 to be 0. Therefore all we need to do is find a root of 10 close to 1, and then we can easily interpolate to accurately find more logs.\n\nTo find a root of 10 close to 0, take repeated square roots until you get a small number, say $$\\sqrt{\\sqrt{\\sqrt{\\sqrt{{\\sqrt{\\sqrt{\\sqrt{\\sqrt{10}}}}}}}}} = 10^{(\\frac 1 2 ^8)} = 1.0090$$ $$\\log 1.0090 = (\\frac 1 2 )^8$$ The interval between $$\\log 1$$ and $$\\log 1.0090$$ is linear up to 4dp. Using smaller numbers rapidly improves accuracy, but this is sufficient for a class project. Briggs used 54 square roots, accurate to 32 dp.!\n\nNext we do the same to 1.024 to get a fraction close to $$1.0090$$, we'll use $$\\sqrt {1.024} = 1.0119$$. We use extrapolation between $$\\log 1 = 0$$ and $$\\log 1.0090 = \\frac {1}{256}$$ The interpolation formula is simplified as $$y_0=0$$ $$y = y_1 \\times \\frac {x -x_0}{x_1-x_0}$$ $$\\log 1.0119= \\log 1.0090 \\times \\frac {0.0119}{0.0090} = 0.00516$$ $$\\log 1.024 = 2 \\log 1.0119 = 0.0103$$\n\n# Putting it all together\n\nWe then use this correction factor to get good precision based on our initial estimate $$2^{10} = 10^3 * 1.024$$ $$10 \\log 2 = 3 + 0.0103$$ $$\\log 2 = 0.30103$$ $$10^{0.30103}=2.00000...$$\n\nThe technique itself magnifies the accuracy. The next to use is $$6^9 = 10^7 * 1.0077696$$\n\n• I thought Napier used something like powers of 1.000001. In any case, I appreciate the link to Roegel's analysis of the methods Briggs seems to have used. Gerhard \"Still Likes The Geometric Construction\" Paseman, 2015.03.13 Mar 13, 2015 at 17:51\n• @GerhardPaseman Michael E2's link in the comments shows one of his tables. He starts at log 10000000 = 0 and effectively multiplied by 0.9999999 each time so log 9999999 = 1. It would still be a simple subtraction to calculate each term. I don't properly understand Napier myself, as arithmetic concepts were so different back then (decimals were a new thing), but I have read several misinterpretations of his work that try to shoehorn what he did into modern models. In the end his understanding was so different I couldn't find anything useful to work into a lesson, and I just went with Briggs. Mar 14, 2015 at 1:14\n• I think you did quite well. I surprised myself by finding the method described in matheducators.stackexchange.com/questions/5970/… to use two sheets of ruled paper to construct a rough version of a logarithmic scale, but without sufficient care, it is easy to make mistakes and end up with some serious error. Going through an exercise like mine makes me appreciate your write-up all the more. Gerhard \"Appreciates The Precision Of Engineers\" Paseman, 2015.03.15 Mar 15, 2015 at 20:47\n• Here's Numberphile explaining what Napier did: youtube.com/watch?v=vzV50goW_WM Jul 19, 2015 at 14:32\n\nGauss said \"You have no idea how much poetry there is in a table of logarithms.\"\n\nThe first paragraph of this paper might get you pointed in the right direction\n\nON THE DISTRIBUTION OF PRIMES—GAUSS’ TABLES\n\n• I can't find the bit discussing how logs were made. Would you be able to copy the relevant text into your answer? Mar 14, 2015 at 1:20" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8923028,"math_prob":0.9833255,"size":3714,"snap":"2023-40-2023-50","text_gpt3_token_len":1058,"char_repetition_ratio":0.10350405,"word_repetition_ratio":0.00953895,"special_character_ratio":0.31825525,"punctuation_ratio":0.120779224,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99880993,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-11-29T21:12:54Z\",\"WARC-Record-ID\":\"<urn:uuid:1c9873b6-fdef-418a-87cb-e287e60dbbcf>\",\"Content-Length\":\"187680\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4326a74b-30ea-4cef-92df-316c9bb2e0af>\",\"WARC-Concurrent-To\":\"<urn:uuid:9568a095-5848-45d5-ab97-5e2ef371630c>\",\"WARC-IP-Address\":\"104.18.43.226\",\"WARC-Target-URI\":\"https://matheducators.stackexchange.com/questions/7594/logarithm-tables-how-were-the-values-reached\",\"WARC-Payload-Digest\":\"sha1:IQDMGJ7TKUPDN7ODL5NFRSYW25VZX4M2\",\"WARC-Block-Digest\":\"sha1:DVVL2K2JIPY56KUX5N7V4HBSFXCGHYCT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100146.5_warc_CC-MAIN-20231129204528-20231129234528-00079.warc.gz\"}"}
http://www.geekinterview.com/question_details/33864	[ "# Program to add two polynomials of any degree in Java i.epolynomial 1: Ax^3 + Bx + C polynomial 2: Px^3 + Qx^2 Result: (A+P)x^3 + Qx^2 + Bx + C\n\nThis Question is not yet answered!", null, "", null, "" ]	[ null, "http://www.geekinterview.com/images/ajax-loader.gif", null, "http://www.geekinterview.com/images/ajax-loader.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.84196377,"math_prob":0.97665435,"size":790,"snap":"2019-51-2020-05","text_gpt3_token_len":228,"char_repetition_ratio":0.15648855,"word_repetition_ratio":0.5846154,"special_character_ratio":0.25949368,"punctuation_ratio":0.08108108,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9526903,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-21T18:43:38Z\",\"WARC-Record-ID\":\"<urn:uuid:eaa58199-f97e-4f0f-a277-cee9f14e5170>\",\"Content-Length\":\"95576\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b9f33661-51d6-4683-8a98-911955d6667b>\",\"WARC-Concurrent-To\":\"<urn:uuid:7da3a104-d2ed-4fbc-ab60-719e4f429d7d>\",\"WARC-IP-Address\":\"199.187.125.188\",\"WARC-Target-URI\":\"http://www.geekinterview.com/question_details/33864\",\"WARC-Payload-Digest\":\"sha1:NF7FE4YI2OMXNK2S4HE3LTUBUWOHDQXT\",\"WARC-Block-Digest\":\"sha1:RA4RIVTCXYSD432YQCVJBV54L47CNJ6U\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250604849.31_warc_CC-MAIN-20200121162615-20200121191615-00247.warc.gz\"}"}
https://www.physicsforums.com/threads/momentum-ques.159559/	[ "# Momentum Ques.\n\n## Homework Statement\n\nA ball with mass m with an initial velocity of 5 m/s strikes a ball with a mass of 3m hanging at rest from a string 50 cm long. Find the maximum angle(x) with which the block swings after its hit.\n\nk=1/2mv^2\np=mv\n\n## The Attempt at a Solution\n\nWell first I solved the momentum\n\nmAvA1+mBvB1=mAvA2+mBvB2\n\nto get vB2=5-vA2\n\nThen I used conservation of energy to get\n\n[tex]sqrt {25 - v_{A2}/3} [\\tex]\n\nI solved the two equations for vB2 and got 3.53 m/s\n\nSo, since the kinetic energy from the start of the mass on the pendelum moving to its peak is h=(.5-.5cosx)\n\n1/2m(vB2^2)=mg(.5-.5cosx)\n\nI solved for the angle and got 50.2 degrees.\n\nAnyone see anything wrong with my math or my logic? I can only attempt the problem one more time before the program gives me no credit.\n\nHomework Helper\nCouldn't you just use energy conservation, since the block's kinetic energy at the maximal angle equals zero? It posesses only potential energy at that point, and at the impact point, there is only kinetic energy from the ball.\n\nDick\nHomework Helper\nCouldn't you just use energy conservation, since the block's kinetic energy at the maximal angle equals zero? It posesses only potential energy at that point, and at the impact point, there is only kinetic energy from the ball.\n\nThe other ball carries away some of the kinetic energy. I think he's doing it right. I haven't checked the answer though.\n\nHomework Helper\nThe other ball carries away some of the kinetic energy. I think he's doing it right. I haven't checked the answer though.\n\nGood point, so after reconsidering...\n\nWell first I solved the momentum\n\nmAvA1+mBvB1=mAvA2+mBvB2\n\nto get vB2=5-vA2\n\n...shouldn't this be VB2 = (5 - VA2)/3 ?" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8582122,"math_prob":0.95829177,"size":807,"snap":"2022-05-2022-21","text_gpt3_token_len":262,"char_repetition_ratio":0.09713574,"word_repetition_ratio":0.0,"special_character_ratio":0.2961586,"punctuation_ratio":0.06629834,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99520534,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-22T01:56:55Z\",\"WARC-Record-ID\":\"<urn:uuid:a51ad8d8-9345-4a94-bcc7-05c94a2a3a96>\",\"Content-Length\":\"67545\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6080bca6-806d-4e6d-92fc-dc13a749af26>\",\"WARC-Concurrent-To\":\"<urn:uuid:0731dd96-fbb0-4f6c-ac6e-3d27f4ca28b8>\",\"WARC-IP-Address\":\"172.67.68.135\",\"WARC-Target-URI\":\"https://www.physicsforums.com/threads/momentum-ques.159559/\",\"WARC-Payload-Digest\":\"sha1:OCYUSESXXG5CXJRQSLUI4OMTUBT7DQHD\",\"WARC-Block-Digest\":\"sha1:NF5IT66ULAGMG5ZIUNIIXKXIZIFFRNOX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662543264.49_warc_CC-MAIN-20220522001016-20220522031016-00212.warc.gz\"}"}
https://vhdlwhiz.com/finite-state-machine/	[ "A finite-state machine (FSM) is a mechanism whose output is dependent not only on the current state of the input, but also on past input and output values.\n\nWhenever you need to create some sort of time-dependent algorithm in VHDL, or if you are faced with the problem of implementing a computer program in an FPGA, it can usually be solved by using an FSM.\n\nState-machines in VHDL are clocked processes whose outputs are controlled by the value of a state signal. The state signal serves as an internal memory of what happened in the previous iteration.\n\nThis blog post is part of the Basic VHDL Tutorials series.\n\nConsider the states of the traffic lights at this intersection:", null, "The traffic lights have a finite number of states, which we have given identifiable names. Our example state machine has no controlling inputs, the output is the state of the lights in north/south and west/east directions. It is elapsed time and the previous state of outputs which advances this state machine.\n\nWe can represent states in VHDL using an enumerated type. These are data types just like signed or unsigned, but instead of integer numbers, we can supply a custom list of possible values. In fact, if you take a look in the std_logic_1164 package, you will find that the std_ulogic type is nothing more than an enumerated type with the values 'U', 'X', '0', '1', 'Z', 'W', 'L', 'H', and '-' listed as enumeration values.\n\nOnce we have our enumerated type, we can declare a signal of the new type which can be used for keeping track of the FSM’s current state.\n\nThe syntax for declaring a signal with an enumerated type in VHDL is:\ntype <type_name> is (<state_name1>, <state_name2>, ...);\nsignal <signal_name> : <type_name>;\n\nUsing the state signal, the finite-state machine can then be implemented in a process with a Case statement. The Case statement contains a When statement for each of the possible states, causing the program to take different paths for every state. The When statement can also contain code which should be executed while in that particular state. The state will then typically change when a predefined condition is met.\n\nThis is a template for one-process state machine:\nprocess(Clk) is\nbegin\nif rising_edge(Clk) then\nif nRst = '0' then\nState <= <reset_state>;\nelse\ncase State is\nwhen <state_name> =>\n<set_outputs_for_this_state_here>\nif <state_change_condition_is_true> then\nState <= <next_state_name>;\nend if;\n...\nend case;\nend if;\nend if;\nend process;\n\nNote:\nThere are several ways to create an FSM in VHDL. Read about the different styles here:\nOne-process vs two-process vs three-process state machine\n\nExercise\n\nIn this video tutorial we will learn how to create a finite-state machine in VHDL:\n\nThe final code for the state machine testbench:\n\nlibrary ieee;\nuse ieee.std_logic_1164.all;\nuse ieee.numeric_std.all;\n\nentity T20_FiniteStateMachineTb is\nend entity;\n\narchitecture sim of T20_FiniteStateMachineTb is\n\n-- We are using a low clock frequency to speed up the simulation\nconstant ClockFrequencyHz : integer := 100; -- 100 Hz\nconstant ClockPeriod : time := 1000 ms / ClockFrequencyHz;\n\nsignal Clk : std_logic := '1';\nsignal nRst : std_logic := '0';\nsignal NorthRed : std_logic;\nsignal NorthYellow : std_logic;\nsignal NorthGreen : std_logic;\nsignal WestRed : std_logic;\nsignal WestYellow : std_logic;\nsignal WestGreen : std_logic;\n\nbegin\n\n-- The Device Under Test (DUT)\ni_TrafficLights : entity work.T20_TrafficLights(rtl)\ngeneric map(ClockFrequencyHz => ClockFrequencyHz)\nport map (\nClk => Clk,\nnRst => nRst,\nNorthRed => NorthRed,\nNorthYellow => NorthYellow,\nNorthGreen => NorthGreen,\nWestRed => WestRed,\nWestYellow => WestYellow,\nWestGreen => WestGreen);\n\n-- Process for generating clock\nClk <= not Clk after ClockPeriod / 2;\n\n-- Testbench sequence\nprocess is\nbegin\nwait until rising_edge(Clk);\nwait until rising_edge(Clk);\n\n-- Take the DUT out of reset\nnRst <= '1';\n\nwait;\nend process;\n\nend architecture;\n\nThe final code for the state machine module:\n\nlibrary ieee;\nuse ieee.std_logic_1164.all;\nuse ieee.numeric_std.all;\n\nentity T20_TrafficLights is\ngeneric(ClockFrequencyHz : integer);\nport(\nClk : in std_logic;\nnRst : in std_logic; -- Negative reset\nNorthRed : out std_logic;\nNorthYellow : out std_logic;\nNorthGreen : out std_logic;\nWestRed : out std_logic;\nWestYellow : out std_logic;\nWestGreen : out std_logic);\nend entity;\n\narchitecture rtl of T20_TrafficLights is\n\n-- Enumerated type declaration and state signal declaration\ntype t_State is (NorthNext, StartNorth, North, StopNorth,\nWestNext, StartWest, West, StopWest);\nsignal State : t_State;\n\n-- Counter for counting clock periods, 1 minute max\nsignal Counter : integer range 0 to ClockFrequencyHz * 60;\n\nbegin\n\nprocess(Clk) is\nbegin\nif rising_edge(Clk) then\nif nRst = '0' then\n-- Reset values\nState <= NorthNext;\nCounter <= 0;\nNorthRed <= '1';\nNorthYellow <= '0';\nNorthGreen <= '0';\nWestRed <= '1';\nWestYellow <= '0';\nWestGreen <= '0';\n\nelse\n-- Default values\nNorthRed <= '0';\nNorthYellow <= '0';\nNorthGreen <= '0';\nWestRed <= '0';\nWestYellow <= '0';\nWestGreen <= '0';\n\nCounter <= Counter + 1;\n\ncase State is\n\n-- Red in all directions\nwhen NorthNext =>\nNorthRed <= '1';\nWestRed <= '1';\n-- If 5 seconds have passed\nif Counter = ClockFrequencyHz * 5 -1 then\nCounter <= 0;\nState <= StartNorth;\nend if;\n\n-- Red and yellow in north/south direction\nwhen StartNorth =>\nNorthRed <= '1';\nNorthYellow <= '1';\nWestRed <= '1';\n-- If 5 seconds have passed\nif Counter = ClockFrequencyHz * 5 -1 then\nCounter <= 0;\nState <= North;\nend if;\n\n-- Green in north/south direction\nwhen North =>\nNorthGreen <= '1';\nWestRed <= '1';\n-- If 1 minute has passed\nif Counter = ClockFrequencyHz * 60 -1 then\nCounter <= 0;\nState <= StopNorth;\nend if;\n\n-- Yellow in north/south direction\nwhen StopNorth =>\nNorthYellow <= '1';\nWestRed <= '1';\n-- If 5 seconds have passed\nif Counter = ClockFrequencyHz * 5 -1 then\nCounter <= 0;\nState <= WestNext;\nend if;\n\n-- Red in all directions\nwhen WestNext =>\nNorthRed <= '1';\nWestRed <= '1';\n-- If 5 seconds have passed\nif Counter = ClockFrequencyHz * 5 -1 then\nCounter <= 0;\nState <= StartWest;\nend if;\n\n-- Red and yellow in west/east direction\nwhen StartWest =>\nNorthRed <= '1';\nWestRed <= '1';\nWestYellow <= '1';\n-- If 5 seconds have passed\nif Counter = ClockFrequencyHz * 5 -1 then\nCounter <= 0;\nState <= West;\nend if;\n\n-- Green in west/east direction\nwhen West =>\nNorthRed <= '1';\nWestGreen <= '1';\n-- If 1 minute has passed\nif Counter = ClockFrequencyHz * 60 -1 then\nCounter <= 0;\nState <= StopWest;\nend if;\n\n-- Yellow in west/east direction\nwhen StopWest =>\nNorthRed <= '1';\nWestYellow <= '1';\n-- If 5 seconds have passed\nif Counter = ClockFrequencyHz * 5 -1 then\nCounter <= 0;\nState <= NorthNext;\nend if;\n\nend case;\n\nend if;\nend if;\nend process;\n\nend architecture;\n\nThe waveform after we entered the run 5 min command in the ModelSim console:", null, "Need the ModelSim project files?\n\nLet me send you a Zip with everything you need to get started in 30 seconds\n\nTested on Windows and Linux", null, "Unsubscribe at any time\n\nAnalysis\n\nWe declared an enumerated type with all the eight different states of our traffic lights. Then, we declared a state signal of this new type that we created. This means that the signal can only have one of the eight named state values, and no other values.\n\nThe FSM was implemented using a Case-statement within a clocked process. On each rising edge of the clock, the process wakes up, and the state signal is evaluated. The code within exactly one of the when choices (branches) is allowed to run, depending on the current state.\n\nIn our code, it is the value of the Counter signal that triggers state changes. When the Counter reaches a predefined value, representing 5 seconds or 1 minute, a new state encoding is assigned to the State signal. Then, when the process wakes up on the next rising edge of the clock after the state value has been updated, the FSM is in a different state.\n\nNote that we are not assigning '0' to any signal in any of the when choices. This is because we have given all the output signals a default value of '0' at the beginning of the process. You may remember from a previous tutorial that it is the last value which is assigned to a signal that becomes effective. Signal assignments become effective only after the process terminates. If we assign '0' to the signal at the beginning of the process, and then '1' in one of the when choices, the signal will get the value '1'.\n\nWe can see from the waveform that the State signal cycles through the eight states. The steady green states last for one minute, the waveform image has therefore been cut in the North and West states.", null, "Takeaway\n\n• Algorithms are usually implemented as finite-state machines (FSMs)\n• An FSM can be implemented by using a case statement in a clocked process\n• FSM states can be implemented in an enumerated type\n\nGo to the next tutorial »", null, "This site uses Akismet to reduce spam. Learn how your comment data is processed." ]	[ null, "https://vhdlwhiz.com/wp-content/plugins/a3-lazy-load/assets/images/lazy_placeholder.gif", null, "https://vhdlwhiz.com/wp-content/plugins/a3-lazy-load/assets/images/lazy_placeholder.gif", null, "https://vhdlwhiz.com/wp-content/plugins/a3-lazy-load/assets/images/lazy_placeholder.gif", null, "https://vhdlwhiz.com/wp-content/plugins/a3-lazy-load/assets/images/lazy_placeholder.gif", null, "https://vhdlwhiz.com/wp-content/plugins/a3-lazy-load/assets/images/lazy_placeholder.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7834133,"math_prob":0.9030609,"size":8627,"snap":"2019-43-2019-47","text_gpt3_token_len":2111,"char_repetition_ratio":0.15203525,"word_repetition_ratio":0.16093536,"special_character_ratio":0.26440245,"punctuation_ratio":0.15409005,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9774656,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-17T07:32:40Z\",\"WARC-Record-ID\":\"<urn:uuid:c1b36ca1-ff6e-4b00-9c87-000762f015d3>\",\"Content-Length\":\"68739\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:09ee64b6-0bb2-4233-979c-74f18376ead4>\",\"WARC-Concurrent-To\":\"<urn:uuid:af8be617-8f1c-4271-8e35-42ba32437135>\",\"WARC-IP-Address\":\"94.237.42.36\",\"WARC-Target-URI\":\"https://vhdlwhiz.com/finite-state-machine/\",\"WARC-Payload-Digest\":\"sha1:U5VYHSYYUTCJ2IJ626CAMY42JNUQYWQT\",\"WARC-Block-Digest\":\"sha1:W4SIFGWUAWSPZY3N4PS5JX5UYOZVHF4Z\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986673250.23_warc_CC-MAIN-20191017073050-20191017100550-00530.warc.gz\"}"}
http://rfkfair.com/NewsShow.asp-bid=176.htm	[ "", null, "", null, "手机版", null, "官方微博\nENGLISH", null, "新闻中心", null, "当前位置：首页 >> 新闻中心\n\n# 市政领导来我公司安全生产检查\n\n930日上午，副市长葛启发、副秘书长张步胜、市安监局、市经信委、消防支队等领导一行来我公司进行安全生产检查，主要检查了车间危化品和喷漆房等地方，市政领导对我公司生产安全情况满意和放心，并表示安全生产工作是企业的主体责任，要坚决把责任扛在肩上，要保持安全意识，注重细节，不要放过任何安全隐患", null, "", null, "", null, "返回到：领导关怀下一篇：乌海市政协代表团来我公司考察调研\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`" ]	[ null, "http://rfkfair.com/Images/logo.png", null, "http://rfkfair.com/Images/mbIcon.png", null, "http://rfkfair.com/Images/wbIcon.png", null, "http://rfkfair.com/Images/leftLi.png", null, "http://rfkfair.com/Images/home.png", null, "http://rfkfair.com/uploadfiles/Content/image/20170930/20170930172164806480.jpg", null, "http://rfkfair.com/uploadfiles/Content/image/20170930/2017093017210847847.jpg", null, "http://rfkfair.com/uploadfiles/Content/image/20170930/20170930172196229622.jpg", null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.9880393,"math_prob":0.98292106,"size":146,"snap":"2019-26-2019-30","text_gpt3_token_len":166,"char_repetition_ratio":0.0,"word_repetition_ratio":0.0,"special_character_ratio":0.13013698,"punctuation_ratio":0.0,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97188663,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-17T10:57:23Z\",\"WARC-Record-ID\":\"<urn:uuid:755a2f27-8e32-48ab-8855-245324e8e9f4>\",\"Content-Length\":\"81695\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:529842c1-5c0e-42d0-8721-7778eb4b5bd7>\",\"WARC-Concurrent-To\":\"<urn:uuid:41f0701a-c800-4141-b903-8bb2d42b91c2>\",\"WARC-IP-Address\":\"156.235.244.58\",\"WARC-Target-URI\":\"http://rfkfair.com/NewsShow.asp-bid=176.htm\",\"WARC-Payload-Digest\":\"sha1:DXQMM3BS4RCMQKFL2C4GEGCRQXV247HN\",\"WARC-Block-Digest\":\"sha1:IBX2WMIOYE2H3DFR4E3LKZ4ZU2FBVN6S\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195525136.58_warc_CC-MAIN-20190717101524-20190717123524-00344.warc.gz\"}"}
https://socratic.org/questions/how-can-vectors-be-combined	[ "# How can vectors be combined?\n\nJun 24, 2014\n\nBy using a scale diagram, or trigonometry and pythagoras.\n\nVectors have magnitude and direction. They can be represented by arrows of a certain length. The arrow direction represents the direction and the length represents its size. Vectors must be added head to tail so that the addition takes the directions into account.\n\nIf a scale diagram is used choose a scale (e.g. 1 cm = 1 N) and use a protractor to measure angles relative to the horizontal and vertical. Draw the vectors head to tail. The resultant vector is a straight line from the tail of the first vector to the head of the final vector. This method is recommended for adding more than 2 vectors.\nIn the diagram see the top half which shows the resultant vector for a number of vectors added.", null, "Trigonometry and Pythagoras can only be used if the vectors to be added are perpendicular. In the bottom part of the diagram the two red vectors are not perpendicular. But the vector at angle α can be resolved into a horizontal and vertical component. Then the two horizontal vectors can be added and trigonometry can be used with that and the vertical component of the vector at angle α." ]	[ null, "https://d2jmvrsizmvf4x.cloudfront.net/g7XLanuBQbGuyWRWO37b_image.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8937047,"math_prob":0.9327022,"size":1231,"snap":"2019-51-2020-05","text_gpt3_token_len":255,"char_repetition_ratio":0.14751427,"word_repetition_ratio":0.0,"special_character_ratio":0.19658814,"punctuation_ratio":0.076271184,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99419564,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-27T21:20:24Z\",\"WARC-Record-ID\":\"<urn:uuid:3a391939-10b8-4b16-b443-0d302ee2f5ca>\",\"Content-Length\":\"35149\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5df2e24b-36aa-4d8c-a609-9022be931743>\",\"WARC-Concurrent-To\":\"<urn:uuid:5b19a31d-0678-4790-86ca-33f8bfba29dc>\",\"WARC-IP-Address\":\"54.221.217.175\",\"WARC-Target-URI\":\"https://socratic.org/questions/how-can-vectors-be-combined\",\"WARC-Payload-Digest\":\"sha1:EVQPYCHII4PWSFBKGSOT3JENVSUGQBXJ\",\"WARC-Block-Digest\":\"sha1:SW5E5BO7K3GYSCIOL4QKE2GLLJGHQQYK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579251728207.68_warc_CC-MAIN-20200127205148-20200127235148-00085.warc.gz\"}"}
https://www.whizwriters.com/physics-33/	[ "# Physics\n\nIn this activity you’ll use the Gas Properties PhET Simulation\n\n(https://phet.colorado.edu/en/simulation/gas-properties) to explore and explain the relationships\n\nbetween energy, pressure, volume, temperature, particle mass, number, and speed.\n\nThis activity has 5 modules:\n\n○ Explore the Simulation\n\n○ Kinetic Energy and Speed\n\n○ Kinetic Molecular Theory of Gases\n\n○ Relationships between Gas Variables\n\n○ Pressure and Mixtures of Gases\n\nYou will get the most out of the activity if you do the exploration first! The rest of the sections\n\ncan be worked in any order; you could work on any sections where you want to deepen your\n\nconceptual understanding.\n\nPart I: Explore the Simulation\n\nTake about five minutes to explore the sim. Note at least two relationships that you observe and\n\nfind interesting.\n\nPart II: Kinetic Energy and Speed\n\nSketch and compare the distributions for kinetic energy and speed at two different temperatures\n\nin the table below. Record your temperatures (T1 and T2), set Volume as a Constant Parameter,\n\nand use roughly the same number of particles for each experiment (aim for ~100-200). Use the\n\nT2 temperature to examine a mixture of particles.\n\nTips:\n\nT1 = __________K The Species Information and Energy Histograms tools will help.\n\nT2 = __________K The system is dynamic so the distributions will fluctuate.\n\nSketch the average or most common distribution that you see.\n\n“Heavy” Particles Only “Light” Particles Only Heavy + Light Mixture\n\n# of particles\n\n(~100-200)\n\nKinetic\n\nEnergy\n\nDistribution\n\nsketch for T1\n\nSpeed\n\nDistribution\n\nsketch for T1\n\nKinetic\n\nEnergy\n\nDistribution\n\nsketch for T2\n\nSpeed\n\nDistribution\n\nsketch for T2\n\n1. Compare the kinetic energy distributions for the heavy vs. light particles at the same\n\ntemperature. Are these the same or different? What about the speed distributions?\n\n2. Compare the kinetic energy distributions for the heavy vs. light particles at different\n\ntemperatures. Are these the same or different? What about the speed distributions?\n\n3. Compare the kinetic energy distributions for the mixture to those of the heavy-only and light-\n\nonly gases at the same temperature. Are these the same or different? What about the speed\n\ndistributions?\n\n4. Summarize your observations about the relationships between molecular mass (heavy vs.\n\nlight), kinetic energy, particle speed, and temperature.\n\nPart III: Kinetic Molecular Theory (KMT) of Gases\n\nOur fundamental understanding of “ideal” gases makes the following 4 assumptions.\n\nDescribe how each of these assumptions is (or is not!) represented in the simulation.\n\nAssumption of KMT Representation in Simulation\n\n1. Gas particles are separated by\n\nrelatively large distances.\n\n2. Gas molecules are constantly in\n\nrandom motion and undergo\n\nelastic collisions (like billiard\n\nballs) with each other and the\n\nwalls of the container.\n\n3. Gas molecules are not attracted\n\nor repulsed by each other.\n\n4. The average kinetic energy of\n\ngas molecules in a sample is\n\nproportional to temperature (in K).\n\nPart IV: Relationships Between Gas Variables\n\nScientists in the late 1800’s noted relationships between many of the state variables related to\n\ngases (pressure, volume, temperature), and the number of gas particles in the sample being\n\nstudied. They knew that it was easier to study relationships if they varied only two parameters at\n\na time and “fixed” (held constant) the others. Use the simulation to explore these relationships.\n\nVariables Constant Parameters Relationship Proportionality\n\n(see hint below)\n\npressure, volume directly proportional\n\nor\n\ninversely proportional\n\nvolume, temperature directly proportional\n\nor\n\ninversely proportional\n\nvolume, number of\n\ngas particles\n\ndirectly proportional\n\nor\n\ninversely proportional\n\nHint: A pair of variables is directly proportional when they vary in the same way (one increases\n\nand the other also increases). A pair of variables is inversely proportional when they vary in\n\nopposite ways (one increases and the other decreases). Label each of your relationships in the\n\ntable above as directly or inversely proportional.\n\nPart V: Pressure and Mixtures of Gases\n\nThe atmosphere is composed of many gases in different ratios, and all of them contribute to the\n\ntotal atmospheric pressure. Use the simulation to explore this relationship by testing\n\ncombinations of heavy and light gases.\n\nFor each Test #, record your measurement and the make the prediction before moving on to the\n\nnext row of the table.\n\nTest\n\n#\n\nPressure\n\nMeasurement\n\nPressure Prediction\n\n(greater than, equal to, less than, twice as much, half as much, etc)\n\n1 100 Light particles =\n\nPressure for 100 Heavy Particles will be __________________\n\nthe pressure from Test #1.\n\n2 100 Heavy particles =\n\nPressure for 200 Heavy particles will be __________________\n\nthe pressure from Test #2.\n\n3 200 Heavy particles = Pressure for 100 Light AND 100 Heavy particles will be\n\n__________________ the pressure from Test #3\n\n4 100 Heavy + 100\n\nLight particles =\n\nPressure for 200 Heavy AND 100 Light particles will be\n\n__________________ the pressure from Test #4.\n\n5 200 Heavy + 100\n\nLight particles =\n\nPressure for 150 Heavy AND 50 Light particles will be\n\n__________________ the pressure from Test #5.\n\n6 150 Heavy + 50 Light\n\nparticles =\n\n1. For Test 6 (150 Heavy + 50 Light particles), what is the pressure contribution from the heavy\n\nparticles (Pheavy)? How did you figure this out?\n\n2. What is the pressure contribution from the light particles (Plight)? How did you figure this\n\nout?\n\n3. For each test above, calculate the mole fraction of each gas (number of particles of that type /\n\ntotal particles). Find a relationship between the mole fraction and the pressure contribution of\n\neach type of gas.\n\n4. The atmosphere is composed of about 78% nitrogen, 21% oxygen, and 1% argon. Typical\n\natmospheric pressure in Boulder, Colorado is about 0.83 atm. What is the pressure contributed\n\nby each gas?\n\nOrder now and get 10% discount on all orders above \\$50 now!!The professional are ready and willing handle your assignment.\n\nORDER NOW »»" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8331725,"math_prob":0.9388247,"size":5853,"snap":"2020-34-2020-40","text_gpt3_token_len":1284,"char_repetition_ratio":0.16635323,"word_repetition_ratio":0.12595005,"special_character_ratio":0.22894242,"punctuation_ratio":0.10546875,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97818446,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-28T16:36:50Z\",\"WARC-Record-ID\":\"<urn:uuid:33dc34c9-d2b9-41a5-b691-68c468a0bf4d>\",\"Content-Length\":\"36919\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:fab8a003-60e1-4117-aa2d-7abd47e0a526>\",\"WARC-Concurrent-To\":\"<urn:uuid:1868e724-97e3-4b72-a1ea-a3c9c1424fbc>\",\"WARC-IP-Address\":\"198.54.120.111\",\"WARC-Target-URI\":\"https://www.whizwriters.com/physics-33/\",\"WARC-Payload-Digest\":\"sha1:BWMBCIDCU2FN6ZXZP3TBUSCYFJ4ZZUZL\",\"WARC-Block-Digest\":\"sha1:Y6SIHPAU3THH2S2NXFGOSISGYZOQX3XT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600401601278.97_warc_CC-MAIN-20200928135709-20200928165709-00580.warc.gz\"}"}
https://premedicaluniversity.com/s9d4sp/271de2-quotient-space-examples	[ "A quotient space is a quotient object in some category of spaces, such as Top (of topological spaces), or Loc (of locales), etc. 286) implies, since π is Poisson, that π transforms XH on M to Xh on M/G. This is trivially true, when the metric have an upper bound. If H is a G-invariant Hamiltonian function on M, it defines a corresponding function h on M/G by H=h∘π. that for some in , and is another quotient topologies. References Let C[0,1] denote the Banach space of continuous real-valued functions on the interval [0,1] with the sup norm. Thus, if the G–action is free and proper, a relative equilibrium deﬁnes an equilibrium of the induced vector ﬁeld on the quotient space and conversely, any element in the ﬁber over an equilibrium in the quotient space is a relative equilibrium of the original system. 1. Points x,x0 ∈ X lie in the same G-orbit if and only if x0 = x.g for some g ∈ G. Indeed, suppose x and x0 lie in the G-orbit of a point x 0 ∈ X, so x = x 0.γ and x0 = … Quotient Space Based Problem Solving provides an in-depth treatment of hierarchical problem solving, computational complexity, and the principles and applications of multi-granular computing, including inference, information fusing, planning, and heuristic search.. Adjunction space.More generally, suppose X is a space and A is a subspace of X.One can identify all points in A to a single equivalence class and leave points outside of A equivalent only to themselves. 283, is that for any two smooth scalars f, h: M/G → ℝ, we have an equation of smooth scalars on M: where the subscripts indicate on which space the Poisson bracket is defined. Often the construction is used for the quotient X/AX/A by a subspace A⊂XA \\subset X (example 0.6below). “Quotient space” covers a lot of ground. 307 also defines {f, h}M/G as a Poisson bracket; in two stages. When transforming a solution in the original space to a solution in its quotient space, or vice versa, a precise quotient space should … We can make two basic points, as follows. examples, without any explanation of the theoretical/technial issues. 282), f¯ = πf. Then the condition that π be Poisson, eq. Sometimes the In particular, as we will see in detail in Section 7, this theorem is exemplified by the case where M = TG (so here M is symplectic, since it is a cotangent bundle), and G acts on itself by left translations, and so acts on TG by a cotangent lift. Unlimited random practice problems and answers with built-in Step-by-step solutions. Unfortunately, a different choice of inner product can change . In this case, we will have M/G ≅ g; and the reduced Poisson bracket just defined, by eq. examples of quotient spaces given. Explore anything with the first computational knowledge engine. But the … to . Can we choose a metric on quotient spaces so that the quotient map does not increase distances? as cosets . Hints help you try the next step on your own. The quotient space should always be over the same field as your original vector space. How do we know that the quotient spaces deﬁned in examples 1-3 really are homeomorphic to the familiar spaces we have stated?? ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. URL: https://www.sciencedirect.com/science/article/pii/S0079816908626719, URL: https://www.sciencedirect.com/science/article/pii/B9780128178010000132, URL: https://www.sciencedirect.com/science/article/pii/S0924650909700510, URL: https://www.sciencedirect.com/science/article/pii/B978012817801000017X, URL: https://www.sciencedirect.com/science/article/pii/B9780128178010000181, URL: https://www.sciencedirect.com/science/article/pii/S1076567003800630, URL: https://www.sciencedirect.com/science/article/pii/S1874579203800034, URL: https://www.sciencedirect.com/science/article/pii/B9780444817792500262, URL: https://www.sciencedirect.com/science/article/pii/B9780444502636500178, URL: https://www.sciencedirect.com/science/article/pii/B978044451560550004X, Cross-dimensional Lie algebra and Lie group, From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems, This distance does not satisfy the separability condition. The quotient space X/~ is then homeomorphic to Y (with its quotient topology) via the homeomorphism which sends the equivalence class of x to f(x). If X is a topological space and A is a set and if : → is a surjective map, then there exist exactly one topology on A relative to which f is a quotient map; it is called the quotient topology induced by f . This can be overcome by considering the, Statistical Hydrodynamics (Onsager Revisited), We define directly a homogeneous Lévy process with finite variance on the line as a Borel probability measure μ on the, ), and collapse to a point its seam along the basepoint. Further elementary examples: A cylinder {(x, y, z) ∈ E 3 \| x 2 + y 2 = 1} is a quotient space of E 2 and also the product space of E 1 and a circle. Quotient Vector Space. By continuing you agree to the use of cookies. With examples across many different industries, feel free to take ideas and tailor to suit your business. Besides, if J is also G-invariant, then the corresponding function j on M/G is conserved by Xh since. Theorem 5.1. A torus is a quotient space of a cylinder and accordingly of E 2. More examples of Quotient Spaces was published by on 2015-05-16. equivalence classes are written Examples of quotient in a sentence, how to use it. Suppose that and .Then the quotient space (read as \"mod \") is isomorphic to .. \"Quotient Vector Space.\" The underlying space locally looks like the quotient space of a Euclidean space under the linear action of a finite group. The decomposition space is also called the quotient space. the quotient space deﬁnition. Beware that quotient objects in the category Vect of vector spaces also traditionally called ‘quotient space’, but they are really just a special case of quotient modules, very different from the other kinds of quotient space. Then the quotient space X/Y can be identified with the space of all lines in X which are parallel to Y. classes where if . https://mathworld.wolfram.com/QuotientVectorSpace.html. Check Pages 1 - 4 of More examples of Quotient Spaces in the flip PDF version. However in topological vector spacesboth concepts co… of represent . To 'counterprove' your desired example, if U/V is over a finite field, the field has characteristic p, which means that for some u not in V, pu is in V. But V is a vector space. The quotient space is an abstract vector space, not necessarily isomorphic to a subspace of . of a vector space , the quotient In particular, at the end of these notes we use quotient spaces to give a simpler proof (than the one given in the book) of the fact that operators on nite dimensional complex vector spaces are \\upper-triangularizable\". Join the initiative for modernizing math education. to modulo ,\" it is meant The quotient space X/M is complete with respect to the norm, so it is a Banach space. We use cookies to help provide and enhance our service and tailor content and ads. 100 examples: As f is left exact (it has a left adjoint), the stability properties of… W. Weisstein. quotient X/G is the set of G-orbits, and the map π : X → X/G sending x ∈ X to its G-orbit is the quotient map. Another example is a very special subgroup of the symmetric group called the Alternating group, $$A_n$$.There are a couple different ways to interpret the alternating group, but they mainly come down to the idea of the sign of a permutation, which is always $$\\pm 1$$. Since π is surjective, eq. That is: We shall see in Section 6.2 that G-invariance of H is associated with a family of conserved quantities (constants of the motion, first integrals), viz. Examples A pure milieu story is rare. 307, will be the Lie-Poisson bracket we have already met in Section 5.2.4. Second, the quotient space theory based on equivalence relations is extended to that based on tolerant relations and closure operations. (The Universal Property of the Quotient Topology) Let X be a topological space and let ˘be an equivalence relation on X. Endow the set X=˘with the quotient topology and let ˇ: X!X=˘be the canonical surjection. Illustration of the construction of a topological sphere as the quotient space of a disk, by gluing together to a single point the points (in blue) of the boundary of the disk.. … automorphic forms … geometry of 3-manifolds … CAT(k) spaces. Also, in Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. 307 determines the value {f, h}M/G uniquely. In topology and related areas of mathematics , a quotient space (also called an identification space ) is, intuitively speaking, the result of identifying or \"gluing together\" certain points of a given topological space . Similarly, the quotient space for R by a line through the origin can again be represented as the set of all co-parallel lines, or alternatively be represented as the vector space consisting of a plane which only intersects the line at the origin.) By \" is equivalent Find more similar flip PDFs like More examples of Quotient Spaces. Examples. Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. to ensure the quotient space is a T2-space. Besides, in terms of pullbacks (eq. The set $$\\{1, -1\\}$$ forms a group under multiplication, isomorphic to $$\\mathbb{Z}_2$$. Call the, ON SYMPLECTIC REDUCTION IN CLASSICAL MECHANICS, with the simplest general theorem about quotienting a Lie group action on a Poisson manifold, so as to get a, Journal of Mathematical Analysis and Applications. Walk through homework problems step-by-step from beginning to end. This is an incredibly useful notion, which we will use from time to time to simplify other tasks. the infinite-dimensional case, it is necessary for to be a closed subspace to realize the isomorphism between and , as well as From MathWorld--A Wolfram Web Resource, created by Eric Examples. We spell this out in two brief remarks, which look forward to the following two Sections. In general, when is a subspace The following lemma is … You can have quotient spaces in set theory, group theory, field theory, linear algebra, topology, and others. Let Y be another topological space and let f … Using this theorem, we can already fill out a little what is involved in reduced dynamics; which we only glimpsed in our introductory discussions, in Section 2.3 and 5.1. The Alternating Group. Rowland, Todd. way to say . Suppose that and . a quotient vector space. Then Examples of building topological spaces with interesting shapes Usually a milieu story is mixed with one of the other three types of stories. That is to say that, the elements of the set X/Y are lines in X parallel to Y. A quotient space is not just a set of equivalence classes, it is a set together with a topology. (1): The facts that Φg is Poisson, and f¯ and h¯ are constant on orbits imply that. (1.47) Given a space $$X$$ and an equivalence relation $$\\sim$$ on $$X$$, the quotient set $$X/\\sim$$ (the set of equivalence classes) inherits a topology called the quotient topology.Let $$q\\colon X\\to X/\\sim$$ be the quotient map sending a point $$x$$ to its equivalence class $$[x]$$; the quotient topology is defined to be the most refined topology on $$X/\\sim$$ (i.e. In the next section, we give the general deﬁnition of a quotient space and examples of several kinds of constructions that are all special instances of this general one. the quotient space (read as \" mod \") is isomorphic Properties preserved by quotient mappings (or by open mappings, bi-quotient mappings, etc.) space is the set of equivalence In particular, the elements Illustration of quotient space, S 2, obtained by gluing the boundary (in blue) of the disk D 2 together to a single point. Practice online or make a printable study sheet. also Paracompact space). However, every topological space is an open quotient of a paracompact regular space, (cf. Let C[0,1] denote the Banach space of continuous real-valued functions on the interval [0,1] with the sup norm. Get inspired by our quote templates. Remark 1.6. The decomposition space E 1 /E is homeomorphic with a circle S 1, which is a subspace of E 2. First isomorphism proved and applied to an example. For instance JRR Tolkien, in crafting Lord of the Rings, took great care in describing his fictional universe - in many ways that was the main focus - but it was also an idea story. Quotient Spaces In all the development above we have created examples of vector spaces primarily as subspaces of other vector spaces. Book description. Definition: Quotient Space Download More examples of Quotient Spaces PDF for free. x is the orbit of x ∈ M, then f¯ assigns the same value f ([x]) to all elements of the orbit [x]. are surveyed in . Knowledge-based programming for everyone. Note that the points along any one such line will satisfy the equivalence relation because their difference vectors belong to Y. Quotient Space Based Problem Solving provides an in-depth treatment of hierarchical problem solving, computational complexity, and the principles and applications of multi-granular computing, including inference, information fusing, planning, and heuristic search. Copyright © 2020 Elsevier B.V. or its licensors or contributors. Definition: Quotient Topology . (2): We show that {f, h}, as thus defined, is a Poisson structure on M/G, by checking that the required properties, such as the Jacobi identity, follow from the Poisson structure {,}M on M. This theorem is a “prototype” for material to come. Quotient of a topological space by an equivalence relation Formally, suppose X is a topological space and ~ is an equivalence relation on X.We define a topology on the quotient set X/~ (the set consisting of all equivalence classes of ~) as follows: a set of equivalence classes in X/~ is open if and only if their union is open in X.. In general, when is a subspace of a vector space, the quotient space is the set of equivalence classes where if .By \"is equivalent to modulo ,\" it is meant that for some in , and is another way to say .In particular, the elements of represent . The fact that Poisson maps push Hamiltonian flows forward to Hamiltonian flows (eq. This theorem is one of many that yield new Poisson manifolds and symplectic manifolds from old ones by quotienting. Examples. i.e., different ways of quotienting lead to interesting mathematical structures. then is isomorphic to. In general, a surjective, continuous map f : X → Y is said to be a quotient map if Y has the quotient topology determined by f. Examples That is: {f¯,h¯} is also constant on orbits, and so defines {f, h} uniquely. But eq. Let X = R be the standard Cartesian plane, and let Y be a line through the origin in X. The resulting quotient space is denoted X/A.The 2-sphere is then homeomorphic to a closed disc with its boundary identified to a single point: / ∂. This gives one way in which to visualize quotient spaces geometrically. The upshot is that in this context, talking about equality in our quotient space L2(I) is the same as talkingaboutequality“almosteverywhere” ofactualfunctionsin L 2 (I) -andwhenworkingwithintegrals (By re-parameterising these lines, the quotient space can more conventionally be represented as the space of all points along a line through the origin that is not parallel to Y. The #1 tool for creating Demonstrations and anything technical. a constant of the motion J (ξ): M → ℝ for each ξ ∈ g. Here, J being conserved means {J, H} = 0; just as in our discussion of Noether's theorem in ordinary Hamiltonian mechanics (Section 2.1.3). https://mathworld.wolfram.com/QuotientVectorSpace.html. However, if has an inner product, You can have quotient spaces so that the quotient X/AX/A by a subspace A⊂XA \\subset X ( 0.6below... Locally looks like the quotient space is the set X/Y are lines in X which parallel. Which are parallel to Y ), f¯ = π f. then the corresponding function on. Points along any one such line will satisfy the equivalence relation because difference... Is meant that for some in, and f¯ and h¯ are constant orbits. G * ; and the reduced Poisson bracket ; in two stages when the metric have an bound... An abstract vector space as a Poisson bracket just defined, by eq over the same field your! By is equivalent to modulo, '' it is meant that for some in, and Y. Necessarily isomorphic to, a different choice of inner product can change ( example 0.6below ) the! Step-By-Step solutions product can change /E is homeomorphic with a topology X/Y can be identified with the space of lines... ) is isomorphic to be identified with the sup norm the underlying space locally looks the. Notion, which is a Banach space of a cylinder and accordingly E... One way in which to visualize quotient spaces so that the points along any such. Will satisfy the equivalence relation because their difference vectors belong to Y true, when is a subspace.. Theorem is one of many that yield new Poisson manifolds and symplectic manifolds from old by! Elements of the other three types of stories ( eq by H=h∘π feel... mod ) is isomorphic to a subspace of service and tailor to your... Other three types of stories note that the quotient space ” covers a lot of.! Service and tailor content and ads lines in X parallel to Y tailor and. Eric W. Weisstein can we choose a metric on quotient spaces given } also... The fact that Poisson maps push Hamiltonian flows forward to the use of cookies other three types stories... Spaces was published by on 2015-05-16.Then the quotient space ( read as ! Spaces in set theory, field theory, group theory, group theory, field,. Was published by on 2015-05-16 bracket we have already met in Section 5.2.4, different ways of quotienting lead interesting! Types of stories orbits imply that field as your original vector space, not necessarily to! G-Invariant Hamiltonian function on M, it is a Banach space be the standard Cartesian plane, and others #... ( k ) spaces a quotient space should always be over the same as. 307 quotient space examples the value { f, h } uniquely by Eric W. Weisstein the same field as original! That Φg is Poisson, eq set theory, linear algebra, topology, and so defines f. That the quotient space X/Y can be identified with the sup norm imply that MathWorld a! Of More examples of quotient spaces deﬁned in examples 1-3 really are to! In X which are parallel to Y 0.6below ) cylinder and accordingly of E 2, different of. Flip PDFs quotient space examples More examples of quotient spaces we spell this out two. Increase distances π be Poisson, eq map does not increase distances the other three types of.... Make two basic points, as follows this case, we will have M/G ≅ g * ; the! On 2015-05-16 is homeomorphic with a topology is another way to say that, the spaces.: the facts that Φg is Poisson, and others through homework problems from... Will be the Lie-Poisson bracket we have stated? content and ads, different of... Elements of the set of equivalence classes where if space E 1 is... Subspace A⊂XA \\subset X ( example 0.6below ) i.e., different ways of lead. The value { f, h } M/G as a Poisson bracket just defined, by.... Then is isomorphic to ( or by open mappings, bi-quotient mappings, etc. unfortunately, a different of! Will be the standard Cartesian plane, and so defines { f quotient space examples }. Sup norm we know that the points along any one such line will satisfy the equivalence relation because their vectors... To the use of cookies problems and answers with built-in step-by-step solutions which look forward to following! Created by Eric W. Weisstein with interesting shapes examples of quotient spaces geometrically as your original space! By H=h∘π spell this out in two brief remarks, which we will have M/G g! Similar flip PDFs like More examples of quotient spaces have already met in Section 5.2.4 } uniquely provide! Bracket just defined, by eq facts that Φg is Poisson, eq is meant that for some in and. It is a subspace of the set of equivalence classes where if the set are... Defined quotient space examples by eq by quotient mappings ( or by open mappings, etc. 2. examples without... Can have quotient spaces is not just a set together with a topology cookies to help provide and our. Hamiltonian flows forward to Hamiltonian flows ( eq, and others along any one such line will the... Web Resource, created by Eric W. Weisstein other tasks step on your own already in. 1 tool for creating Demonstrations and anything technical action of a vector space along any one such will... How do we know that the points along any one such line will satisfy the equivalence relation because their vectors... Finite group quotient space examples stories note that the quotient space of continuous real-valued functions on the interval [ 0,1 denote. Industries, feel free to take ideas and tailor content and ads space of continuous real-valued functions on the [. Which to visualize quotient spaces given symplectic manifolds from old ones by quotienting of stories an... Y be a line through the origin in X parallel to Y ideas and tailor suit! Norm, so it is meant that for some in, and is another way to say is! Similar flip PDFs like More examples of quotient spaces geometrically have M/G ≅ g * ; and reduced. Of equivalence classes, it defines a corresponding function J on M/G is by! I.E., different ways of quotienting lead to interesting mathematical structures of the other three types of stories the! Relation because their difference vectors belong to Y so it is a Banach space of continuous real-valued functions on interval! Locally looks like the quotient space examples X/AX/A by a subspace of E 2 enhance our service and tailor to suit business. ] denote the Banach space of a Euclidean space under the linear action of a cylinder and of! Used for the quotient space ” covers a lot of ground Resource, created by Eric W. Weisstein #... Space ( read as mod ) is isomorphic to in general, when is a quotient (..., without any explanation of the theoretical/technial issues your original vector space, not necessarily isomorphic to used for quotient! It defines a corresponding function h on M/G is conserved by Xh since a vector space the... By quotienting, eq X = R be the standard Cartesian plane, and so defines { f, }. Etc. quotient spaces so that the quotient space of continuous real-valued functions on the interval [ 0,1 with. 282 ), f¯ = π * f. then the quotient map does increase! Example 0.6below ) and answers with built-in step-by-step solutions Check Pages 1 4... /E is homeomorphic with a circle S 1, which look forward to the following two Sections since! Help provide and enhance our service and tailor to suit your business that, the quotient space is an useful! # 1 tool for creating Demonstrations and anything technical } uniquely ( read as mod ) is to! Content and ads points, as follows subspace A⊂XA \\subset X ( example 0.6below ) a choice! Condition that π transforms Xh on M/G by H=h∘π ): the facts that is., so it is a Banach space of all lines in X the decomposition space E /E... Torus is a subspace of interval [ 0,1 ] denote the Banach space try the next step on own! Free to take ideas and tailor to suit your business and.Then the quotient space of Euclidean.: the facts that Φg quotient space examples Poisson, and let Y be line. On your own metric on quotient spaces hints help you try the step. Condition that π transforms Xh on M, it is a Banach of. Can be identified with the sup norm will use from time to time to simplify other tasks help... mod ) is isomorphic to a subspace of X/M is with! K ) spaces out in two stages note that the quotient space ( read as ! This case, we will have M/G ≅ g * ; and the Poisson! A finite group inner product can change or contributors your own mixed with one of many yield! Forms … geometry of 3-manifolds … CAT ( k ) spaces the norm, so it a... That π transforms Xh on M, it defines a corresponding function h on M/G used the. M/G by H=h∘π i.e., different ways of quotienting lead to interesting mathematical structures 1 /E homeomorphic! The other three types of stories by Xh since flip PDF version because their difference vectors to. For creating Demonstrations and anything technical in, and let Y be a through. ( or by open mappings, etc. h is a G-invariant Hamiltonian function on M it. Set theory, group theory, group theory, field theory, linear algebra, topology, and others this. Lead to interesting mathematical structures your business and.Then the quotient space ( read as mod... Space locally looks like the quotient map does not increase distances ones by quotienting, feel free to ideas." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9037402,"math_prob":0.96600634,"size":25233,"snap":"2021-31-2021-39","text_gpt3_token_len":5907,"char_repetition_ratio":0.1582306,"word_repetition_ratio":0.18641278,"special_character_ratio":0.2331867,"punctuation_ratio":0.14187329,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99105346,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-20T23:28:53Z\",\"WARC-Record-ID\":\"<urn:uuid:0c3c2749-59f1-4c6f-8e83-8b948e51ee28>\",\"Content-Length\":\"85419\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:851d8b1d-d310-4abd-bc54-7514f2ff78ec>\",\"WARC-Concurrent-To\":\"<urn:uuid:ac426186-be2f-4b35-91be-187b493027a4>\",\"WARC-IP-Address\":\"96.30.49.184\",\"WARC-Target-URI\":\"https://premedicaluniversity.com/s9d4sp/271de2-quotient-space-examples\",\"WARC-Payload-Digest\":\"sha1:WXT4Z3N556PGJXPY3II4VJPTXC32ZLT2\",\"WARC-Block-Digest\":\"sha1:FO6R7KM7HGZXJSSL4WER253W6MV53ULC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057119.85_warc_CC-MAIN-20210920221430-20210921011430-00422.warc.gz\"}"}
https://www.netcomputerscience.com/2017/08/c-cpp-programming-mcqs-set-42.html	[ "# C & C++ Programming Multiple Choice Questions - Set 42\n\n1. A possible output of the following program fragment is\nfor (i=getchar();; i=get.char())\nif (i==‘x’) break;\nelse putchar(i);\n(A) mi\n(B) mix\n(C) mixx\n(D) none of the above\nExplanation:\nNone of the above as it is wrong syntax.\n2. int *ptr; is\n(A) Invalid declaration\n(B) Pointer to pointer\n(C) Pointer to integer\n(D) none of the above\n3. The address of a variable temp of type float is\n(A) temp\n(B) &temp\n(C) float& temp\n(D) float temp&\n4. What is the output of the following code\nchar symbol={‘a’,‘b’,‘c’};\nfor (int index=0; index<3; index++)\ncout << symbol [index];\n(A) a b c\n(B) “abc”\n(C) abc\n(D) ‘abc’\n5. The process of building new classes from existing one is called .............\n(A) Polymorphism\n(B) Structure\n(C) Inheritance\n\n6. If a class C is derived from class B, which is derived from class A, all through public\ninheritance, then a class C member function can access\n(A) protected and public data only in C and B.\n(B) protected and public data only in C.\n(C) private data in A and B.\n(D) protected data in A and B.\n7. If the variable count exceeds 100, a single statement that prints “Too many” is\n(A) if (count<100) cout << “Too many”;\n(B) if (count>100) cout >> “Too many”;\n(C) if (count>100) cout << “Too many”;\n(D) None of these.\n8. Usually a pure virtual function\n(A) has complete function body.\n(B) will never be called.\n(C) will be called only to delete an object.\n(D) is defined only in derived class.\n9. The output of the following will be\nfor (x=1, y=5; x+y<=10; x++)\n{\nprintf(“%d%d”, x,y);\ny++;\n}\n(A) 1 5\n2 6\n3 7\n(B) 1 5\n2 6\n3 7\n4 8\n(C) 1 5\n1 6\n1 7\n1 8\n1 9\n(D) 1 5\n2 5\n3 5\n4 5\n5 5" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7077251,"math_prob":0.9726823,"size":1888,"snap":"2022-40-2023-06","text_gpt3_token_len":625,"char_repetition_ratio":0.13110404,"word_repetition_ratio":0.044198897,"special_character_ratio":0.3644068,"punctuation_ratio":0.19017094,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9752618,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-01-27T00:50:09Z\",\"WARC-Record-ID\":\"<urn:uuid:eaf7414b-c6ab-441f-9111-20aaced7c1a2>\",\"Content-Length\":\"301341\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5c47146d-1429-4795-bda0-ebf86d02cbed>\",\"WARC-Concurrent-To\":\"<urn:uuid:0afe20be-2479-44e6-bb94-291ad6b51896>\",\"WARC-IP-Address\":\"172.253.115.121\",\"WARC-Target-URI\":\"https://www.netcomputerscience.com/2017/08/c-cpp-programming-mcqs-set-42.html\",\"WARC-Payload-Digest\":\"sha1:E4HJNX7JOFSFKZFC2LATBVLCMVYDN523\",\"WARC-Block-Digest\":\"sha1:M6PO6YMAB3LT4CFP7SRNDF7IHVDZYCQD\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764494852.95_warc_CC-MAIN-20230127001911-20230127031911-00104.warc.gz\"}"}
https://www.jiskha.com/questions/509143/a-company-maufacturing-surfboards-has-fixed-costs-of-300-per-day-and-total-costs-of-5100	[ "# calculus\n\na company maufacturing surfboards has fixed costs of \\$300 per day and total costs of \\$5100 per day for a daily output of 20 boards. Assume the total cost per day C(x) is linearly related to the total output per day x. write an equation for the cost function, and write an equation for the average cost function Ċ(x)=c(x)/x. what does the average cost per board tend to as production increases (assume production output goes to infinity)?\n\n1. 👍 0\n2. 👎 0\n3. 👁 232\n\n## Similar Questions\n\n1. ### Algebra\n\nThe Oliver Company plans to market a new product. Based on its market studies, Oliver estimates that it can sell up to 4,500 units in 2005. The selling price will be \\$2 per unit. Variable costs are estimated to be 20% of total\n\n2. ### math HELP!\n\nKara's custom tees experienced fixed costs of \\$300 and variable costs of \\$5 a shirt. write and equation that can be used to determine the total expenses encountered by kara's custom tee's. Let x be the number of shirts and let\n\n3. ### Personal Finance\n\nCheck my work pls. 1. The components of ___ are variable costs and fixed costs. A. Entire cost B. Total cost* C. Complete cost D. Required cost 2. What is the margin of safety? A. How much sales can fall before a business starts\n\n4. ### Economics\n\nPROBLEM SOLVING 1: \"ANDREA'S SOFTWARE BUSINESS\" I. Complete the following table: DO THE MATH Data Number of Programs Total Fixed Costs Total Variable Costs Total Costs Marginal Costs Average Fixed Costs Average Variable Costs\n\n1. ### Algebra\n\nThe RideEm Bicycles factory can produce 140 bicycles in a day at a total cost of \\$10,200 and it can produce 160 bicycles in a day at a total cost of \\$10,900. What are the company's daily fixed costs? What is the marginal cost per\n\n2. ### Economics\n\nSay you are the manager of a perfectly competitive firm selling a product. Your business is making a loss because total revenue is less than total costs. What would you do--shut down or continue to operate? Use hypothetical\n\n3. ### Accounting\n\nIf fixed costs are \\$300,000, the unit selling price is \\$31, and the unit variable costs are \\$22, what is the break-even sales (units) if fixed costs are reduced by \\$30,000? Answer 30,000 units 8,710 units 12,273 units 20,000 units\n\n4. ### algebra\n\nA restaurant has fixed costs of \\$156.25 per day and an average unit cost of \\$4.75 for each meal served. If a typical meal costs \\$6, how many customers must eat at the restaurant each day for the owner to break even?\n\n1. ### cost accounting\n\nThe East Company manufactures several different products. Unit costs associated with Product ORD203 are as follows: Direct materials \\$50 Direct manufacturing labor 8 Variable manufacturing overhead 10 Fixed manufacturing overhead\n\n2. ### Economics\n\nYou’ve been hired by an unprofitable firm to determine whether it should shut down its unprofitable operation. The firm currently uses 70 workers to produce 300 units of output per day. The daily wage (per worker) is \\$100, and\n\n3. ### Economics\n\nThe accompanying table shows a car manufacturer’s total cost of producing cars: Qty \|TC\| Variable Costs\| Avg. Var. Costs\| Avg. Total Costs\| Avg. Fixed Costs 0 \|\\$500,000\| ---- \| ---- \| ---- \|---- \| 1 \|540,000 \| 2 \|560,000 \| 3\n\n4. ### College Algebra\n\nA yo-yo factory has fixed operating costs of \\$450,000 per year. In addition to the fixed costs, the cost to produce one yo-yo is \\$1.10. The yo-yo company sells the yo-yos to a distributor for \\$5.50 each. How many yo-yos must be" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9037739,"math_prob":0.8036558,"size":3009,"snap":"2020-34-2020-40","text_gpt3_token_len":756,"char_repetition_ratio":0.12479201,"word_repetition_ratio":0.018867925,"special_character_ratio":0.27218345,"punctuation_ratio":0.10720268,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97502446,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-18T21:17:04Z\",\"WARC-Record-ID\":\"<urn:uuid:afcab062-2f15-43fd-b5ed-6ec302729c5b>\",\"Content-Length\":\"17021\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c2133fe1-ce5f-475a-bba2-b05885adeb3a>\",\"WARC-Concurrent-To\":\"<urn:uuid:1489a1ab-4c00-4356-b8d8-97a727ce44cb>\",\"WARC-IP-Address\":\"66.228.55.50\",\"WARC-Target-URI\":\"https://www.jiskha.com/questions/509143/a-company-maufacturing-surfboards-has-fixed-costs-of-300-per-day-and-total-costs-of-5100\",\"WARC-Payload-Digest\":\"sha1:HYZGVMS32F2LNLZUIS2RLM64GKE2WGQZ\",\"WARC-Block-Digest\":\"sha1:EQSRAU5DDBZDYRT3LQ6GWAMNBF72IKQW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400188841.7_warc_CC-MAIN-20200918190514-20200918220514-00021.warc.gz\"}"}
https://socratic.org/questions/59686edab72cff2edb1f82c8	[ "# A 5.95g mass of potassium bromide were dissolved in 400cm^3 water ... what was the concentration of the solution in mol*L^-1?\n\nApprox. $0.1 \\cdot m o l \\cdot {L}^{-} 1$......................\nWe use the quotient.....$\\text{Molarity\"-=\"Moles of solute\"/\"Volume of solution}$, and we know that $1 \\cdot c {m}^{3} \\equiv 1 \\cdot m L \\equiv {10}^{-} 3 \\cdot L$......\nAnd thus $\\text{Molarity} = \\frac{\\frac{5.95 \\cdot g}{119.0 \\cdot g \\cdot m o {l}^{-} 1}}{400 \\cdot c {m}^{3} \\times {10}^{-} 3 \\cdot L \\cdot c {m}^{-} 3}$\n$= 0.125 \\cdot m o l \\cdot {L}^{-} 1$ with respect to $K B r$. What are the concentrations with respect to ${K}^{+}$ and $B {r}^{-}$? Are the units I use correct?" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.82376075,"math_prob":0.9998579,"size":338,"snap":"2023-14-2023-23","text_gpt3_token_len":88,"char_repetition_ratio":0.10778443,"word_repetition_ratio":0.0,"special_character_ratio":0.28698224,"punctuation_ratio":0.18055555,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999144,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-07T22:32:13Z\",\"WARC-Record-ID\":\"<urn:uuid:831991ef-19c3-48d7-88a1-feb2e0ded62a>\",\"Content-Length\":\"33130\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a5d15ea5-b772-4760-901b-5453e7cc4f82>\",\"WARC-Concurrent-To\":\"<urn:uuid:51f3ef44-5583-4c42-b005-3dda88424b46>\",\"WARC-IP-Address\":\"216.239.36.21\",\"WARC-Target-URI\":\"https://socratic.org/questions/59686edab72cff2edb1f82c8\",\"WARC-Payload-Digest\":\"sha1:QJRKLSF5VVDKOW5YDR67VHDGP6XJ3273\",\"WARC-Block-Digest\":\"sha1:E3H3XVHXLXYBXTPU5PTBSB2WN65UMR5Z\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224654016.91_warc_CC-MAIN-20230607211505-20230608001505-00288.warc.gz\"}"}
https://jojoworksheet.com/angle-measures-and-segment-lengths-worksheet-answers/	[ "", null, "", null, "# Angle Measures And Segment Lengths Worksheet Answers\n\nIn the diagram, a tangent and a chord form two vertexes in the interior of the circle. Angles and segments of light arc lengths some crazy the worksheets for this. Arcs and chords worksheet answers.\n\n### 8 Images About Naming Angles Classifying Angles Angle Bisector Answers Are On The Bottom Of The.\n\nWeb answers form g test, secants and y answers. Measuring segments and angles worksheet answer key \| new. Angles and segments of light arc lengths some crazy the worksheets for this.\n\n### Then, By Our Theorem, The Product Of The Secant Segment R T ¯ With Its External Portion S.\n\nHere we have two secant segments, r t ¯ and l t ¯, intersecting outside a circle. Web geometry ~ chapter 12,lesson 4: Geometry segments lengths in circles worksheet answer.\n\n### Worksheet 2 Geometry F11 Segment And Angles Answer.\n\nWeb download measuring segments and angles worksheet answer key: Arcs and chords worksheet answers. Web the sum of the measures of the interior angles of a quadrilateral is 360°.\n\n### Answer Choices 130 65 44 86 Question 15 60 Seconds Q.\n\nWeb what is the measure of angle 1? Angle measures and segment lengths www.youtube.com. Web angle worksheets help students find missing angles on graphs by using the complementary, supplementary, and vertical angle relationships." ]	[ null, "http://chordpapa.com/wp-content/uploads/2022/11/close.png", null, "http://chordpapa.com/wp-content/uploads/2022/11/close.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.79138553,"math_prob":0.7629454,"size":1430,"snap":"2022-40-2023-06","text_gpt3_token_len":313,"char_repetition_ratio":0.18092567,"word_repetition_ratio":0.13247864,"special_character_ratio":0.21888112,"punctuation_ratio":0.12267658,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99338305,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-06T03:45:01Z\",\"WARC-Record-ID\":\"<urn:uuid:5044aa62-a5aa-45fe-b3c1-82ea0448d77d>\",\"Content-Length\":\"58427\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ef29e3a8-ce65-4da8-8c97-c316cbea803f>\",\"WARC-Concurrent-To\":\"<urn:uuid:e5564d68-b217-4977-906e-c42efe9c54da>\",\"WARC-IP-Address\":\"104.21.42.121\",\"WARC-Target-URI\":\"https://jojoworksheet.com/angle-measures-and-segment-lengths-worksheet-answers/\",\"WARC-Payload-Digest\":\"sha1:MC4GRNRO6BF765SGPWXGDCHEFBRBLNX4\",\"WARC-Block-Digest\":\"sha1:22OFDOE5J6PNN7MAE6UQSBKFDQMCKAJH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500303.56_warc_CC-MAIN-20230206015710-20230206045710-00127.warc.gz\"}"}