Delete diff-gaussian-rasterization-camera

diff-gaussian-rasterization-camera/CMakeLists.txt

@@ -1,36 +0,0 @@
-#
-# 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

@@ -1,83 +0,0 @@
-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

@@ -1,35 +0,0 @@
-# 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

@@ -1,175 +0,0 @@
-/*
- * 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

@@ -1,718 +0,0 @@
-/*
- * 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

@@ -1,71 +0,0 @@
-/*
- * 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

@@ -1,19 +0,0 @@
-/*
- * 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

@@ -1,466 +0,0 @@
-/*
- * 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

@@ -1,68 +0,0 @@
-/*
- * 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

@@ -1,95 +0,0 @@
-/*
- * 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

@@ -1,449 +0,0 @@
-/*
- * 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

@@ -1,73 +0,0 @@
-/*
- * 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

@@ -1,263 +0,0 @@
-#
-# 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

@@ -1,19 +0,0 @@
-/*
- * 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

@@ -1,866 +0,0 @@
-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

@@ -1,232 +0,0 @@
-/*
- * 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

@@ -1,70 +0,0 @@
-/*
- * 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

@@ -1,34 +0,0 @@
-#
-# 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

@@ -1,92 +0,0 @@
-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

@@ -1,388 +0,0 @@
-language: cpp
-
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-
-    - name: "Xcode 7.3 C++98 ms release"
-      os: osx
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-        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Debug -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_17=ON -DGLM_TEST_FORCE_PURE=ON"
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-
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-        - CMAKE_ENV="--parallel"
-
-    - name: "Clang C++14 pure release"
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-      env:
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-        - 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
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-        - CTEST_ENV="--parallel 4 --output-on-failure"
-        - CMAKE_ENV="--parallel"
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-    - name: "Clang C++14 sse2 debug"
-      os: linux
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-        - 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"
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-
-    - name: "Clang C++14 sse2 debug"
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-        - 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"
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-
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-
-    - name: "Clang C++17 pure debug"
-      os: linux
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-        - CTEST_ENV="--parallel 4 --output-on-failure"
-        - CMAKE_ENV="--parallel"
-
-    - name: "Clang C++17 pure release"
-      os: linux
-      dist: focal
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-        - 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

@@ -1,45 +0,0 @@
-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
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-endif()

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

@@ -1,21 +0,0 @@
-if(NOT EXISTS "@CMAKE_BINARY_DIR@/install_manifest.txt")
-  message(FATAL_ERROR "Cannot find install manifest: @CMAKE_BINARY_DIR@/install_manifest.txt")
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-
-file(READ "@CMAKE_BINARY_DIR@/install_manifest.txt" files)
-string(REGEX REPLACE "\n" ";" files "${files}")
-foreach(file ${files})
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-    exec_program(
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-      OUTPUT_VARIABLE rm_out
-      RETURN_VALUE rm_retval
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-    if(NOT "${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

@@ -1,54 +0,0 @@
-================================================================================
-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.

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-<tr class="memdesc:gafba2e0674deb5953878d89483cd6323d"><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#gafba2e0674deb5953878d89483cd6323d">More...</a><br /></td></tr>
-<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>
-<tr class="memitem:gaa0f2f12e9108b09e22a3f0b2008a0b5d"><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#gaa0f2f12e9108b09e22a3f0b2008a0b5d">clamp</a> (vec&lt; L, T, Q &gt; const &amp;x, vec&lt; L, T, Q &gt; const &amp;minVal, vec&lt; L, T, Q &gt; const &amp;maxVal)</td></tr>
-<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>
-<tr class="memdesc:ga1425c1c3160ec51214b03a0469a3013d"><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#ga1425c1c3160ec51214b03a0469a3013d">More...</a><br /></td></tr>
-<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>
-<tr class="memitem:ga7a0a8291a1cf3e1c2aee33030a1bd7b0"><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#ga7a0a8291a1cf3e1c2aee33030a1bd7b0">intBitsToFloat</a> (vec&lt; L, int, Q &gt; const &amp;v)</td></tr>
-<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>
-<tr class="memitem:gac1fec0c3303b572a6d4697a637213870"><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#gac1fec0c3303b572a6d4697a637213870">max</a> (vec&lt; L, T, Q &gt; const &amp;x, vec&lt; L, T, Q &gt; const &amp;y)</td></tr>
-<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>
-<tr class="memitem:ga6cf8098827054a270ee36b18e30d471d"><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#ga6cf8098827054a270ee36b18e30d471d">min</a> (genType x, genType y)</td></tr>
-<tr class="memdesc:ga6cf8098827054a270ee36b18e30d471d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns y if y &lt; x; otherwise, it returns x.  <a href="a00241.html#ga6cf8098827054a270ee36b18e30d471d">More...</a><br /></td></tr>
-<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>
-<tr class="memitem:gaa7d015eba1f9f48519251f4abe69b14d"><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#gaa7d015eba1f9f48519251f4abe69b14d">min</a> (vec&lt; L, T, Q &gt; const &amp;x, T y)</td></tr>
-<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>
-<tr class="memitem:ga31f49ef9e7d1beb003160c5e009b0c48"><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#ga31f49ef9e7d1beb003160c5e009b0c48">min</a> (vec&lt; L, T, Q &gt; const &amp;x, vec&lt; L, T, Q &gt; const &amp;y)</td></tr>
-<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:ga015a1261ff23e12650211aa872863cce"><td class="memSeparator" colspan="2">&#160;</td></tr>
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-<tr class="memitem:gaf4a5fc81619c7d3e8b22f53d4a098c7f"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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-<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>
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-<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>
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-<tr class="separator:ga97f46b5f7b42fe44482e13356eb394ae"><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="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>
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-<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;</div>
-<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>
-<div class="line"><a name="l00042"></a><span class="lineno"><a class="line" href="a00315.html#gaa551c0a0e16d2d4608e49f7696df897f">   42</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#gab5477ab69c40de4db5d58d3359529724">lerp</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, T a){<span class="keywordflow">return</span> <a class="code" href="a00241.html#ga8e93f374aae27d1a88b921860351f8d4">mix</a>(x, y, a);}                                                 </div>
-<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;</div>
-<div class="line"><a name="l00044"></a><span class="lineno"><a class="line" href="a00315.html#ga44a8b5fd776320f1713413dec959b32a">   44</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, T a){<span class="keywordflow">return</span> <a class="code" href="a00241.html#ga8e93f374aae27d1a88b921860351f8d4">mix</a>(x, y, a);}                                                 </div>
-<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>
-<div class="line"><a name="l00046"></a><span class="lineno"><a class="line" href="a00315.html#gaf68de5baf72d16135368b8ef4f841604">   46</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#gab5477ab69c40de4db5d58d3359529724">lerp</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="keyword">const</span> vec&lt;2, 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="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>
-<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> genType&gt; GLM_FUNC_DECL <span class="keywordtype">bool</span> <a class="code" href="a00315.html#ga19925badbe10ce61df1d0de00be0b5ad">isfinite</a>(genType <span class="keyword">const</span>&amp; x);                                                                                       </div>
-<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt; GLM_FUNC_DECL vec&lt;1, bool, Q&gt; <a class="code" href="a00315.html#ga19925badbe10ce61df1d0de00be0b5ad">isfinite</a>(<span class="keyword">const</span> vec&lt;1, T, Q&gt;&amp; x);                                </div>
-<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt; GLM_FUNC_DECL vec&lt;2, bool, Q&gt; <a class="code" href="a00315.html#ga19925badbe10ce61df1d0de00be0b5ad">isfinite</a>(<span class="keyword">const</span> vec&lt;2, T, Q&gt;&amp; x);                                </div>
-<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt; GLM_FUNC_DECL vec&lt;3, bool, Q&gt; <a class="code" href="a00315.html#ga19925badbe10ce61df1d0de00be0b5ad">isfinite</a>(<span class="keyword">const</span> vec&lt;3, T, Q&gt;&amp; x);                                </div>
-<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>
-<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;</div>
-<div class="line"><a name="l00066"></a><span class="lineno"><a class="line" href="a00315.html#gaddcd7aa2e30e61af5b38660613d3979e">   66</a></span>&#160;        <span class="keyword">typedef</span> <span class="keywordtype">bool</span>                                            <a class="code" href="a00315.html#gaddcd7aa2e30e61af5b38660613d3979e">bool1</a>;                  </div>
-<div class="line"><a name="l00067"></a><span class="lineno"><a class="line" href="a00315.html#gaa09ab65ec9c3c54305ff502e2b1fe6d9">   67</a></span>&#160;        <span class="keyword">typedef</span> vec&lt;2, bool, highp&gt;                     <a class="code" href="a00315.html#gaa09ab65ec9c3c54305ff502e2b1fe6d9">bool2</a>;                  </div>
-<div class="line"><a name="l00068"></a><span class="lineno"><a class="line" href="a00315.html#ga99629f818737f342204071ef8296b2ed">   68</a></span>&#160;        <span class="keyword">typedef</span> vec&lt;3, bool, highp&gt;                     <a class="code" href="a00315.html#ga99629f818737f342204071ef8296b2ed">bool3</a>;                  </div>
-<div class="line"><a name="l00069"></a><span class="lineno"><a class="line" href="a00315.html#ga13c3200b82708f73faac6d7f09ec91a3">   69</a></span>&#160;        <span class="keyword">typedef</span> vec&lt;4, bool, highp&gt;                     <a class="code" href="a00315.html#ga13c3200b82708f73faac6d7f09ec91a3">bool4</a>;                  </div>
-<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;</div>
-<div class="line"><a name="l00071"></a><span class="lineno"><a class="line" href="a00315.html#ga7f895c936f0c29c8729afbbf22806090">   71</a></span>&#160;        <span class="keyword">typedef</span> <span class="keywordtype">bool</span>                                            <a class="code" href="a00315.html#ga7f895c936f0c29c8729afbbf22806090">bool1x1</a>;                </div>
-<div class="line"><a name="l00072"></a><span class="lineno"><a class="line" href="a00315.html#gadb3703955e513632f98ba12fe051ba3e">   72</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;2, 2, bool, highp&gt;          <a class="code" href="a00315.html#gadb3703955e513632f98ba12fe051ba3e">bool2x2</a>;                </div>
-<div class="line"><a name="l00073"></a><span class="lineno"><a class="line" href="a00315.html#ga9ae6ee155d0f90cb1ae5b6c4546738a0">   73</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;2, 3, bool, highp&gt;          <a class="code" href="a00315.html#ga9ae6ee155d0f90cb1ae5b6c4546738a0">bool2x3</a>;                </div>
-<div class="line"><a name="l00074"></a><span class="lineno"><a class="line" href="a00315.html#ga4d7fa65be8e8e4ad6d920b45c44e471f">   74</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;2, 4, bool, highp&gt;          <a class="code" href="a00315.html#ga4d7fa65be8e8e4ad6d920b45c44e471f">bool2x4</a>;                </div>
-<div class="line"><a name="l00075"></a><span class="lineno"><a class="line" href="a00315.html#gac7d7311f7e0fa8b6163d96dab033a755">   75</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;3, 2, bool, highp&gt;          <a class="code" href="a00315.html#gac7d7311f7e0fa8b6163d96dab033a755">bool3x2</a>;                </div>
-<div class="line"><a name="l00076"></a><span class="lineno"><a class="line" href="a00315.html#ga6c97b99aac3e302053ffb58aace9033c">   76</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;3, 3, bool, highp&gt;          <a class="code" href="a00315.html#ga6c97b99aac3e302053ffb58aace9033c">bool3x3</a>;                </div>
-<div class="line"><a name="l00077"></a><span class="lineno"><a class="line" href="a00315.html#gae7d6b679463d37d6c527d478fb470fdf">   77</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;3, 4, bool, highp&gt;          <a class="code" href="a00315.html#gae7d6b679463d37d6c527d478fb470fdf">bool3x4</a>;                </div>
-<div class="line"><a name="l00078"></a><span class="lineno"><a class="line" href="a00315.html#ga9ed830f52408b2f83c085063a3eaf1d0">   78</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;4, 2, bool, highp&gt;          <a class="code" href="a00315.html#ga9ed830f52408b2f83c085063a3eaf1d0">bool4x2</a>;                </div>
-<div class="line"><a name="l00079"></a><span class="lineno"><a class="line" href="a00315.html#gad0f5dc7f22c2065b1b06d57f1c0658fe">   79</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;4, 3, bool, highp&gt;          <a class="code" href="a00315.html#gad0f5dc7f22c2065b1b06d57f1c0658fe">bool4x3</a>;                </div>
-<div class="line"><a name="l00080"></a><span class="lineno"><a class="line" href="a00315.html#ga7d2a7d13986602ae2896bfaa394235d4">   80</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;4, 4, bool, highp&gt;          <a class="code" href="a00315.html#ga7d2a7d13986602ae2896bfaa394235d4">bool4x4</a>;                </div>
-<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;</div>
-<div class="line"><a name="l00082"></a><span class="lineno"><a class="line" href="a00315.html#ga0670a2111b5e4a6410bd027fa0232fc3">   82</a></span>&#160;        <span class="keyword">typedef</span> <span class="keywordtype">int</span>                                                     <a class="code" href="a00315.html#ga0670a2111b5e4a6410bd027fa0232fc3">int1</a>;                   </div>
-<div class="line"><a name="l00083"></a><span class="lineno"><a class="line" href="a00315.html#gafe3a8fd56354caafe24bfe1b1e3ad22a">   83</a></span>&#160;        <span class="keyword">typedef</span> vec&lt;2, int, highp&gt;                      <a class="code" href="a00315.html#gafe3a8fd56354caafe24bfe1b1e3ad22a">int2</a>;                   </div>
-<div class="line"><a name="l00084"></a><span class="lineno"><a class="line" href="a00315.html#ga909c38a425f215a50c847145d7da09f0">   84</a></span>&#160;        <span class="keyword">typedef</span> vec&lt;3, int, highp&gt;                      <a class="code" href="a00315.html#ga909c38a425f215a50c847145d7da09f0">int3</a>;                   </div>
-<div class="line"><a name="l00085"></a><span class="lineno"><a class="line" href="a00315.html#gaecdef18c819c205aeee9f94dc93de56a">   85</a></span>&#160;        <span class="keyword">typedef</span> vec&lt;4, int, highp&gt;                      <a class="code" href="a00315.html#gaecdef18c819c205aeee9f94dc93de56a">int4</a>;                   </div>
-<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;</div>
-<div class="line"><a name="l00087"></a><span class="lineno"><a class="line" href="a00315.html#ga056ffe02d3a45af626f8e62221881c7a">   87</a></span>&#160;        <span class="keyword">typedef</span> <span class="keywordtype">int</span>                                                     <a class="code" href="a00315.html#ga056ffe02d3a45af626f8e62221881c7a">int1x1</a>;                 </div>
-<div class="line"><a name="l00088"></a><span class="lineno"><a class="line" href="a00315.html#ga4e5ce477c15836b21e3c42daac68554d">   88</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;2, 2, int, highp&gt;           <a class="code" href="a00315.html#ga4e5ce477c15836b21e3c42daac68554d">int2x2</a>;                 </div>
-<div class="line"><a name="l00089"></a><span class="lineno"><a class="line" href="a00315.html#ga197ded5ad8354f6b6fb91189d7a269b3">   89</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;2, 3, int, highp&gt;           <a class="code" href="a00315.html#ga197ded5ad8354f6b6fb91189d7a269b3">int2x3</a>;                 </div>
-<div class="line"><a name="l00090"></a><span class="lineno"><a class="line" href="a00315.html#ga2749d59a7fddbac44f34ba78e57ef807">   90</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;2, 4, int, highp&gt;           <a class="code" href="a00315.html#ga2749d59a7fddbac44f34ba78e57ef807">int2x4</a>;                 </div>
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-<div class="line"><a name="l00096"></a><span class="lineno"><a class="line" href="a00315.html#ga04dee1552424198b8f58b377c2ee00d8">   96</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;4, 4, int, highp&gt;           <a class="code" href="a00315.html#ga04dee1552424198b8f58b377c2ee00d8">int4x4</a>;                 </div>
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-<div class="line"><a name="l00099"></a><span class="lineno"><a class="line" href="a00315.html#ga02d3c013982c183906c61d74aa3166ce">   99</a></span>&#160;        <span class="keyword">typedef</span> vec&lt;2, float, highp&gt;            <a class="code" href="a00315.html#ga02d3c013982c183906c61d74aa3166ce">float2</a>;                 </div>
-<div class="line"><a name="l00100"></a><span class="lineno"><a class="line" href="a00315.html#ga821ff110fc8533a053cbfcc93e078cc0">  100</a></span>&#160;        <span class="keyword">typedef</span> vec&lt;3, float, highp&gt;            <a class="code" href="a00315.html#ga821ff110fc8533a053cbfcc93e078cc0">float3</a>;                 </div>
-<div class="line"><a name="l00101"></a><span class="lineno"><a class="line" href="a00315.html#gae2da7345087db3815a25d8837a727ef1">  101</a></span>&#160;        <span class="keyword">typedef</span> vec&lt;4, float, highp&gt;            <a class="code" href="a00315.html#gae2da7345087db3815a25d8837a727ef1">float4</a>;                 </div>
-<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;</div>
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-<div class="line"><a name="l00110"></a><span class="lineno"><a class="line" href="a00315.html#ga308b9af0c221145bcfe9bfc129d9098e">  110</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;4, 2, float, highp&gt;         <a class="code" href="a00315.html#ga308b9af0c221145bcfe9bfc129d9098e">float4x2</a>;               </div>
-<div class="line"><a name="l00111"></a><span class="lineno"><a class="line" href="a00315.html#gac0a51b4812038aa81d73ffcc37f741ac">  111</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;4, 3, float, highp&gt;         <a class="code" href="a00315.html#gac0a51b4812038aa81d73ffcc37f741ac">float4x3</a>;               </div>
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-<div class="line"><a name="l00115"></a><span class="lineno"><a class="line" href="a00315.html#ga31b729b04facccda73f07ed26958b3c2">  115</a></span>&#160;        <span class="keyword">typedef</span> vec&lt;2, double, highp&gt;           <a class="code" href="a00315.html#ga31b729b04facccda73f07ed26958b3c2">double2</a>;                </div>
-<div class="line"><a name="l00116"></a><span class="lineno"><a class="line" href="a00315.html#ga3d8b9028a1053a44a98902cd1c389472">  116</a></span>&#160;        <span class="keyword">typedef</span> vec&lt;3, double, highp&gt;           <a class="code" href="a00315.html#ga3d8b9028a1053a44a98902cd1c389472">double3</a>;                </div>
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-<div class="line"><a name="l00121"></a><span class="lineno"><a class="line" href="a00315.html#ga3655bc324008553ca61f39952d0b2d08">  121</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;2, 3, double, highp&gt;                <a class="code" href="a00315.html#ga3655bc324008553ca61f39952d0b2d08">double2x3</a>;              </div>
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-<div class="line"><a name="l00123"></a><span class="lineno"><a class="line" href="a00315.html#ga5ec08fc39c9d783dfcc488be240fe975">  123</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;3, 2, double, highp&gt;                <a class="code" href="a00315.html#ga5ec08fc39c9d783dfcc488be240fe975">double3x2</a>;              </div>
-<div class="line"><a name="l00124"></a><span class="lineno"><a class="line" href="a00315.html#ga4bad5bb20c6ddaecfe4006c93841d180">  124</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;3, 3, double, highp&gt;                <a class="code" href="a00315.html#ga4bad5bb20c6ddaecfe4006c93841d180">double3x3</a>;              </div>
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-<div class="line"><a name="l00126"></a><span class="lineno"><a class="line" href="a00315.html#gabca29ccceea53669618b751aae0ba83d">  126</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;4, 2, double, highp&gt;                <a class="code" href="a00315.html#gabca29ccceea53669618b751aae0ba83d">double4x2</a>;              </div>
-<div class="line"><a name="l00127"></a><span class="lineno"><a class="line" href="a00315.html#gafad66a02ccd360c86d6ab9ff9cfbc19c">  127</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;4, 3, double, highp&gt;                <a class="code" href="a00315.html#gafad66a02ccd360c86d6ab9ff9cfbc19c">double4x3</a>;              </div>
-<div class="line"><a name="l00128"></a><span class="lineno"><a class="line" href="a00315.html#gaab541bed2e788e4537852a2492860806">  128</a></span>&#160;        <span class="keyword">typedef</span> mat&lt;4, 4, double, highp&gt;                <a class="code" href="a00315.html#gaab541bed2e788e4537852a2492860806">double4x4</a>;              </div>
-<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;</div>
-<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;}<span class="comment">//namespace glm</span></div>
-<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;</div>
-<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;<span class="preprocessor">#include &quot;compatibility.inl&quot;</span></div>
-<div class="ttc" id="a00315_html_gaab541bed2e788e4537852a2492860806"><div class="ttname"><a href="a00315.html#gaab541bed2e788e4537852a2492860806">glm::double4x4</a></div><div class="ttdeci">mat&lt; 4, 4, double, highp &gt; double4x4</div><div class="ttdoc">double-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#l00128">compatibility.hpp:128</a></div></div>
-<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>
-<div class="ttc" id="a00315_html_gaddcd7aa2e30e61af5b38660613d3979e"><div class="ttname"><a href="a00315.html#gaddcd7aa2e30e61af5b38660613d3979e">glm::bool1</a></div><div class="ttdeci">bool bool1</div><div class="ttdoc">boolean type with 1 component. (From GLM_GTX_compatibility extension) </div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00066">compatibility.hpp:66</a></div></div>
-<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>
-<div class="ttc" id="a00315_html_ga31b729b04facccda73f07ed26958b3c2"><div class="ttname"><a href="a00315.html#ga31b729b04facccda73f07ed26958b3c2">glm::double2</a></div><div class="ttdeci">vec&lt; 2, double, highp &gt; double2</div><div class="ttdoc">double-qualifier floating-point vector with 2 components. (From GLM_GTX_compatibility extension) ...</div><div class="ttdef"><b>Definition:</b> <a href="a00017_source.html#l00115">compatibility.hpp:115</a></div></div>
-<div class="ttc" id="a00315_html_ga6ceb5d38a58becdf420026e12a6562f3"><div class="ttname"><a href="a00315.html#ga6ceb5d38a58becdf420026e12a6562f3">glm::float3x3</a></div><div class="ttdeci">mat&lt; 3, 3, float, highp &gt; float3x3</div><div class="ttdoc">single-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#l00108">compatibility.hpp:108</a></div></div>
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-<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>
-<tr class="memitem:ga4dfb33fa7664aa888eb647999d329b98"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00318.html#ga4dfb33fa7664aa888eb647999d329b98">quarticEaseOut</a> (genType const &amp;a)</td></tr>
-<tr class="memdesc:ga4dfb33fa7664aa888eb647999d329b98"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modelled after the quartic y = 1 - (x - 1)^4.  <a href="a00318.html#ga4dfb33fa7664aa888eb647999d329b98">More...</a><br /></td></tr>
-<tr class="separator:ga4dfb33fa7664aa888eb647999d329b98"><td class="memSeparator" colspan="2">&#160;</td></tr>
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-<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;</div>
-<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
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-<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;                                                                                        T &amp; t1,</div>
-<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;                                                                                        T &amp; t2,</div>
-<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;                                                                                        T &amp; t3);</div>
-<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;</div>
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-<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;                                                                                        T &amp; t1,</div>
-<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;                                                                                        T &amp; t2,</div>
-<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;                                                                                        T &amp; t3);</div>
-<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;</div>
-<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
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-<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;                                                                                        T &amp; t1,</div>
-<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;                                                                                        T &amp; t2,</div>
-<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;                                                                                        T &amp; t3);</div>
-<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;</div>
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-<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;                                                                                        T &amp; t1,</div>
-<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;                                                                                        T &amp; t2,</div>
-<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;                                                                                        T &amp; t3);</div>
-<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;</div>
-<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
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-<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;                                                                                        T &amp; t2,</div>
-<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;                                                                                        T &amp; t3);</div>
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-<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;<span class="preprocessor">#include &quot;euler_angles.inl&quot;</span></div>
-<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>
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-<div class="title">hash.hpp</div>  </div>
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-<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>
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-<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>
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-<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>
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-<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>
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-<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>
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-<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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-<tr class="memitem:gaf39f4e5f78eb29c1a90277d45b9b3feb"><td class="memTemplParams" colspan="2">template&lt;length_t C, length_t R, typename T , qualifier Q&gt; </td></tr>
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-<tr class="memdesc:gaf39f4e5f78eb29c1a90277d45b9b3feb"><td class="mdescLeft">&#160;</td><td class="mdescRight">Flips the matrix columns right and left.  <a href="a00336.html#gaf39f4e5f78eb29c1a90277d45b9b3feb">More...</a><br /></td></tr>
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