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	<html><!-- Created using the cpp_pretty_printer from the dlib C++ library. See http://dlib.net for updates. --><head><title>dlib C++ Library - line_abstract.h</title></head><body bgcolor='white'><pre>
	<font color='#009900'>// Copyright (C) 2018 Davis E. King ([email protected])
	</font><font color='#009900'>// License: Boost Software License See LICENSE.txt for the full license.
	</font><font color='#0000FF'>#undef</font> DLIB_LInE_ABSTRACT_H_
	<font color='#0000FF'>#ifdef</font> DLIB_LInE_ABSTRACT_H_

	<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='../vector_abstract.h.html'>../vector_abstract.h</a>"
	<font color='#0000FF'>#include</font> <font color='#5555FF'><</font>vector<font color='#5555FF'>></font>

	<font color='#0000FF'>namespace</font> dlib
	<b>{</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>class</font> <b><a name='line'></a>line</b>
	<b>{</b>
	<font color='#009900'>/*!
	WHAT THIS OBJECT REPRESENTS
	This object represents a line in the 2D plane. The line is defined by two
	points running through it, p1() and p2(). This object also includes a
	unit normal vector that is perpendicular to the line.
	!*/</font>

	<font color='#0000FF'>public</font>:

	<b><a name='line'></a>line</b><font face='Lucida Console'>(</font>
	<font face='Lucida Console'>)</font>;
	<font color='#009900'>/*!
	ensures
	- p1(), p2(), and normal() are all the 0 vector.
	!*/</font>

	<b><a name='line'></a>line</b><font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> dpoint<font color='#5555FF'>&</font> a,
	<font color='#0000FF'>const</font> dpoint<font color='#5555FF'>&</font> b
	<font face='Lucida Console'>)</font>;
	<font color='#009900'>/*!
	ensures
	- #p1() == a
	- #p2() == b
	- #normal() == A vector normal to the line passing through points a and b.
	In particular, it is given by: (a-b).cross(dlib::vector<double,3>(0,0,1)).normalize().
	Therefore, the normal vector is the vector (a-b) but unit normalized and rotated clockwise 90 degrees.
	!*/</font>

	<font color='#0000FF'>template</font> <font color='#5555FF'><</font><font color='#0000FF'>typename</font> T<font color='#5555FF'>></font>
	<b><a name='line'></a>line</b><font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> std::pair<font color='#5555FF'><</font>vector<font color='#5555FF'><</font>T,<font color='#979000'>2</font><font color='#5555FF'>></font>,vector<font color='#5555FF'><</font>T,<font color='#979000'>2</font><font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#5555FF'>&</font> l
	<font face='Lucida Console'>)</font>;
	<font color='#009900'>/*!
	ensures
	- #*this == line(l.first, l.second)
	!*/</font>

	<font color='#0000FF'>const</font> dpoint<font color='#5555FF'>&</font> <b><a name='p1'></a>p1</b><font face='Lucida Console'>(</font>
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
	<font color='#009900'>/*!
	ensures
	- returns the first endpoint of the line.
	!*/</font>

	<font color='#0000FF'>const</font> dpoint<font color='#5555FF'>&</font> <b><a name='p2'></a>p2</b><font face='Lucida Console'>(</font>
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
	<font color='#009900'>/*!
	ensures
	- returns the second endpoint of the line.
	!*/</font>

	<font color='#0000FF'>const</font> dpoint<font color='#5555FF'>&</font> <b><a name='normal'></a>normal</b><font face='Lucida Console'>(</font>
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
	<font color='#009900'>/*!
	ensures
	- returns a unit vector that is normal to the line passing through p1() and p2().
	!*/</font>

	<b>}</b>;

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>template</font> <font color='#5555FF'><</font><font color='#0000FF'>typename</font> U<font color='#5555FF'>></font>
	<font color='#0000FF'><u>double</u></font> <b><a name='signed_distance_to_line'></a>signed_distance_to_line</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> line<font color='#5555FF'>&</font> l,
	<font color='#0000FF'>const</font> vector<font color='#5555FF'><</font>U,<font color='#979000'>2</font><font color='#5555FF'>></font><font color='#5555FF'>&</font> p
	<font face='Lucida Console'>)</font>;
	<font color='#009900'>/*!
	ensures
	- returns how far p is from the line l. This is a signed distance. The sign
	indicates which side of the line the point is on and the magnitude is the
	distance. Moreover, the direction of positive sign is pointed to by the
	vector l.normal().
	- To be specific, this routine returns dot(p-l.p1(), l.normal())
	!*/</font>

	<font color='#0000FF'>template</font> <font color='#5555FF'><</font><font color='#0000FF'>typename</font> T, <font color='#0000FF'>typename</font> U<font color='#5555FF'>></font>
	<font color='#0000FF'><u>double</u></font> <b><a name='signed_distance_to_line'></a>signed_distance_to_line</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> std::pair<font color='#5555FF'><</font>vector<font color='#5555FF'><</font>T,<font color='#979000'>2</font><font color='#5555FF'>></font>,vector<font color='#5555FF'><</font>T,<font color='#979000'>2</font><font color='#5555FF'>></font> <font color='#5555FF'>></font><font color='#5555FF'>&</font> l,
	<font color='#0000FF'>const</font> vector<font color='#5555FF'><</font>U,<font color='#979000'>2</font><font color='#5555FF'>></font><font color='#5555FF'>&</font> p
	<font face='Lucida Console'>)</font>;
	<font color='#009900'>/*!
	ensures
	- returns signed_distance_to_line(line(l),p);
	!*/</font>

	<font color='#0000FF'>template</font> <font color='#5555FF'><</font><font color='#0000FF'>typename</font> T, <font color='#0000FF'>typename</font> U<font color='#5555FF'>></font>
	<font color='#0000FF'><u>double</u></font> <b><a name='distance_to_line'></a>distance_to_line</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> std::pair<font color='#5555FF'><</font>vector<font color='#5555FF'><</font>T,<font color='#979000'>2</font><font color='#5555FF'>></font>,vector<font color='#5555FF'><</font>T,<font color='#979000'>2</font><font color='#5555FF'>></font> <font color='#5555FF'>></font><font color='#5555FF'>&</font> l,
	<font color='#0000FF'>const</font> vector<font color='#5555FF'><</font>U,<font color='#979000'>2</font><font color='#5555FF'>></font><font color='#5555FF'>&</font> p
	<font face='Lucida Console'>)</font>;
	<font color='#009900'>/*!
	ensures
	- returns abs(signed_distance_to_line(l,p))
	!*/</font>

	<font color='#0000FF'>template</font> <font color='#5555FF'><</font><font color='#0000FF'>typename</font> U<font color='#5555FF'>></font>
	<font color='#0000FF'><u>double</u></font> <b><a name='distance_to_line'></a>distance_to_line</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> line<font color='#5555FF'>&</font> l,
	<font color='#0000FF'>const</font> vector<font color='#5555FF'><</font>U,<font color='#979000'>2</font><font color='#5555FF'>></font><font color='#5555FF'>&</font> p
	<font face='Lucida Console'>)</font>;
	<font color='#009900'>/*!
	ensures
	- returns abs(signed_distance_to_line(l,p))
	!*/</font>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	line <b><a name='reverse'></a>reverse</b><font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> line<font color='#5555FF'>&</font> l
	<font face='Lucida Console'>)</font>;
	<font color='#009900'>/*!
	ensures
	- returns line(l.p2(), l.p1())
	(i.e. returns a line object that represents the same line as l but with the
	endpoints, and therefore, the normal vector flipped. This means that the
	signed distance of operator() is also flipped).
	!*/</font>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	dpoint <b><a name='intersect'></a>intersect</b><font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> line<font color='#5555FF'>&</font> a,
	<font color='#0000FF'>const</font> line<font color='#5555FF'>&</font> b
	<font face='Lucida Console'>)</font>;
	<font color='#009900'>/*!
	ensures
	- returns the point of intersection between lines a and b. If no such point
	exists then this function returns a point with Inf values in it.
	!*/</font>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>double</u></font> <b><a name='angle_between_lines'></a>angle_between_lines</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> line<font color='#5555FF'>&</font> a,
	<font color='#0000FF'>const</font> line<font color='#5555FF'>&</font> b
	<font face='Lucida Console'>)</font>;
	<font color='#009900'>/*!
	ensures
	- returns the angle, in degrees, between the given lines. This is a number in
	the range [0 90].
	!*/</font>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>template</font> <font color='#5555FF'><</font><font color='#0000FF'>typename</font> T<font color='#5555FF'>></font>
	dpoint <b><a name='intersect'></a>intersect</b><font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> std::pair<font color='#5555FF'><</font>vector<font color='#5555FF'><</font>T,<font color='#979000'>2</font><font color='#5555FF'>></font>,vector<font color='#5555FF'><</font>T,<font color='#979000'>2</font><font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#5555FF'>&</font> a,
	<font color='#0000FF'>const</font> std::pair<font color='#5555FF'><</font>vector<font color='#5555FF'><</font>T,<font color='#979000'>2</font><font color='#5555FF'>></font>,vector<font color='#5555FF'><</font>T,<font color='#979000'>2</font><font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#5555FF'>&</font> b
	<font face='Lucida Console'>)</font>;
	<font color='#009900'>/*!
	ensures
	- returns intersect(line(a), line(b))
	!*/</font>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>template</font> <font color='#5555FF'><</font><font color='#0000FF'>typename</font> T<font color='#5555FF'>></font>
	<font color='#0000FF'><u>size_t</u></font> <b><a name='count_points_on_side_of_line'></a>count_points_on_side_of_line</b><font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> line<font color='#5555FF'>&</font> l,
	<font color='#0000FF'>const</font> dpoint<font color='#5555FF'>&</font> reference_point,
	<font color='#0000FF'>const</font> std::vector<font color='#5555FF'><</font>vector<font color='#5555FF'><</font>T,<font color='#979000'>2</font><font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#5555FF'>&</font> pts,
	<font color='#0000FF'>const</font> <font color='#0000FF'><u>double</u></font><font color='#5555FF'>&</font> dist_thresh_min <font color='#5555FF'>=</font> <font color='#979000'>0</font>,
	<font color='#0000FF'>const</font> <font color='#0000FF'><u>double</u></font><font color='#5555FF'>&</font> dist_thresh_max <font color='#5555FF'>=</font> std::numeric_limits<font color='#5555FF'><</font><font color='#0000FF'><u>double</u></font><font color='#5555FF'>></font>::<font color='#BB00BB'>infinity</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>
	<font face='Lucida Console'>)</font>;
	<font color='#009900'>/*!
	ensures
	- Returns a count of how many points in pts have a distance from the line l
	that is in the range [dist_thresh_min, dist_thresh_max]. This distance is a
	signed value that indicates how far a point is from the line. Moreover, if
	the point is on the same side as reference_point then the distance is
	positive, otherwise it is negative. So for example, If this range is [0,
	infinity] then this function counts how many points are on the same side of l
	as reference_point.
	!*/</font>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>template</font> <font color='#5555FF'><</font><font color='#0000FF'>typename</font> T<font color='#5555FF'>></font>
	<font color='#0000FF'><u>double</u></font> <b><a name='count_points_between_lines'></a>count_points_between_lines</b><font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> line<font color='#5555FF'>&</font> l1,
	<font color='#0000FF'>const</font> line<font color='#5555FF'>&</font> l2,
	<font color='#0000FF'>const</font> dpoint<font color='#5555FF'>&</font> reference_point,
	<font color='#0000FF'>const</font> std::vector<font color='#5555FF'><</font>vector<font color='#5555FF'><</font>T,<font color='#979000'>2</font><font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#5555FF'>&</font> pts
	<font face='Lucida Console'>)</font>;
	<font color='#009900'>/*!
	ensures
	- Counts and returns the number of points in pts that are between lines l1 and
	l2. Since a pair of lines will, in the general case, divide the plane into 4
	regions, we identify the region of interest as the one that contains the
	reference_point. Therefore, this function counts the number of points in pts
	that appear in the same region as reference_point.
	!*/</font>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>struct</font> <b><a name='no_convex_quadrilateral'></a>no_convex_quadrilateral</b> : dlib::error
	<b>{</b>
	<font color='#009900'>/*!
	WHAT THIS OBJECT REPRESENTS
	This is the exception thrown by find_convex_quadrilateral() if the inputs
	can't form a convex quadrilateral.
	!*/</font>
	<b><a name='no_convex_quadrilateral'></a>no_convex_quadrilateral</b><font face='Lucida Console'>(</font>
	<font face='Lucida Console'>)</font> : dlib::error<font face='Lucida Console'>(</font>"<font color='#CC0000'>Lines given to find_convex_quadrilateral() don't form any convex quadrilateral.</font>"<font face='Lucida Console'>)</font>
	<b>{</b><b>}</b>
	<b>}</b>;

	std::array<font color='#5555FF'><</font>dpoint,<font color='#979000'>4</font><font color='#5555FF'>></font> <b><a name='find_convex_quadrilateral'></a>find_convex_quadrilateral</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> std::array<font color='#5555FF'><</font>line,<font color='#979000'>4</font><font color='#5555FF'>></font><font color='#5555FF'>&</font> lines
	<font face='Lucida Console'>)</font>;
	<font color='#009900'>/*!
	ensures
	- Is there a set of 4 points, made up of the intersections of the given lines,
	that forms a convex quadrilateral? If yes then this routine returns those 4
	points and if not throws no_convex_quadrilateral.
	throws
	- no_convex_quadrilateral
	!*/</font>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<b>}</b>

	<font color='#0000FF'>#endif</font> <font color='#009900'>// DLIB_LInE_ABSTRACT_H_
	</font>

	</pre></body></html>