init commit

.gitattributes

@@ -36,3 +36,4 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
 simple-knn/build/lib.linux-x86_64-cpython-39/simple_knn/_C.cpython-39-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text
 simple-knn/build/temp.linux-x86_64-cpython-39/.ninja_deps filter=lfs diff=lfs merge=lfs -text
 simple-knn/build/temp.linux-x86_64-cpython-39/simple_knn.o filter=lfs diff=lfs merge=lfs -text
+diff-gaussian-rasterization-camera/third_party/glm/doc/manual.pdf filter=lfs diff=lfs merge=lfs -text

diff-gaussian-rasterization-camera/CMakeLists.txt

@@ -0,0 +1,36 @@
+#
+# Copyright (C) 2023, Inria
+# GRAPHDECO research group, https://team.inria.fr/graphdeco
+# All rights reserved.
+#
+# This software is free for non-commercial, research and evaluation use 
+# under the terms of the LICENSE.md file.
+#
+# For inquiries contact  [email protected]
+#
+
+cmake_minimum_required(VERSION 3.20)
+
+project(DiffRast LANGUAGES CUDA CXX)
+
+set(CMAKE_CXX_STANDARD 17)
+set(CMAKE_CXX_EXTENSIONS OFF)
+set(CMAKE_CUDA_STANDARD 17)
+
+set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+
+add_library(CudaRasterizer
+	cuda_rasterizer/backward.h
+	cuda_rasterizer/backward.cu
+	cuda_rasterizer/forward.h
+	cuda_rasterizer/forward.cu
+	cuda_rasterizer/auxiliary.h
+	cuda_rasterizer/rasterizer_impl.cu
+	cuda_rasterizer/rasterizer_impl.h
+	cuda_rasterizer/rasterizer.h
+)
+
+set_target_properties(CudaRasterizer PROPERTIES CUDA_ARCHITECTURES "75;86")
+
+target_include_directories(CudaRasterizer PUBLIC ${CMAKE_CURRENT_SOURCE_DIR}/cuda_rasterizer)
+target_include_directories(CudaRasterizer PRIVATE third_party/glm ${CMAKE_CUDA_TOOLKIT_INCLUDE_DIRECTORIES})

diff-gaussian-rasterization-camera/LICENSE.md

@@ -0,0 +1,83 @@
+Gaussian-Splatting License  
+===========================  
+
+**Inria** and **the Max Planck Institut for Informatik (MPII)** hold all the ownership rights on the *Software* named **gaussian-splatting**.  
+The *Software* is in the process of being registered with the Agence pour la Protection des  
+Programmes (APP).  
+
+The *Software* is still being developed by the *Licensor*.  
+
+*Licensor*'s goal is to allow the research community to use, test and evaluate  
+the *Software*.  
+
+## 1.  Definitions  
+
+*Licensee* means any person or entity that uses the *Software* and distributes  
+its *Work*.  
+
+*Licensor* means the owners of the *Software*, i.e Inria and MPII  
+
+*Software* means the original work of authorship made available under this  
+License ie gaussian-splatting.  
+
+*Work* means the *Software* and any additions to or derivative works of the  
+*Software* that are made available under this License.  
+
+
+## 2.  Purpose  
+This license is intended to define the rights granted to the *Licensee* by  
+Licensors under the *Software*.  
+
+## 3.  Rights granted  
+
+For the above reasons Licensors have decided to distribute the *Software*.  
+Licensors grant non-exclusive rights to use the *Software* for research purposes  
+to research users (both academic and industrial), free of charge, without right  
+to sublicense.. The *Software* may be used "non-commercially", i.e., for research  
+and/or evaluation purposes only.  
+
+Subject to the terms and conditions of this License, you are granted a  
+non-exclusive, royalty-free, license to reproduce, prepare derivative works of,  
+publicly display, publicly perform and distribute its *Work* and any resulting  
+derivative works in any form.  
+
+## 4.  Limitations  
+
+**4.1 Redistribution.** You may reproduce or distribute the *Work* only if (a) you do  
+so under this License, (b) you include a complete copy of this License with  
+your distribution, and (c) you retain without modification any copyright,  
+patent, trademark, or attribution notices that are present in the *Work*.  
+
+**4.2 Derivative Works.** You may specify that additional or different terms apply  
+to the use, reproduction, and distribution of your derivative works of the *Work*  
+("Your Terms") only if (a) Your Terms provide that the use limitation in  
+Section 2 applies to your derivative works, and (b) you identify the specific  
+derivative works that are subject to Your Terms. Notwithstanding Your Terms,  
+this License (including the redistribution requirements in Section 3.1) will  
+continue to apply to the *Work* itself.  
+
+**4.3** Any other use without of prior consent of Licensors is prohibited. Research  
+users explicitly acknowledge having received from Licensors all information  
+allowing to appreciate the adequacy between of the *Software* and their needs and  
+to undertake all necessary precautions for its execution and use.  
+
+**4.4** The *Software* is provided both as a compiled library file and as source  
+code. In case of using the *Software* for a publication or other results obtained  
+through the use of the *Software*, users are strongly encouraged to cite the  
+corresponding publications as explained in the documentation of the *Software*.  
+
+## 5.  Disclaimer  
+
+THE USER CANNOT USE, EXPLOIT OR DISTRIBUTE THE *SOFTWARE* FOR COMMERCIAL PURPOSES  
+WITHOUT PRIOR AND EXPLICIT CONSENT OF LICENSORS. YOU MUST CONTACT INRIA FOR ANY  
+UNAUTHORIZED USE: [email protected] . ANY SUCH ACTION WILL  
+CONSTITUTE A FORGERY. THIS *SOFTWARE* IS PROVIDED "AS IS" WITHOUT ANY WARRANTIES  
+OF ANY NATURE AND ANY EXPRESS OR IMPLIED WARRANTIES, WITH REGARDS TO COMMERCIAL  
+USE, PROFESSIONNAL USE, LEGAL OR NOT, OR OTHER, OR COMMERCIALISATION OR  
+ADAPTATION. UNLESS EXPLICITLY PROVIDED BY LAW, IN NO EVENT, SHALL INRIA OR THE  
+AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR  
+CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE  
+GOODS OR SERVICES, LOSS OF USE, DATA, OR PROFITS OR BUSINESS INTERRUPTION)  
+HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT  
+LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING FROM, OUT OF OR  
+IN CONNECTION WITH THE *SOFTWARE* OR THE USE OR OTHER DEALINGS IN THE *SOFTWARE*.  

diff-gaussian-rasterization-camera/README.md

@@ -0,0 +1,35 @@
+# Differential Gaussian Rasterization
+
+**NOTE**: this is a modified version to support depth & alpha rendering (both forward and backward) from the [original repository](https://github.com/graphdeco-inria/diff-gaussian-rasterization). 
+
+```python
+rendered_image, radii, rendered_depth, rendered_alpha = rasterizer(
+    means3D=means3D,
+    means2D=means2D,
+    shs=shs,
+    colors_precomp=colors_precomp,
+    opacities=opacity,
+    scales=scales,
+    rotations=rotations,
+    cov3D_precomp=cov3D_precomp,
+)
+```
+
+
+Used as the rasterization engine for the paper "3D Gaussian Splatting for Real-Time Rendering of Radiance Fields". If you can make use of it in your own research, please be so kind to cite us.
+
+<section class="section" id="BibTeX">
+  <div class="container is-max-desktop content">
+    <h2 class="title">BibTeX</h2>
+    <pre><code>@Article{kerbl3Dgaussians,
+      author       = {Kerbl, Bernhard and Kopanas, Georgios and Leimk{\"u}hler, Thomas and Drettakis, George},
+      title        = {3D Gaussian Splatting for Real-Time Radiance Field Rendering},
+      journal      = {ACM Transactions on Graphics},
+      number       = {4},
+      volume       = {42},
+      month        = {July},
+      year         = {2023},
+      url          = {https://repo-sam.inria.fr/fungraph/3d-gaussian-splatting/}
+}</code></pre>
+  </div>
+</section>

diff-gaussian-rasterization-camera/cuda_rasterizer/auxiliary.h

@@ -0,0 +1,175 @@
+/*
+ * Copyright (C) 2023, Inria
+ * GRAPHDECO research group, https://team.inria.fr/graphdeco
+ * All rights reserved.
+ *
+ * This software is free for non-commercial, research and evaluation use 
+ * under the terms of the LICENSE.md file.
+ *
+ * For inquiries contact  [email protected]
+ */
+
+#ifndef CUDA_RASTERIZER_AUXILIARY_H_INCLUDED
+#define CUDA_RASTERIZER_AUXILIARY_H_INCLUDED
+
+#include "config.h"
+#include "stdio.h"
+
+#define BLOCK_SIZE (BLOCK_X * BLOCK_Y)
+#define NUM_WARPS (BLOCK_SIZE/32)
+
+// Spherical harmonics coefficients
+__device__ const float SH_C0 = 0.28209479177387814f;
+__device__ const float SH_C1 = 0.4886025119029199f;
+__device__ const float SH_C2[] = {
+	1.0925484305920792f,
+	-1.0925484305920792f,
+	0.31539156525252005f,
+	-1.0925484305920792f,
+	0.5462742152960396f
+};
+__device__ const float SH_C3[] = {
+	-0.5900435899266435f,
+	2.890611442640554f,
+	-0.4570457994644658f,
+	0.3731763325901154f,
+	-0.4570457994644658f,
+	1.445305721320277f,
+	-0.5900435899266435f
+};
+
+__forceinline__ __device__ float ndc2Pix(float v, int S)
+{
+	return ((v + 1.0) * S - 1.0) * 0.5;
+}
+
+__forceinline__ __device__ void getRect(const float2 p, int max_radius, uint2& rect_min, uint2& rect_max, dim3 grid)
+{
+	rect_min = {
+		min(grid.x, max((int)0, (int)((p.x - max_radius) / BLOCK_X))),
+		min(grid.y, max((int)0, (int)((p.y - max_radius) / BLOCK_Y)))
+	};
+	rect_max = {
+		min(grid.x, max((int)0, (int)((p.x + max_radius + BLOCK_X - 1) / BLOCK_X))),
+		min(grid.y, max((int)0, (int)((p.y + max_radius + BLOCK_Y - 1) / BLOCK_Y)))
+	};
+}
+
+__forceinline__ __device__ float3 transformPoint4x3(const float3& p, const float* matrix)
+{
+	float3 transformed = {
+		matrix[0] * p.x + matrix[4] * p.y + matrix[8] * p.z + matrix[12],
+		matrix[1] * p.x + matrix[5] * p.y + matrix[9] * p.z + matrix[13],
+		matrix[2] * p.x + matrix[6] * p.y + matrix[10] * p.z + matrix[14],
+	};
+	return transformed;
+}
+
+__forceinline__ __device__ float4 transformPoint4x4(const float3& p, const float* matrix)
+{
+	float4 transformed = {
+		matrix[0] * p.x + matrix[4] * p.y + matrix[8] * p.z + matrix[12],
+		matrix[1] * p.x + matrix[5] * p.y + matrix[9] * p.z + matrix[13],
+		matrix[2] * p.x + matrix[6] * p.y + matrix[10] * p.z + matrix[14],
+		matrix[3] * p.x + matrix[7] * p.y + matrix[11] * p.z + matrix[15]
+	};
+	return transformed;
+}
+
+__forceinline__ __device__ float3 transformVec4x3(const float3& p, const float* matrix)
+{
+	float3 transformed = {
+		matrix[0] * p.x + matrix[4] * p.y + matrix[8] * p.z,
+		matrix[1] * p.x + matrix[5] * p.y + matrix[9] * p.z,
+		matrix[2] * p.x + matrix[6] * p.y + matrix[10] * p.z,
+	};
+	return transformed;
+}
+
+__forceinline__ __device__ float3 transformVec4x3Transpose(const float3& p, const float* matrix)
+{
+	float3 transformed = {
+		matrix[0] * p.x + matrix[1] * p.y + matrix[2] * p.z,
+		matrix[4] * p.x + matrix[5] * p.y + matrix[6] * p.z,
+		matrix[8] * p.x + matrix[9] * p.y + matrix[10] * p.z,
+	};
+	return transformed;
+}
+
+__forceinline__ __device__ float dnormvdz(float3 v, float3 dv)
+{
+	float sum2 = v.x * v.x + v.y * v.y + v.z * v.z;
+	float invsum32 = 1.0f / sqrt(sum2 * sum2 * sum2);
+	float dnormvdz = (-v.x * v.z * dv.x - v.y * v.z * dv.y + (sum2 - v.z * v.z) * dv.z) * invsum32;
+	return dnormvdz;
+}
+
+__forceinline__ __device__ float3 dnormvdv(float3 v, float3 dv)
+{
+	float sum2 = v.x * v.x + v.y * v.y + v.z * v.z;
+	float invsum32 = 1.0f / sqrt(sum2 * sum2 * sum2);
+
+	float3 dnormvdv;
+	dnormvdv.x = ((+sum2 - v.x * v.x) * dv.x - v.y * v.x * dv.y - v.z * v.x * dv.z) * invsum32;
+	dnormvdv.y = (-v.x * v.y * dv.x + (sum2 - v.y * v.y) * dv.y - v.z * v.y * dv.z) * invsum32;
+	dnormvdv.z = (-v.x * v.z * dv.x - v.y * v.z * dv.y + (sum2 - v.z * v.z) * dv.z) * invsum32;
+	return dnormvdv;
+}
+
+__forceinline__ __device__ float4 dnormvdv(float4 v, float4 dv)
+{
+	float sum2 = v.x * v.x + v.y * v.y + v.z * v.z + v.w * v.w;
+	float invsum32 = 1.0f / sqrt(sum2 * sum2 * sum2);
+
+	float4 vdv = { v.x * dv.x, v.y * dv.y, v.z * dv.z, v.w * dv.w };
+	float vdv_sum = vdv.x + vdv.y + vdv.z + vdv.w;
+	float4 dnormvdv;
+	dnormvdv.x = ((sum2 - v.x * v.x) * dv.x - v.x * (vdv_sum - vdv.x)) * invsum32;
+	dnormvdv.y = ((sum2 - v.y * v.y) * dv.y - v.y * (vdv_sum - vdv.y)) * invsum32;
+	dnormvdv.z = ((sum2 - v.z * v.z) * dv.z - v.z * (vdv_sum - vdv.z)) * invsum32;
+	dnormvdv.w = ((sum2 - v.w * v.w) * dv.w - v.w * (vdv_sum - vdv.w)) * invsum32;
+	return dnormvdv;
+}
+
+__forceinline__ __device__ float sigmoid(float x)
+{
+	return 1.0f / (1.0f + expf(-x));
+}
+
+__forceinline__ __device__ bool in_frustum(int idx,
+	const float* orig_points,
+	const float* viewmatrix,
+	const float* projmatrix,
+	bool prefiltered,
+	float3& p_view)
+{
+	float3 p_orig = { orig_points[3 * idx], orig_points[3 * idx + 1], orig_points[3 * idx + 2] };
+
+	// Bring points to screen space
+	float4 p_hom = transformPoint4x4(p_orig, projmatrix);
+	float p_w = 1.0f / (p_hom.w + 0.0000001f);
+	float3 p_proj = { p_hom.x * p_w, p_hom.y * p_w, p_hom.z * p_w };
+	p_view = transformPoint4x3(p_orig, viewmatrix);
+
+	if (p_view.z <= 0.2f)// || ((p_proj.x < -1.3 || p_proj.x > 1.3 || p_proj.y < -1.3 || p_proj.y > 1.3)))
+	{
+		if (prefiltered)
+		{
+			printf("Point is filtered although prefiltered is set. This shouldn't happen!");
+			__trap();
+		}
+		return false;
+	}
+	return true;
+}
+
+#define CHECK_CUDA(A, debug) \
+A; if(debug) { \
+auto ret = cudaDeviceSynchronize(); \
+if (ret != cudaSuccess) { \
+std::cerr << "\n[CUDA ERROR] in " << __FILE__ << "\nLine " << __LINE__ << ": " << cudaGetErrorString(ret); \
+throw std::runtime_error(cudaGetErrorString(ret)); \
+} \
+}
+
+#endif

diff-gaussian-rasterization-camera/cuda_rasterizer/backward.cu

@@ -0,0 +1,718 @@
+/*
+ * Copyright (C) 2023, Inria
+ * GRAPHDECO research group, https://team.inria.fr/graphdeco
+ * All rights reserved.
+ *
+ * This software is free for non-commercial, research and evaluation use 
+ * under the terms of the LICENSE.md file.
+ *
+ * For inquiries contact  [email protected]
+ */
+
+#include "backward.h"
+#include "auxiliary.h"
+#include <cooperative_groups.h>
+#include <cooperative_groups/reduce.h>
+namespace cg = cooperative_groups;
+
+// Backward pass for conversion of spherical harmonics to RGB for
+// each Gaussian.
+__device__ void computeColorFromSH(int idx, int deg, int max_coeffs, const glm::vec3* means, glm::vec3 campos, const float* shs, const bool* clamped, const glm::vec3* dL_dcolor, glm::vec3* dL_dmeans, glm::vec3* dL_dshs)
+{
+	// Compute intermediate values, as it is done during forward
+	glm::vec3 pos = means[idx];
+	glm::vec3 dir_orig = pos - campos;
+	glm::vec3 dir = dir_orig / glm::length(dir_orig);
+
+	glm::vec3* sh = ((glm::vec3*)shs) + idx * max_coeffs;
+
+	// Use PyTorch rule for clamping: if clamping was applied,
+	// gradient becomes 0.
+	glm::vec3 dL_dRGB = dL_dcolor[idx];
+	dL_dRGB.x *= clamped[3 * idx + 0] ? 0 : 1;
+	dL_dRGB.y *= clamped[3 * idx + 1] ? 0 : 1;
+	dL_dRGB.z *= clamped[3 * idx + 2] ? 0 : 1;
+
+	glm::vec3 dRGBdx(0, 0, 0);
+	glm::vec3 dRGBdy(0, 0, 0);
+	glm::vec3 dRGBdz(0, 0, 0);
+	float x = dir.x;
+	float y = dir.y;
+	float z = dir.z;
+
+	// Target location for this Gaussian to write SH gradients to
+	glm::vec3* dL_dsh = dL_dshs + idx * max_coeffs;
+
+	// No tricks here, just high school-level calculus.
+	float dRGBdsh0 = SH_C0;
+	dL_dsh[0] = dRGBdsh0 * dL_dRGB;
+	if (deg > 0)
+	{
+		float dRGBdsh1 = -SH_C1 * y;
+		float dRGBdsh2 = SH_C1 * z;
+		float dRGBdsh3 = -SH_C1 * x;
+		dL_dsh[1] = dRGBdsh1 * dL_dRGB;
+		dL_dsh[2] = dRGBdsh2 * dL_dRGB;
+		dL_dsh[3] = dRGBdsh3 * dL_dRGB;
+
+		dRGBdx = -SH_C1 * sh[3];
+		dRGBdy = -SH_C1 * sh[1];
+		dRGBdz = SH_C1 * sh[2];
+
+		if (deg > 1)
+		{
+			float xx = x * x, yy = y * y, zz = z * z;
+			float xy = x * y, yz = y * z, xz = x * z;
+
+			float dRGBdsh4 = SH_C2[0] * xy;
+			float dRGBdsh5 = SH_C2[1] * yz;
+			float dRGBdsh6 = SH_C2[2] * (2.f * zz - xx - yy);
+			float dRGBdsh7 = SH_C2[3] * xz;
+			float dRGBdsh8 = SH_C2[4] * (xx - yy);
+			dL_dsh[4] = dRGBdsh4 * dL_dRGB;
+			dL_dsh[5] = dRGBdsh5 * dL_dRGB;
+			dL_dsh[6] = dRGBdsh6 * dL_dRGB;
+			dL_dsh[7] = dRGBdsh7 * dL_dRGB;
+			dL_dsh[8] = dRGBdsh8 * dL_dRGB;
+
+			dRGBdx += SH_C2[0] * y * sh[4] + SH_C2[2] * 2.f * -x * sh[6] + SH_C2[3] * z * sh[7] + SH_C2[4] * 2.f * x * sh[8];
+			dRGBdy += SH_C2[0] * x * sh[4] + SH_C2[1] * z * sh[5] + SH_C2[2] * 2.f * -y * sh[6] + SH_C2[4] * 2.f * -y * sh[8];
+			dRGBdz += SH_C2[1] * y * sh[5] + SH_C2[2] * 2.f * 2.f * z * sh[6] + SH_C2[3] * x * sh[7];
+
+			if (deg > 2)
+			{
+				float dRGBdsh9 = SH_C3[0] * y * (3.f * xx - yy);
+				float dRGBdsh10 = SH_C3[1] * xy * z;
+				float dRGBdsh11 = SH_C3[2] * y * (4.f * zz - xx - yy);
+				float dRGBdsh12 = SH_C3[3] * z * (2.f * zz - 3.f * xx - 3.f * yy);
+				float dRGBdsh13 = SH_C3[4] * x * (4.f * zz - xx - yy);
+				float dRGBdsh14 = SH_C3[5] * z * (xx - yy);
+				float dRGBdsh15 = SH_C3[6] * x * (xx - 3.f * yy);
+				dL_dsh[9] = dRGBdsh9 * dL_dRGB;
+				dL_dsh[10] = dRGBdsh10 * dL_dRGB;
+				dL_dsh[11] = dRGBdsh11 * dL_dRGB;
+				dL_dsh[12] = dRGBdsh12 * dL_dRGB;
+				dL_dsh[13] = dRGBdsh13 * dL_dRGB;
+				dL_dsh[14] = dRGBdsh14 * dL_dRGB;
+				dL_dsh[15] = dRGBdsh15 * dL_dRGB;
+
+				dRGBdx += (
+					SH_C3[0] * sh[9] * 3.f * 2.f * xy +
+					SH_C3[1] * sh[10] * yz +
+					SH_C3[2] * sh[11] * -2.f * xy +
+					SH_C3[3] * sh[12] * -3.f * 2.f * xz +
+					SH_C3[4] * sh[13] * (-3.f * xx + 4.f * zz - yy) +
+					SH_C3[5] * sh[14] * 2.f * xz +
+					SH_C3[6] * sh[15] * 3.f * (xx - yy));
+
+				dRGBdy += (
+					SH_C3[0] * sh[9] * 3.f * (xx - yy) +
+					SH_C3[1] * sh[10] * xz +
+					SH_C3[2] * sh[11] * (-3.f * yy + 4.f * zz - xx) +
+					SH_C3[3] * sh[12] * -3.f * 2.f * yz +
+					SH_C3[4] * sh[13] * -2.f * xy +
+					SH_C3[5] * sh[14] * -2.f * yz +
+					SH_C3[6] * sh[15] * -3.f * 2.f * xy);
+
+				dRGBdz += (
+					SH_C3[1] * sh[10] * xy +
+					SH_C3[2] * sh[11] * 4.f * 2.f * yz +
+					SH_C3[3] * sh[12] * 3.f * (2.f * zz - xx - yy) +
+					SH_C3[4] * sh[13] * 4.f * 2.f * xz +
+					SH_C3[5] * sh[14] * (xx - yy));
+			}
+		}
+	}
+
+	// The view direction is an input to the computation. View direction
+	// is influenced by the Gaussian's mean, so SHs gradients
+	// must propagate back into 3D position.
+	glm::vec3 dL_ddir(glm::dot(dRGBdx, dL_dRGB), glm::dot(dRGBdy, dL_dRGB), glm::dot(dRGBdz, dL_dRGB));
+
+	// Account for normalization of direction
+	float3 dL_dmean = dnormvdv(float3{ dir_orig.x, dir_orig.y, dir_orig.z }, float3{ dL_ddir.x, dL_ddir.y, dL_ddir.z });
+
+	// Gradients of loss w.r.t. Gaussian means, but only the portion 
+	// that is caused because the mean affects the view-dependent color.
+	// Additional mean gradient is accumulated in below methods.
+	dL_dmeans[idx] += glm::vec3(dL_dmean.x, dL_dmean.y, dL_dmean.z);
+}
+
+// Backward version of INVERSE 2D covariance matrix computation
+// (due to length launched as separate kernel before other 
+// backward steps contained in preprocess)
+__global__ void computeCov2DCUDA(int P,
+	const float3* means,
+	const int* radii,
+	const float* cov3Ds,
+	const float h_x, float h_y,
+	const float tan_fovx, float tan_fovy,
+	const float* view_matrix,
+	const float* dL_dconics,
+	float3* dL_dmeans,
+	float3* dL_dts,
+	float* dL_dcov)
+{
+	auto idx = cg::this_grid().thread_rank();
+	if (idx >= P || !(radii[idx] > 0))
+		return;
+
+	// Reading location of 3D covariance for this Gaussian
+	const float* cov3D = cov3Ds + 6 * idx;
+
+	// Fetch gradients, recompute 2D covariance and relevant 
+	// intermediate forward results needed in the backward.
+	float3 mean = means[idx];
+	float3 dL_dconic = { dL_dconics[4 * idx], dL_dconics[4 * idx + 1], dL_dconics[4 * idx + 3] };
+	float3 t = transformPoint4x3(mean, view_matrix);
+	
+	const float limx = 1.3f * tan_fovx;
+	const float limy = 1.3f * tan_fovy;
+	const float txtz = t.x / t.z;
+	const float tytz = t.y / t.z;
+	t.x = min(limx, max(-limx, txtz)) * t.z;
+	t.y = min(limy, max(-limy, tytz)) * t.z;
+	
+	const float x_grad_mul = txtz < -limx || txtz > limx ? 0 : 1;
+	const float y_grad_mul = tytz < -limy || tytz > limy ? 0 : 1;
+
+	glm::mat3 J = glm::mat3(h_x / t.z, 0.0f, -(h_x * t.x) / (t.z * t.z),
+		0.0f, h_y / t.z, -(h_y * t.y) / (t.z * t.z),
+		0, 0, 0);
+
+	glm::mat3 W = glm::mat3(
+		view_matrix[0], view_matrix[4], view_matrix[8],
+		view_matrix[1], view_matrix[5], view_matrix[9],
+		view_matrix[2], view_matrix[6], view_matrix[10]);
+
+	glm::mat3 Vrk = glm::mat3(
+		cov3D[0], cov3D[1], cov3D[2],
+		cov3D[1], cov3D[3], cov3D[4],
+		cov3D[2], cov3D[4], cov3D[5]);
+
+	glm::mat3 T = W * J;
+
+	glm::mat3 cov2D = glm::transpose(T) * glm::transpose(Vrk) * T;
+
+	// Use helper variables for 2D covariance entries. More compact.
+	float a = cov2D[0][0] += 0.3f;
+	float b = cov2D[0][1];
+	float c = cov2D[1][1] += 0.3f;
+
+	float denom = a * c - b * b;
+	float dL_da = 0, dL_db = 0, dL_dc = 0;
+	float denom2inv = 1.0f / ((denom * denom) + 0.0000001f);
+
+	if (denom2inv != 0)
+	{
+		// Gradients of loss w.r.t. entries of 2D covariance matrix,
+		// given gradients of loss w.r.t. conic matrix (inverse covariance matrix).
+		// e.g., dL / da = dL / d_conic_a * d_conic_a / d_a
+		dL_da = denom2inv * (-c * c * dL_dconic.x + 2 * b * c * dL_dconic.y + (denom - a * c) * dL_dconic.z);
+		dL_dc = denom2inv * (-a * a * dL_dconic.z + 2 * a * b * dL_dconic.y + (denom - a * c) * dL_dconic.x);
+		dL_db = denom2inv * 2 * (b * c * dL_dconic.x - (denom + 2 * b * b) * dL_dconic.y + a * b * dL_dconic.z);
+
+		// Gradients of loss L w.r.t. each 3D covariance matrix (Vrk) entry, 
+		// given gradients w.r.t. 2D covariance matrix (diagonal).
+		// cov2D = transpose(T) * transpose(Vrk) * T;
+		dL_dcov[6 * idx + 0] = (T[0][0] * T[0][0] * dL_da + T[0][0] * T[1][0] * dL_db + T[1][0] * T[1][0] * dL_dc);
+		dL_dcov[6 * idx + 3] = (T[0][1] * T[0][1] * dL_da + T[0][1] * T[1][1] * dL_db + T[1][1] * T[1][1] * dL_dc);
+		dL_dcov[6 * idx + 5] = (T[0][2] * T[0][2] * dL_da + T[0][2] * T[1][2] * dL_db + T[1][2] * T[1][2] * dL_dc);
+
+		// Gradients of loss L w.r.t. each 3D covariance matrix (Vrk) entry, 
+		// given gradients w.r.t. 2D covariance matrix (off-diagonal).
+		// Off-diagonal elements appear twice --> double the gradient.
+		// cov2D = transpose(T) * transpose(Vrk) * T;
+		dL_dcov[6 * idx + 1] = 2 * T[0][0] * T[0][1] * dL_da + (T[0][0] * T[1][1] + T[0][1] * T[1][0]) * dL_db + 2 * T[1][0] * T[1][1] * dL_dc;
+		dL_dcov[6 * idx + 2] = 2 * T[0][0] * T[0][2] * dL_da + (T[0][0] * T[1][2] + T[0][2] * T[1][0]) * dL_db + 2 * T[1][0] * T[1][2] * dL_dc;
+		dL_dcov[6 * idx + 4] = 2 * T[0][2] * T[0][1] * dL_da + (T[0][1] * T[1][2] + T[0][2] * T[1][1]) * dL_db + 2 * T[1][1] * T[1][2] * dL_dc;
+	}
+	else
+	{
+		for (int i = 0; i < 6; i++)
+			dL_dcov[6 * idx + i] = 0;
+	}
+
+	// Gradients of loss w.r.t. upper 2x3 portion of intermediate matrix T
+	// cov2D = transpose(T) * transpose(Vrk) * T;
+	float dL_dT00 = 2 * (T[0][0] * Vrk[0][0] + T[0][1] * Vrk[0][1] + T[0][2] * Vrk[0][2]) * dL_da +
+		(T[1][0] * Vrk[0][0] + T[1][1] * Vrk[0][1] + T[1][2] * Vrk[0][2]) * dL_db;
+	float dL_dT01 = 2 * (T[0][0] * Vrk[1][0] + T[0][1] * Vrk[1][1] + T[0][2] * Vrk[1][2]) * dL_da +
+		(T[1][0] * Vrk[1][0] + T[1][1] * Vrk[1][1] + T[1][2] * Vrk[1][2]) * dL_db;
+	float dL_dT02 = 2 * (T[0][0] * Vrk[2][0] + T[0][1] * Vrk[2][1] + T[0][2] * Vrk[2][2]) * dL_da +
+		(T[1][0] * Vrk[2][0] + T[1][1] * Vrk[2][1] + T[1][2] * Vrk[2][2]) * dL_db;
+	float dL_dT10 = 2 * (T[1][0] * Vrk[0][0] + T[1][1] * Vrk[0][1] + T[1][2] * Vrk[0][2]) * dL_dc +
+		(T[0][0] * Vrk[0][0] + T[0][1] * Vrk[0][1] + T[0][2] * Vrk[0][2]) * dL_db;
+	float dL_dT11 = 2 * (T[1][0] * Vrk[1][0] + T[1][1] * Vrk[1][1] + T[1][2] * Vrk[1][2]) * dL_dc +
+		(T[0][0] * Vrk[1][0] + T[0][1] * Vrk[1][1] + T[0][2] * Vrk[1][2]) * dL_db;
+	float dL_dT12 = 2 * (T[1][0] * Vrk[2][0] + T[1][1] * Vrk[2][1] + T[1][2] * Vrk[2][2]) * dL_dc +
+		(T[0][0] * Vrk[2][0] + T[0][1] * Vrk[2][1] + T[0][2] * Vrk[2][2]) * dL_db;
+
+	// Gradients of loss w.r.t. upper 3x2 non-zero entries of Jacobian matrix
+	// T = W * J
+	float dL_dJ00 = W[0][0] * dL_dT00 + W[0][1] * dL_dT01 + W[0][2] * dL_dT02;
+	float dL_dJ02 = W[2][0] * dL_dT00 + W[2][1] * dL_dT01 + W[2][2] * dL_dT02;
+	float dL_dJ11 = W[1][0] * dL_dT10 + W[1][1] * dL_dT11 + W[1][2] * dL_dT12;
+	float dL_dJ12 = W[2][0] * dL_dT10 + W[2][1] * dL_dT11 + W[2][2] * dL_dT12;
+
+	float tz = 1.f / t.z;
+	float tz2 = tz * tz;
+	float tz3 = tz2 * tz;
+
+	// Gradients of loss w.r.t. transformed Gaussian mean t
+	float dL_dtx = x_grad_mul * -h_x * tz2 * dL_dJ02;
+	float dL_dty = y_grad_mul * -h_y * tz2 * dL_dJ12;
+	float dL_dtz = -h_x * tz2 * dL_dJ00 - h_y * tz2 * dL_dJ11 + (2 * h_x * t.x) * tz3 * dL_dJ02 + (2 * h_y * t.y) * tz3 * dL_dJ12;
+
+	// Account for transformation of mean to t
+	// t = transformPoint4x3(mean, view_matrix);
+	float3 dL_dmean = transformVec4x3Transpose({ dL_dtx, dL_dty, dL_dtz }, view_matrix);
+
+	// Gradients of loss w.r.t. Gaussian means, but only the portion 
+	// that is caused because the mean affects the covariance matrix.
+	// Additional mean gradient is accumulated in BACKWARD::preprocess.
+	dL_dmeans[idx] = dL_dmean;
+
+	// Created by Qitao
+	dL_dts[idx] = { dL_dtx, dL_dty, dL_dtz };
+}
+
+// Backward pass for the conversion of scale and rotation to a 
+// 3D covariance matrix for each Gaussian. 
+__device__ void computeCov3D(int idx, const glm::vec3 scale, float mod, const glm::vec4 rot, const float* dL_dcov3Ds, glm::vec3* dL_dscales, glm::vec4* dL_drots)
+{
+	// Recompute (intermediate) results for the 3D covariance computation.
+	glm::vec4 q = rot;// / glm::length(rot);
+	float r = q.x;
+	float x = q.y;
+	float y = q.z;
+	float z = q.w;
+
+	glm::mat3 R = glm::mat3(
+		1.f - 2.f * (y * y + z * z), 2.f * (x * y - r * z), 2.f * (x * z + r * y),
+		2.f * (x * y + r * z), 1.f - 2.f * (x * x + z * z), 2.f * (y * z - r * x),
+		2.f * (x * z - r * y), 2.f * (y * z + r * x), 1.f - 2.f * (x * x + y * y)
+	);
+
+	glm::mat3 S = glm::mat3(1.0f);
+
+	glm::vec3 s = mod * scale;
+	S[0][0] = s.x;
+	S[1][1] = s.y;
+	S[2][2] = s.z;
+
+	glm::mat3 M = S * R;
+
+	const float* dL_dcov3D = dL_dcov3Ds + 6 * idx;
+
+	glm::vec3 dunc(dL_dcov3D[0], dL_dcov3D[3], dL_dcov3D[5]);
+	glm::vec3 ounc = 0.5f * glm::vec3(dL_dcov3D[1], dL_dcov3D[2], dL_dcov3D[4]);
+
+	// Convert per-element covariance loss gradients to matrix form
+	glm::mat3 dL_dSigma = glm::mat3(
+		dL_dcov3D[0], 0.5f * dL_dcov3D[1], 0.5f * dL_dcov3D[2],
+		0.5f * dL_dcov3D[1], dL_dcov3D[3], 0.5f * dL_dcov3D[4],
+		0.5f * dL_dcov3D[2], 0.5f * dL_dcov3D[4], dL_dcov3D[5]
+	);
+
+	// Compute loss gradient w.r.t. matrix M
+	// dSigma_dM = 2 * M
+	glm::mat3 dL_dM = 2.0f * M * dL_dSigma;
+
+	glm::mat3 Rt = glm::transpose(R);
+	glm::mat3 dL_dMt = glm::transpose(dL_dM);
+
+	// Gradients of loss w.r.t. scale
+	glm::vec3* dL_dscale = dL_dscales + idx;
+	dL_dscale->x = glm::dot(Rt[0], dL_dMt[0]);
+	dL_dscale->y = glm::dot(Rt[1], dL_dMt[1]);
+	dL_dscale->z = glm::dot(Rt[2], dL_dMt[2]);
+
+	dL_dMt[0] *= s.x;
+	dL_dMt[1] *= s.y;
+	dL_dMt[2] *= s.z;
+
+	// Gradients of loss w.r.t. normalized quaternion
+	glm::vec4 dL_dq;
+	dL_dq.x = 2 * z * (dL_dMt[0][1] - dL_dMt[1][0]) + 2 * y * (dL_dMt[2][0] - dL_dMt[0][2]) + 2 * x * (dL_dMt[1][2] - dL_dMt[2][1]);
+	dL_dq.y = 2 * y * (dL_dMt[1][0] + dL_dMt[0][1]) + 2 * z * (dL_dMt[2][0] + dL_dMt[0][2]) + 2 * r * (dL_dMt[1][2] - dL_dMt[2][1]) - 4 * x * (dL_dMt[2][2] + dL_dMt[1][1]);
+	dL_dq.z = 2 * x * (dL_dMt[1][0] + dL_dMt[0][1]) + 2 * r * (dL_dMt[2][0] - dL_dMt[0][2]) + 2 * z * (dL_dMt[1][2] + dL_dMt[2][1]) - 4 * y * (dL_dMt[2][2] + dL_dMt[0][0]);
+	dL_dq.w = 2 * r * (dL_dMt[0][1] - dL_dMt[1][0]) + 2 * x * (dL_dMt[2][0] + dL_dMt[0][2]) + 2 * y * (dL_dMt[1][2] + dL_dMt[2][1]) - 4 * z * (dL_dMt[1][1] + dL_dMt[0][0]);
+
+	// Gradients of loss w.r.t. unnormalized quaternion
+	float4* dL_drot = (float4*)(dL_drots + idx);
+	*dL_drot = float4{ dL_dq.x, dL_dq.y, dL_dq.z, dL_dq.w };//dnormvdv(float4{ rot.x, rot.y, rot.z, rot.w }, float4{ dL_dq.x, dL_dq.y, dL_dq.z, dL_dq.w });
+}
+
+// Backward pass of the preprocessing steps, except
+// for the covariance computation and inversion
+// (those are handled by a previous kernel call)
+template<int C>
+__global__ void preprocessCUDA(
+	int P, int D, int M,
+	const float3* means,
+	const int* radii,
+	const float* shs,
+	const bool* clamped,
+	const glm::vec3* scales,
+	const glm::vec4* rotations,
+	const float scale_modifier,
+	const float* view,
+	const float* proj,
+	const glm::vec3* campos,
+	const float3* dL_dmean2D,
+	glm::vec3* dL_dmeans,
+	float* dL_dcolor,
+	float* dL_ddepth,
+	float* dL_dcov3D,
+	float* dL_dsh,
+	glm::vec3* dL_dscale,
+	glm::vec4* dL_drot)
+{
+	auto idx = cg::this_grid().thread_rank();
+	if (idx >= P || !(radii[idx] > 0))
+		return;
+
+	float3 m = means[idx];
+
+	// Taking care of gradients from the screenspace points
+	float4 m_hom = transformPoint4x4(m, proj);
+	float m_w = 1.0f / (m_hom.w + 0.0000001f);
+
+	// Compute loss gradient w.r.t. 3D means due to gradients of 2D means
+	// from rendering procedure
+	glm::vec3 dL_dmean;
+	float mul1 = (proj[0] * m.x + proj[4] * m.y + proj[8] * m.z + proj[12]) * m_w * m_w;
+	float mul2 = (proj[1] * m.x + proj[5] * m.y + proj[9] * m.z + proj[13]) * m_w * m_w;
+	dL_dmean.x = (proj[0] * m_w - proj[3] * mul1) * dL_dmean2D[idx].x + (proj[1] * m_w - proj[3] * mul2) * dL_dmean2D[idx].y;
+	dL_dmean.y = (proj[4] * m_w - proj[7] * mul1) * dL_dmean2D[idx].x + (proj[5] * m_w - proj[7] * mul2) * dL_dmean2D[idx].y;
+	dL_dmean.z = (proj[8] * m_w - proj[11] * mul1) * dL_dmean2D[idx].x + (proj[9] * m_w - proj[11] * mul2) * dL_dmean2D[idx].y;
+
+	// That's the second part of the mean gradient. Previous computation
+	// of cov2D and following SH conversion also affects it.
+	dL_dmeans[idx] += dL_dmean;
+
+	// the w must be equal to 1 for view^T * [x,y,z,1]
+	float3 m_view = transformPoint4x3(m, view);
+
+	// Compute loss gradient w.r.t. 3D means due to gradients of depth
+	// from rendering procedure
+	glm::vec3 dL_dmean2;
+	float mul3 = view[2] * m.x + view[6] * m.y + view[10] * m.z + view[14];
+	dL_dmean2.x = (view[2] - view[3] * mul3) * dL_ddepth[idx];
+	dL_dmean2.y = (view[6] - view[7] * mul3) * dL_ddepth[idx];
+	dL_dmean2.z = (view[10] - view[11] * mul3) * dL_ddepth[idx];
+
+	// That's the third part of the mean gradient.
+	dL_dmeans[idx] += dL_dmean2;
+
+	// Compute gradient updates due to computing colors from SHs
+	if (shs)
+		computeColorFromSH(idx, D, M, (glm::vec3*)means, *campos, shs, clamped, (glm::vec3*)dL_dcolor, (glm::vec3*)dL_dmeans, (glm::vec3*)dL_dsh);
+
+	// Compute gradient updates due to computing covariance from scale/rotation
+	if (scales)
+		computeCov3D(idx, scales[idx], scale_modifier, rotations[idx], dL_dcov3D, dL_dscale, dL_drot);
+}
+
+// Backward version of the rendering procedure.
+template <uint32_t C>
+__global__ void __launch_bounds__(BLOCK_X * BLOCK_Y)
+renderCUDA(
+	const uint2* __restrict__ ranges,
+	const uint32_t* __restrict__ point_list,
+	int W, int H,
+	const float* __restrict__ bg_color,
+	const float2* __restrict__ points_xy_image,
+	const float4* __restrict__ conic_opacity,
+	const float* __restrict__ colors,
+	const float* __restrict__ depths,
+	const float* __restrict__ alphas,
+	const uint32_t* __restrict__ n_contrib,
+	const float* __restrict__ dL_dpixels,
+	const float* __restrict__ dL_dpixel_depths,
+	const float* __restrict__ dL_dalphas,
+	float3* __restrict__ dL_dmean2D,
+	float4* __restrict__ dL_dconic2D,
+	float* __restrict__ dL_dopacity,
+	float* __restrict__ dL_dcolors,
+	float* __restrict__ dL_ddepths
+)
+{
+	// We rasterize again. Compute necessary block info.
+	auto block = cg::this_thread_block();
+	const uint32_t horizontal_blocks = (W + BLOCK_X - 1) / BLOCK_X;
+	const uint2 pix_min = { block.group_index().x * BLOCK_X, block.group_index().y * BLOCK_Y };
+	const uint2 pix_max = { min(pix_min.x + BLOCK_X, W), min(pix_min.y + BLOCK_Y , H) };
+	const uint2 pix = { pix_min.x + block.thread_index().x, pix_min.y + block.thread_index().y };
+	const uint32_t pix_id = W * pix.y + pix.x;
+	const float2 pixf = { (float)pix.x, (float)pix.y };
+
+	const bool inside = pix.x < W&& pix.y < H;
+	const uint2 range = ranges[block.group_index().y * horizontal_blocks + block.group_index().x];
+
+	const int rounds = ((range.y - range.x + BLOCK_SIZE - 1) / BLOCK_SIZE);
+
+	bool done = !inside;
+	int toDo = range.y - range.x;
+
+	__shared__ int collected_id[BLOCK_SIZE];
+	__shared__ float2 collected_xy[BLOCK_SIZE];
+	__shared__ float4 collected_conic_opacity[BLOCK_SIZE];
+	__shared__ float collected_colors[C * BLOCK_SIZE];
+	__shared__ float collected_depths[BLOCK_SIZE];
+
+	// In the forward, we stored the final value for T, the
+	// product of all (1 - alpha) factors. 
+	const float T_final = inside ? (1 - alphas[pix_id]) : 0;
+	float T = T_final;
+
+	// We start from the back. The ID of the last contributing
+	// Gaussian is known from each pixel from the forward.
+	uint32_t contributor = toDo;
+	const int last_contributor = inside ? n_contrib[pix_id] : 0;
+
+	float accum_rec[C] = { 0 };
+	float dL_dpixel[C];
+	float accum_depth_rec = 0;
+	float dL_dpixel_depth;
+	float accum_alpha_rec = 0;
+	float dL_dalpha;
+	if (inside) {
+		for (int i = 0; i < C; i++)
+			dL_dpixel[i] = dL_dpixels[i * H * W + pix_id];
+		dL_dpixel_depth = dL_dpixel_depths[pix_id];
+		dL_dalpha = dL_dalphas[pix_id];
+	}
+
+	float last_alpha = 0;
+	float last_color[C] = { 0 };
+	float last_depth = 0;
+
+	// Gradient of pixel coordinate w.r.t. normalized 
+	// screen-space viewport corrdinates (-1 to 1)
+	const float ddelx_dx = 0.5 * W;
+	const float ddely_dy = 0.5 * H;
+
+	// Traverse all Gaussians
+	for (int i = 0; i < rounds; i++, toDo -= BLOCK_SIZE)
+	{
+		// Load auxiliary data into shared memory, start in the BACK
+		// and load them in revers order.
+		block.sync();
+		const int progress = i * BLOCK_SIZE + block.thread_rank();
+		if (range.x + progress < range.y)
+		{
+			const int coll_id = point_list[range.y - progress - 1];
+			collected_id[block.thread_rank()] = coll_id;
+			collected_xy[block.thread_rank()] = points_xy_image[coll_id];
+			collected_conic_opacity[block.thread_rank()] = conic_opacity[coll_id];
+			for (int i = 0; i < C; i++)
+				collected_colors[i * BLOCK_SIZE + block.thread_rank()] = colors[coll_id * C + i];
+			collected_depths[block.thread_rank()] = depths[coll_id];
+		}
+		block.sync();
+
+		// Iterate over Gaussians
+		for (int j = 0; !done && j < min(BLOCK_SIZE, toDo); j++)
+		{
+			// Keep track of current Gaussian ID. Skip, if this one
+			// is behind the last contributor for this pixel.
+			contributor--;
+			if (contributor >= last_contributor)
+				continue;
+
+			// Compute blending values, as before.
+			const float2 xy = collected_xy[j];
+			const float2 d = { xy.x - pixf.x, xy.y - pixf.y };
+			const float4 con_o = collected_conic_opacity[j];
+			const float power = -0.5f * (con_o.x * d.x * d.x + con_o.z * d.y * d.y) - con_o.y * d.x * d.y;
+			if (power > 0.0f)
+				continue;
+
+			const float G = exp(power);
+			const float alpha = min(0.99f, con_o.w * G);
+			if (alpha < 1.0f / 255.0f)
+				continue;
+
+			T = T / (1.f - alpha);
+			const float dchannel_dcolor = alpha * T;
+			const float dpixel_depth_ddepth = alpha * T;
+
+			// Propagate gradients to per-Gaussian colors and keep
+			// gradients w.r.t. alpha (blending factor for a Gaussian/pixel
+			// pair).
+			float dL_dopa = 0.0f;
+			const int global_id = collected_id[j];
+			for (int ch = 0; ch < C; ch++)
+			{
+				const float c = collected_colors[ch * BLOCK_SIZE + j];
+				// Update last color (to be used in the next iteration)
+				accum_rec[ch] = last_alpha * last_color[ch] + (1.f - last_alpha) * accum_rec[ch];
+				last_color[ch] = c;
+
+				const float dL_dchannel = dL_dpixel[ch];
+				dL_dopa += (c - accum_rec[ch]) * dL_dchannel;
+				// Update the gradients w.r.t. color of the Gaussian. 
+				// Atomic, since this pixel is just one of potentially
+				// many that were affected by this Gaussian.
+				atomicAdd(&(dL_dcolors[global_id * C + ch]), dchannel_dcolor * dL_dchannel);
+			}
+			
+			// Propagate gradients from pixel depth to opacity
+			const float c_d = collected_depths[j];
+			accum_depth_rec = last_alpha * last_depth + (1.f - last_alpha) * accum_depth_rec;
+			last_depth = c_d;
+			dL_dopa += (c_d - accum_depth_rec) * dL_dpixel_depth;
+			atomicAdd(&(dL_ddepths[global_id]), dpixel_depth_ddepth * dL_dpixel_depth);
+
+			// Propagate gradients from pixel alpha (weights_sum) to opacity
+			accum_alpha_rec = last_alpha + (1.f - last_alpha) * accum_alpha_rec;
+			dL_dopa += (1 - accum_alpha_rec) * dL_dalpha; //- (alpha - accum_alpha_rec) * dL_dalpha;
+
+			dL_dopa *= T;
+			// Update last alpha (to be used in the next iteration)
+			last_alpha = alpha;
+
+			// Account for fact that alpha also influences how much of
+			// the background color is added if nothing left to blend
+			float bg_dot_dpixel = 0;
+			for (int i = 0; i < C; i++)
+				bg_dot_dpixel += bg_color[i] * dL_dpixel[i];
+			dL_dopa += (-T_final / (1.f - alpha)) * bg_dot_dpixel;
+
+
+			// Helpful reusable temporary variables
+			const float dL_dG = con_o.w * dL_dopa;
+			const float gdx = G * d.x;
+			const float gdy = G * d.y;
+			const float dG_ddelx = -gdx * con_o.x - gdy * con_o.y;
+			const float dG_ddely = -gdy * con_o.z - gdx * con_o.y;
+
+			// Update gradients w.r.t. 2D mean position of the Gaussian
+			atomicAdd(&dL_dmean2D[global_id].x, dL_dG * dG_ddelx * ddelx_dx);
+			atomicAdd(&dL_dmean2D[global_id].y, dL_dG * dG_ddely * ddely_dy);
+
+			// Update gradients w.r.t. 2D covariance (2x2 matrix, symmetric)
+			atomicAdd(&dL_dconic2D[global_id].x, -0.5f * gdx * d.x * dL_dG);
+			atomicAdd(&dL_dconic2D[global_id].y, -0.5f * gdx * d.y * dL_dG);
+			atomicAdd(&dL_dconic2D[global_id].w, -0.5f * gdy * d.y * dL_dG);
+
+			// Update gradients w.r.t. opacity of the Gaussian
+			atomicAdd(&(dL_dopacity[global_id]), G * dL_dopa);
+		}
+	}
+}
+
+void BACKWARD::preprocess(
+	int P, int D, int M,
+	const float3* means3D,
+	const int* radii,
+	const float* shs,
+	const bool* clamped,
+	const glm::vec3* scales,
+	const glm::vec4* rotations,
+	const float scale_modifier,
+	const float* cov3Ds,
+	const float* viewmatrix,
+	const float* projmatrix,
+	const float focal_x, float focal_y,
+	const float tan_fovx, float tan_fovy,
+	const glm::vec3* campos,
+	const float3* dL_dmean2D,
+	float3* dL_dts,
+	const float* dL_dconic,
+	glm::vec3* dL_dmean3D,
+	float* dL_dcolor,
+	float* dL_ddepth,
+	float* dL_dcov3D,
+	float* dL_dsh,
+	glm::vec3* dL_dscale,
+	glm::vec4* dL_drot)
+{
+	// Propagate gradients for the path of 2D conic matrix computation. 
+	// Somewhat long, thus it is its own kernel rather than being part of 
+	// "preprocess". When done, loss gradient w.r.t. 3D means has been
+	// modified and gradient w.r.t. 3D covariance matrix has been computed.	
+	computeCov2DCUDA << <(P + 255) / 256, 256 >> > (
+		P,
+		means3D,
+		radii,
+		cov3Ds,
+		focal_x,
+		focal_y,
+		tan_fovx,
+		tan_fovy,
+		viewmatrix,
+		dL_dconic,
+		(float3*)dL_dmean3D,
+		(float3*)dL_dts,
+		dL_dcov3D);
+
+	// Propagate gradients for remaining steps: finish 3D mean gradients,
+	// propagate color gradients to SH (if desireD), propagate 3D covariance
+	// matrix gradients to scale and rotation.
+	preprocessCUDA<NUM_CHANNELS> << < (P + 255) / 256, 256 >> > (
+		P, D, M,
+		(float3*)means3D,
+		radii,
+		shs,
+		clamped,
+		(glm::vec3*)scales,
+		(glm::vec4*)rotations,
+		scale_modifier,
+		viewmatrix,
+		projmatrix,
+		campos,
+		(float3*)dL_dmean2D,
+		(glm::vec3*)dL_dmean3D,
+		dL_dcolor,
+		dL_ddepth,
+		dL_dcov3D,
+		dL_dsh,
+		dL_dscale,
+		dL_drot);
+}
+
+void BACKWARD::render(
+	const dim3 grid, const dim3 block,
+	const uint2* ranges,
+	const uint32_t* point_list,
+	int W, int H,
+	const float* bg_color,
+	const float2* means2D,
+	const float4* conic_opacity,
+	const float* colors,
+	const float* depths,
+	const float* alphas,
+	const uint32_t* n_contrib,
+	const float* dL_dpixels,
+	const float* dL_dpixel_depths,
+	const float* dL_dalphas,
+	float3* dL_dmean2D,
+	float4* dL_dconic2D,
+	float* dL_dopacity,
+	float* dL_dcolors,
+	float* dL_ddepths)
+{
+	renderCUDA<NUM_CHANNELS> << <grid, block >> >(
+		ranges,
+		point_list,
+		W, H,
+		bg_color,
+		means2D,
+		conic_opacity,
+		colors,
+		depths,
+		alphas,
+		n_contrib,
+		dL_dpixels,
+		dL_dpixel_depths,
+		dL_dalphas,
+		dL_dmean2D,
+		dL_dconic2D,
+		dL_dopacity,
+		dL_dcolors,
+		dL_ddepths
+		);
+}

diff-gaussian-rasterization-camera/cuda_rasterizer/backward.h

@@ -0,0 +1,71 @@
+/*
+ * Copyright (C) 2023, Inria
+ * GRAPHDECO research group, https://team.inria.fr/graphdeco
+ * All rights reserved.
+ *
+ * This software is free for non-commercial, research and evaluation use 
+ * under the terms of the LICENSE.md file.
+ *
+ * For inquiries contact  [email protected]
+ */
+
+#ifndef CUDA_RASTERIZER_BACKWARD_H_INCLUDED
+#define CUDA_RASTERIZER_BACKWARD_H_INCLUDED
+
+#include <cuda.h>
+#include "cuda_runtime.h"
+#include "device_launch_parameters.h"
+#define GLM_FORCE_CUDA
+#include <glm/glm.hpp>
+
+namespace BACKWARD
+{
+	void render(
+		const dim3 grid, dim3 block,
+		const uint2* ranges,
+		const uint32_t* point_list,
+		int W, int H,
+		const float* bg_color,
+		const float2* means2D,
+		const float4* conic_opacity,
+		const float* colors,
+		const float* depths,
+		const float* alphas,
+		const uint32_t* n_contrib,
+		const float* dL_dpixels,
+		const float* dL_dpixel_depths,
+		const float* dL_dalphas,
+		float3* dL_dmean2D,
+		float4* dL_dconic2D,
+		float* dL_dopacity,
+		float* dL_dcolors,
+		float* dL_ddepths);
+
+	void preprocess(
+		int P, int D, int M,
+		const float3* means,
+		const int* radii,
+		const float* shs,
+		const bool* clamped,
+		const glm::vec3* scales,
+		const glm::vec4* rotations,
+		const float scale_modifier,
+		const float* cov3Ds,
+		const float* view,
+		const float* proj,
+		const float focal_x, float focal_y,
+		const float tan_fovx, float tan_fovy,
+		const glm::vec3* campos,
+		const float3* dL_dmean2D,
+		float3* dL_dts,
+		const float* dL_dconics,
+		glm::vec3* dL_dmeans,
+		float* dL_dcolor,
+		float* dL_ddepth,
+		float* dL_dcov3D,
+		float* dL_dsh,
+		glm::vec3* dL_dscale,
+		glm::vec4* dL_drot);
+}
+
+#endif

diff-gaussian-rasterization-camera/cuda_rasterizer/config.h

@@ -0,0 +1,19 @@
+/*
+ * Copyright (C) 2023, Inria
+ * GRAPHDECO research group, https://team.inria.fr/graphdeco
+ * All rights reserved.
+ *
+ * This software is free for non-commercial, research and evaluation use 
+ * under the terms of the LICENSE.md file.
+ *
+ * For inquiries contact  [email protected]
+ */
+
+#ifndef CUDA_RASTERIZER_CONFIG_H_INCLUDED
+#define CUDA_RASTERIZER_CONFIG_H_INCLUDED
+
+#define NUM_CHANNELS 3 // Default 3, RGB
+#define BLOCK_X 16
+#define BLOCK_Y 16
+
+#endif

diff-gaussian-rasterization-camera/cuda_rasterizer/forward.cu

@@ -0,0 +1,466 @@
+/*
+ * Copyright (C) 2023, Inria
+ * GRAPHDECO research group, https://team.inria.fr/graphdeco
+ * All rights reserved.
+ *
+ * This software is free for non-commercial, research and evaluation use 
+ * under the terms of the LICENSE.md file.
+ *
+ * For inquiries contact  [email protected]
+ */
+
+#include "forward.h"
+#include "auxiliary.h"
+#include <cooperative_groups.h>
+#include <cooperative_groups/reduce.h>
+namespace cg = cooperative_groups;
+
+// Forward method for converting the input spherical harmonics
+// coefficients of each Gaussian to a simple RGB color.
+__device__ glm::vec3 computeColorFromSH(int idx, int deg, int max_coeffs, const glm::vec3* means, glm::vec3 campos, const float* shs, bool* clamped)
+{
+	// The implementation is loosely based on code for 
+	// "Differentiable Point-Based Radiance Fields for 
+	// Efficient View Synthesis" by Zhang et al. (2022)
+	glm::vec3 pos = means[idx];
+	glm::vec3 dir = pos - campos;
+	dir = dir / glm::length(dir);
+
+	glm::vec3* sh = ((glm::vec3*)shs) + idx * max_coeffs;
+	glm::vec3 result = SH_C0 * sh[0];
+
+	if (deg > 0)
+	{
+		float x = dir.x;
+		float y = dir.y;
+		float z = dir.z;
+		result = result - SH_C1 * y * sh[1] + SH_C1 * z * sh[2] - SH_C1 * x * sh[3];
+
+		if (deg > 1)
+		{
+			float xx = x * x, yy = y * y, zz = z * z;
+			float xy = x * y, yz = y * z, xz = x * z;
+			result = result +
+				SH_C2[0] * xy * sh[4] +
+				SH_C2[1] * yz * sh[5] +
+				SH_C2[2] * (2.0f * zz - xx - yy) * sh[6] +
+				SH_C2[3] * xz * sh[7] +
+				SH_C2[4] * (xx - yy) * sh[8];
+
+			if (deg > 2)
+			{
+				result = result +
+					SH_C3[0] * y * (3.0f * xx - yy) * sh[9] +
+					SH_C3[1] * xy * z * sh[10] +
+					SH_C3[2] * y * (4.0f * zz - xx - yy) * sh[11] +
+					SH_C3[3] * z * (2.0f * zz - 3.0f * xx - 3.0f * yy) * sh[12] +
+					SH_C3[4] * x * (4.0f * zz - xx - yy) * sh[13] +
+					SH_C3[5] * z * (xx - yy) * sh[14] +
+					SH_C3[6] * x * (xx - 3.0f * yy) * sh[15];
+			}
+		}
+	}
+	result += 0.5f;
+
+	// RGB colors are clamped to positive values. If values are
+	// clamped, we need to keep track of this for the backward pass.
+	clamped[3 * idx + 0] = (result.x < 0);
+	clamped[3 * idx + 1] = (result.y < 0);
+	clamped[3 * idx + 2] = (result.z < 0);
+	return glm::max(result, 0.0f);
+}
+
+// Forward version of 2D covariance matrix computation
+__device__ float3 computeCov2D(const float3& mean, float focal_x, float focal_y, float tan_fovx, float tan_fovy, const float* cov3D, const float* viewmatrix)
+{
+	// The following models the steps outlined by equations 29
+	// and 31 in "EWA Splatting" (Zwicker et al., 2002). 
+	// Additionally considers aspect / scaling of viewport.
+	// Transposes used to account for row-/column-major conventions.
+	float3 t = transformPoint4x3(mean, viewmatrix);
+
+	const float limx = 1.3f * tan_fovx;
+	const float limy = 1.3f * tan_fovy;
+	const float txtz = t.x / t.z;
+	const float tytz = t.y / t.z;
+	t.x = min(limx, max(-limx, txtz)) * t.z;
+	t.y = min(limy, max(-limy, tytz)) * t.z;
+
+	glm::mat3 J = glm::mat3(
+		focal_x / t.z, 0.0f, -(focal_x * t.x) / (t.z * t.z),
+		0.0f, focal_y / t.z, -(focal_y * t.y) / (t.z * t.z),
+		0, 0, 0);
+
+	glm::mat3 W = glm::mat3(
+		viewmatrix[0], viewmatrix[4], viewmatrix[8],
+		viewmatrix[1], viewmatrix[5], viewmatrix[9],
+		viewmatrix[2], viewmatrix[6], viewmatrix[10]);
+
+	glm::mat3 T = W * J;
+
+	glm::mat3 Vrk = glm::mat3(
+		cov3D[0], cov3D[1], cov3D[2],
+		cov3D[1], cov3D[3], cov3D[4],
+		cov3D[2], cov3D[4], cov3D[5]);
+
+	glm::mat3 cov = glm::transpose(T) * glm::transpose(Vrk) * T;
+
+	// Apply low-pass filter: every Gaussian should be at least
+	// one pixel wide/high. Discard 3rd row and column.
+	cov[0][0] += 0.3f;
+	cov[1][1] += 0.3f;
+	return { float(cov[0][0]), float(cov[0][1]), float(cov[1][1]) };
+}
+
+// Forward method for converting scale and rotation properties of each
+// Gaussian to a 3D covariance matrix in world space. Also takes care
+// of quaternion normalization.
+__device__ void computeCov3D(const glm::vec3 scale, float mod, const glm::vec4 rot, float* cov3D)
+{
+	// Create scaling matrix
+	glm::mat3 S = glm::mat3(1.0f);
+	S[0][0] = mod * scale.x;
+	S[1][1] = mod * scale.y;
+	S[2][2] = mod * scale.z;
+
+	// Normalize quaternion to get valid rotation
+	glm::vec4 q = rot;// / glm::length(rot);
+	float r = q.x;
+	float x = q.y;
+	float y = q.z;
+	float z = q.w;
+
+	// Compute rotation matrix from quaternion
+	glm::mat3 R = glm::mat3(
+		1.f - 2.f * (y * y + z * z), 2.f * (x * y - r * z), 2.f * (x * z + r * y),
+		2.f * (x * y + r * z), 1.f - 2.f * (x * x + z * z), 2.f * (y * z - r * x),
+		2.f * (x * z - r * y), 2.f * (y * z + r * x), 1.f - 2.f * (x * x + y * y)
+	);
+
+	glm::mat3 M = S * R;
+
+	// Compute 3D world covariance matrix Sigma
+	glm::mat3 Sigma = glm::transpose(M) * M;
+
+	// Covariance is symmetric, only store upper right
+	cov3D[0] = Sigma[0][0];
+	cov3D[1] = Sigma[0][1];
+	cov3D[2] = Sigma[0][2];
+	cov3D[3] = Sigma[1][1];
+	cov3D[4] = Sigma[1][2];
+	cov3D[5] = Sigma[2][2];
+}
+
+// Perform initial steps for each Gaussian prior to rasterization.
+template<int C>
+__global__ void preprocessCUDA(int P, int D, int M,
+	const float* orig_points,
+	const glm::vec3* scales,
+	const float scale_modifier,
+	const glm::vec4* rotations,
+	const float* opacities,
+	const float* shs,
+	bool* clamped,
+	const float* cov3D_precomp,
+	const float* colors_precomp,
+	const float* viewmatrix,
+	const float* projmatrix,
+	const glm::vec3* cam_pos,
+	const int W, int H,
+	const float tan_fovx, float tan_fovy,
+	const float focal_x, float focal_y,
+	int* radii,
+	float2* points_xy_image,
+	float* depths,
+	float* cov3Ds,
+	float* rgb,
+	float4* conic_opacity,
+	const dim3 grid,
+	uint32_t* tiles_touched,
+	bool prefiltered)
+{
+	auto idx = cg::this_grid().thread_rank();
+	if (idx >= P)
+		return;
+
+	// Initialize radius and touched tiles to 0. If this isn't changed,
+	// this Gaussian will not be processed further.
+	radii[idx] = 0;
+	tiles_touched[idx] = 0;
+
+	// Perform near culling, quit if outside.
+	float3 p_view;
+	if (!in_frustum(idx, orig_points, viewmatrix, projmatrix, prefiltered, p_view))
+		return;
+
+	// Transform point by projecting
+	float3 p_orig = { orig_points[3 * idx], orig_points[3 * idx + 1], orig_points[3 * idx + 2] };
+	float4 p_hom = transformPoint4x4(p_orig, projmatrix);
+	float p_w = 1.0f / (p_hom.w + 0.0000001f);
+	float3 p_proj = { p_hom.x * p_w, p_hom.y * p_w, p_hom.z * p_w };
+
+	// If 3D covariance matrix is precomputed, use it, otherwise compute
+	// from scaling and rotation parameters. 
+	const float* cov3D;
+	if (cov3D_precomp != nullptr)
+	{
+		cov3D = cov3D_precomp + idx * 6;
+	}
+	else
+	{
+		computeCov3D(scales[idx], scale_modifier, rotations[idx], cov3Ds + idx * 6);
+		cov3D = cov3Ds + idx * 6;
+	}
+
+	// Compute 2D screen-space covariance matrix
+	float3 cov = computeCov2D(p_orig, focal_x, focal_y, tan_fovx, tan_fovy, cov3D, viewmatrix);
+
+	// Invert covariance (EWA algorithm)
+	float det = (cov.x * cov.z - cov.y * cov.y);
+	if (det == 0.0f)
+		return;
+	float det_inv = 1.f / det;
+	float3 conic = { cov.z * det_inv, -cov.y * det_inv, cov.x * det_inv };
+
+	// Compute extent in screen space (by finding eigenvalues of
+	// 2D covariance matrix). Use extent to compute a bounding rectangle
+	// of screen-space tiles that this Gaussian overlaps with. Quit if
+	// rectangle covers 0 tiles. 
+	float mid = 0.5f * (cov.x + cov.z);
+	float lambda1 = mid + sqrt(max(0.1f, mid * mid - det));
+	float lambda2 = mid - sqrt(max(0.1f, mid * mid - det));
+	float my_radius = ceil(3.f * sqrt(max(lambda1, lambda2)));
+	float2 point_image = { ndc2Pix(p_proj.x, W), ndc2Pix(p_proj.y, H) };
+	uint2 rect_min, rect_max;
+	getRect(point_image, my_radius, rect_min, rect_max, grid);
+	if ((rect_max.x - rect_min.x) * (rect_max.y - rect_min.y) == 0)
+		return;
+
+	// If colors have been precomputed, use them, otherwise convert
+	// spherical harmonics coefficients to RGB color.
+	if (colors_precomp == nullptr)
+	{
+		glm::vec3 result = computeColorFromSH(idx, D, M, (glm::vec3*)orig_points, *cam_pos, shs, clamped);
+		rgb[idx * C + 0] = result.x;
+		rgb[idx * C + 1] = result.y;
+		rgb[idx * C + 2] = result.z;
+	}
+
+	// Store some useful helper data for the next steps.
+	depths[idx] = p_view.z;
+	radii[idx] = my_radius;
+	points_xy_image[idx] = point_image;
+	// Inverse 2D covariance and opacity neatly pack into one float4
+	conic_opacity[idx] = { conic.x, conic.y, conic.z, opacities[idx] };
+	tiles_touched[idx] = (rect_max.y - rect_min.y) * (rect_max.x - rect_min.x);
+}
+
+// Main rasterization method. Collaboratively works on one tile per
+// block, each thread treats one pixel. Alternates between fetching 
+// and rasterizing data.
+template <uint32_t CHANNELS>
+__global__ void __launch_bounds__(BLOCK_X * BLOCK_Y)
+renderCUDA(
+	const uint2* __restrict__ ranges,
+	const uint32_t* __restrict__ point_list,
+	int W, int H,
+	const float2* __restrict__ points_xy_image,
+	const float* __restrict__ features,
+	const float* __restrict__ depths,
+	const float4* __restrict__ conic_opacity,
+	float* __restrict__ out_alpha,
+	uint32_t* __restrict__ n_contrib,
+	const float* __restrict__ bg_color,
+	float* __restrict__ out_color,
+	float* __restrict__ out_depth)
+{
+	// Identify current tile and associated min/max pixel range.
+	auto block = cg::this_thread_block();
+	uint32_t horizontal_blocks = (W + BLOCK_X - 1) / BLOCK_X;
+	uint2 pix_min = { block.group_index().x * BLOCK_X, block.group_index().y * BLOCK_Y };
+	uint2 pix_max = { min(pix_min.x + BLOCK_X, W), min(pix_min.y + BLOCK_Y , H) };
+	uint2 pix = { pix_min.x + block.thread_index().x, pix_min.y + block.thread_index().y };
+	uint32_t pix_id = W * pix.y + pix.x;
+	float2 pixf = { (float)pix.x, (float)pix.y };
+
+	// Check if this thread is associated with a valid pixel or outside.
+	bool inside = pix.x < W&& pix.y < H;
+	// Done threads can help with fetching, but don't rasterize
+	bool done = !inside;
+
+	// Load start/end range of IDs to process in bit sorted list.
+	uint2 range = ranges[block.group_index().y * horizontal_blocks + block.group_index().x];
+	const int rounds = ((range.y - range.x + BLOCK_SIZE - 1) / BLOCK_SIZE);
+	int toDo = range.y - range.x;
+
+	// Allocate storage for batches of collectively fetched data.
+	__shared__ int collected_id[BLOCK_SIZE];
+	__shared__ float2 collected_xy[BLOCK_SIZE];
+	__shared__ float4 collected_conic_opacity[BLOCK_SIZE];
+
+	// Initialize helper variables
+	float T = 1.0f;
+	uint32_t contributor = 0;
+	uint32_t last_contributor = 0;
+	float C[CHANNELS] = { 0 };
+	float weight = 0;
+	float D = 0;
+
+	// Iterate over batches until all done or range is complete
+	for (int i = 0; i < rounds; i++, toDo -= BLOCK_SIZE)
+	{
+		// End if entire block votes that it is done rasterizing
+		int num_done = __syncthreads_count(done);
+		if (num_done == BLOCK_SIZE)
+			break;
+
+		// Collectively fetch per-Gaussian data from global to shared
+		int progress = i * BLOCK_SIZE + block.thread_rank();
+		if (range.x + progress < range.y)
+		{
+			int coll_id = point_list[range.x + progress];
+			collected_id[block.thread_rank()] = coll_id;
+			collected_xy[block.thread_rank()] = points_xy_image[coll_id];
+			collected_conic_opacity[block.thread_rank()] = conic_opacity[coll_id];
+		}
+		block.sync();
+
+		// Iterate over current batch
+		for (int j = 0; !done && j < min(BLOCK_SIZE, toDo); j++)
+		{
+			// Keep track of current position in range
+			contributor++;
+
+			// Resample using conic matrix (cf. "Surface 
+			// Splatting" by Zwicker et al., 2001)
+			float2 xy = collected_xy[j];
+			float2 d = { xy.x - pixf.x, xy.y - pixf.y };
+			float4 con_o = collected_conic_opacity[j];
+			float power = -0.5f * (con_o.x * d.x * d.x + con_o.z * d.y * d.y) - con_o.y * d.x * d.y;
+			if (power > 0.0f)
+				continue;
+
+			// Eq. (2) from 3D Gaussian splatting paper.
+			// Obtain alpha by multiplying with Gaussian opacity
+			// and its exponential falloff from mean.
+			// Avoid numerical instabilities (see paper appendix). 
+			float alpha = min(0.99f, con_o.w * exp(power));
+			if (alpha < 1.0f / 255.0f)
+				continue;
+			float test_T = T * (1 - alpha);
+			if (test_T < 0.0001f)
+			{
+				done = true;
+				continue;
+			}
+
+			// Eq. (3) from 3D Gaussian splatting paper.
+			for (int ch = 0; ch < CHANNELS; ch++)
+				C[ch] += features[collected_id[j] * CHANNELS + ch] * alpha * T;
+			weight += alpha * T;
+			D += depths[collected_id[j]] * alpha * T;
+
+			T = test_T;
+
+			// Keep track of last range entry to update this
+			// pixel.
+			last_contributor = contributor;
+		}
+	}
+
+	// All threads that treat valid pixel write out their final
+	// rendering data to the frame and auxiliary buffers.
+	if (inside)
+	{
+		n_contrib[pix_id] = last_contributor;
+		for (int ch = 0; ch < CHANNELS; ch++)
+			out_color[ch * H * W + pix_id] = C[ch] + T * bg_color[ch];
+		out_alpha[pix_id] = weight; //1 - T;
+		out_depth[pix_id] = D;
+	}
+}
+
+void FORWARD::render(
+	const dim3 grid, dim3 block,
+	const uint2* ranges,
+	const uint32_t* point_list,
+	int W, int H,
+	const float2* means2D,
+	const float* colors,
+	const float* depths,
+	const float4* conic_opacity,
+	float* out_alpha,
+	uint32_t* n_contrib,
+	const float* bg_color,
+	float* out_color,
+	float* out_depth)
+{
+	renderCUDA<NUM_CHANNELS> << <grid, block >> > (
+		ranges,
+		point_list,
+		W, H,
+		means2D,
+		colors,
+		depths,
+		conic_opacity,
+		out_alpha,
+		n_contrib,
+		bg_color,
+		out_color,
+		out_depth);
+}
+
+void FORWARD::preprocess(int P, int D, int M,
+	const float* means3D,
+	const glm::vec3* scales,
+	const float scale_modifier,
+	const glm::vec4* rotations,
+	const float* opacities,
+	const float* shs,
+	bool* clamped,
+	const float* cov3D_precomp,
+	const float* colors_precomp,
+	const float* viewmatrix,
+	const float* projmatrix,
+	const glm::vec3* cam_pos,
+	const int W, int H,
+	const float focal_x, float focal_y,
+	const float tan_fovx, float tan_fovy,
+	int* radii,
+	float2* means2D,
+	float* depths,
+	float* cov3Ds,
+	float* rgb,
+	float4* conic_opacity,
+	const dim3 grid,
+	uint32_t* tiles_touched,
+	bool prefiltered)
+{
+	preprocessCUDA<NUM_CHANNELS> << <(P + 255) / 256, 256 >> > (
+		P, D, M,
+		means3D,
+		scales,
+		scale_modifier,
+		rotations,
+		opacities,
+		shs,
+		clamped,
+		cov3D_precomp,
+		colors_precomp,
+		viewmatrix, 
+		projmatrix,
+		cam_pos,
+		W, H,
+		tan_fovx, tan_fovy,
+		focal_x, focal_y,
+		radii,
+		means2D,
+		depths,
+		cov3Ds,
+		rgb,
+		conic_opacity,
+		grid,
+		tiles_touched,
+		prefiltered
+		);
+}

diff-gaussian-rasterization-camera/cuda_rasterizer/forward.h

@@ -0,0 +1,68 @@
+/*
+ * Copyright (C) 2023, Inria
+ * GRAPHDECO research group, https://team.inria.fr/graphdeco
+ * All rights reserved.
+ *
+ * This software is free for non-commercial, research and evaluation use 
+ * under the terms of the LICENSE.md file.
+ *
+ * For inquiries contact  [email protected]
+ */
+
+#ifndef CUDA_RASTERIZER_FORWARD_H_INCLUDED
+#define CUDA_RASTERIZER_FORWARD_H_INCLUDED
+
+#include <cuda.h>
+#include "cuda_runtime.h"
+#include "device_launch_parameters.h"
+#define GLM_FORCE_CUDA
+#include <glm/glm.hpp>
+
+namespace FORWARD
+{
+	// Perform initial steps for each Gaussian prior to rasterization.
+	void preprocess(int P, int D, int M,
+		const float* orig_points,
+		const glm::vec3* scales,
+		const float scale_modifier,
+		const glm::vec4* rotations,
+		const float* opacities,
+		const float* shs,
+		bool* clamped,
+		const float* cov3D_precomp,
+		const float* colors_precomp,
+		const float* viewmatrix,
+		const float* projmatrix,
+		const glm::vec3* cam_pos,
+		const int W, int H,
+		const float focal_x, float focal_y,
+		const float tan_fovx, float tan_fovy,
+		int* radii,
+		float2* points_xy_image,
+		float* depths,
+		float* cov3Ds,
+		float* colors,
+		float4* conic_opacity,
+		const dim3 grid,
+		uint32_t* tiles_touched,
+		bool prefiltered);
+
+	// Main rasterization method.
+	void render(
+		const dim3 grid, dim3 block,
+		const uint2* ranges,
+		const uint32_t* point_list,
+		int W, int H,
+		const float2* points_xy_image,
+		const float* features,
+		const float* depths,
+		const float4* conic_opacity,
+		float* out_alpha,
+		uint32_t* n_contrib,
+		const float* bg_color,
+		float* out_color,
+		float* out_depth);
+}
+
+
+#endif

diff-gaussian-rasterization-camera/cuda_rasterizer/rasterizer.h

@@ -0,0 +1,95 @@
+/*
+ * Copyright (C) 2023, Inria
+ * GRAPHDECO research group, https://team.inria.fr/graphdeco
+ * All rights reserved.
+ *
+ * This software is free for non-commercial, research and evaluation use 
+ * under the terms of the LICENSE.md file.
+ *
+ * For inquiries contact  [email protected]
+ */
+
+#ifndef CUDA_RASTERIZER_H_INCLUDED
+#define CUDA_RASTERIZER_H_INCLUDED
+
+#include <vector>
+#include <functional>
+
+namespace CudaRasterizer
+{
+	class Rasterizer
+	{
+	public:
+
+		static void markVisible(
+			int P,
+			float* means3D,
+			float* viewmatrix,
+			float* projmatrix,
+			bool* present);
+
+		static int forward(
+			std::function<char* (size_t)> geometryBuffer,
+			std::function<char* (size_t)> binningBuffer,
+			std::function<char* (size_t)> imageBuffer,
+			const int P, int D, int M,
+			const float* background,
+			const int width, int height,
+			const float* means3D,
+			const float* shs,
+			const float* colors_precomp,
+			const float* opacities,
+			const float* scales,
+			const float scale_modifier,
+			const float* rotations,
+			const float* cov3D_precomp,
+			const float* viewmatrix,
+			const float* projmatrix,
+			const float* cam_pos,
+			const float tan_fovx, float tan_fovy,
+			const bool prefiltered,
+			float* out_color,
+			float* out_depth,
+			float* out_alpha,
+			int* radii = nullptr,
+			bool debug = false);
+
+		static void backward(
+			const int P, int D, int M, int R,
+			const float* background,
+			const int width, int height,
+			const float* means3D,
+			const float* shs,
+			const float* colors_precomp,
+			const float* alphas,
+			const float* scales,
+			const float scale_modifier,
+			const float* rotations,
+			const float* cov3D_precomp,
+			const float* viewmatrix,
+			const float* projmatrix,
+			const float* campos,
+			const float tan_fovx, float tan_fovy,
+			const int* radii,
+			char* geom_buffer,
+			char* binning_buffer,
+			char* image_buffer,
+			const float* dL_dpix,
+			const float* dL_dpix_depth,
+			const float* dL_dalphas,
+			float* dL_dmean2D,
+			float* dL_dts,
+			float* dL_dconic,
+			float* dL_dopacity,
+			float* dL_dcolor,
+			float* dL_ddepth,
+			float* dL_dmean3D,
+			float* dL_dcov3D,
+			float* dL_dsh,
+			float* dL_dscale,
+			float* dL_drot,
+			bool debug);
+	};
+};
+
+#endif

diff-gaussian-rasterization-camera/cuda_rasterizer/rasterizer_impl.cu

@@ -0,0 +1,449 @@
+/*
+ * Copyright (C) 2023, Inria
+ * GRAPHDECO research group, https://team.inria.fr/graphdeco
+ * All rights reserved.
+ *
+ * This software is free for non-commercial, research and evaluation use 
+ * under the terms of the LICENSE.md file.
+ *
+ * For inquiries contact  [email protected]
+ */
+
+#include "rasterizer_impl.h"
+#include <iostream>
+#include <fstream>
+#include <algorithm>
+#include <numeric>
+#include <cuda.h>
+#include "cuda_runtime.h"
+#include "device_launch_parameters.h"
+#include <cub/cub.cuh>
+#include <cub/device/device_radix_sort.cuh>
+#define GLM_FORCE_CUDA
+#include <glm/glm.hpp>
+
+#include <cooperative_groups.h>
+#include <cooperative_groups/reduce.h>
+namespace cg = cooperative_groups;
+
+#include "auxiliary.h"
+#include "forward.h"
+#include "backward.h"
+
+// Helper function to find the next-highest bit of the MSB
+// on the CPU.
+uint32_t getHigherMsb(uint32_t n)
+{
+	uint32_t msb = sizeof(n) * 4;
+	uint32_t step = msb;
+	while (step > 1)
+	{
+		step /= 2;
+		if (n >> msb)
+			msb += step;
+		else
+			msb -= step;
+	}
+	if (n >> msb)
+		msb++;
+	return msb;
+}
+
+// Wrapper method to call auxiliary coarse frustum containment test.
+// Mark all Gaussians that pass it.
+__global__ void checkFrustum(int P,
+	const float* orig_points,
+	const float* viewmatrix,
+	const float* projmatrix,
+	bool* present)
+{
+	auto idx = cg::this_grid().thread_rank();
+	if (idx >= P)
+		return;
+
+	float3 p_view;
+	present[idx] = in_frustum(idx, orig_points, viewmatrix, projmatrix, false, p_view);
+}
+
+// Generates one key/value pair for all Gaussian / tile overlaps. 
+// Run once per Gaussian (1:N mapping).
+__global__ void duplicateWithKeys(
+	int P,
+	const float2* points_xy,
+	const float* depths,
+	const uint32_t* offsets,
+	uint64_t* gaussian_keys_unsorted,
+	uint32_t* gaussian_values_unsorted,
+	int* radii,
+	dim3 grid)
+{
+	auto idx = cg::this_grid().thread_rank();
+	if (idx >= P)
+		return;
+
+	// Generate no key/value pair for invisible Gaussians
+	if (radii[idx] > 0)
+	{
+		// Find this Gaussian's offset in buffer for writing keys/values.
+		uint32_t off = (idx == 0) ? 0 : offsets[idx - 1];
+		uint2 rect_min, rect_max;
+
+		getRect(points_xy[idx], radii[idx], rect_min, rect_max, grid);
+
+		// For each tile that the bounding rect overlaps, emit a 
+		// key/value pair. The key is |  tile ID  |      depth      |,
+		// and the value is the ID of the Gaussian. Sorting the values 
+		// with this key yields Gaussian IDs in a list, such that they
+		// are first sorted by tile and then by depth. 
+		for (int y = rect_min.y; y < rect_max.y; y++)
+		{
+			for (int x = rect_min.x; x < rect_max.x; x++)
+			{
+				uint64_t key = y * grid.x + x;
+				key <<= 32;
+				key |= *((uint32_t*)&depths[idx]);
+				gaussian_keys_unsorted[off] = key;
+				gaussian_values_unsorted[off] = idx;
+				off++;
+			}
+		}
+	}
+}
+
+// Check keys to see if it is at the start/end of one tile's range in 
+// the full sorted list. If yes, write start/end of this tile. 
+// Run once per instanced (duplicated) Gaussian ID.
+__global__ void identifyTileRanges(int L, uint64_t* point_list_keys, uint2* ranges)
+{
+	auto idx = cg::this_grid().thread_rank();
+	if (idx >= L)
+		return;
+
+	// Read tile ID from key. Update start/end of tile range if at limit.
+	uint64_t key = point_list_keys[idx];
+	uint32_t currtile = key >> 32;
+	if (idx == 0)
+		ranges[currtile].x = 0;
+	else
+	{
+		uint32_t prevtile = point_list_keys[idx - 1] >> 32;
+		if (currtile != prevtile)
+		{
+			ranges[prevtile].y = idx;
+			ranges[currtile].x = idx;
+		}
+	}
+	if (idx == L - 1)
+		ranges[currtile].y = L;
+}
+
+// Mark Gaussians as visible/invisible, based on view frustum testing
+void CudaRasterizer::Rasterizer::markVisible(
+	int P,
+	float* means3D,
+	float* viewmatrix,
+	float* projmatrix,
+	bool* present)
+{
+	checkFrustum << <(P + 255) / 256, 256 >> > (
+		P,
+		means3D,
+		viewmatrix, projmatrix,
+		present);
+}
+
+CudaRasterizer::GeometryState CudaRasterizer::GeometryState::fromChunk(char*& chunk, size_t P)
+{
+	GeometryState geom;
+	obtain(chunk, geom.depths, P, 128);
+	obtain(chunk, geom.clamped, P * 3, 128);
+	obtain(chunk, geom.internal_radii, P, 128);
+	obtain(chunk, geom.means2D, P, 128);
+	obtain(chunk, geom.cov3D, P * 6, 128);
+	obtain(chunk, geom.conic_opacity, P, 128);
+	obtain(chunk, geom.rgb, P * 3, 128);
+	obtain(chunk, geom.tiles_touched, P, 128);
+	cub::DeviceScan::InclusiveSum(nullptr, geom.scan_size, geom.tiles_touched, geom.tiles_touched, P);
+	obtain(chunk, geom.scanning_space, geom.scan_size, 128);
+	obtain(chunk, geom.point_offsets, P, 128);
+	return geom;
+}
+
+CudaRasterizer::ImageState CudaRasterizer::ImageState::fromChunk(char*& chunk, size_t N)
+{
+	ImageState img;
+	obtain(chunk, img.n_contrib, N, 128);
+	obtain(chunk, img.ranges, N, 128);
+	return img;
+}
+
+CudaRasterizer::BinningState CudaRasterizer::BinningState::fromChunk(char*& chunk, size_t P)
+{
+	BinningState binning;
+	obtain(chunk, binning.point_list, P, 128);
+	obtain(chunk, binning.point_list_unsorted, P, 128);
+	obtain(chunk, binning.point_list_keys, P, 128);
+	obtain(chunk, binning.point_list_keys_unsorted, P, 128);
+	cub::DeviceRadixSort::SortPairs(
+		nullptr, binning.sorting_size,
+		binning.point_list_keys_unsorted, binning.point_list_keys,
+		binning.point_list_unsorted, binning.point_list, P);
+	obtain(chunk, binning.list_sorting_space, binning.sorting_size, 128);
+	return binning;
+}
+
+// Forward rendering procedure for differentiable rasterization
+// of Gaussians.
+int CudaRasterizer::Rasterizer::forward(
+	std::function<char* (size_t)> geometryBuffer,
+	std::function<char* (size_t)> binningBuffer,
+	std::function<char* (size_t)> imageBuffer,
+	const int P, int D, int M,
+	const float* background,
+	const int width, int height,
+	const float* means3D,
+	const float* shs,
+	const float* colors_precomp,
+	const float* opacities,
+	const float* scales,
+	const float scale_modifier,
+	const float* rotations,
+	const float* cov3D_precomp,
+	const float* viewmatrix,
+	const float* projmatrix,
+	const float* cam_pos,
+	const float tan_fovx, float tan_fovy,
+	const bool prefiltered,
+	float* out_color,
+	float* out_depth,
+	float* out_alpha,
+	int* radii,
+	bool debug)
+{
+	const float focal_y = height / (2.0f * tan_fovy);
+	const float focal_x = width / (2.0f * tan_fovx);
+
+	size_t chunk_size = required<GeometryState>(P);
+	char* chunkptr = geometryBuffer(chunk_size);
+	GeometryState geomState = GeometryState::fromChunk(chunkptr, P);
+
+	if (radii == nullptr)
+	{
+		radii = geomState.internal_radii;
+	}
+
+	dim3 tile_grid((width + BLOCK_X - 1) / BLOCK_X, (height + BLOCK_Y - 1) / BLOCK_Y, 1);
+	dim3 block(BLOCK_X, BLOCK_Y, 1);
+
+	// Dynamically resize image-based auxiliary buffers during training
+	size_t img_chunk_size = required<ImageState>(width * height);
+	char* img_chunkptr = imageBuffer(img_chunk_size);
+	ImageState imgState = ImageState::fromChunk(img_chunkptr, width * height);
+
+	if (NUM_CHANNELS != 3 && colors_precomp == nullptr)
+	{
+		throw std::runtime_error("For non-RGB, provide precomputed Gaussian colors!");
+	}
+
+	// Run preprocessing per-Gaussian (transformation, bounding, conversion of SHs to RGB)
+	CHECK_CUDA(FORWARD::preprocess(
+		P, D, M,
+		means3D,
+		(glm::vec3*)scales,
+		scale_modifier,
+		(glm::vec4*)rotations,
+		opacities,
+		shs,
+		geomState.clamped,
+		cov3D_precomp,
+		colors_precomp,
+		viewmatrix, projmatrix,
+		(glm::vec3*)cam_pos,
+		width, height,
+		focal_x, focal_y,
+		tan_fovx, tan_fovy,
+		radii,
+		geomState.means2D,
+		geomState.depths,
+		geomState.cov3D,
+		geomState.rgb,
+		geomState.conic_opacity,
+		tile_grid,
+		geomState.tiles_touched,
+		prefiltered
+	), debug)
+
+	// Compute prefix sum over full list of touched tile counts by Gaussians
+	// E.g., [2, 3, 0, 2, 1] -> [2, 5, 5, 7, 8]
+	CHECK_CUDA(cub::DeviceScan::InclusiveSum(geomState.scanning_space, geomState.scan_size, geomState.tiles_touched, geomState.point_offsets, P), debug)
+
+	// Retrieve total number of Gaussian instances to launch and resize aux buffers
+	int num_rendered;
+	CHECK_CUDA(cudaMemcpy(&num_rendered, geomState.point_offsets + P - 1, sizeof(int), cudaMemcpyDeviceToHost), debug);
+
+	size_t binning_chunk_size = required<BinningState>(num_rendered);
+	char* binning_chunkptr = binningBuffer(binning_chunk_size);
+	BinningState binningState = BinningState::fromChunk(binning_chunkptr, num_rendered);
+
+	// For each instance to be rendered, produce adequate [ tile | depth ] key 
+	// and corresponding dublicated Gaussian indices to be sorted
+	duplicateWithKeys << <(P + 255) / 256, 256 >> > (
+		P,
+		geomState.means2D,
+		geomState.depths,
+		geomState.point_offsets,
+		binningState.point_list_keys_unsorted,
+		binningState.point_list_unsorted,
+		radii,
+		tile_grid)
+	CHECK_CUDA(, debug)
+
+	int bit = getHigherMsb(tile_grid.x * tile_grid.y);
+
+	// Sort complete list of (duplicated) Gaussian indices by keys
+	CHECK_CUDA(cub::DeviceRadixSort::SortPairs(
+		binningState.list_sorting_space,
+		binningState.sorting_size,
+		binningState.point_list_keys_unsorted, binningState.point_list_keys,
+		binningState.point_list_unsorted, binningState.point_list,
+		num_rendered, 0, 32 + bit), debug)
+
+	CHECK_CUDA(cudaMemset(imgState.ranges, 0, tile_grid.x * tile_grid.y * sizeof(uint2)), debug);
+
+	// Identify start and end of per-tile workloads in sorted list
+	if (num_rendered > 0)
+		identifyTileRanges << <(num_rendered + 255) / 256, 256 >> > (
+			num_rendered,
+			binningState.point_list_keys,
+			imgState.ranges);
+	CHECK_CUDA(, debug);
+
+	// Let each tile blend its range of Gaussians independently in parallel
+	const float* feature_ptr = colors_precomp != nullptr ? colors_precomp : geomState.rgb;
+	CHECK_CUDA(FORWARD::render(
+		tile_grid, block,
+		imgState.ranges,
+		binningState.point_list,
+		width, height,
+		geomState.means2D,
+		feature_ptr,
+		geomState.depths,
+		geomState.conic_opacity,
+		out_alpha,
+		imgState.n_contrib,
+		background,
+		out_color,
+		out_depth), debug);
+
+	return num_rendered;
+}
+
+// Produce necessary gradients for optimization, corresponding
+// to forward render pass
+void CudaRasterizer::Rasterizer::backward(
+	const int P, int D, int M, int R,
+	const float* background,
+	const int width, int height,
+	const float* means3D,
+	const float* shs,
+	const float* colors_precomp,
+	const float* alphas,
+	const float* scales,
+	const float scale_modifier,
+	const float* rotations,
+	const float* cov3D_precomp,
+	const float* viewmatrix,
+	const float* projmatrix,
+	const float* campos,
+	const float tan_fovx, float tan_fovy,
+	const int* radii,
+	char* geom_buffer,
+	char* binning_buffer,
+	char* img_buffer,
+	const float* dL_dpix,
+	const float* dL_dpix_depth,
+	const float* dL_dalphas,
+	float* dL_dmean2D,
+	float* dL_dts,
+	float* dL_dconic,
+	float* dL_dopacity,
+	float* dL_dcolor,
+	float* dL_ddepth,
+	float* dL_dmean3D,
+	float* dL_dcov3D,
+	float* dL_dsh,
+	float* dL_dscale,
+	float* dL_drot,
+	bool debug)
+{
+	GeometryState geomState = GeometryState::fromChunk(geom_buffer, P);
+	BinningState binningState = BinningState::fromChunk(binning_buffer, R);
+	ImageState imgState = ImageState::fromChunk(img_buffer, width * height);
+
+	if (radii == nullptr)
+	{
+		radii = geomState.internal_radii;
+	}
+
+	const float focal_y = height / (2.0f * tan_fovy);
+	const float focal_x = width / (2.0f * tan_fovx);
+
+	const dim3 tile_grid((width + BLOCK_X - 1) / BLOCK_X, (height + BLOCK_Y - 1) / BLOCK_Y, 1);
+	const dim3 block(BLOCK_X, BLOCK_Y, 1);
+
+	// Compute loss gradients w.r.t. 2D mean position, conic matrix,
+	// opacity and RGB of Gaussians from per-pixel loss gradients.
+	// If we were given precomputed colors and not SHs, use them.
+	const float* color_ptr = (colors_precomp != nullptr) ? colors_precomp : geomState.rgb;
+	const float* depth_ptr = geomState.depths;
+	CHECK_CUDA(BACKWARD::render(
+		tile_grid,
+		block,
+		imgState.ranges,
+		binningState.point_list,
+		width, height,
+		background,
+		geomState.means2D,
+		geomState.conic_opacity,
+		color_ptr,
+		depth_ptr,
+		alphas,
+		imgState.n_contrib,
+		dL_dpix,
+		dL_dpix_depth,
+		dL_dalphas,
+		(float3*)dL_dmean2D,
+		(float4*)dL_dconic,
+		dL_dopacity,
+		dL_dcolor,
+		dL_ddepth), debug)
+
+	// Take care of the rest of preprocessing. Was the precomputed covariance
+	// given to us or a scales/rot pair? If precomputed, pass that. If not,
+	// use the one we computed ourselves.
+	const float* cov3D_ptr = (cov3D_precomp != nullptr) ? cov3D_precomp : geomState.cov3D;
+	CHECK_CUDA(BACKWARD::preprocess(P, D, M,
+		(float3*)means3D,
+		radii,
+		shs,
+		geomState.clamped,
+		(glm::vec3*)scales,
+		(glm::vec4*)rotations,
+		scale_modifier,
+		cov3D_ptr,
+		viewmatrix,
+		projmatrix,
+		focal_x, focal_y,
+		tan_fovx, tan_fovy,
+		(glm::vec3*)campos,
+		(float3*)dL_dmean2D,
+		(float3*)dL_dts,
+		dL_dconic,
+		(glm::vec3*)dL_dmean3D,
+		dL_dcolor,
+		dL_ddepth,
+		dL_dcov3D,
+		dL_dsh,
+		(glm::vec3*)dL_dscale,
+		(glm::vec4*)dL_drot), debug)
+}

diff-gaussian-rasterization-camera/cuda_rasterizer/rasterizer_impl.h

@@ -0,0 +1,73 @@
+/*
+ * Copyright (C) 2023, Inria
+ * GRAPHDECO research group, https://team.inria.fr/graphdeco
+ * All rights reserved.
+ *
+ * This software is free for non-commercial, research and evaluation use 
+ * under the terms of the LICENSE.md file.
+ *
+ * For inquiries contact  [email protected]
+ */
+
+#pragma once
+
+#include <iostream>
+#include <vector>
+#include "rasterizer.h"
+#include <cuda_runtime_api.h>
+
+namespace CudaRasterizer
+{
+	template <typename T>
+	static void obtain(char*& chunk, T*& ptr, std::size_t count, std::size_t alignment)
+	{
+		std::size_t offset = (reinterpret_cast<std::uintptr_t>(chunk) + alignment - 1) & ~(alignment - 1);
+		ptr = reinterpret_cast<T*>(offset);
+		chunk = reinterpret_cast<char*>(ptr + count);
+	}
+
+	struct GeometryState
+	{
+		size_t scan_size;
+		float* depths;
+		char* scanning_space;
+		bool* clamped;
+		int* internal_radii;
+		float2* means2D;
+		float* cov3D;
+		float4* conic_opacity;
+		float* rgb;
+		uint32_t* point_offsets;
+		uint32_t* tiles_touched;
+
+		static GeometryState fromChunk(char*& chunk, size_t P);
+	};
+
+	struct ImageState
+	{
+		uint2* ranges;
+		uint32_t* n_contrib;
+
+		static ImageState fromChunk(char*& chunk, size_t N);
+	};
+
+	struct BinningState
+	{
+		size_t sorting_size;
+		uint64_t* point_list_keys_unsorted;
+		uint64_t* point_list_keys;
+		uint32_t* point_list_unsorted;
+		uint32_t* point_list;
+		char* list_sorting_space;
+
+		static BinningState fromChunk(char*& chunk, size_t P);
+	};
+
+	template<typename T> 
+	size_t required(size_t P)
+	{
+		char* size = nullptr;
+		T::fromChunk(size, P);
+		return ((size_t)size) + 128;
+	}
+};

diff-gaussian-rasterization-camera/diff_gaussian_rasterization/__init__.py

@@ -0,0 +1,263 @@
+#
+# Copyright (C) 2023, Inria
+# GRAPHDECO research group, https://team.inria.fr/graphdeco
+# All rights reserved.
+#
+# This software is free for non-commercial, research and evaluation use 
+# under the terms of the LICENSE.md file.
+#
+# For inquiries contact  [email protected]
+#
+
+from typing import NamedTuple
+import torch.nn as nn
+import torch
+from . import _C
+
+def cpu_deep_copy_tuple(input_tuple):
+    copied_tensors = [item.cpu().clone() if isinstance(item, torch.Tensor) else item for item in input_tuple]
+    return tuple(copied_tensors)
+
+def rasterize_gaussians(
+    means3D,
+    means2D,
+    sh,
+    colors_precomp,
+    opacities,
+    scales,
+    rotations,
+    cov3Ds_precomp,
+    viewmat,
+    raster_settings,
+):
+    return _RasterizeGaussians.apply(
+        means3D,
+        means2D,
+        sh,
+        colors_precomp,
+        opacities,
+        scales,
+        rotations,
+        cov3Ds_precomp,
+        viewmat,
+        raster_settings,
+    )
+
+class _RasterizeGaussians(torch.autograd.Function):
+    @staticmethod
+    def forward(
+        ctx,
+        means3D,
+        means2D,
+        sh,
+        colors_precomp,
+        opacities,
+        scales,
+        rotations,
+        cov3Ds_precomp,
+        viewmat,
+        raster_settings,
+    ):
+
+        # Restructure arguments the way that the C++ lib expects them
+        args = (
+            raster_settings.bg, 
+            means3D,
+            colors_precomp,
+            opacities,
+            scales,
+            rotations,
+            raster_settings.scale_modifier,
+            cov3Ds_precomp,
+            raster_settings.viewmatrix,
+            raster_settings.projmatrix,
+            raster_settings.tanfovx,
+            raster_settings.tanfovy,
+            raster_settings.image_height,
+            raster_settings.image_width,
+            sh,
+            raster_settings.sh_degree,
+            raster_settings.campos,
+            raster_settings.prefiltered,
+            raster_settings.debug
+        )
+
+        # Invoke C++/CUDA rasterizer
+        if raster_settings.debug:
+            cpu_args = cpu_deep_copy_tuple(args) # Copy them before they can be corrupted
+            try:
+                num_rendered, color, depth, alpha, radii, geomBuffer, binningBuffer, imgBuffer = _C.rasterize_gaussians(*args)
+            except Exception as ex:
+                torch.save(cpu_args, "snapshot_fw.dump")
+                print("\nAn error occured in forward. Please forward snapshot_fw.dump for debugging.")
+                raise ex
+        else:
+            num_rendered, color, depth, alpha, radii, geomBuffer, binningBuffer, imgBuffer = _C.rasterize_gaussians(*args)
+
+        # Keep relevant tensors for backward
+        ctx.raster_settings = raster_settings
+        ctx.num_rendered = num_rendered
+        ctx.save_for_backward(colors_precomp, means3D, scales, rotations, cov3Ds_precomp, radii, sh, geomBuffer, binningBuffer, imgBuffer, alpha)
+        return color, radii, depth, alpha
+
+    @staticmethod
+    def backward(ctx, grad_color, grad_radii, grad_depth, grad_alpha):
+
+        # Restore necessary values from context
+        num_rendered = ctx.num_rendered
+        raster_settings = ctx.raster_settings
+        colors_precomp, means3D, scales, rotations, cov3Ds_precomp, radii, sh, geomBuffer, binningBuffer, imgBuffer, alpha = ctx.saved_tensors
+
+        # Restructure args as C++ method expects them
+        args = (raster_settings.bg,
+                means3D, 
+                radii, 
+                colors_precomp, 
+                scales, 
+                rotations, 
+                raster_settings.scale_modifier, 
+                cov3Ds_precomp, 
+                raster_settings.viewmatrix, 
+                raster_settings.projmatrix, 
+                raster_settings.tanfovx, 
+                raster_settings.tanfovy, 
+                grad_color,
+                grad_depth,
+                grad_alpha,
+                sh, 
+                raster_settings.sh_degree, 
+                raster_settings.campos,
+                geomBuffer,
+                num_rendered,
+                binningBuffer,
+                imgBuffer,
+                alpha,
+                raster_settings.debug)
+
+        # Compute gradients for relevant tensors by invoking backward method
+        if raster_settings.debug:
+            cpu_args = cpu_deep_copy_tuple(args) # Copy them before they can be corrupted
+            try:
+                grad_means2D, grad_ts, grad_colors_precomp, grad_opacities, grad_means3D, grad_cov3Ds_precomp, grad_sh, grad_scales, grad_rotations = _C.rasterize_gaussians_backward(*args)
+            except Exception as ex:
+                torch.save(cpu_args, "snapshot_bw.dump")
+                print("\nAn error occured in backward. Writing snapshot_bw.dump for debugging.\n")
+                raise ex
+        else:
+             grad_means2D, grad_ts, grad_colors_precomp, grad_opacities, grad_means3D, grad_cov3Ds_precomp, grad_sh, grad_scales, grad_rotations = _C.rasterize_gaussians_backward(*args)
+        
+        with torch.no_grad():
+            # return viewmat gradients
+            projmat = raster_settings.projmatrix.T
+            means_h = torch.cat([means3D, torch.ones_like(means3D[..., :1])], dim=-1)
+            p_hom = torch.einsum("ij,nj->ni", projmat, means_h)
+            rw = 1 / (p_hom[..., 3] + 1e-5)
+
+            proj = raster_settings.perspectivematrix.flatten()
+            # v_t is the grad w.r.t. the 3D mean in camera coordinates
+            # Math reference (https://arxiv.org/pdf/2312.02121.pdf)
+            # One source is from grad_means2D (the grad w.r.t. the mean in ND coordinates, t' in the paper)
+            v_tx = grad_means2D[:, 0] * (proj[0] * rw - proj[3] * p_hom[:, 0] * torch.square(rw))
+            v_tx += grad_means2D[:, 1] * (proj[1] * rw - proj[3] * p_hom[:, 1] * torch.square(rw))
+            v_ty = grad_means2D[:, 0] * (proj[4] * rw - proj[7] * p_hom[:, 0] * torch.square(rw))
+            v_ty += grad_means2D[:, 1] * (proj[5] * rw - proj[7] * p_hom[:, 1] * torch.square(rw))
+            v_tz = grad_means2D[:, 0] * (proj[8] * rw - proj[11] * p_hom[:, 0] * torch.square(rw))
+            v_tz += grad_means2D[:, 1] * (proj[9] * rw - proj[11] * p_hom[:, 1] * torch.square(rw))
+            v_t = torch.stack(
+                [
+                    v_tx,
+                    v_ty,
+                    v_tz,
+                    torch.zeros_like(v_tx),
+                ],
+                dim=-1,
+            )
+            # Another source of gradients (grad_ts) 
+            # t is involved in the affine transform J when computing the 2D covariance matrix
+            # grad_ts is gathered from "cuda_rasterizer/backward.cu"
+            v_t[:, :3] += grad_ts
+            # Finally, we compute the grad w.r.t. the viewmatrix from v_t
+            grad_viewmat = torch.einsum("ni,nj->ij", v_t, means_h).T # We transposed the viewmatrix
+
+        grads = (
+            grad_means3D,
+            grad_means2D,
+            grad_sh,
+            grad_colors_precomp,
+            grad_opacities,
+            grad_scales,
+            grad_rotations,
+            grad_cov3Ds_precomp,
+            grad_viewmat,
+            None,
+        )
+
+        return grads
+
+class GaussianRasterizationSettings(NamedTuple):
+    image_height: int
+    image_width: int 
+    tanfovx : float
+    tanfovy : float
+    bg : torch.Tensor
+    scale_modifier : float
+    viewmatrix : torch.Tensor
+    perspectivematrix: torch.Tensor
+    projmatrix : torch.Tensor
+    sh_degree : int
+    campos : torch.Tensor
+    prefiltered : bool
+    debug : bool
+
+class GaussianRasterizer(nn.Module):
+    def __init__(self, raster_settings):
+        super().__init__()
+        self.raster_settings = raster_settings
+
+    def markVisible(self, positions):
+        # Mark visible points (based on frustum culling for camera) with a boolean 
+        with torch.no_grad():
+            raster_settings = self.raster_settings
+            visible = _C.mark_visible(
+                positions,
+                raster_settings.viewmatrix,
+                raster_settings.projmatrix)
+            
+        return visible
+
+    def forward(self, means3D, means2D, opacities, shs = None, colors_precomp = None, scales = None, rotations = None, cov3D_precomp = None, viewmat = None):
+        
+        raster_settings = self.raster_settings
+
+        if (shs is None and colors_precomp is None) or (shs is not None and colors_precomp is not None):
+            raise Exception('Please provide excatly one of either SHs or precomputed colors!')
+        
+        if ((scales is None or rotations is None) and cov3D_precomp is None) or ((scales is not None or rotations is not None) and cov3D_precomp is not None):
+            raise Exception('Please provide exactly one of either scale/rotation pair or precomputed 3D covariance!')
+        
+        if shs is None:
+            shs = torch.Tensor([])
+        if colors_precomp is None:
+            colors_precomp = torch.Tensor([])
+
+        if scales is None:
+            scales = torch.Tensor([])
+        if rotations is None:
+            rotations = torch.Tensor([])
+        if cov3D_precomp is None:
+            cov3D_precomp = torch.Tensor([])
+
+        # Invoke C++/CUDA rasterization routine
+        return rasterize_gaussians(
+            means3D,
+            means2D,
+            shs,
+            colors_precomp,
+            opacities,
+            scales, 
+            rotations,
+            cov3D_precomp,
+            viewmat,
+            raster_settings, 
+        )
+

diff-gaussian-rasterization-camera/ext.cpp

@@ -0,0 +1,19 @@
+/*
+ * Copyright (C) 2023, Inria
+ * GRAPHDECO research group, https://team.inria.fr/graphdeco
+ * All rights reserved.
+ *
+ * This software is free for non-commercial, research and evaluation use 
+ * under the terms of the LICENSE.md file.
+ *
+ * For inquiries contact  [email protected]
+ */
+
+#include <torch/extension.h>
+#include "rasterize_points.h"
+
+PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) {
+  m.def("rasterize_gaussians", &RasterizeGaussiansCUDA);
+  m.def("rasterize_gaussians_backward", &RasterizeGaussiansBackwardCUDA);
+  m.def("mark_visible", &markVisible);
+}

diff-gaussian-rasterization-camera/gs_renderer.py

@@ -0,0 +1,866 @@
+import os
+import math
+import numpy as np
+from typing import NamedTuple
+from plyfile import PlyData, PlyElement
+
+import torch
+from torch import nn
+
+from diff_gaussian_rasterization import (
+    GaussianRasterizationSettings,
+    GaussianRasterizer,
+)
+from simple_knn._C import distCUDA2
+
+from sh_utils import eval_sh, SH2RGB, RGB2SH
+from mesh import Mesh
+from mesh_utils import decimate_mesh, clean_mesh
+from cam_utils_torch import orbit_camera
+
+import kiui
+
+def inverse_sigmoid(x):
+    return torch.log(x/(1-x))
+
+def get_expon_lr_func(
+    lr_init, lr_final, lr_delay_steps=0, lr_delay_mult=1.0, max_steps=1000000
+):
+    
+    def helper(step):
+        if lr_init == lr_final:
+            # constant lr, ignore other params
+            return lr_init
+        if step < 0 or (lr_init == 0.0 and lr_final == 0.0):
+            # Disable this parameter
+            return 0.0
+        if lr_delay_steps > 0:
+            # A kind of reverse cosine decay.
+            delay_rate = lr_delay_mult + (1 - lr_delay_mult) * np.sin(
+                0.5 * np.pi * np.clip(step / lr_delay_steps, 0, 1)
+            )
+        else:
+            delay_rate = 1.0
+        t = np.clip(step / max_steps, 0, 1)
+        log_lerp = np.exp(np.log(lr_init) * (1 - t) + np.log(lr_final) * t)
+        return delay_rate * log_lerp
+
+    return helper
+
+
+def strip_lowerdiag(L):
+    uncertainty = torch.zeros((L.shape[0], 6), dtype=torch.float, device="cuda")
+
+    uncertainty[:, 0] = L[:, 0, 0]
+    uncertainty[:, 1] = L[:, 0, 1]
+    uncertainty[:, 2] = L[:, 0, 2]
+    uncertainty[:, 3] = L[:, 1, 1]
+    uncertainty[:, 4] = L[:, 1, 2]
+    uncertainty[:, 5] = L[:, 2, 2]
+    return uncertainty
+
+def strip_symmetric(sym):
+    return strip_lowerdiag(sym)
+
+def gaussian_3d_coeff(xyzs, covs):
+    # xyzs: [N, 3]
+    # covs: [N, 6]
+    x, y, z = xyzs[:, 0], xyzs[:, 1], xyzs[:, 2]
+    a, b, c, d, e, f = covs[:, 0], covs[:, 1], covs[:, 2], covs[:, 3], covs[:, 4], covs[:, 5]
+
+    # eps must be small enough !!!
+    inv_det = 1 / (a * d * f + 2 * e * c * b - e**2 * a - c**2 * d - b**2 * f + 1e-24)
+    inv_a = (d * f - e**2) * inv_det
+    inv_b = (e * c - b * f) * inv_det
+    inv_c = (e * b - c * d) * inv_det
+    inv_d = (a * f - c**2) * inv_det
+    inv_e = (b * c - e * a) * inv_det
+    inv_f = (a * d - b**2) * inv_det
+
+    power = -0.5 * (x**2 * inv_a + y**2 * inv_d + z**2 * inv_f) - x * y * inv_b - x * z * inv_c - y * z * inv_e
+
+    power[power > 0] = -1e10 # abnormal values... make weights 0
+        
+    return torch.exp(power)
+
+def build_rotation(r):
+    norm = torch.sqrt(r[:,0]*r[:,0] + r[:,1]*r[:,1] + r[:,2]*r[:,2] + r[:,3]*r[:,3])
+
+    q = r / norm[:, None]
+
+    R = torch.zeros((q.size(0), 3, 3), device='cuda')
+
+    r = q[:, 0]
+    x = q[:, 1]
+    y = q[:, 2]
+    z = q[:, 3]
+
+    R[:, 0, 0] = 1 - 2 * (y*y + z*z)
+    R[:, 0, 1] = 2 * (x*y - r*z)
+    R[:, 0, 2] = 2 * (x*z + r*y)
+    R[:, 1, 0] = 2 * (x*y + r*z)
+    R[:, 1, 1] = 1 - 2 * (x*x + z*z)
+    R[:, 1, 2] = 2 * (y*z - r*x)
+    R[:, 2, 0] = 2 * (x*z - r*y)
+    R[:, 2, 1] = 2 * (y*z + r*x)
+    R[:, 2, 2] = 1 - 2 * (x*x + y*y)
+    return R
+
+def build_scaling_rotation(s, r):
+    L = torch.zeros((s.shape[0], 3, 3), dtype=torch.float, device="cuda")
+    R = build_rotation(r)
+
+    L[:,0,0] = s[:,0]
+    L[:,1,1] = s[:,1]
+    L[:,2,2] = s[:,2]
+
+    L = R @ L
+    return L
+
+class BasicPointCloud(NamedTuple):
+    points: np.array
+    colors: np.array
+    normals: np.array
+
+
+class GaussianModel:
+
+    def setup_functions(self):
+        def build_covariance_from_scaling_rotation(scaling, scaling_modifier, rotation):
+            L = build_scaling_rotation(scaling_modifier * scaling, rotation)
+            actual_covariance = L @ L.transpose(1, 2)
+            symm = strip_symmetric(actual_covariance)
+            return symm
+        
+        self.scaling_activation = torch.exp
+        self.scaling_inverse_activation = torch.log
+
+        self.covariance_activation = build_covariance_from_scaling_rotation
+
+        self.opacity_activation = torch.sigmoid
+        self.inverse_opacity_activation = inverse_sigmoid
+
+        self.rotation_activation = torch.nn.functional.normalize
+
+
+    def __init__(self, sh_degree : int):
+        self.active_sh_degree = 0
+        self.max_sh_degree = sh_degree  
+        self._xyz = torch.empty(0)
+        self._features_dc = torch.empty(0)
+        self._features_rest = torch.empty(0)
+        self._scaling = torch.empty(0)
+        self._rotation = torch.empty(0)
+        self._opacity = torch.empty(0)
+        self.max_radii2D = torch.empty(0)
+        self.xyz_gradient_accum = torch.empty(0)
+        self.denom = torch.empty(0)
+        self.optimizer = None
+        self.percent_dense = 0
+        self.spatial_lr_scale = 0
+        self.setup_functions()
+
+    def capture(self):
+        return (
+            self.active_sh_degree,
+            self._xyz,
+            self._features_dc,
+            self._features_rest,
+            self._scaling,
+            self._rotation,
+            self._opacity,
+            self.max_radii2D,
+            self.xyz_gradient_accum,
+            self.denom,
+            self.optimizer.state_dict(),
+            self.spatial_lr_scale,
+        )
+    
+    def restore(self, model_args, training_args):
+        (self.active_sh_degree, 
+        self._xyz, 
+        self._features_dc, 
+        self._features_rest,
+        self._scaling, 
+        self._rotation, 
+        self._opacity,
+        self.max_radii2D, 
+        xyz_gradient_accum, 
+        denom,
+        opt_dict, 
+        self.spatial_lr_scale) = model_args
+        self.training_setup(training_args)
+        self.xyz_gradient_accum = xyz_gradient_accum
+        self.denom = denom
+        self.optimizer.load_state_dict(opt_dict)
+
+    @property
+    def get_scaling(self):
+        return self.scaling_activation(self._scaling)
+    
+    @property
+    def get_rotation(self):
+        return self.rotation_activation(self._rotation)
+    
+    @property
+    def get_xyz(self):
+        return self._xyz
+    
+    @property
+    def get_features(self):
+        features_dc = self._features_dc
+        features_rest = self._features_rest
+        return torch.cat((features_dc, features_rest), dim=1)
+    
+    @property
+    def get_opacity(self):
+        return self.opacity_activation(self._opacity)
+
+    @torch.no_grad()
+    def extract_fields(self, resolution=128, num_blocks=16, relax_ratio=1.5):
+        # resolution: resolution of field
+        
+        block_size = 2 / num_blocks
+
+        assert resolution % block_size == 0
+        split_size = resolution // num_blocks
+
+        opacities = self.get_opacity
+
+        # pre-filter low opacity gaussians to save computation
+        mask = (opacities > 0.005).squeeze(1)
+
+        opacities = opacities[mask]
+        xyzs = self.get_xyz[mask]
+        stds = self.get_scaling[mask]
+        
+        # normalize to ~ [-1, 1]
+        mn, mx = xyzs.amin(0), xyzs.amax(0)
+        self.center = (mn + mx) / 2
+        self.scale = 1.8 / (mx - mn).amax().item()
+
+        xyzs = (xyzs - self.center) * self.scale
+        stds = stds * self.scale
+
+        covs = self.covariance_activation(stds, 1, self._rotation[mask])
+
+        # tile
+        device = opacities.device
+        occ = torch.zeros([resolution] * 3, dtype=torch.float32, device=device)
+
+        X = torch.linspace(-1, 1, resolution).split(split_size)
+        Y = torch.linspace(-1, 1, resolution).split(split_size)
+        Z = torch.linspace(-1, 1, resolution).split(split_size)
+
+
+        # loop blocks (assume max size of gaussian is small than relax_ratio * block_size !!!)
+        for xi, xs in enumerate(X):
+            for yi, ys in enumerate(Y):
+                for zi, zs in enumerate(Z):
+                    xx, yy, zz = torch.meshgrid(xs, ys, zs)
+                    # sample points [M, 3]
+                    pts = torch.cat([xx.reshape(-1, 1), yy.reshape(-1, 1), zz.reshape(-1, 1)], dim=-1).to(device)
+                    # in-tile gaussians mask
+                    vmin, vmax = pts.amin(0), pts.amax(0)
+                    vmin -= block_size * relax_ratio
+                    vmax += block_size * relax_ratio
+                    mask = (xyzs < vmax).all(-1) & (xyzs > vmin).all(-1)
+                    # if hit no gaussian, continue to next block
+                    if not mask.any():
+                        continue
+                    mask_xyzs = xyzs[mask] # [L, 3]
+                    mask_covs = covs[mask] # [L, 6]
+                    mask_opas = opacities[mask].view(1, -1) # [L, 1] --> [1, L]
+
+                    # query per point-gaussian pair.
+                    g_pts = pts.unsqueeze(1).repeat(1, mask_covs.shape[0], 1) - mask_xyzs.unsqueeze(0) # [M, L, 3]
+                    g_covs = mask_covs.unsqueeze(0).repeat(pts.shape[0], 1, 1) # [M, L, 6]
+
+                    # batch on gaussian to avoid OOM
+                    batch_g = 1024
+                    val = 0
+                    for start in range(0, g_covs.shape[1], batch_g):
+                        end = min(start + batch_g, g_covs.shape[1])
+                        w = gaussian_3d_coeff(g_pts[:, start:end].reshape(-1, 3), g_covs[:, start:end].reshape(-1, 6)).reshape(pts.shape[0], -1) # [M, l]
+                        val += (mask_opas[:, start:end] * w).sum(-1)
+                    
+                    # kiui.lo(val, mask_opas, w)
+                
+                    occ[xi * split_size: xi * split_size + len(xs), 
+                        yi * split_size: yi * split_size + len(ys), 
+                        zi * split_size: zi * split_size + len(zs)] = val.reshape(len(xs), len(ys), len(zs)) 
+        
+        kiui.lo(occ, verbose=1)
+
+        return occ
+    
+    def extract_mesh(self, path, density_thresh=1, resolution=128, decimate_target=1e5):
+
+        os.makedirs(os.path.dirname(path), exist_ok=True)
+
+        occ = self.extract_fields(resolution).detach().cpu().numpy()
+
+        import mcubes
+        vertices, triangles = mcubes.marching_cubes(occ, density_thresh)
+        vertices = vertices / (resolution - 1.0) * 2 - 1
+
+        # transform back to the original space
+        vertices = vertices / self.scale + self.center.detach().cpu().numpy()
+
+        vertices, triangles = clean_mesh(vertices, triangles, remesh=True, remesh_size=0.015)
+        if decimate_target > 0 and triangles.shape[0] > decimate_target:
+            vertices, triangles = decimate_mesh(vertices, triangles, decimate_target)
+
+        v = torch.from_numpy(vertices.astype(np.float32)).contiguous().cuda()
+        f = torch.from_numpy(triangles.astype(np.int32)).contiguous().cuda()
+
+        print(
+            f"[INFO] marching cubes result: {v.shape} ({v.min().item()}-{v.max().item()}), {f.shape}"
+        )
+
+        mesh = Mesh(v=v, f=f, device='cuda')
+
+        return mesh
+    
+    def get_covariance(self, scaling_modifier = 1):
+        return self.covariance_activation(self.get_scaling, scaling_modifier, self._rotation)
+
+    def oneupSHdegree(self):
+        if self.active_sh_degree < self.max_sh_degree:
+            self.active_sh_degree += 1
+
+    def create_from_pcd(self, pcd : BasicPointCloud, spatial_lr_scale : float = 1):
+        self.spatial_lr_scale = spatial_lr_scale
+        fused_point_cloud = torch.tensor(np.asarray(pcd.points)).float().cuda()
+        fused_color = RGB2SH(torch.tensor(np.asarray(pcd.colors)).float().cuda())
+        features = torch.zeros((fused_color.shape[0], 3, (self.max_sh_degree + 1) ** 2)).float().cuda()
+        features[:, :3, 0 ] = fused_color
+        features[:, 3:, 1:] = 0.0
+
+        print("Number of points at initialisation : ", fused_point_cloud.shape[0])
+
+        dist2 = torch.clamp_min(distCUDA2(torch.from_numpy(np.asarray(pcd.points)).float().cuda()), 0.0000001)
+        scales = torch.log(torch.sqrt(dist2))[...,None].repeat(1, 3)
+        rots = torch.zeros((fused_point_cloud.shape[0], 4), device="cuda")
+        rots[:, 0] = 1
+
+        opacities = inverse_sigmoid(0.1 * torch.ones((fused_point_cloud.shape[0], 1), dtype=torch.float, device="cuda"))
+
+        self._xyz = nn.Parameter(fused_point_cloud.requires_grad_(True))
+        self._features_dc = nn.Parameter(features[:,:,0:1].transpose(1, 2).contiguous().requires_grad_(True))
+        self._features_rest = nn.Parameter(features[:,:,1:].transpose(1, 2).contiguous().requires_grad_(True))
+        self._scaling = nn.Parameter(scales.requires_grad_(True))
+        self._rotation = nn.Parameter(rots.requires_grad_(True))
+        self._opacity = nn.Parameter(opacities.requires_grad_(True))
+        self.max_radii2D = torch.zeros((self.get_xyz.shape[0]), device="cuda")
+
+    def training_setup(self, training_args):
+        self.percent_dense = training_args.percent_dense
+        self.xyz_gradient_accum = torch.zeros((self.get_xyz.shape[0], 1), device="cuda")
+        self.denom = torch.zeros((self.get_xyz.shape[0], 1), device="cuda")
+
+        l = [
+            {'params': [self._xyz], 'lr': training_args.position_lr_init * self.spatial_lr_scale, "name": "xyz"},
+            {'params': [self._features_dc], 'lr': training_args.feature_lr, "name": "f_dc"},
+            {'params': [self._features_rest], 'lr': training_args.feature_lr / 20.0, "name": "f_rest"},
+            {'params': [self._opacity], 'lr': training_args.opacity_lr, "name": "opacity"},
+            {'params': [self._scaling], 'lr': training_args.scaling_lr, "name": "scaling"},
+            {'params': [self._rotation], 'lr': training_args.rotation_lr, "name": "rotation"},
+        ]
+
+        if training_args.opt_cam:
+            # Learnable parameters for camera, i.e., radius, azimuth and elevation
+            l.append({'params': self.cam_params, 'lr': training_args.rotation_lr * 10, "name": "cam_params"})
+
+        self.optimizer = torch.optim.Adam(l, lr=0.0, eps=1e-15)
+        self.xyz_scheduler_args = get_expon_lr_func(lr_init=training_args.position_lr_init*self.spatial_lr_scale,
+                                                    lr_final=training_args.position_lr_final*self.spatial_lr_scale,
+                                                    lr_delay_mult=training_args.position_lr_delay_mult,
+                                                    max_steps=training_args.position_lr_max_steps)
+
+    def update_learning_rate(self, iteration):
+        ''' Learning rate scheduling per step '''
+        for param_group in self.optimizer.param_groups:
+            if param_group["name"] == "xyz":
+                lr = self.xyz_scheduler_args(iteration)
+                param_group['lr'] = lr
+                return lr
+
+    def construct_list_of_attributes(self):
+        l = ['x', 'y', 'z', 'nx', 'ny', 'nz']
+        # All channels except the 3 DC
+        for i in range(self._features_dc.shape[1]*self._features_dc.shape[2]):
+            l.append('f_dc_{}'.format(i))
+        for i in range(self._features_rest.shape[1]*self._features_rest.shape[2]):
+            l.append('f_rest_{}'.format(i))
+        l.append('opacity')
+        for i in range(self._scaling.shape[1]):
+            l.append('scale_{}'.format(i))
+        for i in range(self._rotation.shape[1]):
+            l.append('rot_{}'.format(i))
+        return l
+
+    def save_ply(self, path):
+        os.makedirs(os.path.dirname(path), exist_ok=True)
+
+        xyz = self._xyz.detach().cpu().numpy()
+        normals = np.zeros_like(xyz)
+        f_dc = self._features_dc.detach().transpose(1, 2).flatten(start_dim=1).contiguous().cpu().numpy()
+        f_rest = self._features_rest.detach().transpose(1, 2).flatten(start_dim=1).contiguous().cpu().numpy()
+        opacities = self._opacity.detach().cpu().numpy()
+        scale = self._scaling.detach().cpu().numpy()
+        rotation = self._rotation.detach().cpu().numpy()
+
+        dtype_full = [(attribute, 'f4') for attribute in self.construct_list_of_attributes()]
+
+        elements = np.empty(xyz.shape[0], dtype=dtype_full)
+        attributes = np.concatenate((xyz, normals, f_dc, f_rest, opacities, scale, rotation), axis=1)
+        elements[:] = list(map(tuple, attributes))
+        el = PlyElement.describe(elements, 'vertex')
+        PlyData([el]).write(path)
+
+    def reset_opacity(self):
+        opacities_new = inverse_sigmoid(torch.min(self.get_opacity, torch.ones_like(self.get_opacity)*0.01))
+        optimizable_tensors = self.replace_tensor_to_optimizer(opacities_new, "opacity")
+        self._opacity = optimizable_tensors["opacity"]
+
+    def load_ply(self, path):
+        plydata = PlyData.read(path)
+
+        xyz = np.stack((np.asarray(plydata.elements[0]["x"]),
+                        np.asarray(plydata.elements[0]["y"]),
+                        np.asarray(plydata.elements[0]["z"])),  axis=1)
+        opacities = np.asarray(plydata.elements[0]["opacity"])[..., np.newaxis]
+
+        print("Number of points at loading : ", xyz.shape[0])
+
+        features_dc = np.zeros((xyz.shape[0], 3, 1))
+        features_dc[:, 0, 0] = np.asarray(plydata.elements[0]["f_dc_0"])
+        features_dc[:, 1, 0] = np.asarray(plydata.elements[0]["f_dc_1"])
+        features_dc[:, 2, 0] = np.asarray(plydata.elements[0]["f_dc_2"])
+
+        extra_f_names = [p.name for p in plydata.elements[0].properties if p.name.startswith("f_rest_")]
+        assert len(extra_f_names)==3*(self.max_sh_degree + 1) ** 2 - 3
+        features_extra = np.zeros((xyz.shape[0], len(extra_f_names)))
+        for idx, attr_name in enumerate(extra_f_names):
+            features_extra[:, idx] = np.asarray(plydata.elements[0][attr_name])
+        # Reshape (P,F*SH_coeffs) to (P, F, SH_coeffs except DC)
+        features_extra = features_extra.reshape((features_extra.shape[0], 3, (self.max_sh_degree + 1) ** 2 - 1))
+
+        scale_names = [p.name for p in plydata.elements[0].properties if p.name.startswith("scale_")]
+        scales = np.zeros((xyz.shape[0], len(scale_names)))
+        for idx, attr_name in enumerate(scale_names):
+            scales[:, idx] = np.asarray(plydata.elements[0][attr_name])
+
+        rot_names = [p.name for p in plydata.elements[0].properties if p.name.startswith("rot")]
+        rots = np.zeros((xyz.shape[0], len(rot_names)))
+        for idx, attr_name in enumerate(rot_names):
+            rots[:, idx] = np.asarray(plydata.elements[0][attr_name])
+
+        self._xyz = nn.Parameter(torch.tensor(xyz, dtype=torch.float, device="cuda").requires_grad_(True))
+        self._features_dc = nn.Parameter(torch.tensor(features_dc, dtype=torch.float, device="cuda").transpose(1, 2).contiguous().requires_grad_(True))
+        self._features_rest = nn.Parameter(torch.tensor(features_extra, dtype=torch.float, device="cuda").transpose(1, 2).contiguous().requires_grad_(True))
+        self._opacity = nn.Parameter(torch.tensor(opacities, dtype=torch.float, device="cuda").requires_grad_(True))
+        self._scaling = nn.Parameter(torch.tensor(scales, dtype=torch.float, device="cuda").requires_grad_(True))
+        self._rotation = nn.Parameter(torch.tensor(rots, dtype=torch.float, device="cuda").requires_grad_(True))
+
+        self.active_sh_degree = self.max_sh_degree
+
+    def replace_tensor_to_optimizer(self, tensor, name):
+        optimizable_tensors = {}
+        for group in self.optimizer.param_groups:
+            if len(group["params"]) != 1:
+                continue
+            if group["name"] == name:
+                stored_state = self.optimizer.state.get(group['params'][0], None)
+                stored_state["exp_avg"] = torch.zeros_like(tensor)
+                stored_state["exp_avg_sq"] = torch.zeros_like(tensor)
+
+                del self.optimizer.state[group['params'][0]]
+                group["params"][0] = nn.Parameter(tensor.requires_grad_(True))
+                self.optimizer.state[group['params'][0]] = stored_state
+
+                optimizable_tensors[group["name"]] = group["params"][0]
+        return optimizable_tensors
+
+    def _prune_optimizer(self, mask):
+        optimizable_tensors = {}
+        for group in self.optimizer.param_groups:
+            if len(group["params"]) != 1:
+                continue
+            stored_state = self.optimizer.state.get(group['params'][0], None)
+            if stored_state is not None:
+                stored_state["exp_avg"] = stored_state["exp_avg"][mask]
+                stored_state["exp_avg_sq"] = stored_state["exp_avg_sq"][mask]
+
+                del self.optimizer.state[group['params'][0]]
+                group["params"][0] = nn.Parameter((group["params"][0][mask].requires_grad_(True)))
+                self.optimizer.state[group['params'][0]] = stored_state
+
+                optimizable_tensors[group["name"]] = group["params"][0]
+            else:
+                group["params"][0] = nn.Parameter(group["params"][0][mask].requires_grad_(True))
+                optimizable_tensors[group["name"]] = group["params"][0]
+        return optimizable_tensors
+
+    def prune_points(self, mask):
+        valid_points_mask = ~mask
+        optimizable_tensors = self._prune_optimizer(valid_points_mask)
+
+        self._xyz = optimizable_tensors["xyz"]
+        self._features_dc = optimizable_tensors["f_dc"]
+        self._features_rest = optimizable_tensors["f_rest"]
+        self._opacity = optimizable_tensors["opacity"]
+        self._scaling = optimizable_tensors["scaling"]
+        self._rotation = optimizable_tensors["rotation"]
+
+        self.xyz_gradient_accum = self.xyz_gradient_accum[valid_points_mask]
+
+        self.denom = self.denom[valid_points_mask]
+        self.max_radii2D = self.max_radii2D[valid_points_mask]
+
+    def cat_tensors_to_optimizer(self, tensors_dict):
+        optimizable_tensors = {}
+        for group in self.optimizer.param_groups:
+            if len(group["params"]) != 1:
+                continue
+            assert len(group["params"]) == 1
+            extension_tensor = tensors_dict[group["name"]]
+            stored_state = self.optimizer.state.get(group['params'][0], None)
+            if stored_state is not None:
+
+                stored_state["exp_avg"] = torch.cat((stored_state["exp_avg"], torch.zeros_like(extension_tensor)), dim=0)
+                stored_state["exp_avg_sq"] = torch.cat((stored_state["exp_avg_sq"], torch.zeros_like(extension_tensor)), dim=0)
+
+                del self.optimizer.state[group['params'][0]]
+                group["params"][0] = nn.Parameter(torch.cat((group["params"][0], extension_tensor), dim=0).requires_grad_(True))
+                self.optimizer.state[group['params'][0]] = stored_state
+
+                optimizable_tensors[group["name"]] = group["params"][0]
+            else:
+                group["params"][0] = nn.Parameter(torch.cat((group["params"][0], extension_tensor), dim=0).requires_grad_(True))
+                optimizable_tensors[group["name"]] = group["params"][0]
+
+        return optimizable_tensors
+
+    def densification_postfix(self, new_xyz, new_features_dc, new_features_rest, new_opacities, new_scaling, new_rotation):
+        d = {"xyz": new_xyz,
+        "f_dc": new_features_dc,
+        "f_rest": new_features_rest,
+        "opacity": new_opacities,
+        "scaling" : new_scaling,
+        "rotation" : new_rotation}
+
+        optimizable_tensors = self.cat_tensors_to_optimizer(d)
+        self._xyz = optimizable_tensors["xyz"]
+        self._features_dc = optimizable_tensors["f_dc"]
+        self._features_rest = optimizable_tensors["f_rest"]
+        self._opacity = optimizable_tensors["opacity"]
+        self._scaling = optimizable_tensors["scaling"]
+        self._rotation = optimizable_tensors["rotation"]
+
+        self.xyz_gradient_accum = torch.zeros((self.get_xyz.shape[0], 1), device="cuda")
+        self.denom = torch.zeros((self.get_xyz.shape[0], 1), device="cuda")
+        self.max_radii2D = torch.zeros((self.get_xyz.shape[0]), device="cuda")
+
+    def densify_and_split(self, grads, grad_threshold, scene_extent, N=2):
+        n_init_points = self.get_xyz.shape[0]
+        # Extract points that satisfy the gradient condition
+        padded_grad = torch.zeros((n_init_points), device="cuda")
+        padded_grad[:grads.shape[0]] = grads.squeeze()
+        selected_pts_mask = torch.where(padded_grad >= grad_threshold, True, False)
+        selected_pts_mask = torch.logical_and(selected_pts_mask,
+            torch.max(self.get_scaling, dim=1).values > self.percent_dense*scene_extent
+        )
+
+        stds = self.get_scaling[selected_pts_mask].repeat(N,1)
+        means =torch.zeros((stds.size(0), 3),device="cuda")
+        samples = torch.normal(mean=means, std=stds)
+        rots = build_rotation(self._rotation[selected_pts_mask]).repeat(N,1,1)
+        new_xyz = torch.bmm(rots, samples.unsqueeze(-1)).squeeze(-1) + self.get_xyz[selected_pts_mask].repeat(N, 1)
+        new_scaling = self.scaling_inverse_activation(self.get_scaling[selected_pts_mask].repeat(N,1) / (0.8*N))
+        new_rotation = self._rotation[selected_pts_mask].repeat(N,1)
+        new_features_dc = self._features_dc[selected_pts_mask].repeat(N,1,1)
+        new_features_rest = self._features_rest[selected_pts_mask].repeat(N,1,1)
+        new_opacity = self._opacity[selected_pts_mask].repeat(N,1)
+
+        self.densification_postfix(new_xyz, new_features_dc, new_features_rest, new_opacity, new_scaling, new_rotation)
+
+        prune_filter = torch.cat((selected_pts_mask, torch.zeros(N * selected_pts_mask.sum(), device="cuda", dtype=bool)))
+        self.prune_points(prune_filter)
+
+    def densify_and_clone(self, grads, grad_threshold, scene_extent):
+        # Extract points that satisfy the gradient condition
+        selected_pts_mask = torch.where(torch.norm(grads, dim=-1) >= grad_threshold, True, False)
+        selected_pts_mask = torch.logical_and(selected_pts_mask,
+            torch.max(self.get_scaling, dim=1).values <= self.percent_dense*scene_extent
+        )
+        
+        new_xyz = self._xyz[selected_pts_mask]
+        new_features_dc = self._features_dc[selected_pts_mask]
+        new_features_rest = self._features_rest[selected_pts_mask]
+        new_opacities = self._opacity[selected_pts_mask]
+        new_scaling = self._scaling[selected_pts_mask]
+        new_rotation = self._rotation[selected_pts_mask]
+
+        self.densification_postfix(new_xyz, new_features_dc, new_features_rest, new_opacities, new_scaling, new_rotation)
+
+    def densify_and_prune(self, max_grad, min_opacity, extent, max_screen_size):
+        grads = self.xyz_gradient_accum / self.denom
+        grads[grads.isnan()] = 0.0
+
+        self.densify_and_clone(grads, max_grad, extent)
+        self.densify_and_split(grads, max_grad, extent)
+
+        prune_mask = (self.get_opacity < min_opacity).squeeze()
+        if max_screen_size:
+            big_points_vs = self.max_radii2D > max_screen_size
+            big_points_ws = self.get_scaling.max(dim=1).values > 0.1 * extent
+            prune_mask = torch.logical_or(torch.logical_or(prune_mask, big_points_vs), big_points_ws)
+        self.prune_points(prune_mask)
+
+        torch.cuda.empty_cache()
+
+    def prune(self, min_opacity, extent, max_screen_size):
+
+        prune_mask = (self.get_opacity < min_opacity).squeeze()
+        if max_screen_size:
+            big_points_vs = self.max_radii2D > max_screen_size
+            big_points_ws = self.get_scaling.max(dim=1).values > 0.1 * extent
+            prune_mask = torch.logical_or(torch.logical_or(prune_mask, big_points_vs), big_points_ws)
+        self.prune_points(prune_mask)
+
+        torch.cuda.empty_cache()
+
+
+    def add_densification_stats(self, viewspace_point_tensor, update_filter):
+        self.xyz_gradient_accum[update_filter] += torch.norm(viewspace_point_tensor.grad[update_filter,:2], dim=-1, keepdim=True)
+        self.denom[update_filter] += 1
+
+def getProjectionMatrix(znear, zfar, fovX, fovY):
+    tanHalfFovY = math.tan((fovY / 2))
+    tanHalfFovX = math.tan((fovX / 2))
+
+    P = torch.zeros(4, 4)
+
+    z_sign = 1.0
+
+    P[0, 0] = 1 / tanHalfFovX
+    P[1, 1] = 1 / tanHalfFovY
+    P[3, 2] = z_sign
+    P[2, 2] = z_sign * zfar / (zfar - znear)
+    P[2, 3] = -(zfar * znear) / (zfar - znear)
+    return P
+
+
+class MiniCam:
+    def __init__(self, c2w, width, height, fovy, fovx, znear, zfar, cam_params=None, opt_pose=False):
+        # c2w (pose) should be in NeRF convention.
+
+        self.image_width = width
+        self.image_height = height
+        self.FoVy = fovy
+        self.FoVx = fovx
+        self.znear = znear
+        self.zfar = zfar
+        self.opt_pose = opt_pose
+
+        self.projection_matrix = (
+            getProjectionMatrix(
+                znear=self.znear, zfar=self.zfar, fovX=self.FoVx, fovY=self.FoVy
+            )
+            .transpose(0, 1)
+            .cuda()
+        )
+
+        if not opt_pose:
+            w2c = np.linalg.inv(c2w)
+
+            # rectify...
+            w2c[1:3, :3] *= -1
+            w2c[:3, 3] *= -1
+
+            self.world_view_transform = torch.tensor(w2c).transpose(0, 1).cuda()
+            self.full_proj_transform = self.world_view_transform @ self.projection_matrix
+            self.camera_center = -torch.tensor(c2w[:3, 3]).cuda()
+        else:
+            # Enable camera pose optimization.
+            self.cam_params = torch.tensor(cam_params, dtype=torch.float32, requires_grad=True)
+            # Place holders, computed when rendering
+            self.world_view_transform = None
+            self.camera_center = None
+            self.full_proj_transform = None
+
+
+class Renderer:
+    def __init__(self, sh_degree=3, white_background=True, radius=1):
+        
+        self.sh_degree = sh_degree
+        self.white_background = white_background
+        self.radius = radius
+
+        self.gaussians = GaussianModel(sh_degree)
+
+        self.bg_color = torch.tensor(
+            [1, 1, 1] if white_background else [0, 0, 0],
+            dtype=torch.float32,
+            device="cuda",
+        )
+    
+    def initialize(self, input=None, num_pts=5000, radius=0.5):
+        # load checkpoint
+        if input is None:
+            # init from random point cloud
+            
+            phis = np.random.random((num_pts,)) * 2 * np.pi
+            costheta = np.random.random((num_pts,)) * 2 - 1
+            thetas = np.arccos(costheta)
+            mu = np.random.random((num_pts,))
+            radius = radius * np.cbrt(mu)
+            x = radius * np.sin(thetas) * np.cos(phis)
+            y = radius * np.sin(thetas) * np.sin(phis)
+            z = radius * np.cos(thetas)
+            xyz = np.stack((x, y, z), axis=1)
+            # xyz = np.random.random((num_pts, 3)) * 2.6 - 1.3
+
+            shs = np.random.random((num_pts, 3)) / 255.0
+            pcd = BasicPointCloud(
+                points=xyz, colors=SH2RGB(shs), normals=np.zeros((num_pts, 3))
+            )
+            self.gaussians.create_from_pcd(pcd, 10)
+        elif isinstance(input, BasicPointCloud):
+            # load from a provided pcd
+            self.gaussians.create_from_pcd(input, 1)
+        else:
+            # load from saved ply
+            self.gaussians.load_ply(input)
+
+    def render(
+        self,
+        viewpoint_camera,
+        scaling_modifier=1.0,
+        bg_color=None,
+        override_color=None,
+        compute_cov3D_python=False,
+        convert_SHs_python=False,
+    ):
+        if viewpoint_camera.opt_pose:
+            # Because c2w matrix is updated in each iter, recompute some parameters when rendering
+            # Create c2w matrix from radius, azimuth and elevation
+            c2w = orbit_camera(viewpoint_camera.cam_params).to("cuda")
+            R = c2w[:3, :3]  # 3 x 3
+            T = c2w[:3, 3:4]  # 3 x 1
+            R_inv = R.T
+            T_inv = torch.matmul(-R_inv, T)
+            upper = torch.cat([R_inv, T_inv], dim=1)  # Upper 3x4 part of the matrix
+            lower = torch.tensor([[0, 0, 0, 1]], device=R.device, dtype=R.dtype)  # Last row
+            w2c = torch.cat([upper, lower], dim=0)
+
+            # rectify...
+            w2c[1:3, :3] *= -1
+            w2c[:3, 3] *= -1
+
+            viewpoint_camera.world_view_transform = w2c.transpose(0, 1)
+            viewpoint_camera.full_proj_transform = viewpoint_camera.world_view_transform @ viewpoint_camera.projection_matrix
+            viewpoint_camera.camera_center = -c2w[:3, 3]
+
+        # Create zero tensor. We will use it to make pytorch return gradients of the 2D (screen-space) means
+        screenspace_points = (
+            torch.zeros_like(
+                self.gaussians.get_xyz,
+                dtype=self.gaussians.get_xyz.dtype,
+                requires_grad=True,
+                device="cuda",
+            )
+            + 0
+        )
+        try:
+            screenspace_points.retain_grad()
+        except:
+            pass
+
+        # Set up rasterization configuration
+        tanfovx = math.tan(viewpoint_camera.FoVx * 0.5)
+        tanfovy = math.tan(viewpoint_camera.FoVy * 0.5)
+
+        raster_settings = GaussianRasterizationSettings(
+            image_height=int(viewpoint_camera.image_height),
+            image_width=int(viewpoint_camera.image_width),
+            tanfovx=tanfovx,
+            tanfovy=tanfovy,
+            bg=self.bg_color if bg_color is None else bg_color,
+            scale_modifier=scaling_modifier,
+            viewmatrix=viewpoint_camera.world_view_transform,
+            perspectivematrix=viewpoint_camera.projection_matrix, # Added for computing gradients for viewmatrix
+            projmatrix=viewpoint_camera.full_proj_transform,
+            sh_degree=self.gaussians.active_sh_degree,
+            campos=viewpoint_camera.camera_center,
+            prefiltered=False,
+            debug=False,
+        )
+
+        rasterizer = GaussianRasterizer(raster_settings=raster_settings)
+
+        means3D = self.gaussians.get_xyz
+        means2D = screenspace_points
+        opacity = self.gaussians.get_opacity
+
+        # If precomputed 3d covariance is provided, use it. If not, then it will be computed from
+        # scaling / rotation by the rasterizer.
+        scales = None
+        rotations = None
+        cov3D_precomp = None
+        if compute_cov3D_python:
+            cov3D_precomp = self.gaussians.get_covariance(scaling_modifier)
+        else:
+            scales = self.gaussians.get_scaling
+            rotations = self.gaussians.get_rotation
+
+        # If precomputed colors are provided, use them. Otherwise, if it is desired to precompute colors
+        # from SHs in Python, do it. If not, then SH -> RGB conversion will be done by rasterizer.
+        shs = None
+        colors_precomp = None
+        if colors_precomp is None:
+            if convert_SHs_python:
+                shs_view = self.gaussians.get_features.transpose(1, 2).view(
+                    -1, 3, (self.gaussians.max_sh_degree + 1) ** 2
+                )
+                dir_pp = self.gaussians.get_xyz - viewpoint_camera.camera_center.repeat(
+                    self.gaussians.get_features.shape[0], 1
+                )
+                dir_pp_normalized = dir_pp / dir_pp.norm(dim=1, keepdim=True)
+                sh2rgb = eval_sh(
+                    self.gaussians.active_sh_degree, shs_view, dir_pp_normalized
+                )
+                colors_precomp = torch.clamp_min(sh2rgb + 0.5, 0.0)
+            else:
+                shs = self.gaussians.get_features
+        else:
+            colors_precomp = override_color
+
+        # Rasterize visible Gaussians to image, obtain their radii (on screen).
+        rendered_image, radii, rendered_depth, rendered_alpha = rasterizer(
+            means3D=means3D,
+            means2D=means2D,
+            shs=shs,
+            colors_precomp=colors_precomp,
+            opacities=opacity,
+            scales=scales,
+            rotations=rotations,
+            cov3D_precomp=cov3D_precomp,
+            viewmat=viewpoint_camera.world_view_transform, # Added for receiving gradients
+        )
+
+        # Those Gaussians that were frustum culled or had a radius of 0 were not visible.
+        # They will be excluded from value updates used in the splitting criteria.
+        ret =  {
+            "image": rendered_image.clamp(0, 1),
+            "depth": rendered_depth,
+            "alpha": rendered_alpha,
+            "viewspace_points": screenspace_points,
+            "visibility_filter": radii > 0,
+            "radii": radii,
+        }
+
+        return ret
+

diff-gaussian-rasterization-camera/rasterize_points.cu

@@ -0,0 +1,232 @@
+/*
+ * Copyright (C) 2023, Inria
+ * GRAPHDECO research group, https://team.inria.fr/graphdeco
+ * All rights reserved.
+ *
+ * This software is free for non-commercial, research and evaluation use 
+ * under the terms of the LICENSE.md file.
+ *
+ * For inquiries contact  [email protected]
+ */
+
+#include <math.h>
+#include <torch/extension.h>
+#include <cstdio>
+#include <sstream>
+#include <iostream>
+#include <tuple>
+#include <stdio.h>
+#include <cuda_runtime_api.h>
+#include <memory>
+#include "cuda_rasterizer/config.h"
+#include "cuda_rasterizer/rasterizer.h"
+#include <fstream>
+#include <string>
+#include <functional>
+
+std::function<char*(size_t N)> resizeFunctional(torch::Tensor& t) {
+    auto lambda = [&t](size_t N) {
+        t.resize_({(long long)N});
+		return reinterpret_cast<char*>(t.contiguous().data_ptr());
+    };
+    return lambda;
+}
+
+std::tuple<int, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor>
+RasterizeGaussiansCUDA(
+	const torch::Tensor& background,
+	const torch::Tensor& means3D,
+    const torch::Tensor& colors,
+    const torch::Tensor& opacity,
+	const torch::Tensor& scales,
+	const torch::Tensor& rotations,
+	const float scale_modifier,
+	const torch::Tensor& cov3D_precomp,
+	const torch::Tensor& viewmatrix,
+	const torch::Tensor& projmatrix,
+	const float tan_fovx, 
+	const float tan_fovy,
+    const int image_height,
+    const int image_width,
+	const torch::Tensor& sh,
+	const int degree,
+	const torch::Tensor& campos,
+	const bool prefiltered,
+	const bool debug)
+{
+  if (means3D.ndimension() != 2 || means3D.size(1) != 3) {
+    AT_ERROR("means3D must have dimensions (num_points, 3)");
+  }
+  
+  const int P = means3D.size(0);
+  const int H = image_height;
+  const int W = image_width;
+
+  auto int_opts = means3D.options().dtype(torch::kInt32);
+  auto float_opts = means3D.options().dtype(torch::kFloat32);
+
+  torch::Tensor out_color = torch::full({NUM_CHANNELS, H, W}, 0.0, float_opts);
+  torch::Tensor out_depth = torch::full({1, H, W}, 0.0, float_opts);
+  torch::Tensor out_alpha = torch::full({1, H, W}, 0.0, float_opts);
+  torch::Tensor radii = torch::full({P}, 0, means3D.options().dtype(torch::kInt32));
+  
+  torch::Device device(torch::kCUDA);
+  torch::TensorOptions options(torch::kByte);
+  torch::Tensor geomBuffer = torch::empty({0}, options.device(device));
+  torch::Tensor binningBuffer = torch::empty({0}, options.device(device));
+  torch::Tensor imgBuffer = torch::empty({0}, options.device(device));
+  std::function<char*(size_t)> geomFunc = resizeFunctional(geomBuffer);
+  std::function<char*(size_t)> binningFunc = resizeFunctional(binningBuffer);
+  std::function<char*(size_t)> imgFunc = resizeFunctional(imgBuffer);
+  
+  int rendered = 0;
+  if(P != 0)
+  {
+	  int M = 0;
+	  if(sh.size(0) != 0)
+	  {
+		M = sh.size(1);
+      }
+
+	  rendered = CudaRasterizer::Rasterizer::forward(
+	    geomFunc,
+		binningFunc,
+		imgFunc,
+	    P, degree, M,
+		background.contiguous().data<float>(),
+		W, H,
+		means3D.contiguous().data<float>(),
+		sh.contiguous().data_ptr<float>(),
+		colors.contiguous().data<float>(), 
+		opacity.contiguous().data<float>(), 
+		scales.contiguous().data_ptr<float>(),
+		scale_modifier,
+		rotations.contiguous().data_ptr<float>(),
+		cov3D_precomp.contiguous().data<float>(), 
+		viewmatrix.contiguous().data<float>(), 
+		projmatrix.contiguous().data<float>(),
+		campos.contiguous().data<float>(),
+		tan_fovx,
+		tan_fovy,
+		prefiltered,
+		out_color.contiguous().data<float>(),
+		out_depth.contiguous().data<float>(),
+		out_alpha.contiguous().data<float>(),
+		radii.contiguous().data<int>(),
+		debug);
+  }
+  return std::make_tuple(rendered, out_color, out_depth, out_alpha, radii, geomBuffer, binningBuffer, imgBuffer);
+}
+
+std::tuple<torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor>
+ RasterizeGaussiansBackwardCUDA(
+ 	const torch::Tensor& background,
+	const torch::Tensor& means3D,
+	const torch::Tensor& radii,
+    const torch::Tensor& colors,
+	const torch::Tensor& scales,
+	const torch::Tensor& rotations,
+	const float scale_modifier,
+	const torch::Tensor& cov3D_precomp,
+	const torch::Tensor& viewmatrix,
+    const torch::Tensor& projmatrix,
+	const float tan_fovx,
+	const float tan_fovy,
+    const torch::Tensor& dL_dout_color,
+	const torch::Tensor& dL_dout_depth,
+	const torch::Tensor& dL_dout_alpha,
+	const torch::Tensor& sh,
+	const int degree,
+	const torch::Tensor& campos,
+	const torch::Tensor& geomBuffer,
+	const int R,
+	const torch::Tensor& binningBuffer,
+	const torch::Tensor& imageBuffer,
+	const torch::Tensor& alphas,
+	const bool debug) 
+{
+  const int P = means3D.size(0);
+  const int H = dL_dout_color.size(1);
+  const int W = dL_dout_color.size(2);
+  
+  int M = 0;
+  if(sh.size(0) != 0)
+  {	
+	M = sh.size(1);
+  }
+
+  torch::Tensor dL_dmeans3D = torch::zeros({P, 3}, means3D.options());
+  torch::Tensor dL_dmeans2D = torch::zeros({P, 3}, means3D.options());
+  torch::Tensor dL_dcolors = torch::zeros({P, NUM_CHANNELS}, means3D.options());
+  torch::Tensor dL_ddepths = torch::zeros({P, 1}, means3D.options());
+  torch::Tensor dL_dconic = torch::zeros({P, 2, 2}, means3D.options());
+  torch::Tensor dL_dopacity = torch::zeros({P, 1}, means3D.options());
+  torch::Tensor dL_dcov3D = torch::zeros({P, 6}, means3D.options());
+  torch::Tensor dL_dsh = torch::zeros({P, M, 3}, means3D.options());
+  torch::Tensor dL_dscales = torch::zeros({P, 3}, means3D.options());
+  torch::Tensor dL_drotations = torch::zeros({P, 4}, means3D.options());
+	// Created by Qitao
+  torch::Tensor dL_dts = torch::zeros({P, 3}, means3D.options());  
+  
+  if(P != 0)
+  {  
+	  CudaRasterizer::Rasterizer::backward(P, degree, M, R,
+	  background.contiguous().data<float>(),
+	  W, H, 
+	  means3D.contiguous().data<float>(),
+	  sh.contiguous().data<float>(),
+	  colors.contiguous().data<float>(),
+	  alphas.contiguous().data<float>(),
+	  scales.data_ptr<float>(),
+	  scale_modifier,
+	  rotations.data_ptr<float>(),
+	  cov3D_precomp.contiguous().data<float>(),
+	  viewmatrix.contiguous().data<float>(),
+	  projmatrix.contiguous().data<float>(),
+	  campos.contiguous().data<float>(),
+	  tan_fovx,
+	  tan_fovy,
+	  radii.contiguous().data<int>(),
+	  reinterpret_cast<char*>(geomBuffer.contiguous().data_ptr()),
+	  reinterpret_cast<char*>(binningBuffer.contiguous().data_ptr()),
+	  reinterpret_cast<char*>(imageBuffer.contiguous().data_ptr()),
+	  dL_dout_color.contiguous().data<float>(),
+	  dL_dout_depth.contiguous().data<float>(),
+	  dL_dout_alpha.contiguous().data<float>(),
+	  dL_dmeans2D.contiguous().data<float>(),
+		dL_dts.contiguous().data<float>(),
+	  dL_dconic.contiguous().data<float>(),  
+	  dL_dopacity.contiguous().data<float>(),
+	  dL_dcolors.contiguous().data<float>(),
+	  dL_ddepths.contiguous().data<float>(),
+	  dL_dmeans3D.contiguous().data<float>(),
+	  dL_dcov3D.contiguous().data<float>(),
+	  dL_dsh.contiguous().data<float>(),
+	  dL_dscales.contiguous().data<float>(),
+	  dL_drotations.contiguous().data<float>(),
+	  debug);
+  }
+
+  return std::make_tuple(dL_dmeans2D, dL_dts, dL_dcolors, dL_dopacity, dL_dmeans3D, dL_dcov3D, dL_dsh, dL_dscales, dL_drotations);
+}
+
+torch::Tensor markVisible(
+		torch::Tensor& means3D,
+		torch::Tensor& viewmatrix,
+		torch::Tensor& projmatrix)
+{ 
+  const int P = means3D.size(0);
+  
+  torch::Tensor present = torch::full({P}, false, means3D.options().dtype(at::kBool));
+ 
+  if(P != 0)
+  {
+	CudaRasterizer::Rasterizer::markVisible(P,
+		means3D.contiguous().data<float>(),
+		viewmatrix.contiguous().data<float>(),
+		projmatrix.contiguous().data<float>(),
+		present.contiguous().data<bool>());
+  }
+  
+  return present;
+}

diff-gaussian-rasterization-camera/rasterize_points.h

@@ -0,0 +1,70 @@
+/*
+ * Copyright (C) 2023, Inria
+ * GRAPHDECO research group, https://team.inria.fr/graphdeco
+ * All rights reserved.
+ *
+ * This software is free for non-commercial, research and evaluation use 
+ * under the terms of the LICENSE.md file.
+ *
+ * For inquiries contact  [email protected]
+ */
+
+#pragma once
+#include <torch/extension.h>
+#include <cstdio>
+#include <tuple>
+#include <string>
+	
+std::tuple<int, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor>
+RasterizeGaussiansCUDA(
+	const torch::Tensor& background,
+	const torch::Tensor& means3D,
+    const torch::Tensor& colors,
+    const torch::Tensor& opacity,
+	const torch::Tensor& scales,
+	const torch::Tensor& rotations,
+	const float scale_modifier,
+	const torch::Tensor& cov3D_precomp,
+	const torch::Tensor& viewmatrix,
+	const torch::Tensor& projmatrix,
+	const float tan_fovx, 
+	const float tan_fovy,
+    const int image_height,
+    const int image_width,
+	const torch::Tensor& sh,
+	const int degree,
+	const torch::Tensor& campos,
+	const bool prefiltered,
+	const bool debug);
+
+std::tuple<torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor>
+ RasterizeGaussiansBackwardCUDA(
+ 	const torch::Tensor& background,
+	const torch::Tensor& means3D,
+	const torch::Tensor& radii,
+    const torch::Tensor& colors,
+	const torch::Tensor& scales,
+	const torch::Tensor& rotations,
+	const float scale_modifier,
+	const torch::Tensor& cov3D_precomp,
+	const torch::Tensor& viewmatrix,
+    const torch::Tensor& projmatrix,
+	const float tan_fovx, 
+	const float tan_fovy,
+    const torch::Tensor& dL_dout_color,
+	const torch::Tensor& dL_dout_depth,
+	const torch::Tensor& dL_dout_alpha,
+	const torch::Tensor& sh,
+	const int degree,
+	const torch::Tensor& campos,
+	const torch::Tensor& geomBuffer,
+	const int R,
+	const torch::Tensor& binningBuffer,
+	const torch::Tensor& imageBuffer,
+	const torch::Tensor& alpha,
+	const bool debug);
+		
+torch::Tensor markVisible(
+		torch::Tensor& means3D,
+		torch::Tensor& viewmatrix,
+		torch::Tensor& projmatrix);

diff-gaussian-rasterization-camera/setup.py

@@ -0,0 +1,34 @@
+#
+# Copyright (C) 2023, Inria
+# GRAPHDECO research group, https://team.inria.fr/graphdeco
+# All rights reserved.
+#
+# This software is free for non-commercial, research and evaluation use 
+# under the terms of the LICENSE.md file.
+#
+# For inquiries contact  [email protected]
+#
+
+from setuptools import setup
+from torch.utils.cpp_extension import CUDAExtension, BuildExtension
+import os
+os.path.dirname(os.path.abspath(__file__))
+
+setup(
+    name="diff_gaussian_rasterization",
+    packages=['diff_gaussian_rasterization'],
+    ext_modules=[
+        CUDAExtension(
+            name="diff_gaussian_rasterization._C",
+            sources=[
+            "cuda_rasterizer/rasterizer_impl.cu",
+            "cuda_rasterizer/forward.cu",
+            "cuda_rasterizer/backward.cu",
+            "rasterize_points.cu",
+            "ext.cpp"],
+            extra_compile_args={"nvcc": ["-I" + os.path.join(os.path.dirname(os.path.abspath(__file__)), "third_party/glm/")]})
+        ],
+    cmdclass={
+        'build_ext': BuildExtension
+    }
+)

diff-gaussian-rasterization-camera/third_party/glm/.appveyor.yml

@@ -0,0 +1,92 @@
+shallow_clone: true
+
+platform:
+  - x86
+  - x64
+
+configuration:
+  - Debug
+  - Release
+
+image:
+  - Visual Studio 2013
+  - Visual Studio 2015
+  - Visual Studio 2017
+  - Visual Studio 2019
+
+environment:
+  matrix:
+    - GLM_ARGUMENTS: -DGLM_TEST_FORCE_PURE=ON
+    - GLM_ARGUMENTS: -DGLM_TEST_ENABLE_SIMD_SSE2=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON
+    - GLM_ARGUMENTS: -DGLM_TEST_ENABLE_SIMD_AVX=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON
+    - GLM_ARGUMENTS: -DGLM_TEST_ENABLE_SIMD_AVX=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_CXX_14=ON
+    - GLM_ARGUMENTS: -DGLM_TEST_ENABLE_SIMD_AVX=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_CXX_17=ON
+
+matrix:
+    exclude:
+    - image: Visual Studio 2013
+      GLM_ARGUMENTS: -DGLM_TEST_ENABLE_SIMD_AVX=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON
+    - image: Visual Studio 2013
+      GLM_ARGUMENTS: -DGLM_TEST_ENABLE_SIMD_AVX=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_CXX_14=ON
+    - image: Visual Studio 2013
+      GLM_ARGUMENTS: -DGLM_TEST_ENABLE_SIMD_AVX=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_CXX_17=ON
+    - image: Visual Studio 2013
+      configuration: Debug
+    - image: Visual Studio 2015
+      GLM_ARGUMENTS: -DGLM_TEST_ENABLE_SIMD_SSE2=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON
+    - image: Visual Studio 2015
+      GLM_ARGUMENTS: -DGLM_TEST_ENABLE_SIMD_AVX=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_CXX_14=ON
+    - image: Visual Studio 2015
+      GLM_ARGUMENTS: -DGLM_TEST_ENABLE_SIMD_AVX=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_CXX_17=ON
+    - image: Visual Studio 2015
+      platform: x86
+    - image: Visual Studio 2015
+      configuration: Debug
+    - image: Visual Studio 2017
+      platform: x86
+    - image: Visual Studio 2017
+      configuration: Debug
+    - image: Visual Studio 2019
+      platform: x64
+
+branches:
+  only:
+    - master
+
+before_build:
+  - ps: |
+      mkdir build
+      cd build
+
+      if ("$env:APPVEYOR_JOB_NAME" -match "Image: Visual Studio 2013") {
+          $env:generator="Visual Studio 12 2013"
+      } 
+      if ("$env:APPVEYOR_JOB_NAME" -match "Image: Visual Studio 2015") {
+          $env:generator="Visual Studio 14 2015"
+      } 
+      if ("$env:APPVEYOR_JOB_NAME" -match "Image: Visual Studio 2017") {
+          $env:generator="Visual Studio 15 2017"
+      }
+      if ("$env:APPVEYOR_JOB_NAME" -match "Image: Visual Studio 2019") {
+          $env:generator="Visual Studio 16 2019"
+      }
+      if ($env:PLATFORM -eq "x64") {
+          $env:generator="$env:generator Win64"
+      }
+      echo generator="$env:generator"
+      cmake .. -G "$env:generator" -DCMAKE_INSTALL_PREFIX="$env:APPVEYOR_BUILD_FOLDER/install" -DGLM_QUIET=ON -DGLM_TEST_ENABLE=ON "$env:GLM_ARGUMENTS"
+
+build_script:
+  - cmake --build . --parallel --config %CONFIGURATION% -- /m /v:minimal
+  - cmake --build . --target install --parallel --config %CONFIGURATION% -- /m /v:minimal
+
+test_script:
+  - ctest --parallel 4 --verbose -C %CONFIGURATION%
+  - cd ..
+  - ps: |
+      mkdir build_test_cmake
+      cd build_test_cmake
+      cmake ..\test\cmake\ -G "$env:generator" -DCMAKE_PREFIX_PATH="$env:APPVEYOR_BUILD_FOLDER/install"
+  - cmake --build . --parallel --config %CONFIGURATION% -- /m /v:minimal
+
+deploy: off

diff-gaussian-rasterization-camera/third_party/glm/.travis.yml

@@ -0,0 +1,388 @@
+language: cpp
+
+branches:
+  only:
+    - master
+    - stable
+
+jobs:
+  include:
+    - name: "Xcode 7.3 C++98 pure release"
+      os: osx
+      osx_image: xcode7.3
+      env:
+        - MATRIX_EVAL=""
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Release -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_98=ON -DGLM_TEST_FORCE_PURE=ON"
+
+    - name: "Xcode 7.3 C++98 sse2 release"
+      os: osx
+      osx_image: xcode7.3
+      env:
+        - MATRIX_EVAL=""
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Release -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_98=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_SIMD_SSE2=ON"
+
+    - name: "Xcode 7.3 C++98 ms release"
+      os: osx
+      osx_image: xcode7.3
+      env:
+        - MATRIX_EVAL=""
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Release -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_98=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON"
+
+    - name: "XCode 7.3 C++11 pure release"
+      os: osx
+      osx_image: xcode7.3
+      env:
+        - MATRIX_EVAL=""
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Release -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_11=ON -DGLM_TEST_FORCE_PURE=ON"
+
+    - name: "XCode 7.3 C++11 sse2 release"
+      os: osx
+      osx_image: xcode7.3
+      env:
+        - MATRIX_EVAL=""
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Release -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_11=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_SIMD_SSE3=ON"
+
+    - name: "XCode 10.3 C++11 sse2 release"
+      os: osx
+      osx_image: xcode10.3
+      env:
+        - MATRIX_EVAL=""
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Release -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_11=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_SIMD_SSE3=ON"
+
+    - name: "XCode 12.2 C++11 sse2 release"
+      os: osx
+      osx_image: xcode12.2
+      env:
+        - MATRIX_EVAL=""
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Release -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_11=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_SIMD_SSE3=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "XCode 12.2 C++11 sse2 debug"
+      os: osx
+      osx_image: xcode12.2
+      env:
+        - MATRIX_EVAL=""
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_11=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_SIMD_SSE3=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "XCode 12.2 C++11 avx debug"
+      os: osx
+      osx_image: xcode12.2
+      env:
+        - MATRIX_EVAL=""
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_11=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_SIMD_AVX=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "XCode 12.2 C++14 avx debug"
+      os: osx
+      osx_image: xcode12.2
+      env:
+        - MATRIX_EVAL=""
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_14=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_SIMD_AVX=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "XCode 12.2 C++14 pure debug"
+      os: osx
+      osx_image: xcode12.2
+      env:
+        - MATRIX_EVAL=""
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_14=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_FORCE_PURE=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "XCode 12.2 C++17 pure debug"
+      os: osx
+      osx_image: xcode12.2
+      env:
+        - MATRIX_EVAL=""
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_17=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_FORCE_PURE=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "XCode 12.2 C++17 sse2 debug"
+      os: osx
+      osx_image: xcode12.2
+      env:
+        - MATRIX_EVAL=""
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_17=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_SIMD_SSE2=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "XCode 12.2 C++17 sse2 release"
+      os: osx
+      osx_image: xcode12.2
+      env:
+        - MATRIX_EVAL=""
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Release -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_17=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_SIMD_SSE2=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "XCode 12.2 C++17 avx release"
+      os: osx
+      osx_image: xcode12.2
+      env:
+        - MATRIX_EVAL=""
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Release -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_17=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_SIMD_AVX=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "GCC 4.9 C++98 pure release"
+      os: linux
+      dist: Xenial
+      addons:
+        apt:
+          sources:
+            - ubuntu-toolchain-r-test
+          packages:
+            - g++-4.9
+      env:
+        - MATRIX_EVAL="CC=gcc-4.9 && CXX=g++-4.9"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Release -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_98=ON -DGLM_TEST_FORCE_PURE=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "GCC 4.9 C++98 pure debug"
+      os: linux
+      dist: Xenial
+      addons:
+        apt:
+          sources:
+            - ubuntu-toolchain-r-test
+          packages:
+            - g++-4.9
+      env:
+        - MATRIX_EVAL="CC=gcc-4.9 && CXX=g++-4.9"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_98=ON -DGLM_TEST_FORCE_PURE=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "GCC 4.9 C++98 ms debug"
+      os: linux
+      dist: Xenial
+      addons:
+        apt:
+          sources:
+            - ubuntu-toolchain-r-test
+          packages:
+            - g++-4.9
+      env:
+        - MATRIX_EVAL="CC=gcc-4.9 && CXX=g++-4.9"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_98=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "GCC 4.9 C++11 ms debug"
+      os: linux
+      dist: Xenial
+      addons:
+        apt:
+          sources:
+            - ubuntu-toolchain-r-test
+          packages:
+            - g++-4.9
+      env:
+        - MATRIX_EVAL="CC=gcc-4.9 && CXX=g++-4.9"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_11=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "GCC 4.9 C++11 pure debug"
+      os: linux
+      dist: Xenial
+      addons:
+        apt:
+          sources:
+            - ubuntu-toolchain-r-test
+          packages:
+            - g++-4.9
+      env:
+        - MATRIX_EVAL="CC=gcc-4.9 && CXX=g++-4.9"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_11=ON -DGLM_TEST_FORCE_PURE=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "GCC 6 C++14 pure debug"
+      os: linux
+      dist: bionic
+      addons:
+        apt:
+          sources:
+            - ubuntu-toolchain-r-test
+          packages:
+            - g++-6
+      env:
+        - MATRIX_EVAL="CC=gcc-6 && CXX=g++-6"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_14=ON -DGLM_TEST_FORCE_PURE=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "GCC 6 C++14 ms debug"
+      os: linux
+      dist: bionic
+      addons:
+        apt:
+          sources:
+            - ubuntu-toolchain-r-test
+          packages:
+            - g++-6
+      env:
+        - MATRIX_EVAL="CC=gcc-6 && CXX=g++-6"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_14=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "GCC 7 C++17 ms debug"
+      os: linux
+      dist: bionic
+      addons:
+        apt:
+          sources:
+            - ubuntu-toolchain-r-test
+          packages:
+            - g++-7
+      env:
+        - MATRIX_EVAL="CC=gcc-7 && CXX=g++-7"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_17=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "GCC 7 C++17 pure debug"
+      os: linux
+      dist: bionic
+      addons:
+        apt:
+          sources:
+            - ubuntu-toolchain-r-test
+          packages:
+            - g++-7
+      env:
+        - MATRIX_EVAL="CC=gcc-7 && CXX=g++-7"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_17=ON -DGLM_TEST_FORCE_PURE=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "GCC 10 C++17 pure debug"
+      os: linux
+      dist: bionic
+      addons:
+        apt:
+          sources:
+            - ubuntu-toolchain-r-test
+          packages:
+            - g++-10
+      env:
+        - MATRIX_EVAL="CC=gcc-10 && CXX=g++-10"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_17=ON -DGLM_TEST_FORCE_PURE=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "GCC 10 C++17 pure release"
+      os: linux
+      dist: bionic
+      addons:
+        apt:
+          sources:
+            - ubuntu-toolchain-r-test
+          packages:
+            - g++-10
+      env:
+        - MATRIX_EVAL="CC=gcc-10 && CXX=g++-10"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Release -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_17=ON -DGLM_TEST_FORCE_PURE=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "Clang C++14 pure release"
+      os: linux
+      dist: Xenial
+      env:
+        - MATRIX_EVAL="CC=clang && CXX=clang++"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Release -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_14=ON -DGLM_TEST_FORCE_PURE=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "Clang C++14 pure debug"
+      os: linux
+      dist: Xenial
+      env:
+        - MATRIX_EVAL="CC=clang && CXX=clang++"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_14=ON -DGLM_TEST_FORCE_PURE=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "Clang C++14 sse2 debug"
+      os: linux
+      dist: Xenial
+      env:
+        - MATRIX_EVAL="CC=clang && CXX=clang++"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_14=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_SIMD_SSE2=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "Clang C++14 sse2 debug"
+      os: linux
+      dist: focal
+      env:
+        - MATRIX_EVAL="CC=clang && CXX=clang++"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_14=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_SIMD_SSE2=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "Clang C++17 sse2 debug"
+      os: linux
+      dist: focal
+      env:
+        - MATRIX_EVAL="CC=clang && CXX=clang++"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_17=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_SIMD_SSE2=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "Clang C++17 avx2 debug"
+      os: linux
+      dist: focal
+      env:
+        - MATRIX_EVAL="CC=clang && CXX=clang++"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_17=ON -DGLM_TEST_ENABLE_LANG_EXTENSIONS=ON -DGLM_TEST_ENABLE_SIMD_AVX2=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "Clang C++17 pure debug"
+      os: linux
+      dist: focal
+      env:
+        - MATRIX_EVAL="CC=clang && CXX=clang++"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_17=ON -DGLM_TEST_FORCE_PURE=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "Clang C++17 pure release"
+      os: linux
+      dist: focal
+      env:
+        - MATRIX_EVAL="CC=clang && CXX=clang++"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Release -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_17=ON -DGLM_TEST_FORCE_PURE=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+before_script:
+    - cmake --version
+    - eval "${MATRIX_EVAL}"
+
+script:
+  - ${CC} --version
+  - mkdir ./build
+  - cd ./build
+  - cmake -DCMAKE_INSTALL_PREFIX=$TRAVIS_BUILD_DIR/install -DCMAKE_CXX_COMPILER=$COMPILER ${CMAKE_BUILD_ENV} ..
+  - cmake --build . ${CMAKE_ENV}
+  - ctest ${CTEST_ENV}
+  - cmake --build . --target install ${CMAKE_ENV}
+  - cd $TRAVIS_BUILD_DIR
+  - mkdir ./build_test_cmake
+  - cd ./build_test_cmake
+  - cmake -DCMAKE_CXX_COMPILER=$COMPILER $TRAVIS_BUILD_DIR/test/cmake/ -DCMAKE_PREFIX_PATH=$TRAVIS_BUILD_DIR/install
+  - cmake --build .
+
+

diff-gaussian-rasterization-camera/third_party/glm/CMakeLists.txt

@@ -0,0 +1,45 @@
+cmake_minimum_required(VERSION 3.2 FATAL_ERROR)
+cmake_policy(VERSION 3.2)
+
+
+file(READ "glm/detail/setup.hpp" GLM_SETUP_FILE)
+string(REGEX MATCH "#define[ ]+GLM_VERSION_MAJOR[ ]+([0-9]+)" _ ${GLM_SETUP_FILE})
+set(GLM_VERSION_MAJOR "${CMAKE_MATCH_1}")
+string(REGEX MATCH "#define[ ]+GLM_VERSION_MINOR[ ]+([0-9]+)" _ ${GLM_SETUP_FILE})
+set(GLM_VERSION_MINOR "${CMAKE_MATCH_1}")
+string(REGEX MATCH "#define[ ]+GLM_VERSION_PATCH[ ]+([0-9]+)" _ ${GLM_SETUP_FILE})
+set(GLM_VERSION_PATCH "${CMAKE_MATCH_1}")
+string(REGEX MATCH "#define[ ]+GLM_VERSION_REVISION[ ]+([0-9]+)" _ ${GLM_SETUP_FILE})
+set(GLM_VERSION_REVISION "${CMAKE_MATCH_1}")
+
+set(GLM_VERSION ${GLM_VERSION_MAJOR}.${GLM_VERSION_MINOR}.${GLM_VERSION_PATCH}.${GLM_VERSION_REVISION})
+project(glm VERSION ${GLM_VERSION} LANGUAGES CXX)
+message(STATUS "GLM: Version " ${GLM_VERSION})
+
+add_subdirectory(glm)
+add_library(glm::glm ALIAS glm)
+
+if(${CMAKE_SOURCE_DIR} STREQUAL ${CMAKE_CURRENT_SOURCE_DIR})
+
+	include(CPack)
+	install(DIRECTORY glm DESTINATION ${CMAKE_INSTALL_INCLUDEDIR} PATTERN "CMakeLists.txt" EXCLUDE)
+	install(EXPORT glm FILE glmConfig.cmake DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/glm NAMESPACE glm::)
+	include(CMakePackageConfigHelpers)
+	write_basic_package_version_file("glmConfigVersion.cmake" COMPATIBILITY AnyNewerVersion)
+	install(FILES ${CMAKE_CURRENT_BINARY_DIR}/glmConfigVersion.cmake DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/glm)
+
+	include(CTest)
+	if(BUILD_TESTING)
+		add_subdirectory(test)
+	endif()
+
+endif(${CMAKE_SOURCE_DIR} STREQUAL ${CMAKE_CURRENT_SOURCE_DIR})
+
+if (NOT TARGET uninstall)
+configure_file(cmake/cmake_uninstall.cmake.in
+               cmake_uninstall.cmake IMMEDIATE @ONLY)
+
+add_custom_target(uninstall
+                  "${CMAKE_COMMAND}" -P
+                  "${CMAKE_BINARY_DIR}/cmake_uninstall.cmake")
+endif()

diff-gaussian-rasterization-camera/third_party/glm/cmake/cmake_uninstall.cmake.in

@@ -0,0 +1,21 @@
+if(NOT EXISTS "@CMAKE_BINARY_DIR@/install_manifest.txt")
+  message(FATAL_ERROR "Cannot find install manifest: @CMAKE_BINARY_DIR@/install_manifest.txt")
+endif()
+
+file(READ "@CMAKE_BINARY_DIR@/install_manifest.txt" files)
+string(REGEX REPLACE "\n" ";" files "${files}")
+foreach(file ${files})
+  message(STATUS "Uninstalling $ENV{DESTDIR}${file}")
+  if(IS_SYMLINK "$ENV{DESTDIR}${file}" OR EXISTS "$ENV{DESTDIR}${file}")
+    exec_program(
+      "@CMAKE_COMMAND@" ARGS "-E remove \"$ENV{DESTDIR}${file}\""
+      OUTPUT_VARIABLE rm_out
+      RETURN_VALUE rm_retval
+      )
+    if(NOT "${rm_retval}" STREQUAL 0)
+      message(FATAL_ERROR "Problem when removing $ENV{DESTDIR}${file}")
+    endif()
+  else(IS_SYMLINK "$ENV{DESTDIR}${file}" OR EXISTS "$ENV{DESTDIR}${file}")
+    message(STATUS "File $ENV{DESTDIR}${file} does not exist.")
+  endif()
+endforeach()

diff-gaussian-rasterization-camera/third_party/glm/copying.txt

@@ -0,0 +1,54 @@
+================================================================================
+OpenGL Mathematics (GLM)
+--------------------------------------------------------------------------------
+GLM is licensed under The Happy Bunny License or MIT License
+
+================================================================================
+The Happy Bunny License (Modified MIT License)
+--------------------------------------------------------------------------------
+Copyright (c) 2005 - G-Truc Creation
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+Restrictions:
+ By making use of the Software for military purposes, you choose to make a
+ Bunny unhappy.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
+
+================================================================================
+The MIT License
+--------------------------------------------------------------------------------
+Copyright (c) 2005 - G-Truc Creation
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.

diff-gaussian-rasterization-camera/third_party/glm/doc/api/a00002_source.html

@@ -0,0 +1,121 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml">
+<head>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta http-equiv="X-UA-Compatible" content="IE=9"/>
+<meta name="generator" content="Doxygen 1.8.10"/>
+<title>0.9.9 API documentation: _fixes.hpp Source File</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="jquery.js"></script>
+<script type="text/javascript" src="dynsections.js"></script>
+<link href="search/search.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="search/searchdata.js"></script>
+<script type="text/javascript" src="search/search.js"></script>
+<script type="text/javascript">
+  $(document).ready(function() { init_search(); });
+</script>
+<link href="doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
+<table cellspacing="0" cellpadding="0">
+ <tbody>
+ <tr style="height: 56px;">
+  <td id="projectlogo"><img alt="Logo" src="logo-mini.png"/></td>
+  <td id="projectalign" style="padding-left: 0.5em;">
+   <div id="projectname">0.9.9 API documentation
+   </div>
+  </td>
+ </tr>
+ </tbody>
+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.10 -->
+<script type="text/javascript">
+var searchBox = new SearchBox("searchBox", "search",false,'Search');
+</script>
+  <div id="navrow1" class="tabs">
+    <ul class="tablist">
+      <li><a href="index.html"><span>Main&#160;Page</span></a></li>
+      <li><a href="modules.html"><span>Modules</span></a></li>
+      <li class="current"><a href="files.html"><span>Files</span></a></li>
+      <li>
+        <div id="MSearchBox" class="MSearchBoxInactive">
+        <span class="left">
+          <img id="MSearchSelect" src="search/mag_sel.png"
+               onmouseover="return searchBox.OnSearchSelectShow()"
+               onmouseout="return searchBox.OnSearchSelectHide()"
+               alt=""/>
+          <input type="text" id="MSearchField" value="Search" accesskey="S"
+               onfocus="searchBox.OnSearchFieldFocus(true)" 
+               onblur="searchBox.OnSearchFieldFocus(false)" 
+               onkeyup="searchBox.OnSearchFieldChange(event)"/>
+          </span><span class="right">
+            <a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.png" alt=""/></a>
+          </span>
+        </div>
+      </li>
+    </ul>
+  </div>
+  <div id="navrow2" class="tabs2">
+    <ul class="tablist">
+      <li><a href="files.html"><span>File&#160;List</span></a></li>
+    </ul>
+  </div>
+<!-- window showing the filter options -->
+<div id="MSearchSelectWindow"
+     onmouseover="return searchBox.OnSearchSelectShow()"
+     onmouseout="return searchBox.OnSearchSelectHide()"
+     onkeydown="return searchBox.OnSearchSelectKey(event)">
+</div>
+
+<!-- iframe showing the search results (closed by default) -->
+<div id="MSearchResultsWindow">
+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div id="nav-path" class="navpath">
+  <ul>
+<li class="navelem"><a class="el" href="dir_3a581ba30d25676e4b797b1f96d53b45.html">F:</a></li><li class="navelem"><a class="el" href="dir_9e5fe034a00e89334fd5186c3e7db156.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_d9496f0844b48bc7e53b5af8c99b9ab2.html">Source</a></li><li class="navelem"><a class="el" href="dir_a8bee7be44182a33f3820393ae0b105d.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_44e5e654415abd9ca6fdeaddaff8565e.html">glm</a></li><li class="navelem"><a class="el" href="dir_cef2d71d502cb69a9252bca2297d9549.html">glm</a></li><li class="navelem"><a class="el" href="dir_033f5edb0915b828d2c46ed4804e5503.html">detail</a></li>  </ul>
+</div>
+</div><!-- top -->
+<div class="header">
+  <div class="headertitle">
+<div class="title">_fixes.hpp</div>  </div>
+</div><!--header-->
+<div class="contents">
+<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#include &lt;cmath&gt;</span></div>
+<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;</div>
+<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#ifdef max</span></div>
+<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="preprocessor">#undef max</span></div>
+<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;</div>
+<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="preprocessor">#ifdef min</span></div>
+<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#undef min</span></div>
+<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;</div>
+<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#ifdef isnan</span></div>
+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="preprocessor">#undef isnan</span></div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;</div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="preprocessor">#ifdef isinf</span></div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="preprocessor">#undef isinf</span></div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;</div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="preprocessor">#ifdef log2</span></div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="preprocessor">#undef log2</span></div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;</div>
+</div><!-- fragment --></div><!-- contents -->
+<!-- start footer part -->
+<hr class="footer"/><address class="footer"><small>
+Generated by &#160;<a href="http://www.doxygen.org/index.html">
+<img class="footer" src="doxygen.png" alt="doxygen"/>
+</a> 1.8.10
+</small></address>
+</body>
+</html>

diff-gaussian-rasterization-camera/third_party/glm/doc/api/a00015.html

@@ -0,0 +1,267 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml">
+<head>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta http-equiv="X-UA-Compatible" content="IE=9"/>
+<meta name="generator" content="Doxygen 1.8.10"/>
+<title>0.9.9 API documentation: common.hpp File Reference</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="jquery.js"></script>
+<script type="text/javascript" src="dynsections.js"></script>
+<link href="search/search.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="search/searchdata.js"></script>
+<script type="text/javascript" src="search/search.js"></script>
+<script type="text/javascript">
+  $(document).ready(function() { init_search(); });
+</script>
+<link href="doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
+<table cellspacing="0" cellpadding="0">
+ <tbody>
+ <tr style="height: 56px;">
+  <td id="projectlogo"><img alt="Logo" src="logo-mini.png"/></td>
+  <td id="projectalign" style="padding-left: 0.5em;">
+   <div id="projectname">0.9.9 API documentation
+   </div>
+  </td>
+ </tr>
+ </tbody>
+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.10 -->
+<script type="text/javascript">
+var searchBox = new SearchBox("searchBox", "search",false,'Search');
+</script>
+  <div id="navrow1" class="tabs">
+    <ul class="tablist">
+      <li><a href="index.html"><span>Main&#160;Page</span></a></li>
+      <li><a href="modules.html"><span>Modules</span></a></li>
+      <li class="current"><a href="files.html"><span>Files</span></a></li>
+      <li>
+        <div id="MSearchBox" class="MSearchBoxInactive">
+        <span class="left">
+          <img id="MSearchSelect" src="search/mag_sel.png"
+               onmouseover="return searchBox.OnSearchSelectShow()"
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+               alt=""/>
+          <input type="text" id="MSearchField" value="Search" accesskey="S"
+               onfocus="searchBox.OnSearchFieldFocus(true)" 
+               onblur="searchBox.OnSearchFieldFocus(false)" 
+               onkeyup="searchBox.OnSearchFieldChange(event)"/>
+          </span><span class="right">
+            <a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.png" alt=""/></a>
+          </span>
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+  <div id="navrow2" class="tabs2">
+    <ul class="tablist">
+      <li><a href="files.html"><span>File&#160;List</span></a></li>
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+<div id="MSearchSelectWindow"
+     onmouseover="return searchBox.OnSearchSelectShow()"
+     onmouseout="return searchBox.OnSearchSelectHide()"
+     onkeydown="return searchBox.OnSearchSelectKey(event)">
+</div>
+
+<!-- iframe showing the search results (closed by default) -->
+<div id="MSearchResultsWindow">
+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div id="nav-path" class="navpath">
+  <ul>
+<li class="navelem"><a class="el" href="dir_3a581ba30d25676e4b797b1f96d53b45.html">F:</a></li><li class="navelem"><a class="el" href="dir_9e5fe034a00e89334fd5186c3e7db156.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_d9496f0844b48bc7e53b5af8c99b9ab2.html">Source</a></li><li class="navelem"><a class="el" href="dir_a8bee7be44182a33f3820393ae0b105d.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_44e5e654415abd9ca6fdeaddaff8565e.html">glm</a></li><li class="navelem"><a class="el" href="dir_cef2d71d502cb69a9252bca2297d9549.html">glm</a></li>  </ul>
+</div>
+</div><!-- top -->
+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">common.hpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a class="el" href="a00280.html">Core features</a>  
+<a href="#details">More...</a></p>
+
+<p><a href="a00015_source.html">Go to the source code of this file.</a></p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ga439e60a72eadecfeda2df5449c613a64"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga439e60a72eadecfeda2df5449c613a64"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL GLM_CONSTEXPR genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga439e60a72eadecfeda2df5449c613a64">abs</a> (genType x)</td></tr>
+<tr class="memdesc:ga439e60a72eadecfeda2df5449c613a64"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns x if x &gt;= 0; otherwise, it returns -x.  <a href="a00241.html#ga439e60a72eadecfeda2df5449c613a64">More...</a><br /></td></tr>
+<tr class="separator:ga439e60a72eadecfeda2df5449c613a64"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga81d3abddd0ef0c8de579bc541ecadab6"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga81d3abddd0ef0c8de579bc541ecadab6"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL GLM_CONSTEXPR vec&lt; L, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga81d3abddd0ef0c8de579bc541ecadab6">abs</a> (vec&lt; L, T, Q &gt; const &amp;x)</td></tr>
+<tr class="memdesc:ga81d3abddd0ef0c8de579bc541ecadab6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns x if x &gt;= 0; otherwise, it returns -x.  <a href="a00241.html#ga81d3abddd0ef0c8de579bc541ecadab6">More...</a><br /></td></tr>
+<tr class="separator:ga81d3abddd0ef0c8de579bc541ecadab6"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gafb9d2a645a23aca12d4d6de0104b7657"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:gafb9d2a645a23aca12d4d6de0104b7657"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#gafb9d2a645a23aca12d4d6de0104b7657">ceil</a> (vec&lt; L, T, Q &gt; const &amp;x)</td></tr>
+<tr class="memdesc:gafb9d2a645a23aca12d4d6de0104b7657"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a value equal to the nearest integer that is greater than or equal to x.  <a href="a00241.html#gafb9d2a645a23aca12d4d6de0104b7657">More...</a><br /></td></tr>
+<tr class="separator:gafb9d2a645a23aca12d4d6de0104b7657"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga7cd77683da6361e297c56443fc70806d"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga7cd77683da6361e297c56443fc70806d"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL GLM_CONSTEXPR genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga7cd77683da6361e297c56443fc70806d">clamp</a> (genType x, genType minVal, genType maxVal)</td></tr>
+<tr class="memdesc:ga7cd77683da6361e297c56443fc70806d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns min(max(x, minVal), maxVal) for each component in x using the floating-point values minVal and maxVal.  <a href="a00241.html#ga7cd77683da6361e297c56443fc70806d">More...</a><br /></td></tr>
+<tr class="separator:ga7cd77683da6361e297c56443fc70806d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gafba2e0674deb5953878d89483cd6323d"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="separator:gafba2e0674deb5953878d89483cd6323d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaa0f2f12e9108b09e22a3f0b2008a0b5d"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:gaa0f2f12e9108b09e22a3f0b2008a0b5d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns min(max(x, minVal), maxVal) for each component in x using the floating-point values minVal and maxVal.  <a href="a00241.html#gaa0f2f12e9108b09e22a3f0b2008a0b5d">More...</a><br /></td></tr>
+<tr class="separator:gaa0f2f12e9108b09e22a3f0b2008a0b5d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga1425c1c3160ec51214b03a0469a3013d"><td class="memItemLeft" align="right" valign="top">GLM_FUNC_DECL int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00241.html#ga1425c1c3160ec51214b03a0469a3013d">floatBitsToInt</a> (float const &amp;v)</td></tr>
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+<tr class="separator:ga1425c1c3160ec51214b03a0469a3013d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga99f7d62f78ac5ea3b49bae715c9488ed"><td class="memTemplParams" colspan="2">template&lt;length_t L, qualifier Q&gt; </td></tr>
+<tr class="memitem:ga99f7d62f78ac5ea3b49bae715c9488ed"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, int, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga99f7d62f78ac5ea3b49bae715c9488ed">floatBitsToInt</a> (vec&lt; L, float, Q &gt; const &amp;v)</td></tr>
+<tr class="memdesc:ga99f7d62f78ac5ea3b49bae715c9488ed"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a signed integer value representing the encoding of a floating-point value.  <a href="a00241.html#ga99f7d62f78ac5ea3b49bae715c9488ed">More...</a><br /></td></tr>
+<tr class="separator:ga99f7d62f78ac5ea3b49bae715c9488ed"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga70e0271c34af52f3100c7960e18c3f2b"><td class="memItemLeft" align="right" valign="top">GLM_FUNC_DECL uint&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00241.html#ga70e0271c34af52f3100c7960e18c3f2b">floatBitsToUint</a> (float const &amp;v)</td></tr>
+<tr class="memdesc:ga70e0271c34af52f3100c7960e18c3f2b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a unsigned integer value representing the encoding of a floating-point value.  <a href="a00241.html#ga70e0271c34af52f3100c7960e18c3f2b">More...</a><br /></td></tr>
+<tr class="separator:ga70e0271c34af52f3100c7960e18c3f2b"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga49418ba4c8a60fbbb5d57b705f3e26db"><td class="memTemplParams" colspan="2">template&lt;length_t L, qualifier Q&gt; </td></tr>
+<tr class="memitem:ga49418ba4c8a60fbbb5d57b705f3e26db"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, uint, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga49418ba4c8a60fbbb5d57b705f3e26db">floatBitsToUint</a> (vec&lt; L, float, Q &gt; const &amp;v)</td></tr>
+<tr class="memdesc:ga49418ba4c8a60fbbb5d57b705f3e26db"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a unsigned integer value representing the encoding of a floating-point value.  <a href="a00241.html#ga49418ba4c8a60fbbb5d57b705f3e26db">More...</a><br /></td></tr>
+<tr class="separator:ga49418ba4c8a60fbbb5d57b705f3e26db"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaa9d0742639e85b29c7c5de11cfd6840d"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:gaa9d0742639e85b29c7c5de11cfd6840d"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#gaa9d0742639e85b29c7c5de11cfd6840d">floor</a> (vec&lt; L, T, Q &gt; const &amp;x)</td></tr>
+<tr class="memdesc:gaa9d0742639e85b29c7c5de11cfd6840d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a value equal to the nearest integer that is less then or equal to x.  <a href="a00241.html#gaa9d0742639e85b29c7c5de11cfd6840d">More...</a><br /></td></tr>
+<tr class="separator:gaa9d0742639e85b29c7c5de11cfd6840d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gad0f444d4b81cc53c3b6edf5aa25078c2"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:gad0f444d4b81cc53c3b6edf5aa25078c2"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#gad0f444d4b81cc53c3b6edf5aa25078c2">fma</a> (genType const &amp;a, genType const &amp;b, genType const &amp;c)</td></tr>
+<tr class="memdesc:gad0f444d4b81cc53c3b6edf5aa25078c2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes and returns a * b + c.  <a href="a00241.html#gad0f444d4b81cc53c3b6edf5aa25078c2">More...</a><br /></td></tr>
+<tr class="separator:gad0f444d4b81cc53c3b6edf5aa25078c2"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga8ba89e40e55ae5cdf228548f9b7639c7"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga8ba89e40e55ae5cdf228548f9b7639c7"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga8ba89e40e55ae5cdf228548f9b7639c7">fract</a> (genType x)</td></tr>
+<tr class="memdesc:ga8ba89e40e55ae5cdf228548f9b7639c7"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return x - floor(x).  <a href="a00241.html#ga8ba89e40e55ae5cdf228548f9b7639c7">More...</a><br /></td></tr>
+<tr class="separator:ga8ba89e40e55ae5cdf228548f9b7639c7"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga2df623004f634b440d61e018d62c751b"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga2df623004f634b440d61e018d62c751b"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga2df623004f634b440d61e018d62c751b">fract</a> (vec&lt; L, T, Q &gt; const &amp;x)</td></tr>
+<tr class="memdesc:ga2df623004f634b440d61e018d62c751b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return x - floor(x).  <a href="a00241.html#ga2df623004f634b440d61e018d62c751b">More...</a><br /></td></tr>
+<tr class="separator:ga2df623004f634b440d61e018d62c751b"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaddf5ef73283c171730e0bcc11833fa81"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:gaddf5ef73283c171730e0bcc11833fa81"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#gaddf5ef73283c171730e0bcc11833fa81">frexp</a> (genType x, int &amp;exp)</td></tr>
+<tr class="memdesc:gaddf5ef73283c171730e0bcc11833fa81"><td class="mdescLeft">&#160;</td><td class="mdescRight">Splits x into a floating-point significand in the range [0.5, 1.0) and an integral exponent of two, such that: x = significand * exp(2, exponent)  <a href="a00241.html#gaddf5ef73283c171730e0bcc11833fa81">More...</a><br /></td></tr>
+<tr class="separator:gaddf5ef73283c171730e0bcc11833fa81"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga4fb7c21c2dce064b26fd9ccdaf9adcd4"><td class="memItemLeft" align="right" valign="top">GLM_FUNC_DECL float&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00241.html#ga4fb7c21c2dce064b26fd9ccdaf9adcd4">intBitsToFloat</a> (int const &amp;v)</td></tr>
+<tr class="memdesc:ga4fb7c21c2dce064b26fd9ccdaf9adcd4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a floating-point value corresponding to a signed integer encoding of a floating-point value.  <a href="a00241.html#ga4fb7c21c2dce064b26fd9ccdaf9adcd4">More...</a><br /></td></tr>
+<tr class="separator:ga4fb7c21c2dce064b26fd9ccdaf9adcd4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga7a0a8291a1cf3e1c2aee33030a1bd7b0"><td class="memTemplParams" colspan="2">template&lt;length_t L, qualifier Q&gt; </td></tr>
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+<tr class="memdesc:ga7a0a8291a1cf3e1c2aee33030a1bd7b0"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a floating-point value corresponding to a signed integer encoding of a floating-point value.  <a href="a00241.html#ga7a0a8291a1cf3e1c2aee33030a1bd7b0">More...</a><br /></td></tr>
+<tr class="separator:ga7a0a8291a1cf3e1c2aee33030a1bd7b0"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga2885587c23a106301f20443896365b62"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga2885587c23a106301f20443896365b62"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, bool, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga2885587c23a106301f20443896365b62">isinf</a> (vec&lt; L, T, Q &gt; const &amp;x)</td></tr>
+<tr class="memdesc:ga2885587c23a106301f20443896365b62"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns true if x holds a positive infinity or negative infinity representation in the underlying implementation's set of floating point representations.  <a href="a00241.html#ga2885587c23a106301f20443896365b62">More...</a><br /></td></tr>
+<tr class="separator:ga2885587c23a106301f20443896365b62"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga29ef934c00306490de837b4746b4e14d"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga29ef934c00306490de837b4746b4e14d"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, bool, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga29ef934c00306490de837b4746b4e14d">isnan</a> (vec&lt; L, T, Q &gt; const &amp;x)</td></tr>
+<tr class="memdesc:ga29ef934c00306490de837b4746b4e14d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns true if x holds a NaN (not a number) representation in the underlying implementation's set of floating point representations.  <a href="a00241.html#ga29ef934c00306490de837b4746b4e14d">More...</a><br /></td></tr>
+<tr class="separator:ga29ef934c00306490de837b4746b4e14d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gac3010e0a0c35a1b514540f2fb579c58c"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:gac3010e0a0c35a1b514540f2fb579c58c"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#gac3010e0a0c35a1b514540f2fb579c58c">ldexp</a> (genType const &amp;x, int const &amp;exp)</td></tr>
+<tr class="memdesc:gac3010e0a0c35a1b514540f2fb579c58c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Builds a floating-point number from x and the corresponding integral exponent of two in exp, returning: significand * exp(2, exponent)  <a href="a00241.html#gac3010e0a0c35a1b514540f2fb579c58c">More...</a><br /></td></tr>
+<tr class="separator:gac3010e0a0c35a1b514540f2fb579c58c"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gae02d42887fc5570451f880e3c624b9ac"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:gae02d42887fc5570451f880e3c624b9ac"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL GLM_CONSTEXPR genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#gae02d42887fc5570451f880e3c624b9ac">max</a> (genType x, genType y)</td></tr>
+<tr class="memdesc:gae02d42887fc5570451f880e3c624b9ac"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns y if x &lt; y; otherwise, it returns x.  <a href="a00241.html#gae02d42887fc5570451f880e3c624b9ac">More...</a><br /></td></tr>
+<tr class="separator:gae02d42887fc5570451f880e3c624b9ac"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga03e45d6e60d1c36edb00c52edeea0f31"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga03e45d6e60d1c36edb00c52edeea0f31"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL GLM_CONSTEXPR vec&lt; L, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga03e45d6e60d1c36edb00c52edeea0f31">max</a> (vec&lt; L, T, Q &gt; const &amp;x, T y)</td></tr>
+<tr class="memdesc:ga03e45d6e60d1c36edb00c52edeea0f31"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns y if x &lt; y; otherwise, it returns x.  <a href="a00241.html#ga03e45d6e60d1c36edb00c52edeea0f31">More...</a><br /></td></tr>
+<tr class="separator:ga03e45d6e60d1c36edb00c52edeea0f31"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gac1fec0c3303b572a6d4697a637213870"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:gac1fec0c3303b572a6d4697a637213870"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns y if x &lt; y; otherwise, it returns x.  <a href="a00241.html#gac1fec0c3303b572a6d4697a637213870">More...</a><br /></td></tr>
+<tr class="separator:gac1fec0c3303b572a6d4697a637213870"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga6cf8098827054a270ee36b18e30d471d"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
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+<tr class="separator:ga6cf8098827054a270ee36b18e30d471d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaa7d015eba1f9f48519251f4abe69b14d"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:gaa7d015eba1f9f48519251f4abe69b14d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns y if y &lt; x; otherwise, it returns x.  <a href="a00241.html#gaa7d015eba1f9f48519251f4abe69b14d">More...</a><br /></td></tr>
+<tr class="separator:gaa7d015eba1f9f48519251f4abe69b14d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga31f49ef9e7d1beb003160c5e009b0c48"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:ga31f49ef9e7d1beb003160c5e009b0c48"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns y if y &lt; x; otherwise, it returns x.  <a href="a00241.html#ga31f49ef9e7d1beb003160c5e009b0c48">More...</a><br /></td></tr>
+<tr class="separator:ga31f49ef9e7d1beb003160c5e009b0c48"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga8e93f374aae27d1a88b921860351f8d4"><td class="memTemplParams" colspan="2">template&lt;typename genTypeT , typename genTypeU &gt; </td></tr>
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+<tr class="separator:ga8e93f374aae27d1a88b921860351f8d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga9b197a452cd52db3c5c18bac72bd7798"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="separator:ga9b197a452cd52db3c5c18bac72bd7798"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga85e33f139b8db1b39b590a5713b9e679"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
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+<tr class="memdesc:ga85e33f139b8db1b39b590a5713b9e679"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the fractional part of x and sets i to the integer part (as a whole number floating point value).  <a href="a00241.html#ga85e33f139b8db1b39b590a5713b9e679">More...</a><br /></td></tr>
+<tr class="separator:ga85e33f139b8db1b39b590a5713b9e679"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gafa03aca8c4713e1cc892aa92ca135a7e"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:gafa03aca8c4713e1cc892aa92ca135a7e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a value equal to the nearest integer to x.  <a href="a00241.html#gafa03aca8c4713e1cc892aa92ca135a7e">More...</a><br /></td></tr>
+<tr class="separator:gafa03aca8c4713e1cc892aa92ca135a7e"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga76b81785045a057989a84d99aeeb1578"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga76b81785045a057989a84d99aeeb1578"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga76b81785045a057989a84d99aeeb1578">roundEven</a> (vec&lt; L, T, Q &gt; const &amp;x)</td></tr>
+<tr class="memdesc:ga76b81785045a057989a84d99aeeb1578"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a value equal to the nearest integer to x.  <a href="a00241.html#ga76b81785045a057989a84d99aeeb1578">More...</a><br /></td></tr>
+<tr class="separator:ga76b81785045a057989a84d99aeeb1578"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga1e2e5cfff800056540e32f6c9b604b28"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga1e2e5cfff800056540e32f6c9b604b28"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga1e2e5cfff800056540e32f6c9b604b28">sign</a> (vec&lt; L, T, Q &gt; const &amp;x)</td></tr>
+<tr class="memdesc:ga1e2e5cfff800056540e32f6c9b604b28"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns 1.0 if x &gt; 0, 0.0 if x == 0, or -1.0 if x &lt; 0.  <a href="a00241.html#ga1e2e5cfff800056540e32f6c9b604b28">More...</a><br /></td></tr>
+<tr class="separator:ga1e2e5cfff800056540e32f6c9b604b28"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga562edf7eca082cc5b7a0aaf180436daf"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga562edf7eca082cc5b7a0aaf180436daf"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga562edf7eca082cc5b7a0aaf180436daf">smoothstep</a> (genType edge0, genType edge1, genType x)</td></tr>
+<tr class="memdesc:ga562edf7eca082cc5b7a0aaf180436daf"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns 0.0 if x &lt;= edge0 and 1.0 if x &gt;= edge1 and performs smooth Hermite interpolation between 0 and 1 when edge0 &lt; x &lt; edge1.  <a href="a00241.html#ga562edf7eca082cc5b7a0aaf180436daf">More...</a><br /></td></tr>
+<tr class="separator:ga562edf7eca082cc5b7a0aaf180436daf"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga015a1261ff23e12650211aa872863cce"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga015a1261ff23e12650211aa872863cce"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga015a1261ff23e12650211aa872863cce">step</a> (genType edge, genType x)</td></tr>
+<tr class="memdesc:ga015a1261ff23e12650211aa872863cce"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns 0.0 if x &lt; edge, otherwise it returns 1.0 for each component of a genType.  <a href="a00241.html#ga015a1261ff23e12650211aa872863cce">More...</a><br /></td></tr>
+<tr class="separator:ga015a1261ff23e12650211aa872863cce"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga8f9a911a48ef244b51654eaefc81c551"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga8f9a911a48ef244b51654eaefc81c551"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga8f9a911a48ef244b51654eaefc81c551">step</a> (T edge, vec&lt; L, T, Q &gt; const &amp;x)</td></tr>
+<tr class="memdesc:ga8f9a911a48ef244b51654eaefc81c551"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns 0.0 if x &lt; edge, otherwise it returns 1.0.  <a href="a00241.html#ga8f9a911a48ef244b51654eaefc81c551">More...</a><br /></td></tr>
+<tr class="separator:ga8f9a911a48ef244b51654eaefc81c551"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaf4a5fc81619c7d3e8b22f53d4a098c7f"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:gaf4a5fc81619c7d3e8b22f53d4a098c7f"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#gaf4a5fc81619c7d3e8b22f53d4a098c7f">step</a> (vec&lt; L, T, Q &gt; const &amp;edge, vec&lt; L, T, Q &gt; const &amp;x)</td></tr>
+<tr class="memdesc:gaf4a5fc81619c7d3e8b22f53d4a098c7f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns 0.0 if x &lt; edge, otherwise it returns 1.0.  <a href="a00241.html#gaf4a5fc81619c7d3e8b22f53d4a098c7f">More...</a><br /></td></tr>
+<tr class="separator:gaf4a5fc81619c7d3e8b22f53d4a098c7f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaf9375e3e06173271d49e6ffa3a334259"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:gaf9375e3e06173271d49e6ffa3a334259"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#gaf9375e3e06173271d49e6ffa3a334259">trunc</a> (vec&lt; L, T, Q &gt; const &amp;x)</td></tr>
+<tr class="memdesc:gaf9375e3e06173271d49e6ffa3a334259"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a value equal to the nearest integer to x whose absolute value is not larger than the absolute value of x.  <a href="a00241.html#gaf9375e3e06173271d49e6ffa3a334259">More...</a><br /></td></tr>
+<tr class="separator:gaf9375e3e06173271d49e6ffa3a334259"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gab2bae0d15dcdca6093f88f76b3975d97"><td class="memItemLeft" align="right" valign="top">GLM_FUNC_DECL float&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00241.html#gab2bae0d15dcdca6093f88f76b3975d97">uintBitsToFloat</a> (uint const &amp;v)</td></tr>
+<tr class="memdesc:gab2bae0d15dcdca6093f88f76b3975d97"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a floating-point value corresponding to a unsigned integer encoding of a floating-point value.  <a href="a00241.html#gab2bae0d15dcdca6093f88f76b3975d97">More...</a><br /></td></tr>
+<tr class="separator:gab2bae0d15dcdca6093f88f76b3975d97"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga97f46b5f7b42fe44482e13356eb394ae"><td class="memTemplParams" colspan="2">template&lt;length_t L, qualifier Q&gt; </td></tr>
+<tr class="memitem:ga97f46b5f7b42fe44482e13356eb394ae"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, float, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga97f46b5f7b42fe44482e13356eb394ae">uintBitsToFloat</a> (vec&lt; L, uint, Q &gt; const &amp;v)</td></tr>
+<tr class="memdesc:ga97f46b5f7b42fe44482e13356eb394ae"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a floating-point value corresponding to a unsigned integer encoding of a floating-point value.  <a href="a00241.html#ga97f46b5f7b42fe44482e13356eb394ae">More...</a><br /></td></tr>
+<tr class="separator:ga97f46b5f7b42fe44482e13356eb394ae"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a class="el" href="a00280.html">Core features</a> </p>
+<dl class="section see"><dt>See also</dt><dd><a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> </dd></dl>
+
+<p>Definition in file <a class="el" href="a00015_source.html">common.hpp</a>.</p>
+</div></div><!-- contents -->
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+Generated by &#160;<a href="http://www.doxygen.org/index.html">
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+<li class="navelem"><a class="el" href="dir_3a581ba30d25676e4b797b1f96d53b45.html">F:</a></li><li class="navelem"><a class="el" href="dir_9e5fe034a00e89334fd5186c3e7db156.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_d9496f0844b48bc7e53b5af8c99b9ab2.html">Source</a></li><li class="navelem"><a class="el" href="dir_a8bee7be44182a33f3820393ae0b105d.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_44e5e654415abd9ca6fdeaddaff8565e.html">glm</a></li><li class="navelem"><a class="el" href="dir_cef2d71d502cb69a9252bca2297d9549.html">glm</a></li><li class="navelem"><a class="el" href="dir_f35778ec600a1b9bbc4524e62e226aa2.html">gtx</a></li>  </ul>
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+<div class="title">compatibility.hpp</div>  </div>
+</div><!--header-->
+<div class="contents">
+<a href="a00017.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;</div>
+<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#pragma once</span></div>
+<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;</div>
+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">// Dependency:</span></div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#include &quot;../glm.hpp&quot;</span></div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="preprocessor">#include &quot;../gtc/quaternion.hpp&quot;</span></div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;</div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="preprocessor">#if GLM_MESSAGES == GLM_ENABLE &amp;&amp; !defined(GLM_EXT_INCLUDED)</span></div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="preprocessor">#       ifndef GLM_ENABLE_EXPERIMENTAL</span></div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="preprocessor">#               pragma message(&quot;GLM: GLM_GTX_compatibility is an experimental extension and may change in the future. Use #define GLM_ENABLE_EXPERIMENTAL before including it, if you really want to use it.&quot;)</span></div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="preprocessor">#       else</span></div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="preprocessor">#               pragma message(&quot;GLM: GLM_GTX_compatibility extension included&quot;)</span></div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="preprocessor">#if GLM_COMPILER &amp; GLM_COMPILER_VC</span></div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="preprocessor">#       include &lt;cfloat&gt;</span></div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="preprocessor">#elif GLM_COMPILER &amp; GLM_COMPILER_GCC</span></div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="preprocessor">#       include &lt;cmath&gt;</span></div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="preprocessor">#       if(GLM_PLATFORM &amp; GLM_PLATFORM_ANDROID)</span></div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="preprocessor">#               undef isfinite</span></div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="preprocessor">#endif//GLM_COMPILER</span></div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;</div>
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+<div class="line"><a name="l00041"></a><span class="lineno"><a class="line" href="a00315.html#ga5494ba3a95ea6594c86fc75236886864">   41</a></span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; GLM_FUNC_QUALIFIER T <a class="code" href="a00315.html#gab5477ab69c40de4db5d58d3359529724">lerp</a>(T x, T y, T a){<span class="keywordflow">return</span> <a class="code" href="a00241.html#ga8e93f374aae27d1a88b921860351f8d4">mix</a>(x, y, a);}                                                                                                                                                                     </div>
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+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;</div>
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+<div class="line"><a name="l00045"></a><span class="lineno"><a class="line" href="a00315.html#ga89ac8e000199292ec7875519d27e214b">   45</a></span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt; GLM_FUNC_QUALIFIER vec&lt;4, T, Q&gt; <a class="code" href="a00315.html#gab5477ab69c40de4db5d58d3359529724">lerp</a>(<span class="keyword">const</span> vec&lt;4, T, Q&gt;&amp; x, <span class="keyword">const</span> vec&lt;4, T, Q&gt;&amp; y, T a){<span class="keywordflow">return</span> <a class="code" href="a00241.html#ga8e93f374aae27d1a88b921860351f8d4">mix</a>(x, y, a);}                                                 </div>
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+<div class="line"><a name="l00047"></a><span class="lineno"><a class="line" href="a00315.html#ga4ae1a616c8540a2649eab8e0cd051bb3">   47</a></span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt; GLM_FUNC_QUALIFIER vec&lt;3, T, Q&gt; <a class="code" href="a00315.html#gab5477ab69c40de4db5d58d3359529724">lerp</a>(<span class="keyword">const</span> vec&lt;3, T, Q&gt;&amp; x, <span class="keyword">const</span> vec&lt;3, T, Q&gt;&amp; y, <span class="keyword">const</span> vec&lt;3, T, Q&gt;&amp; a){<span class="keywordflow">return</span> <a class="code" href="a00241.html#ga8e93f374aae27d1a88b921860351f8d4">mix</a>(x, y, a);}       </div>
+<div class="line"><a name="l00048"></a><span class="lineno"><a class="line" href="a00315.html#gab5477ab69c40de4db5d58d3359529724">   48</a></span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt; GLM_FUNC_QUALIFIER vec&lt;4, T, Q&gt; <a class="code" href="a00315.html#gab5477ab69c40de4db5d58d3359529724">lerp</a>(<span class="keyword">const</span> vec&lt;4, T, Q&gt;&amp; x, <span class="keyword">const</span> vec&lt;4, T, Q&gt;&amp; y, <span class="keyword">const</span> vec&lt;4, T, Q&gt;&amp; a){<span class="keywordflow">return</span> <a class="code" href="a00241.html#ga8e93f374aae27d1a88b921860351f8d4">mix</a>(x, y, a);}       </div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;</div>
+<div class="line"><a name="l00050"></a><span class="lineno"><a class="line" href="a00315.html#ga0fd09e616d122bc2ed9726682ffd44b7">   50</a></span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt; GLM_FUNC_QUALIFIER T <a class="code" href="a00315.html#ga356f8c3a7e7d6376d3d4b0a026407183">saturate</a>(T x){<span class="keywordflow">return</span> <a class="code" href="a00241.html#ga7cd77683da6361e297c56443fc70806d">clamp</a>(x, T(0), T(1));}                                                                                                              </div>
+<div class="line"><a name="l00051"></a><span class="lineno"><a class="line" href="a00315.html#gaee97b8001c794a78a44f5d59f62a8aba">   51</a></span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt; GLM_FUNC_QUALIFIER vec&lt;2, T, Q&gt; <a class="code" href="a00315.html#ga356f8c3a7e7d6376d3d4b0a026407183">saturate</a>(<span class="keyword">const</span> vec&lt;2, T, Q&gt;&amp; x){<span class="keywordflow">return</span> <a class="code" href="a00241.html#ga7cd77683da6361e297c56443fc70806d">clamp</a>(x, T(0), T(1));}                                 </div>
+<div class="line"><a name="l00052"></a><span class="lineno"><a class="line" href="a00315.html#ga39bfe3a421286ee31680d45c31ccc161">   52</a></span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt; GLM_FUNC_QUALIFIER vec&lt;3, T, Q&gt; <a class="code" href="a00315.html#ga356f8c3a7e7d6376d3d4b0a026407183">saturate</a>(<span class="keyword">const</span> vec&lt;3, T, Q&gt;&amp; x){<span class="keywordflow">return</span> <a class="code" href="a00241.html#ga7cd77683da6361e297c56443fc70806d">clamp</a>(x, T(0), T(1));}                                 </div>
+<div class="line"><a name="l00053"></a><span class="lineno"><a class="line" href="a00315.html#ga356f8c3a7e7d6376d3d4b0a026407183">   53</a></span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt; GLM_FUNC_QUALIFIER vec&lt;4, T, Q&gt; <a class="code" href="a00315.html#ga356f8c3a7e7d6376d3d4b0a026407183">saturate</a>(<span class="keyword">const</span> vec&lt;4, T, Q&gt;&amp; x){<span class="keywordflow">return</span> <a class="code" href="a00241.html#ga7cd77683da6361e297c56443fc70806d">clamp</a>(x, T(0), T(1));}                                 </div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;</div>
+<div class="line"><a name="l00055"></a><span class="lineno"><a class="line" href="a00315.html#gac63011205bf6d0be82589dc56dd26708">   55</a></span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt; GLM_FUNC_QUALIFIER T <a class="code" href="a00315.html#gaba86c28da7bf5bdac64fecf7d56e8ff3">atan2</a>(T x, T y){<span class="keywordflow">return</span> <a class="code" href="a00373.html#gac61629f3a4aa14057e7a8cae002291db">atan</a>(x, y);}                                                                                                                              </div>
+<div class="line"><a name="l00056"></a><span class="lineno"><a class="line" href="a00315.html#ga83bc41bd6f89113ee8006576b12bfc50">   56</a></span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt; GLM_FUNC_QUALIFIER vec&lt;2, T, Q&gt; <a class="code" href="a00315.html#gaba86c28da7bf5bdac64fecf7d56e8ff3">atan2</a>(<span class="keyword">const</span> vec&lt;2, T, Q&gt;&amp; x, <span class="keyword">const</span> vec&lt;2, T, Q&gt;&amp; y){<span class="keywordflow">return</span> <a class="code" href="a00373.html#gac61629f3a4aa14057e7a8cae002291db">atan</a>(x, y);}       </div>
+<div class="line"><a name="l00057"></a><span class="lineno"><a class="line" href="a00315.html#gac39314f5087e7e51e592897cabbc1927">   57</a></span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt; GLM_FUNC_QUALIFIER vec&lt;3, T, Q&gt; <a class="code" href="a00315.html#gaba86c28da7bf5bdac64fecf7d56e8ff3">atan2</a>(<span class="keyword">const</span> vec&lt;3, T, Q&gt;&amp; x, <span class="keyword">const</span> vec&lt;3, T, Q&gt;&amp; y){<span class="keywordflow">return</span> <a class="code" href="a00373.html#gac61629f3a4aa14057e7a8cae002291db">atan</a>(x, y);}       </div>
+<div class="line"><a name="l00058"></a><span class="lineno"><a class="line" href="a00315.html#gaba86c28da7bf5bdac64fecf7d56e8ff3">   58</a></span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt; GLM_FUNC_QUALIFIER vec&lt;4, T, Q&gt; <a class="code" href="a00315.html#gaba86c28da7bf5bdac64fecf7d56e8ff3">atan2</a>(<span class="keyword">const</span> vec&lt;4, T, Q&gt;&amp; x, <span class="keyword">const</span> vec&lt;4, T, Q&gt;&amp; y){<span class="keywordflow">return</span> <a class="code" href="a00373.html#gac61629f3a4aa14057e7a8cae002291db">atan</a>(x, y);}       </div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;</div>
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+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt; GLM_FUNC_DECL vec&lt;4, bool, Q&gt; <a class="code" href="a00315.html#ga19925badbe10ce61df1d0de00be0b5ad">isfinite</a>(<span class="keyword">const</span> vec&lt;4, T, Q&gt;&amp; x);                                </div>
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+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;</div>
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+<div class="ttc" id="a00315_html_gaacac46ddc7d15d0f9529d05c92946a0f"><div class="ttname"><a href="a00315.html#gaacac46ddc7d15d0f9529d05c92946a0f">glm::int3x4</a></div><div class="ttdeci">mat&lt; 3, 4, int, highp &gt; int3x4</div><div class="ttdoc">integer matrix with 3 x 4 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00093">compatibility.hpp:93</a></div></div>
+<div class="ttc" id="a00373_html_gac61629f3a4aa14057e7a8cae002291db"><div class="ttname"><a href="a00373.html#gac61629f3a4aa14057e7a8cae002291db">glm::atan</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, T, Q &gt; atan(vec&lt; L, T, Q &gt; const &amp;y, vec&lt; L, T, Q &gt; const &amp;x)</div><div class="ttdoc">Arc tangent. </div></div>
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+<div class="ttc" id="a00315_html_gac0a51b4812038aa81d73ffcc37f741ac"><div class="ttname"><a href="a00315.html#gac0a51b4812038aa81d73ffcc37f741ac">glm::float4x3</a></div><div class="ttdeci">mat&lt; 4, 3, float, highp &gt; float4x3</div><div class="ttdoc">single-qualifier floating-point matrix with 4 x 3 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00111">compatibility.hpp:111</a></div></div>
+<div class="ttc" id="a00315_html_gad3051649b3715d828a4ab92cdae7c3bf"><div class="ttname"><a href="a00315.html#gad3051649b3715d828a4ab92cdae7c3bf">glm::float4x4</a></div><div class="ttdeci">mat&lt; 4, 4, float, highp &gt; float4x4</div><div class="ttdoc">single-qualifier floating-point matrix with 4 x 4 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00112">compatibility.hpp:112</a></div></div>
+<div class="ttc" id="a00315_html_gacd33061fc64a7b2dcfd7322c49d9557a"><div class="ttname"><a href="a00315.html#gacd33061fc64a7b2dcfd7322c49d9557a">glm::double2x4</a></div><div class="ttdeci">mat&lt; 2, 4, double, highp &gt; double2x4</div><div class="ttdoc">double-qualifier floating-point matrix with 2 x 4 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00122">compatibility.hpp:122</a></div></div>
+<div class="ttc" id="a00315_html_gae57d0201096834d25f2b91b319e7cdbd"><div class="ttname"><a href="a00315.html#gae57d0201096834d25f2b91b319e7cdbd">glm::double2x2</a></div><div class="ttdeci">mat&lt; 2, 2, double, highp &gt; double2x2</div><div class="ttdoc">double-qualifier floating-point matrix with 2 x 2 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00120">compatibility.hpp:120</a></div></div>
+<div class="ttc" id="a00315_html_ga5ec08fc39c9d783dfcc488be240fe975"><div class="ttname"><a href="a00315.html#ga5ec08fc39c9d783dfcc488be240fe975">glm::double3x2</a></div><div class="ttdeci">mat&lt; 3, 2, double, highp &gt; double3x2</div><div class="ttdoc">double-qualifier floating-point matrix with 3 x 2 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00123">compatibility.hpp:123</a></div></div>
+<div class="ttc" id="a00315_html_gaba86c28da7bf5bdac64fecf7d56e8ff3"><div class="ttname"><a href="a00315.html#gaba86c28da7bf5bdac64fecf7d56e8ff3">glm::atan2</a></div><div class="ttdeci">GLM_FUNC_QUALIFIER vec&lt; 4, T, Q &gt; atan2(const vec&lt; 4, T, Q &gt; &amp;x, const vec&lt; 4, T, Q &gt; &amp;y)</div><div class="ttdoc">Arc tangent. Returns an angle whose tangent is y/x. The signs of x and y are used to determine what q...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00058">compatibility.hpp:58</a></div></div>
+<div class="ttc" id="a00315_html_ga45f16a4dd0db1f199afaed9fd12fe9a8"><div class="ttname"><a href="a00315.html#ga45f16a4dd0db1f199afaed9fd12fe9a8">glm::double1x1</a></div><div class="ttdeci">double double1x1</div><div class="ttdoc">double-qualifier floating-point matrix with 1 component. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00119">compatibility.hpp:119</a></div></div>
+<div class="ttc" id="a00315_html_gab5477ab69c40de4db5d58d3359529724"><div class="ttname"><a href="a00315.html#gab5477ab69c40de4db5d58d3359529724">glm::lerp</a></div><div class="ttdeci">GLM_FUNC_QUALIFIER vec&lt; 4, T, Q &gt; lerp(const vec&lt; 4, T, Q &gt; &amp;x, const vec&lt; 4, T, Q &gt; &amp;y, const vec&lt; 4, T, Q &gt; &amp;a)</div><div class="ttdoc">Returns the component-wise result of x * (1.0 - a) + y * a, i.e., the linear blend of x and y using v...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00048">compatibility.hpp:48</a></div></div>
+<div class="ttc" id="a00315_html_ga4bad5bb20c6ddaecfe4006c93841d180"><div class="ttname"><a href="a00315.html#ga4bad5bb20c6ddaecfe4006c93841d180">glm::double3x3</a></div><div class="ttdeci">mat&lt; 3, 3, double, highp &gt; double3x3</div><div class="ttdoc">double-qualifier floating-point matrix with 3 x 3 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00124">compatibility.hpp:124</a></div></div>
+<div class="ttc" id="a00315_html_gae2da7345087db3815a25d8837a727ef1"><div class="ttname"><a href="a00315.html#gae2da7345087db3815a25d8837a727ef1">glm::float4</a></div><div class="ttdeci">vec&lt; 4, float, highp &gt; float4</div><div class="ttdoc">single-qualifier floating-point vector with 4 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00101">compatibility.hpp:101</a></div></div>
+<div class="ttc" id="a00315_html_ga056ffe02d3a45af626f8e62221881c7a"><div class="ttname"><a href="a00315.html#ga056ffe02d3a45af626f8e62221881c7a">glm::int1x1</a></div><div class="ttdeci">int int1x1</div><div class="ttdoc">integer matrix with 1 component. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00087">compatibility.hpp:87</a></div></div>
+<div class="ttc" id="a00315_html_ga02d3c013982c183906c61d74aa3166ce"><div class="ttname"><a href="a00315.html#ga02d3c013982c183906c61d74aa3166ce">glm::float2</a></div><div class="ttdeci">vec&lt; 2, float, highp &gt; float2</div><div class="ttdoc">single-qualifier floating-point vector with 2 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00099">compatibility.hpp:99</a></div></div>
+<div class="ttc" id="a00315_html_ga19925badbe10ce61df1d0de00be0b5ad"><div class="ttname"><a href="a00315.html#ga19925badbe10ce61df1d0de00be0b5ad">glm::isfinite</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; 4, bool, Q &gt; isfinite(const vec&lt; 4, T, Q &gt; &amp;x)</div><div class="ttdoc">Test whether or not a scalar or each vector component is a finite value. (From GLM_GTX_compatibility)...</div></div>
+<div class="ttc" id="a00315_html_ga9ae6ee155d0f90cb1ae5b6c4546738a0"><div class="ttname"><a href="a00315.html#ga9ae6ee155d0f90cb1ae5b6c4546738a0">glm::bool2x3</a></div><div class="ttdeci">mat&lt; 2, 3, bool, highp &gt; bool2x3</div><div class="ttdoc">boolean matrix with 2 x 3 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00073">compatibility.hpp:73</a></div></div>
+<div class="ttc" id="a00315_html_ga197ded5ad8354f6b6fb91189d7a269b3"><div class="ttname"><a href="a00315.html#ga197ded5ad8354f6b6fb91189d7a269b3">glm::int2x3</a></div><div class="ttdeci">mat&lt; 2, 3, int, highp &gt; int2x3</div><div class="ttdoc">integer matrix with 2 x 3 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00089">compatibility.hpp:89</a></div></div>
+<div class="ttc" id="a00315_html_ga0670a2111b5e4a6410bd027fa0232fc3"><div class="ttname"><a href="a00315.html#ga0670a2111b5e4a6410bd027fa0232fc3">glm::int1</a></div><div class="ttdeci">int int1</div><div class="ttdoc">integer vector with 1 component. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00082">compatibility.hpp:82</a></div></div>
+<div class="ttc" id="a00315_html_ga821ff110fc8533a053cbfcc93e078cc0"><div class="ttname"><a href="a00315.html#ga821ff110fc8533a053cbfcc93e078cc0">glm::float3</a></div><div class="ttdeci">vec&lt; 3, float, highp &gt; float3</div><div class="ttdoc">single-qualifier floating-point vector with 3 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00100">compatibility.hpp:100</a></div></div>
+<div class="ttc" id="a00315_html_gafec3cfd901ab334a92e0242b8f2269b4"><div class="ttname"><a href="a00315.html#gafec3cfd901ab334a92e0242b8f2269b4">glm::float2x4</a></div><div class="ttdeci">mat&lt; 2, 4, float, highp &gt; float2x4</div><div class="ttdoc">single-qualifier floating-point matrix with 2 x 4 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00106">compatibility.hpp:106</a></div></div>
+<div class="ttc" id="a00315_html_gadb3703955e513632f98ba12fe051ba3e"><div class="ttname"><a href="a00315.html#gadb3703955e513632f98ba12fe051ba3e">glm::bool2x2</a></div><div class="ttdeci">mat&lt; 2, 2, bool, highp &gt; bool2x2</div><div class="ttdoc">boolean matrix with 2 x 2 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00072">compatibility.hpp:72</a></div></div>
+<div class="ttc" id="a00315_html_ga7d2a7d13986602ae2896bfaa394235d4"><div class="ttname"><a href="a00315.html#ga7d2a7d13986602ae2896bfaa394235d4">glm::bool4x4</a></div><div class="ttdeci">mat&lt; 4, 4, bool, highp &gt; bool4x4</div><div class="ttdoc">boolean matrix with 4 x 4 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00080">compatibility.hpp:80</a></div></div>
+<div class="ttc" id="a00315_html_gaf5208d01f6c6fbcb7bb55d610b9c0ead"><div class="ttname"><a href="a00315.html#gaf5208d01f6c6fbcb7bb55d610b9c0ead">glm::float1</a></div><div class="ttdeci">float float1</div><div class="ttdoc">single-qualifier floating-point vector with 1 component. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00098">compatibility.hpp:98</a></div></div>
+<div class="ttc" id="a00315_html_ga73720b8dc4620835b17f74d428f98c0c"><div class="ttname"><a href="a00315.html#ga73720b8dc4620835b17f74d428f98c0c">glm::float1x1</a></div><div class="ttdeci">float float1x1</div><div class="ttdoc">single-qualifier floating-point matrix with 1 component. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00103">compatibility.hpp:103</a></div></div>
+<div class="ttc" id="a00315_html_gabca29ccceea53669618b751aae0ba83d"><div class="ttname"><a href="a00315.html#gabca29ccceea53669618b751aae0ba83d">glm::double4x2</a></div><div class="ttdeci">mat&lt; 4, 2, double, highp &gt; double4x2</div><div class="ttdoc">double-qualifier floating-point matrix with 4 x 2 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00126">compatibility.hpp:126</a></div></div>
+<div class="ttc" id="a00315_html_gae4a2c53f14aeec9a17c2b81142b7e82d"><div class="ttname"><a href="a00315.html#gae4a2c53f14aeec9a17c2b81142b7e82d">glm::int4x3</a></div><div class="ttdeci">mat&lt; 4, 3, int, highp &gt; int4x3</div><div class="ttdoc">integer matrix with 4 x 3 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00095">compatibility.hpp:95</a></div></div>
+<div class="ttc" id="a00315_html_ga9ed830f52408b2f83c085063a3eaf1d0"><div class="ttname"><a href="a00315.html#ga9ed830f52408b2f83c085063a3eaf1d0">glm::bool4x2</a></div><div class="ttdeci">mat&lt; 4, 2, bool, highp &gt; bool4x2</div><div class="ttdoc">boolean matrix with 4 x 2 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00078">compatibility.hpp:78</a></div></div>
+<div class="ttc" id="a00315_html_ga33d43ecbb60a85a1366ff83f8a0ec85f"><div class="ttname"><a href="a00315.html#ga33d43ecbb60a85a1366ff83f8a0ec85f">glm::float2x2</a></div><div class="ttdeci">mat&lt; 2, 2, float, highp &gt; float2x2</div><div class="ttdoc">single-qualifier floating-point matrix with 2 x 2 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00104">compatibility.hpp:104</a></div></div>
+<div class="ttc" id="a00315_html_ga909c38a425f215a50c847145d7da09f0"><div class="ttname"><a href="a00315.html#ga909c38a425f215a50c847145d7da09f0">glm::int3</a></div><div class="ttdeci">vec&lt; 3, int, highp &gt; int3</div><div class="ttdoc">integer vector with 3 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00084">compatibility.hpp:84</a></div></div>
+<div class="ttc" id="a00315_html_ga308b9af0c221145bcfe9bfc129d9098e"><div class="ttname"><a href="a00315.html#ga308b9af0c221145bcfe9bfc129d9098e">glm::float4x2</a></div><div class="ttdeci">mat&lt; 4, 2, float, highp &gt; float4x2</div><div class="ttdoc">single-qualifier floating-point matrix with 4 x 2 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00110">compatibility.hpp:110</a></div></div>
+<div class="ttc" id="a00315_html_ga3655bc324008553ca61f39952d0b2d08"><div class="ttname"><a href="a00315.html#ga3655bc324008553ca61f39952d0b2d08">glm::double2x3</a></div><div class="ttdeci">mat&lt; 2, 3, double, highp &gt; double2x3</div><div class="ttdoc">double-qualifier floating-point matrix with 2 x 3 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00121">compatibility.hpp:121</a></div></div>
+<div class="ttc" id="a00315_html_ga939b0cff15cee3030f75c1b2e36f89fe"><div class="ttname"><a href="a00315.html#ga939b0cff15cee3030f75c1b2e36f89fe">glm::float2x3</a></div><div class="ttdeci">mat&lt; 2, 3, float, highp &gt; float2x3</div><div class="ttdoc">single-qualifier floating-point matrix with 2 x 3 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00105">compatibility.hpp:105</a></div></div>
+<div class="ttc" id="a00315_html_gaa4cbe16a92cf3664376c7a2fc5126aa8"><div class="ttname"><a href="a00315.html#gaa4cbe16a92cf3664376c7a2fc5126aa8">glm::int3x2</a></div><div class="ttdeci">mat&lt; 3, 2, int, highp &gt; int3x2</div><div class="ttdoc">integer matrix with 3 x 2 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00091">compatibility.hpp:91</a></div></div>
+<div class="ttc" id="a00315_html_ga13c3200b82708f73faac6d7f09ec91a3"><div class="ttname"><a href="a00315.html#ga13c3200b82708f73faac6d7f09ec91a3">glm::bool4</a></div><div class="ttdeci">vec&lt; 4, bool, highp &gt; bool4</div><div class="ttdoc">boolean type with 4 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00069">compatibility.hpp:69</a></div></div>
+<div class="ttc" id="a00315_html_ga97a39dd9bc7d572810d80b8467cbffa1"><div class="ttname"><a href="a00315.html#ga97a39dd9bc7d572810d80b8467cbffa1">glm::int4x2</a></div><div class="ttdeci">mat&lt; 4, 2, int, highp &gt; int4x2</div><div class="ttdoc">integer matrix with 4 x 2 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00094">compatibility.hpp:94</a></div></div>
+<div class="ttc" id="a00315_html_ga7f895c936f0c29c8729afbbf22806090"><div class="ttname"><a href="a00315.html#ga7f895c936f0c29c8729afbbf22806090">glm::bool1x1</a></div><div class="ttdeci">bool bool1x1</div><div class="ttdoc">boolean matrix with 1 x 1 component. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00071">compatibility.hpp:71</a></div></div>
+<div class="ttc" id="a00315_html_ga356f8c3a7e7d6376d3d4b0a026407183"><div class="ttname"><a href="a00315.html#ga356f8c3a7e7d6376d3d4b0a026407183">glm::saturate</a></div><div class="ttdeci">GLM_FUNC_QUALIFIER vec&lt; 4, T, Q &gt; saturate(const vec&lt; 4, T, Q &gt; &amp;x)</div><div class="ttdoc">Returns clamp(x, 0, 1) for each component in x. (From GLM_GTX_compatibility) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00053">compatibility.hpp:53</a></div></div>
+<div class="ttc" id="a00315_html_ga99629f818737f342204071ef8296b2ed"><div class="ttname"><a href="a00315.html#ga99629f818737f342204071ef8296b2ed">glm::bool3</a></div><div class="ttdeci">vec&lt; 3, bool, highp &gt; bool3</div><div class="ttdoc">boolean type with 3 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00068">compatibility.hpp:68</a></div></div>
+<div class="ttc" id="a00241_html_ga7cd77683da6361e297c56443fc70806d"><div class="ttname"><a href="a00241.html#ga7cd77683da6361e297c56443fc70806d">glm::clamp</a></div><div class="ttdeci">GLM_FUNC_DECL GLM_CONSTEXPR genType clamp(genType x, genType minVal, genType maxVal)</div><div class="ttdoc">Returns min(max(x, minVal), maxVal) for each component in x using the floating-point values minVal an...</div></div>
+<div class="ttc" id="a00315_html_ga4e5ce477c15836b21e3c42daac68554d"><div class="ttname"><a href="a00315.html#ga4e5ce477c15836b21e3c42daac68554d">glm::int2x2</a></div><div class="ttdeci">mat&lt; 2, 2, int, highp &gt; int2x2</div><div class="ttdoc">integer matrix with 2 x 2 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00088">compatibility.hpp:88</a></div></div>
+<div class="ttc" id="a00315_html_gafe3a8fd56354caafe24bfe1b1e3ad22a"><div class="ttname"><a href="a00315.html#gafe3a8fd56354caafe24bfe1b1e3ad22a">glm::int2</a></div><div class="ttdeci">vec&lt; 2, int, highp &gt; int2</div><div class="ttdoc">integer vector with 2 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00083">compatibility.hpp:83</a></div></div>
+<div class="ttc" id="a00315_html_ga04dee1552424198b8f58b377c2ee00d8"><div class="ttname"><a href="a00315.html#ga04dee1552424198b8f58b377c2ee00d8">glm::int4x4</a></div><div class="ttdeci">mat&lt; 4, 4, int, highp &gt; int4x4</div><div class="ttdoc">integer matrix with 4 x 4 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00096">compatibility.hpp:96</a></div></div>
+<div class="ttc" id="a00315_html_gac7d7311f7e0fa8b6163d96dab033a755"><div class="ttname"><a href="a00315.html#gac7d7311f7e0fa8b6163d96dab033a755">glm::bool3x2</a></div><div class="ttdeci">mat&lt; 3, 2, bool, highp &gt; bool3x2</div><div class="ttdoc">boolean matrix with 3 x 2 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00075">compatibility.hpp:75</a></div></div>
+<div class="ttc" id="a00315_html_gafad66a02ccd360c86d6ab9ff9cfbc19c"><div class="ttname"><a href="a00315.html#gafad66a02ccd360c86d6ab9ff9cfbc19c">glm::double4x3</a></div><div class="ttdeci">mat&lt; 4, 3, double, highp &gt; double4x3</div><div class="ttdoc">double-qualifier floating-point matrix with 4 x 3 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00127">compatibility.hpp:127</a></div></div>
+<div class="ttc" id="a00315_html_gad0f5dc7f22c2065b1b06d57f1c0658fe"><div class="ttname"><a href="a00315.html#gad0f5dc7f22c2065b1b06d57f1c0658fe">glm::bool4x3</a></div><div class="ttdeci">mat&lt; 4, 3, bool, highp &gt; bool4x3</div><div class="ttdoc">boolean matrix with 4 x 3 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00079">compatibility.hpp:79</a></div></div>
+<div class="ttc" id="a00315_html_ga20b861a9b6e2a300323671c57a02525b"><div class="ttname"><a href="a00315.html#ga20b861a9b6e2a300323671c57a02525b">glm::double1</a></div><div class="ttdeci">double double1</div><div class="ttdoc">double-qualifier floating-point vector with 1 component. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00114">compatibility.hpp:114</a></div></div>
+<div class="ttc" id="a00315_html_ga3d8b9028a1053a44a98902cd1c389472"><div class="ttname"><a href="a00315.html#ga3d8b9028a1053a44a98902cd1c389472">glm::double3</a></div><div class="ttdeci">vec&lt; 3, double, highp &gt; double3</div><div class="ttdoc">double-qualifier floating-point vector with 3 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00116">compatibility.hpp:116</a></div></div>
+<div class="ttc" id="a00315_html_gaf92f58af24f35617518aeb3d4f63fda6"><div class="ttname"><a href="a00315.html#gaf92f58af24f35617518aeb3d4f63fda6">glm::double4</a></div><div class="ttdeci">vec&lt; 4, double, highp &gt; double4</div><div class="ttdoc">double-qualifier floating-point vector with 4 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00117">compatibility.hpp:117</a></div></div>
+<div class="ttc" id="a00315_html_ga15c9649286f0bf431bdf9b3509580048"><div class="ttname"><a href="a00315.html#ga15c9649286f0bf431bdf9b3509580048">glm::int3x3</a></div><div class="ttdeci">mat&lt; 3, 3, int, highp &gt; int3x3</div><div class="ttdoc">integer matrix with 3 x 3 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00092">compatibility.hpp:92</a></div></div>
+<div class="ttc" id="a00315_html_ga6c97b99aac3e302053ffb58aace9033c"><div class="ttname"><a href="a00315.html#ga6c97b99aac3e302053ffb58aace9033c">glm::bool3x3</a></div><div class="ttdeci">mat&lt; 3, 3, bool, highp &gt; bool3x3</div><div class="ttdoc">boolean matrix with 3 x 3 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00076">compatibility.hpp:76</a></div></div>
+<div class="ttc" id="a00315_html_gaa6c69f04ba95f3faedf95dae874de576"><div class="ttname"><a href="a00315.html#gaa6c69f04ba95f3faedf95dae874de576">glm::float3x2</a></div><div class="ttdeci">mat&lt; 3, 2, float, highp &gt; float3x2</div><div class="ttdoc">single-qualifier floating-point matrix with 3 x 2 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00107">compatibility.hpp:107</a></div></div>
+<div class="ttc" id="a00315_html_gaecdef18c819c205aeee9f94dc93de56a"><div class="ttname"><a href="a00315.html#gaecdef18c819c205aeee9f94dc93de56a">glm::int4</a></div><div class="ttdeci">vec&lt; 4, int, highp &gt; int4</div><div class="ttdoc">integer vector with 4 components. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00085">compatibility.hpp:85</a></div></div>
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+<div class="title">easing.hpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a class="el" href="a00318.html">GLM_GTX_easing</a>  
+<a href="#details">More...</a></p>
+
+<p><a href="a00023_source.html">Go to the source code of this file.</a></p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ga93cddcdb6347a44d5927cc2bf2570816"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga93cddcdb6347a44d5927cc2bf2570816"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga93cddcdb6347a44d5927cc2bf2570816">backEaseIn</a> (genType const &amp;a)</td></tr>
+<tr class="separator:ga93cddcdb6347a44d5927cc2bf2570816"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga33777c9dd98f61d9472f96aafdf2bd36"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga33777c9dd98f61d9472f96aafdf2bd36"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga33777c9dd98f61d9472f96aafdf2bd36">backEaseIn</a> (genType const &amp;a, genType const &amp;o)</td></tr>
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+<tr class="memitem:gace6d24722a2f6722b56398206eb810bb"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:gace6d24722a2f6722b56398206eb810bb"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#gace6d24722a2f6722b56398206eb810bb">backEaseInOut</a> (genType const &amp;a)</td></tr>
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+<tr class="memitem:ga68a7b760f2afdfab298d5cd6d7611fb1"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
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+<tr class="separator:ga68a7b760f2afdfab298d5cd6d7611fb1"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gabf25069fa906413c858fd46903d520b9"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:gabf25069fa906413c858fd46903d520b9"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#gabf25069fa906413c858fd46903d520b9">backEaseOut</a> (genType const &amp;a)</td></tr>
+<tr class="separator:gabf25069fa906413c858fd46903d520b9"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga640c1ac6fe9d277a197da69daf60ee4f"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga640c1ac6fe9d277a197da69daf60ee4f"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga640c1ac6fe9d277a197da69daf60ee4f">backEaseOut</a> (genType const &amp;a, genType const &amp;o)</td></tr>
+<tr class="separator:ga640c1ac6fe9d277a197da69daf60ee4f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaac30767f2e430b0c3fc859a4d59c7b5b"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:gaac30767f2e430b0c3fc859a4d59c7b5b"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#gaac30767f2e430b0c3fc859a4d59c7b5b">bounceEaseIn</a> (genType const &amp;a)</td></tr>
+<tr class="separator:gaac30767f2e430b0c3fc859a4d59c7b5b"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gadf9f38eff1e5f4c2fa5b629a25ae413e"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:gadf9f38eff1e5f4c2fa5b629a25ae413e"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#gadf9f38eff1e5f4c2fa5b629a25ae413e">bounceEaseInOut</a> (genType const &amp;a)</td></tr>
+<tr class="separator:gadf9f38eff1e5f4c2fa5b629a25ae413e"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga94007005ff0dcfa0749ebfa2aec540b2"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga94007005ff0dcfa0749ebfa2aec540b2"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga94007005ff0dcfa0749ebfa2aec540b2">bounceEaseOut</a> (genType const &amp;a)</td></tr>
+<tr class="separator:ga94007005ff0dcfa0749ebfa2aec540b2"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga34508d4b204a321ec26d6086aa047997"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga34508d4b204a321ec26d6086aa047997"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga34508d4b204a321ec26d6086aa047997">circularEaseIn</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:ga34508d4b204a321ec26d6086aa047997"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after shifted quadrant IV of unit circle.  <a href="a00318.html#ga34508d4b204a321ec26d6086aa047997">More...</a><br /></td></tr>
+<tr class="separator:ga34508d4b204a321ec26d6086aa047997"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga0c1027637a5b02d4bb3612aa12599d69"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga0c1027637a5b02d4bb3612aa12599d69"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga0c1027637a5b02d4bb3612aa12599d69">circularEaseInOut</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:ga0c1027637a5b02d4bb3612aa12599d69"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the piecewise circular function y = (1/2)(1 - sqrt(1 - 4x^2)) ; [0, 0.5) y = (1/2)(sqrt(-(2x - 3)*(2x - 1)) + 1) ; [0.5, 1].  <a href="a00318.html#ga0c1027637a5b02d4bb3612aa12599d69">More...</a><br /></td></tr>
+<tr class="separator:ga0c1027637a5b02d4bb3612aa12599d69"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga26fefde9ced9b72745fe21f1a3fe8da7"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga26fefde9ced9b72745fe21f1a3fe8da7"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga26fefde9ced9b72745fe21f1a3fe8da7">circularEaseOut</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:ga26fefde9ced9b72745fe21f1a3fe8da7"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after shifted quadrant II of unit circle.  <a href="a00318.html#ga26fefde9ced9b72745fe21f1a3fe8da7">More...</a><br /></td></tr>
+<tr class="separator:ga26fefde9ced9b72745fe21f1a3fe8da7"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaff52f746102b94864d105563ba8895ae"><td class="memTemplParams" colspan="2"><a class="anchor" id="gaff52f746102b94864d105563ba8895ae"></a>
+template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:gaff52f746102b94864d105563ba8895ae"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#gaff52f746102b94864d105563ba8895ae">cubicEaseIn</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:gaff52f746102b94864d105563ba8895ae"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the cubic y = x^3. <br /></td></tr>
+<tr class="separator:gaff52f746102b94864d105563ba8895ae"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga55134072b42d75452189321d4a2ad91c"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga55134072b42d75452189321d4a2ad91c"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga55134072b42d75452189321d4a2ad91c">cubicEaseInOut</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:ga55134072b42d75452189321d4a2ad91c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the piecewise cubic y = (1/2)((2x)^3) ; [0, 0.5) y = (1/2)((2x-2)^3 + 2) ; [0.5, 1].  <a href="a00318.html#ga55134072b42d75452189321d4a2ad91c">More...</a><br /></td></tr>
+<tr class="separator:ga55134072b42d75452189321d4a2ad91c"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga40d746385d8bcc5973f5bc6a2340ca91"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga40d746385d8bcc5973f5bc6a2340ca91"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga40d746385d8bcc5973f5bc6a2340ca91">cubicEaseOut</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:ga40d746385d8bcc5973f5bc6a2340ca91"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the cubic y = (x - 1)^3 + 1.  <a href="a00318.html#ga40d746385d8bcc5973f5bc6a2340ca91">More...</a><br /></td></tr>
+<tr class="separator:ga40d746385d8bcc5973f5bc6a2340ca91"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga230918eccee4e113d10ec5b8cdc58695"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga230918eccee4e113d10ec5b8cdc58695"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga230918eccee4e113d10ec5b8cdc58695">elasticEaseIn</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:ga230918eccee4e113d10ec5b8cdc58695"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the damped sine wave y = sin(13pi/2*x)*pow(2, 10 * (x - 1))  <a href="a00318.html#ga230918eccee4e113d10ec5b8cdc58695">More...</a><br /></td></tr>
+<tr class="separator:ga230918eccee4e113d10ec5b8cdc58695"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga2db4ac8959559b11b4029e54812908d6"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga2db4ac8959559b11b4029e54812908d6"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga2db4ac8959559b11b4029e54812908d6">elasticEaseInOut</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:ga2db4ac8959559b11b4029e54812908d6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the piecewise exponentially-damped sine wave: y = (1/2)*sin(13pi/2*(2*x))*pow(2, 10 * ((2*x) - 1)) ; [0,0.5) y = (1/2)*(sin(-13pi/2*((2x-1)+1))*pow(2,-10(2*x-1)) + 2) ; [0.5, 1].  <a href="a00318.html#ga2db4ac8959559b11b4029e54812908d6">More...</a><br /></td></tr>
+<tr class="separator:ga2db4ac8959559b11b4029e54812908d6"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gace9c9d1bdf88bf2ab1e7cdefa54c7365"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:gace9c9d1bdf88bf2ab1e7cdefa54c7365"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#gace9c9d1bdf88bf2ab1e7cdefa54c7365">elasticEaseOut</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:gace9c9d1bdf88bf2ab1e7cdefa54c7365"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the damped sine wave y = sin(-13pi/2*(x + 1))*pow(2, -10x) + 1.  <a href="a00318.html#gace9c9d1bdf88bf2ab1e7cdefa54c7365">More...</a><br /></td></tr>
+<tr class="separator:gace9c9d1bdf88bf2ab1e7cdefa54c7365"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga7f24ee9219ab4c84dc8de24be84c1e3c"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga7f24ee9219ab4c84dc8de24be84c1e3c"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga7f24ee9219ab4c84dc8de24be84c1e3c">exponentialEaseIn</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:ga7f24ee9219ab4c84dc8de24be84c1e3c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the exponential function y = 2^(10(x - 1))  <a href="a00318.html#ga7f24ee9219ab4c84dc8de24be84c1e3c">More...</a><br /></td></tr>
+<tr class="separator:ga7f24ee9219ab4c84dc8de24be84c1e3c"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga232fb6dc093c5ce94bee105ff2947501"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga232fb6dc093c5ce94bee105ff2947501"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga232fb6dc093c5ce94bee105ff2947501">exponentialEaseInOut</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:ga232fb6dc093c5ce94bee105ff2947501"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the piecewise exponential y = (1/2)2^(10(2x - 1)) ; [0,0.5) y = -(1/2)*2^(-10(2x - 1))) + 1 ; [0.5,1].  <a href="a00318.html#ga232fb6dc093c5ce94bee105ff2947501">More...</a><br /></td></tr>
+<tr class="separator:ga232fb6dc093c5ce94bee105ff2947501"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga517f2bcfd15bc2c25c466ae50808efc3"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga517f2bcfd15bc2c25c466ae50808efc3"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga517f2bcfd15bc2c25c466ae50808efc3">exponentialEaseOut</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:ga517f2bcfd15bc2c25c466ae50808efc3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the exponential function y = -2^(-10x) + 1.  <a href="a00318.html#ga517f2bcfd15bc2c25c466ae50808efc3">More...</a><br /></td></tr>
+<tr class="separator:ga517f2bcfd15bc2c25c466ae50808efc3"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga290c3e47cb0a49f2e8abe90b1872b649"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga290c3e47cb0a49f2e8abe90b1872b649"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga290c3e47cb0a49f2e8abe90b1872b649">linearInterpolation</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:ga290c3e47cb0a49f2e8abe90b1872b649"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the line y = x.  <a href="a00318.html#ga290c3e47cb0a49f2e8abe90b1872b649">More...</a><br /></td></tr>
+<tr class="separator:ga290c3e47cb0a49f2e8abe90b1872b649"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaf42089d35855695132d217cd902304a0"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:gaf42089d35855695132d217cd902304a0"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#gaf42089d35855695132d217cd902304a0">quadraticEaseIn</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:gaf42089d35855695132d217cd902304a0"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the parabola y = x^2.  <a href="a00318.html#gaf42089d35855695132d217cd902304a0">More...</a><br /></td></tr>
+<tr class="separator:gaf42089d35855695132d217cd902304a0"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga03e8fc2d7945a4e63ee33b2159c14cea"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga03e8fc2d7945a4e63ee33b2159c14cea"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga03e8fc2d7945a4e63ee33b2159c14cea">quadraticEaseInOut</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:ga03e8fc2d7945a4e63ee33b2159c14cea"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the piecewise quadratic y = (1/2)((2x)^2) ; [0, 0.5) y = -(1/2)((2x-1)*(2x-3) - 1) ; [0.5, 1].  <a href="a00318.html#ga03e8fc2d7945a4e63ee33b2159c14cea">More...</a><br /></td></tr>
+<tr class="separator:ga03e8fc2d7945a4e63ee33b2159c14cea"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga283717bc2d937547ad34ec0472234ee3"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga283717bc2d937547ad34ec0472234ee3"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga283717bc2d937547ad34ec0472234ee3">quadraticEaseOut</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:ga283717bc2d937547ad34ec0472234ee3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the parabola y = -x^2 + 2x.  <a href="a00318.html#ga283717bc2d937547ad34ec0472234ee3">More...</a><br /></td></tr>
+<tr class="separator:ga283717bc2d937547ad34ec0472234ee3"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga808b41f14514f47dad5dcc69eb924afd"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga808b41f14514f47dad5dcc69eb924afd"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga808b41f14514f47dad5dcc69eb924afd">quarticEaseIn</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:ga808b41f14514f47dad5dcc69eb924afd"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the quartic x^4.  <a href="a00318.html#ga808b41f14514f47dad5dcc69eb924afd">More...</a><br /></td></tr>
+<tr class="separator:ga808b41f14514f47dad5dcc69eb924afd"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga6d000f852de12b197e154f234b20c505"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga6d000f852de12b197e154f234b20c505"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga6d000f852de12b197e154f234b20c505">quarticEaseInOut</a> (genType const &amp;a)</td></tr>
+<tr class="memdesc:ga6d000f852de12b197e154f234b20c505"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the piecewise quartic y = (1/2)((2x)^4) ; [0, 0.5) y = -(1/2)((2x-2)^4 - 2) ; [0.5, 1].  <a href="a00318.html#ga6d000f852de12b197e154f234b20c505">More...</a><br /></td></tr>
+<tr class="separator:ga6d000f852de12b197e154f234b20c505"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga4dfb33fa7664aa888eb647999d329b98"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
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+<tr class="separator:gaa46e3d5fbf7a15caa28eff9ef192d7c7"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="memdesc:gab3e454f883afc1606ef91363881bf5a3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after quarter-cycle of sine wave (different phase)  <a href="a00318.html#gab3e454f883afc1606ef91363881bf5a3">More...</a><br /></td></tr>
+<tr class="separator:gab3e454f883afc1606ef91363881bf5a3"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a class="el" href="a00318.html">GLM_GTX_easing</a> </p>
+<dl class="section author"><dt>Author</dt><dd>Robert Chisholm</dd></dl>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00280.html" title="Features that implement in C++ the GLSL specification as closely as possible. ">Core features</a> (dependence) </dd></dl>
+
+<p>Definition in file <a class="el" href="a00023_source.html">easing.hpp</a>.</p>
+</div></div><!-- contents -->
+<!-- start footer part -->
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+Generated by &#160;<a href="http://www.doxygen.org/index.html">
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+<li class="navelem"><a class="el" href="dir_3a581ba30d25676e4b797b1f96d53b45.html">F:</a></li><li class="navelem"><a class="el" href="dir_9e5fe034a00e89334fd5186c3e7db156.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_d9496f0844b48bc7e53b5af8c99b9ab2.html">Source</a></li><li class="navelem"><a class="el" href="dir_a8bee7be44182a33f3820393ae0b105d.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_44e5e654415abd9ca6fdeaddaff8565e.html">glm</a></li><li class="navelem"><a class="el" href="dir_cef2d71d502cb69a9252bca2297d9549.html">glm</a></li><li class="navelem"><a class="el" href="dir_f35778ec600a1b9bbc4524e62e226aa2.html">gtx</a></li>  </ul>
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+<div class="title">euler_angles.hpp</div>  </div>
+</div><!--header-->
+<div class="contents">
+<a href="a00025.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;</div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#pragma once</span></div>
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+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment">// Dependency:</span></div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="preprocessor">#include &quot;../glm.hpp&quot;</span></div>
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+<div class="ttc" id="a00319_html_ga64036577ee17a2d24be0dbc05881d4e2"><div class="ttname"><a href="a00319.html#ga64036577ee17a2d24be0dbc05881d4e2">glm::eulerAngleXY</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleXY(T const &amp;angleX, T const &amp;angleY)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (X * Y). </div></div>
+<div class="ttc" id="a00319_html_ga5e5e40abc27630749b42b3327c76d6e4"><div class="ttname"><a href="a00319.html#ga5e5e40abc27630749b42b3327c76d6e4">glm::eulerAngleYZY</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleYZY(T const &amp;t1, T const &amp;t2, T const &amp;t3)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (Y * Z * Y). </div></div>
+<div class="ttc" id="a00319_html_gaf0937518e63037335a0e8358b6f053c5"><div class="ttname"><a href="a00319.html#gaf0937518e63037335a0e8358b6f053c5">glm::extractEulerAngleYXZ</a></div><div class="ttdeci">GLM_FUNC_DECL void extractEulerAngleYXZ(mat&lt; 4, 4, T, defaultp &gt; const &amp;M, T &amp;t1, T &amp;t2, T &amp;t3)</div><div class="ttdoc">Extracts the (Y * X * Z) Euler angles from the rotation matrix M. </div></div>
+<div class="ttc" id="a00319_html_ga1975e0f0e9bed7f716dc9946da2ab645"><div class="ttname"><a href="a00319.html#ga1975e0f0e9bed7f716dc9946da2ab645">glm::eulerAngleXYZ</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleXYZ(T const &amp;t1, T const &amp;t2, T const &amp;t3)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (X * Y * Z). </div></div>
+<div class="ttc" id="a00319_html_ga996dce12a60d8a674ba6737a535fa910"><div class="ttname"><a href="a00319.html#ga996dce12a60d8a674ba6737a535fa910">glm::eulerAngleXZY</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleXZY(T const &amp;t1, T const &amp;t2, T const &amp;t3)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (X * Z * Y). </div></div>
+<div class="ttc" id="a00319_html_gae8b397348201c42667be983ba3f344df"><div class="ttname"><a href="a00319.html#gae8b397348201c42667be983ba3f344df">glm::derivedEulerAngleZ</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; derivedEulerAngleZ(T const &amp;angleZ, T const &amp;angularVelocityZ)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous derived matrix from the rotation matrix about Z-axis. </div></div>
+<div class="ttc" id="a00319_html_ga4f57e6dd25c3cffbbd4daa6ef3f4486d"><div class="ttname"><a href="a00319.html#ga4f57e6dd25c3cffbbd4daa6ef3f4486d">glm::eulerAngleYX</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleYX(T const &amp;angleY, T const &amp;angleX)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (Y * X). </div></div>
+<div class="ttc" id="a00319_html_gab84bf4746805fd69b8ecbb230e3974c5"><div class="ttname"><a href="a00319.html#gab84bf4746805fd69b8ecbb230e3974c5">glm::eulerAngleY</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleY(T const &amp;angleY)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from an euler angle Y. </div></div>
+<div class="ttc" id="a00257_html_ga8aa248b31d5ade470c87304df5eb7bd8"><div class="ttname"><a href="a00257.html#ga8aa248b31d5ade470c87304df5eb7bd8">glm::angle</a></div><div class="ttdeci">GLM_FUNC_DECL T angle(qua&lt; T, Q &gt; const &amp;x)</div><div class="ttdoc">Returns the quaternion rotation angle. </div></div>
+<div class="ttc" id="a00319_html_gafdfa880a64b565223550c2d3938b1aeb"><div class="ttname"><a href="a00319.html#gafdfa880a64b565223550c2d3938b1aeb">glm::extractEulerAngleZYZ</a></div><div class="ttdeci">GLM_FUNC_DECL void extractEulerAngleZYZ(mat&lt; 4, 4, T, defaultp &gt; const &amp;M, T &amp;t1, T &amp;t2, T &amp;t3)</div><div class="ttdoc">Extracts the (Z * Y * Z) Euler angles from the rotation matrix M. </div></div>
+<div class="ttc" id="a00319_html_ga994b8186b3b80d91cf90bc403164692f"><div class="ttname"><a href="a00319.html#ga994b8186b3b80d91cf90bc403164692f">glm::derivedEulerAngleX</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; derivedEulerAngleX(T const &amp;angleX, T const &amp;angularVelocityX)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous derived matrix from the rotation matrix about X-axis. </div></div>
+<div class="ttc" id="a00319_html_gaf1077a72171d0f3b08f022ab5ff88af7"><div class="ttname"><a href="a00319.html#gaf1077a72171d0f3b08f022ab5ff88af7">glm::extractEulerAngleXYX</a></div><div class="ttdeci">GLM_FUNC_DECL void extractEulerAngleXYX(mat&lt; 4, 4, T, defaultp &gt; const &amp;M, T &amp;t1, T &amp;t2, T &amp;t3)</div><div class="ttdoc">Extracts the (X * Y * X) Euler angles from the rotation matrix M. </div></div>
+<div class="ttc" id="a00319_html_gab4505c54d2dd654df4569fd1f04c43aa"><div class="ttname"><a href="a00319.html#gab4505c54d2dd654df4569fd1f04c43aa">glm::eulerAngleZXY</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleZXY(T const &amp;t1, T const &amp;t2, T const &amp;t3)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (Z * X * Y). </div></div>
+<div class="ttc" id="a00299_html_ga0cc5ad970d0b00829b139fe0fe5a1e13"><div class="ttname"><a href="a00299.html#ga0cc5ad970d0b00829b139fe0fe5a1e13">glm::roll</a></div><div class="ttdeci">GLM_FUNC_DECL T roll(qua&lt; T, Q &gt; const &amp;x)</div><div class="ttdoc">Returns roll value of euler angles expressed in radians. </div></div>
+<div class="ttc" id="a00319_html_gafba6282e4ed3ff8b5c75331abfba3489"><div class="ttname"><a href="a00319.html#gafba6282e4ed3ff8b5c75331abfba3489">glm::eulerAngleX</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleX(T const &amp;angleX)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from an euler angle X. </div></div>
+<div class="ttc" id="a00319_html_gae16738a9f1887cf4e4db6a124637608d"><div class="ttname"><a href="a00319.html#gae16738a9f1887cf4e4db6a124637608d">glm::orientate2</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 2, 2, T, defaultp &gt; orientate2(T const &amp;angle)</div><div class="ttdoc">Creates a 2D 2 * 2 rotation matrix from an euler angle. </div></div>
+<div class="ttc" id="a00319_html_ga29bd0787a28a6648159c0d6e69706066"><div class="ttname"><a href="a00319.html#ga29bd0787a28a6648159c0d6e69706066">glm::eulerAngleXYX</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleXYX(T const &amp;t1, T const &amp;t2, T const &amp;t3)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (X * Y * X). </div></div>
+<div class="ttc" id="a00319_html_gab8ba99a9814f6d9edf417b6c6d5b0c10"><div class="ttname"><a href="a00319.html#gab8ba99a9814f6d9edf417b6c6d5b0c10">glm::eulerAngleYXZ</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleYXZ(T const &amp;yaw, T const &amp;pitch, T const &amp;roll)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (Y * X * Z). </div></div>
+<div class="ttc" id="a00319_html_gacf0bc6c031f25fa3ee0055b62c8260d0"><div class="ttname"><a href="a00319.html#gacf0bc6c031f25fa3ee0055b62c8260d0">glm::extractEulerAngleXZX</a></div><div class="ttdeci">GLM_FUNC_DECL void extractEulerAngleXZX(mat&lt; 4, 4, T, defaultp &gt; const &amp;M, T &amp;t1, T &amp;t2, T &amp;t3)</div><div class="ttdoc">Extracts the (X * Z * X) Euler angles from the rotation matrix M. </div></div>
+<div class="ttc" id="a00299_html_ga8da38cdfdc452dafa660c2f46506bad5"><div class="ttname"><a href="a00299.html#ga8da38cdfdc452dafa660c2f46506bad5">glm::yaw</a></div><div class="ttdeci">GLM_FUNC_DECL T yaw(qua&lt; T, Q &gt; const &amp;x)</div><div class="ttdoc">Returns yaw value of euler angles expressed in radians. </div></div>
+<div class="ttc" id="a00319_html_gaab8868556361a190db94374e9983ed39"><div class="ttname"><a href="a00319.html#gaab8868556361a190db94374e9983ed39">glm::extractEulerAngleYXY</a></div><div class="ttdeci">GLM_FUNC_DECL void extractEulerAngleYXY(mat&lt; 4, 4, T, defaultp &gt; const &amp;M, T &amp;t1, T &amp;t2, T &amp;t3)</div><div class="ttdoc">Extracts the (Y * X * Y) Euler angles from the rotation matrix M. </div></div>
+<div class="ttc" id="a00319_html_ga81fbbca2ba0c778b9662d5355b4e2363"><div class="ttname"><a href="a00319.html#ga81fbbca2ba0c778b9662d5355b4e2363">glm::extractEulerAngleZXY</a></div><div class="ttdeci">GLM_FUNC_DECL void extractEulerAngleZXY(mat&lt; 4, 4, T, defaultp &gt; const &amp;M, T &amp;t1, T &amp;t2, T &amp;t3)</div><div class="ttdoc">Extracts the (Z * X * Y) Euler angles from the rotation matrix M. </div></div>
+<div class="ttc" id="a00319_html_gabe5a65d8eb1cd873c8de121cce1a15ed"><div class="ttname"><a href="a00319.html#gabe5a65d8eb1cd873c8de121cce1a15ed">glm::extractEulerAngleXZY</a></div><div class="ttdeci">GLM_FUNC_DECL void extractEulerAngleXZY(mat&lt; 4, 4, T, defaultp &gt; const &amp;M, T &amp;t1, T &amp;t2, T &amp;t3)</div><div class="ttdoc">Extracts the (X * Z * Y) Euler angles from the rotation matrix M. </div></div>
+<div class="ttc" id="a00319_html_ga9049b78466796c0de2971756e25b93d3"><div class="ttname"><a href="a00319.html#ga9049b78466796c0de2971756e25b93d3">glm::extractEulerAngleYZX</a></div><div class="ttdeci">GLM_FUNC_DECL void extractEulerAngleYZX(mat&lt; 4, 4, T, defaultp &gt; const &amp;M, T &amp;t1, T &amp;t2, T &amp;t3)</div><div class="ttdoc">Extracts the (Y * Z * X) Euler angles from the rotation matrix M. </div></div>
+<div class="ttc" id="a00319_html_ga60171c79a17aec85d7891ae1d1533ec9"><div class="ttname"><a href="a00319.html#ga60171c79a17aec85d7891ae1d1533ec9">glm::eulerAngleXZX</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleXZX(T const &amp;t1, T const &amp;t2, T const &amp;t3)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (X * Z * X). </div></div>
+<div class="ttc" id="a00319_html_ga2e61f1e39069c47530acab9167852dd6"><div class="ttname"><a href="a00319.html#ga2e61f1e39069c47530acab9167852dd6">glm::eulerAngleZYX</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleZYX(T const &amp;t1, T const &amp;t2, T const &amp;t3)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (Z * Y * X). </div></div>
+<div class="ttc" id="a00319_html_ga4a044653f71a4ecec68e0b623382b48a"><div class="ttname"><a href="a00319.html#ga4a044653f71a4ecec68e0b623382b48a">glm::orientate4</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, Q &gt; orientate4(vec&lt; 3, T, Q &gt; const &amp;angles)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (Y * X * Z). </div></div>
+<div class="ttc" id="a00319_html_ga2d6c11a4abfa60c565483cee2d3f7665"><div class="ttname"><a href="a00319.html#ga2d6c11a4abfa60c565483cee2d3f7665">glm::extractEulerAngleZYX</a></div><div class="ttdeci">GLM_FUNC_DECL void extractEulerAngleZYX(mat&lt; 4, 4, T, defaultp &gt; const &amp;M, T &amp;t1, T &amp;t2, T &amp;t3)</div><div class="ttdoc">Extracts the (Z * Y * X) Euler angles from the rotation matrix M. </div></div>
+<div class="ttc" id="a00319_html_ga5b3935248bb6c3ec6b0d9297d406e251"><div class="ttname"><a href="a00319.html#ga5b3935248bb6c3ec6b0d9297d406e251">glm::eulerAngleZ</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleZ(T const &amp;angleZ)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from an euler angle Z. </div></div>
+<div class="ttc" id="a00319_html_ga750fba9894117f87bcc529d7349d11de"><div class="ttname"><a href="a00319.html#ga750fba9894117f87bcc529d7349d11de">glm::eulerAngleYXY</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleYXY(T const &amp;t1, T const &amp;t2, T const &amp;t3)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (Y * X * Y). </div></div>
+<div class="ttc" id="a00319_html_ga11dad972c109e4bf8694c915017c44a6"><div class="ttname"><a href="a00319.html#ga11dad972c109e4bf8694c915017c44a6">glm::extractEulerAngleYZY</a></div><div class="ttdeci">GLM_FUNC_DECL void extractEulerAngleYZY(mat&lt; 4, 4, T, defaultp &gt; const &amp;M, T &amp;t1, T &amp;t2, T &amp;t3)</div><div class="ttdoc">Extracts the (Y * Z * Y) Euler angles from the rotation matrix M. </div></div>
+<div class="ttc" id="a00319_html_gae6aa26ccb020d281b449619e419a609e"><div class="ttname"><a href="a00319.html#gae6aa26ccb020d281b449619e419a609e">glm::yawPitchRoll</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; yawPitchRoll(T const &amp;yaw, T const &amp;pitch, T const &amp;roll)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (Y * X * Z). </div></div>
+<div class="ttc" id="a00319_html_gaa39bd323c65c2fc0a1508be33a237ce9"><div class="ttname"><a href="a00319.html#gaa39bd323c65c2fc0a1508be33a237ce9">glm::eulerAngleXZ</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleXZ(T const &amp;angleX, T const &amp;angleZ)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (X * Z). </div></div>
+<div class="ttc" id="a00319_html_gacea701562f778c1da4d3a0a1cf091000"><div class="ttname"><a href="a00319.html#gacea701562f778c1da4d3a0a1cf091000">glm::extractEulerAngleXYZ</a></div><div class="ttdeci">GLM_FUNC_DECL void extractEulerAngleXYZ(mat&lt; 4, 4, T, defaultp &gt; const &amp;M, T &amp;t1, T &amp;t2, T &amp;t3)</div><div class="ttdoc">Extracts the (X * Y * Z) Euler angles from the rotation matrix M. </div></div>
+<div class="ttc" id="a00319_html_ga178f966c52b01e4d65e31ebd007e3247"><div class="ttname"><a href="a00319.html#ga178f966c52b01e4d65e31ebd007e3247">glm::eulerAngleZXZ</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleZXZ(T const &amp;t1, T const &amp;t2, T const &amp;t3)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (Z * X * Z). </div></div>
+<div class="ttc" id="a00319_html_ga08bef16357b8f9b3051b3dcaec4b7848"><div class="ttname"><a href="a00319.html#ga08bef16357b8f9b3051b3dcaec4b7848">glm::eulerAngleYZX</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleYZX(T const &amp;t1, T const &amp;t2, T const &amp;t3)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (Y * Z * X). </div></div>
+<div class="ttc" id="a00319_html_ga400b2bd5984999efab663f3a68e1d020"><div class="ttname"><a href="a00319.html#ga400b2bd5984999efab663f3a68e1d020">glm::eulerAngleZY</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleZY(T const &amp;angleZ, T const &amp;angleY)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (Z * Y). </div></div>
+<div class="ttc" id="a00319_html_gacd795f1dbecaf74974f9c76bbcca6830"><div class="ttname"><a href="a00319.html#gacd795f1dbecaf74974f9c76bbcca6830">glm::eulerAngleZYZ</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleZYZ(T const &amp;t1, T const &amp;t2, T const &amp;t3)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (Z * Y * Z). </div></div>
+<div class="ttc" id="a00319_html_ga220379e10ac8cca55e275f0c9018fed9"><div class="ttname"><a href="a00319.html#ga220379e10ac8cca55e275f0c9018fed9">glm::eulerAngleYZ</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleYZ(T const &amp;angleY, T const &amp;angleZ)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (Y * Z). </div></div>
+<div class="ttc" id="a00319_html_ga7238c8e15c7720e3ca6a45ab151eeabb"><div class="ttname"><a href="a00319.html#ga7238c8e15c7720e3ca6a45ab151eeabb">glm::orientate3</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 3, 3, T, Q &gt; orientate3(vec&lt; 3, T, Q &gt; const &amp;angles)</div><div class="ttdoc">Creates a 3D 3 * 3 rotation matrix from euler angles (Y * X * Z). </div></div>
+<div class="ttc" id="a00319_html_ga59359fef9bad92afaca55e193f91e702"><div class="ttname"><a href="a00319.html#ga59359fef9bad92afaca55e193f91e702">glm::extractEulerAngleZXZ</a></div><div class="ttdeci">GLM_FUNC_DECL void extractEulerAngleZXZ(mat&lt; 4, 4, T, defaultp &gt; const &amp;M, T &amp;t1, T &amp;t2, T &amp;t3)</div><div class="ttdoc">Extracts the (Z * X * Z) Euler angles from the rotation matrix M. </div></div>
+<div class="ttc" id="a00319_html_ga0a4c56ecce7abcb69508ebe6313e9d10"><div class="ttname"><a href="a00319.html#ga0a4c56ecce7abcb69508ebe6313e9d10">glm::derivedEulerAngleY</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; derivedEulerAngleY(T const &amp;angleY, T const &amp;angularVelocityY)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous derived matrix from the rotation matrix about Y-axis. </div></div>
+<div class="ttc" id="a00299_html_ga7603e81477b46ddb448896909bc04928"><div class="ttname"><a href="a00299.html#ga7603e81477b46ddb448896909bc04928">glm::pitch</a></div><div class="ttdeci">GLM_FUNC_DECL T pitch(qua&lt; T, Q &gt; const &amp;x)</div><div class="ttdoc">Returns pitch value of euler angles expressed in radians. </div></div>
+<div class="ttc" id="a00319_html_ga483903115cd4059228961046a28d69b5"><div class="ttname"><a href="a00319.html#ga483903115cd4059228961046a28d69b5">glm::eulerAngleZX</a></div><div class="ttdeci">GLM_FUNC_DECL mat&lt; 4, 4, T, defaultp &gt; eulerAngleZX(T const &amp;angle, T const &amp;angleX)</div><div class="ttdoc">Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (Z * X). </div></div>
+<div class="ttc" id="a00236_html"><div class="ttname"><a href="a00236.html">glm</a></div><div class="ttdef"><b>Definition:</b> <a href="a00015_source.html#l00020">common.hpp:20</a></div></div>
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+<a href="a00030.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;</div>
+<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#pragma once</span></div>
+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;</div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment">// Dependencies</span></div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="preprocessor">#include &quot;../detail/setup.hpp&quot;</span></div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="preprocessor">#include &quot;../detail/qualifier.hpp&quot;</span></div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;</div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="preprocessor">#if GLM_MESSAGES == GLM_ENABLE &amp;&amp; !defined(GLM_EXT_INCLUDED)</span></div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="preprocessor">#       ifndef GLM_ENABLE_EXPERIMENTAL</span></div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="preprocessor">#               pragma message(&quot;GLM: GLM_GTX_exterior_product is an experimental extension and may change in the future. Use #define GLM_ENABLE_EXPERIMENTAL before including it, if you really want to use it.&quot;)</span></div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="preprocessor">#       else</span></div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="preprocessor">#               pragma message(&quot;GLM: GLM_GTX_exterior_product extension included&quot;)</span></div>
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+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="keyword">namespace </span><a class="code" href="a00236.html">glm</a></div>
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+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;</div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt;</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;        GLM_FUNC_DECL T <a class="code" href="a00322.html#gac36e72b934ea6a9dd313772d7e78fa93">cross</a>(vec&lt;2, T, Q&gt; <span class="keyword">const</span>&amp; v, vec&lt;2, T, Q&gt; <span class="keyword">const</span>&amp; u);</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;} <span class="comment">//namespace glm</span></div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;</div>
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+<div class="ttc" id="a00322_html_gac36e72b934ea6a9dd313772d7e78fa93"><div class="ttname"><a href="a00322.html#gac36e72b934ea6a9dd313772d7e78fa93">glm::cross</a></div><div class="ttdeci">GLM_FUNC_DECL T cross(vec&lt; 2, T, Q &gt; const &amp;v, vec&lt; 2, T, Q &gt; const &amp;u)</div><div class="ttdoc">Returns the cross product of x and y. </div></div>
+<div class="ttc" id="a00236_html"><div class="ttname"><a href="a00236.html">glm</a></div><div class="ttdef"><b>Definition:</b> <a href="a00015_source.html#l00020">common.hpp:20</a></div></div>
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+Functions</h2></td></tr>
+<tr class="memitem:ga849241df1e55129b8ce9476200307419"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
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+<tr class="separator:ga849241df1e55129b8ce9476200307419"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="memdesc:gaaecb1e93de4cbe0758b882812d4da294"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return a color from a radial gradient.  <a href="a00327.html#gaaecb1e93de4cbe0758b882812d4da294">More...</a><br /></td></tr>
+<tr class="separator:gaaecb1e93de4cbe0758b882812d4da294"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a class="el" href="a00327.html">GLM_GTX_gradient_paint</a> </p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00280.html" title="Features that implement in C++ the GLSL specification as closely as possible. ">Core features</a> (dependence) </dd>
+<dd>
+<a class="el" href="a00347.html" title="Include <glm/gtx/optimum_pow.hpp> to use the features of this extension. ">GLM_GTX_optimum_pow</a> (dependence) </dd></dl>
+
+<p>Definition in file <a class="el" href="a00038_source.html">gradient_paint.hpp</a>.</p>
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+<div class="title">handed_coordinate_space.hpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a class="el" href="a00328.html">GLM_GTX_handed_coordinate_space</a>  
+<a href="#details">More...</a></p>
+
+<p><a href="a00039_source.html">Go to the source code of this file.</a></p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ga6f1bad193b9a3b048543d1935cf04dd3"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga6f1bad193b9a3b048543d1935cf04dd3"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL bool&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00328.html#ga6f1bad193b9a3b048543d1935cf04dd3">leftHanded</a> (vec&lt; 3, T, Q &gt; const &amp;tangent, vec&lt; 3, T, Q &gt; const &amp;binormal, vec&lt; 3, T, Q &gt; const &amp;normal)</td></tr>
+<tr class="memdesc:ga6f1bad193b9a3b048543d1935cf04dd3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return if a trihedron left handed or not.  <a href="a00328.html#ga6f1bad193b9a3b048543d1935cf04dd3">More...</a><br /></td></tr>
+<tr class="separator:ga6f1bad193b9a3b048543d1935cf04dd3"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga99386a5ab5491871b947076e21699cc8"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:ga99386a5ab5491871b947076e21699cc8"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return if a trihedron right handed or not.  <a href="a00328.html#ga99386a5ab5491871b947076e21699cc8">More...</a><br /></td></tr>
+<tr class="separator:ga99386a5ab5491871b947076e21699cc8"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a class="el" href="a00328.html">GLM_GTX_handed_coordinate_space</a> </p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00280.html" title="Features that implement in C++ the GLSL specification as closely as possible. ">Core features</a> (dependence) </dd></dl>
+
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+<a href="a00039.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;</div>
+<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#pragma once</span></div>
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+<li class="navelem"><a class="el" href="dir_3a581ba30d25676e4b797b1f96d53b45.html">F:</a></li><li class="navelem"><a class="el" href="dir_9e5fe034a00e89334fd5186c3e7db156.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_d9496f0844b48bc7e53b5af8c99b9ab2.html">Source</a></li><li class="navelem"><a class="el" href="dir_a8bee7be44182a33f3820393ae0b105d.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_44e5e654415abd9ca6fdeaddaff8565e.html">glm</a></li><li class="navelem"><a class="el" href="dir_cef2d71d502cb69a9252bca2297d9549.html">glm</a></li><li class="navelem"><a class="el" href="dir_f35778ec600a1b9bbc4524e62e226aa2.html">gtx</a></li>  </ul>
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+<div class="title">hash.hpp</div>  </div>
+</div><!--header-->
+<div class="contents">
+<a href="a00040.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;</div>
+<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#pragma once</span></div>
+<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;</div>
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+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#       ifndef GLM_ENABLE_EXPERIMENTAL</span></div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="preprocessor">#               pragma message(&quot;GLM: GLM_GTX_hash is an experimental extension and may change in the future. Use #define GLM_ENABLE_EXPERIMENTAL before including it, if you really want to use it.&quot;)</span></div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="preprocessor">#       else</span></div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="preprocessor">#               pragma message(&quot;GLM: GLM_GTX_hash extension included&quot;)</span></div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="preprocessor">#       endif</span></div>
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+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="preprocessor">#include &quot;../vec2.hpp&quot;</span></div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="preprocessor">#include &quot;../vec3.hpp&quot;</span></div>
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+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;</div>
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+
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+<a href="#details">More...</a></p>
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+<p><a href="a00058_source.html">Go to the source code of this file.</a></p>
+<table class="memberdecls">
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+Functions</h2></td></tr>
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+<tr class="memdesc:ga96022eb0d3fae39d89fc7a954e59b374"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get a specific column of a matrix.  <a href="a00293.html#ga96022eb0d3fae39d89fc7a954e59b374">More...</a><br /></td></tr>
+<tr class="separator:ga96022eb0d3fae39d89fc7a954e59b374"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="memdesc:ga9e757377523890e8b80c5843dbe4dd15"><td class="mdescLeft">&#160;</td><td class="mdescRight">Set a specific column to a matrix.  <a href="a00293.html#ga9e757377523890e8b80c5843dbe4dd15">More...</a><br /></td></tr>
+<tr class="separator:ga9e757377523890e8b80c5843dbe4dd15"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga259e5ebd0f31ec3f83440f8cae7f5dba"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga259e5ebd0f31ec3f83440f8cae7f5dba"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType::row_type&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00293.html#ga259e5ebd0f31ec3f83440f8cae7f5dba">row</a> (genType const &amp;m, length_t index)</td></tr>
+<tr class="memdesc:ga259e5ebd0f31ec3f83440f8cae7f5dba"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get a specific row of a matrix.  <a href="a00293.html#ga259e5ebd0f31ec3f83440f8cae7f5dba">More...</a><br /></td></tr>
+<tr class="separator:ga259e5ebd0f31ec3f83440f8cae7f5dba"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaadcc64829aadf4103477679e48c7594f"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
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+<tr class="memdesc:gaadcc64829aadf4103477679e48c7594f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Set a specific row to a matrix.  <a href="a00293.html#gaadcc64829aadf4103477679e48c7594f">More...</a><br /></td></tr>
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+<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00280.html" title="Features that implement in C++ the GLSL specification as closely as possible. ">Core features</a> (dependence) </dd></dl>
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+Functions</h2></td></tr>
+<tr class="memitem:gac0e342656ba09a9bc97c57182ba73124"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:gac0e342656ba09a9bc97c57182ba73124"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL bool&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00335.html#gac0e342656ba09a9bc97c57182ba73124">decompose</a> (mat&lt; 4, 4, T, Q &gt; const &amp;modelMatrix, vec&lt; 3, T, Q &gt; &amp;scale, qua&lt; T, Q &gt; &amp;orientation, vec&lt; 3, T, Q &gt; &amp;translation, vec&lt; 3, T, Q &gt; &amp;skew, vec&lt; 4, T, Q &gt; &amp;perspective)</td></tr>
+<tr class="memdesc:gac0e342656ba09a9bc97c57182ba73124"><td class="mdescLeft">&#160;</td><td class="mdescRight">Decomposes a model matrix to translations, rotation and scale components.  <a href="a00335.html#gac0e342656ba09a9bc97c57182ba73124">More...</a><br /></td></tr>
+<tr class="separator:gac0e342656ba09a9bc97c57182ba73124"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<div class="textblock"><p><a class="el" href="a00335.html">GLM_GTX_matrix_decompose</a> </p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00280.html" title="Features that implement in C++ the GLSL specification as closely as possible. ">Core features</a> (dependence) </dd></dl>
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+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="typedef-members"></a>
+Typedefs</h2></td></tr>
+<tr class="memitem:ga945254f459860741138bceb74da496b9"><td class="memItemLeft" align="right" valign="top">typedef mat&lt; 4, 4, double, highp &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00284.html#ga945254f459860741138bceb74da496b9">highp_dmat4</a></td></tr>
+<tr class="memdesc:ga945254f459860741138bceb74da496b9"><td class="mdescLeft">&#160;</td><td class="mdescRight">4 columns of 4 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.  <a href="a00284.html#ga945254f459860741138bceb74da496b9">More...</a><br /></td></tr>
+<tr class="separator:ga945254f459860741138bceb74da496b9"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga118d24a3d12c034e7cccef7bf2f01b8a"><td class="memItemLeft" align="right" valign="top">typedef mat&lt; 4, 4, double, highp &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00284.html#ga118d24a3d12c034e7cccef7bf2f01b8a">highp_dmat4x4</a></td></tr>
+<tr class="memdesc:ga118d24a3d12c034e7cccef7bf2f01b8a"><td class="mdescLeft">&#160;</td><td class="mdescRight">4 columns of 4 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.  <a href="a00284.html#ga118d24a3d12c034e7cccef7bf2f01b8a">More...</a><br /></td></tr>
+<tr class="separator:ga118d24a3d12c034e7cccef7bf2f01b8a"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga708bc5b91bbfedd21debac8dcf2a64cd"><td class="memItemLeft" align="right" valign="top">typedef mat&lt; 4, 4, double, lowp &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00284.html#ga708bc5b91bbfedd21debac8dcf2a64cd">lowp_dmat4</a></td></tr>
+<tr class="memdesc:ga708bc5b91bbfedd21debac8dcf2a64cd"><td class="mdescLeft">&#160;</td><td class="mdescRight">4 columns of 4 components matrix of double-precision floating-point numbers using low precision arithmetic in term of ULPs.  <a href="a00284.html#ga708bc5b91bbfedd21debac8dcf2a64cd">More...</a><br /></td></tr>
+<tr class="separator:ga708bc5b91bbfedd21debac8dcf2a64cd"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga5b0413198b7e9f061f7534a221c9dac9"><td class="memItemLeft" align="right" valign="top">typedef mat&lt; 4, 4, double, lowp &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00284.html#ga5b0413198b7e9f061f7534a221c9dac9">lowp_dmat4x4</a></td></tr>
+<tr class="memdesc:ga5b0413198b7e9f061f7534a221c9dac9"><td class="mdescLeft">&#160;</td><td class="mdescRight">4 columns of 4 components matrix of double-precision floating-point numbers using low precision arithmetic in term of ULPs.  <a href="a00284.html#ga5b0413198b7e9f061f7534a221c9dac9">More...</a><br /></td></tr>
+<tr class="separator:ga5b0413198b7e9f061f7534a221c9dac9"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaf650bc667bf2a0e496b5a9182bc8d378"><td class="memItemLeft" align="right" valign="top">typedef mat&lt; 4, 4, double, mediump &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00284.html#gaf650bc667bf2a0e496b5a9182bc8d378">mediump_dmat4</a></td></tr>
+<tr class="memdesc:gaf650bc667bf2a0e496b5a9182bc8d378"><td class="mdescLeft">&#160;</td><td class="mdescRight">4 columns of 4 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.  <a href="a00284.html#gaf650bc667bf2a0e496b5a9182bc8d378">More...</a><br /></td></tr>
+<tr class="separator:gaf650bc667bf2a0e496b5a9182bc8d378"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga5389b3ab32dc0d72bea00057ab6d1dd3"><td class="memItemLeft" align="right" valign="top">typedef mat&lt; 4, 4, double, mediump &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00284.html#ga5389b3ab32dc0d72bea00057ab6d1dd3">mediump_dmat4x4</a></td></tr>
+<tr class="memdesc:ga5389b3ab32dc0d72bea00057ab6d1dd3"><td class="mdescLeft">&#160;</td><td class="mdescRight">4 columns of 4 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.  <a href="a00284.html#ga5389b3ab32dc0d72bea00057ab6d1dd3">More...</a><br /></td></tr>
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