Add UniSHARP Gradio Space

.gitattributes

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-*.arrow filter=lfs diff=lfs merge=lfs -text
-*.bin filter=lfs diff=lfs merge=lfs -text
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-*.lfs.* filter=lfs diff=lfs merge=lfs -text
-*.mlmodel filter=lfs diff=lfs merge=lfs -text
-*.model filter=lfs diff=lfs merge=lfs -text
-*.msgpack filter=lfs diff=lfs merge=lfs -text
-*.npy filter=lfs diff=lfs merge=lfs -text
-*.npz filter=lfs diff=lfs merge=lfs -text
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-*.pickle filter=lfs diff=lfs merge=lfs -text
-*.pkl filter=lfs diff=lfs merge=lfs -text
 *.pt filter=lfs diff=lfs merge=lfs -text
 *.pth filter=lfs diff=lfs merge=lfs -text
-*.rar filter=lfs diff=lfs merge=lfs -text
 *.safetensors filter=lfs diff=lfs merge=lfs -text
-saved_model/**/* filter=lfs diff=lfs merge=lfs -text
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-*tfevents* filter=lfs diff=lfs merge=lfs -text
+*.bin filter=lfs diff=lfs merge=lfs -text
+
+3dgeer/submodules/geer-rasterizer/third_party/glm/doc/manual/frontpage1.png filter=lfs diff=lfs merge=lfs -text
+3dgeer/submodules/geer-rasterizer/third_party/glm/doc/manual/frontpage2.png filter=lfs diff=lfs merge=lfs -text
+3dgeer/submodules/geer-rasterizer/third_party/glm/doc/manual.pdf filter=lfs diff=lfs merge=lfs -text
+UniK3D/unik3d/ops/losses/resources/partition_spline.npz filter=lfs diff=lfs merge=lfs -text
+examples/photo1.jpeg filter=lfs diff=lfs merge=lfs -text
+examples/photo2.jpeg filter=lfs diff=lfs merge=lfs -text
+examples/photo3.jpeg filter=lfs diff=lfs merge=lfs -text
+examples/photo4.jpeg filter=lfs diff=lfs merge=lfs -text
+examples/photo5.jpeg filter=lfs diff=lfs merge=lfs -text

.gitignore

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+__pycache__/
+*.pyc
+/outputs/
+/checkpoints/huggingface/
+/checkpoints/torchhub/
+/checkpoints/*.tmp
+

3dgeer/submodules/geer-rasterizer/CMakeLists.txt

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+#
+# 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  george.drettakis@inria.fr
+#
+
+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 "70;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})

3dgeer/submodules/geer-rasterizer/LICENSE.md

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+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: stip-sophia.transfert@inria.fr . 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*.  

3dgeer/submodules/geer-rasterizer/README.md

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+# 3DGEER-CUDA-Rasterizer
+Used as the rasterization engine for the paper "3DGEER: 3D Gaussian Rendering Made Exact and Efficient for Generic Cameras". 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>@misc{huang20263dgeer3dgaussianrendering,
+      title={3DGEER: 3D Gaussian Rendering Made Exact and Efficient for Generic Cameras}, 
+      author={Zixun Huang and Cho-Ying Wu and Yuliang Guo and Xinyu Huang and Liu Ren},
+      year={2026},
+      eprint={2505.24053},
+      archivePrefix={arXiv},
+      primaryClass={cs.GR},
+      url={https://arxiv.org/abs/2505.24053}, 
+}</code></pre>
+  </div>
+</section>
+
+
+
+<!-- <div>
+<p align="center">
+  <img src="../../assets/intgral.png" alt="teaser" style="width: 60%;">
+  Gradient Flow and Canonical Transformation for Ray-Gaussian Integral
+</p>
+<p align="center">
+  <img src="../../assets/asso.png" alt="teaser" style="width: 70%;">
+  EWA vs. UT vs. PBF: Fix Linear Approximation Error in Ray-Particle Association.
+</p>
+</div> -->

3dgeer/submodules/geer-rasterizer/cuda_rasterizer/auxiliary.h

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+/*
+ * 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  george.drettakis@inria.fr
+ */
+
+#ifndef CUDA_RASTERIZER_AUXILIARY_H_INCLUDED
+#define CUDA_RASTERIZER_AUXILIARY_H_INCLUDED
+
+#include "config.h"
+#include "stdio.h"
+
+#include <thrust/sort.h>
+#include <thrust/binary_search.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
+};
+
+__device__ const float ut_alpha = 1.0f;
+__device__ const float ut_beta = 2.0f;
+__device__ const float ut_kappa = 0.0f;
+__device__ const float ut_lambda = ut_alpha * ut_alpha * (3.f + ut_kappa) - 3.f;
+
+__device__ __forceinline__ float sq(float x) { return x * x; }
+__device__ __forceinline__ float cube(float x) { return x * x * x; }
+
+
+__device__ __forceinline__ float dot(const float3 &a, const float3 &b) {
+    return a.x * b.x + a.y * b.y + a.z * b.z;
+}
+
+__device__ __forceinline__ float3 cross(const float3 &a, const float3 &b) {
+    return make_float3(a.y * b.z - a.z * b.y, 
+                       a.z * b.x - a.x * b.z, 
+                       a.x * b.y - a.y * b.x);
+}
+
+__device__ __forceinline__ float2 divide_z(const glm::vec3& v) {
+    return make_float2(v.x / v.z, v.y / v.z);
+}
+
+__device__ __forceinline__ float2 atan(const float2& v) {
+	return make_float2(atan(v.x), atan(v.y));
+}
+
+__device__ __forceinline__ float3 toFloat3(const glm::vec3& v) {
+    return make_float3(v.x, v.y, v.z);
+}
+
+__forceinline__ __device__ float ndc2Pix(float v, int S)
+{
+	return ((v + 1.0) * S - 1.0) * 0.5;
+}
+
+__forceinline__ __device__ float2 invinterpolated_uv(
+	const float focal_x, const float focal_y, 
+	const float principal_x, const float principal_y, 
+	const float4 dist_coeff, 
+	const float tan_x, const float tan_y) {
+	// Compute the inverse interpolation for the UV coordinates
+	float2 uv_indices;
+	float radius = sqrtf(sq(tan_x) + sq(tan_y));
+	float angle = atanf(radius);
+	float angle_sq = sq(angle);
+	float angle_sq_sq = sq(angle_sq);
+
+	float r = angle * (1.0 + dist_coeff.x * angle_sq + dist_coeff.y * angle_sq_sq + dist_coeff.z * angle_sq * angle_sq_sq + dist_coeff.w * angle_sq_sq * angle_sq_sq);
+	uv_indices.x = (tan_x * r * focal_x) / radius + principal_x;
+	uv_indices.y = (tan_y * r * focal_y) / radius + principal_y;
+	return uv_indices;
+}
+
+__forceinline__ __device__ void getRect2(const int4 pbf, uint2& rect_min, uint2& rect_max, dim3 grid)
+{
+	rect_min = {
+		min(grid.x, max((int)0, (int)((pbf.x) / BLOCK_X))),
+		min(grid.y, max((int)0, (int)((pbf.z) / BLOCK_Y)))
+	};
+	rect_max = {
+		min(grid.x, max((int)0, (int)((pbf.y + BLOCK_X - 1) / BLOCK_X))),
+		min(grid.y, max((int)0, (int)((pbf.w + BLOCK_Y - 1) / BLOCK_Y)))
+	};
+}
+
+
+__forceinline__ __device__ void searchsorted_intersect(
+	const float* ref_start, int span,
+	const float* values,
+	int* indices
+) {
+	thrust::lower_bound(thrust::device, ref_start, ref_start + span, values, values + 2, indices);
+}
+
+// Check whether the ray direction for pixel `idx` falls within the
+// Particle Bounding Frustum (PBF) defined in tan-space as pbf_tan.
+// pbf_tan: (.x=tan_theta_min, .y=tan_theta_max, .z=tan_phi_min, .w=tan_phi_max)
+__forceinline__ __device__ bool checkValid(
+	const float* raymap,
+	const int idx,
+	const float4 pbf_tan
+) {
+	float2 rayf = {(float)raymap[idx * 3] / (float)raymap[idx * 3 + 2], (float)raymap[idx * 3 + 1] / (float)raymap[idx * 3 + 2]};
+	if (rayf.x < pbf_tan.x || rayf.x > pbf_tan.y) return false;
+	if (rayf.y < pbf_tan.z || rayf.y > pbf_tan.w) return false;
+	return true;
+}
+
+// Emit (tile_id | depth, gaussian_id) key/value pairs for every tile that the
+// Particle Bounding Frustum (PBF) of this Gaussian overlaps.  When xmap/ymap
+// are provided the PBF is projected onto the KB image grid via sorted intersection;
+// otherwise a simple tile-rectangle loop is used (BEAP mode).
+__forceinline__ __device__ uint32_t duplicateToTilesTouched(    
+	const float3 points_xyz,
+	const float3* w2o,
+	const float opac,
+	int4 pbf,
+	float4 pbf_tan,
+	const dim3 grid,
+	const int W, int H,
+    uint32_t idx, uint32_t off, float depth,
+	uint64_t* gaussian_keys_unsorted,
+	uint32_t* gaussian_values_unsorted,
+	const float* xmap,
+	const float* ymap
+	)
+{
+	uint2 rect_min, rect_max;
+
+	getRect2(pbf, rect_min, rect_max, grid);
+
+	int y_span = rect_max.y - rect_min.y;
+	int x_span = rect_max.x - rect_min.x;
+
+	// If no tiles are touched, return 0
+	if (y_span * x_span == 0) {
+		return 0;
+	}
+
+	bool isY = y_span > x_span;
+	const uint2 rect_max_ = isY ? rect_max : make_uint2(rect_max.y, rect_max.x);
+	const uint2 rect_min_ = isY ? rect_min : make_uint2(rect_min.y, rect_min.x);
+	const int4 pbf_ = isY ? pbf : make_int4(pbf.z, pbf.w, pbf.x, pbf.y);
+	const float2 pbf_tan_ = isY ? make_float2(pbf_tan.x, pbf_tan.y) : make_float2(pbf_tan.z, pbf_tan.w);
+	const float* cmap = isY ? xmap : ymap;
+	const int W_ = isY ? W : H;
+	// const int H_ = isY ? H : W;
+
+	uint32_t tiles_count = 0;
+    int2 slice_intersect_top, slice_intersect_bottom;
+	int slice_lefttop, slice_leftbottom;
+
+	// 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++)
+	{
+		// Get original BEAP ranged slice;
+		slice_leftbottom = min(max(pbf_.z, y * BLOCK_Y), pbf_.w) * W_ + pbf_.x;
+		searchsorted_intersect(cmap + slice_leftbottom, pbf_.y - pbf_.x + 1, (float*)(&pbf_tan_), (int*)(&slice_intersect_bottom));
+
+		slice_lefttop = min(max(pbf_.z, (y * BLOCK_Y + BLOCK_Y - 1)), pbf_.w) * W_ + pbf_.x;
+		searchsorted_intersect(cmap + slice_lefttop, pbf_.y - pbf_.x + 1, (float*)(&pbf_tan_), (int*)(&slice_intersect_top));
+
+		// Cull out useless tiles;
+		int tmp_left = min(max(0, min(slice_intersect_top.x, slice_intersect_bottom.x)), pbf_.y - pbf_.x);
+		int tmp_right = min(max(0, max(slice_intersect_top.y, slice_intersect_bottom.y)), pbf_.y - pbf_.x);
+		if (tmp_left >= tmp_right) {
+			continue;
+		}
+		int min_tile_x = max(rect_min_.x,
+            min(rect_max_.x, (int)((pbf_.x + tmp_left) / BLOCK_X))
+        );
+        int max_tile_x = max(rect_min_.x,
+            min(rect_max_.x, (int)((pbf_.x + tmp_right + BLOCK_X - 1) / BLOCK_X))
+        );
+		tiles_count += (max_tile_x - min_tile_x);
+		for (int x = min_tile_x; x < max_tile_x; x++)
+		{
+
+			if (gaussian_keys_unsorted != nullptr) {
+				uint64_t key = isY ? y * grid.x + x : x * grid.x + y;
+				key <<= 32;
+				key |= *((uint32_t*)&depth);
+				gaussian_keys_unsorted[off] = key;
+				gaussian_values_unsorted[off] = idx;
+				off++;
+			}
+		}
+	}
+	return tiles_count;
+}
+
+__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));
+}
+
+// ── Packed-type conventions used throughout the rasterizer ──────────────────
+// float2 h_opacity  : { x = antialiasing variance h_var,
+//                       y = antialiasing-scaled Gaussian opacity }
+// float4 pbf_tan    : PBF (Particle Bounding Frustum) in ray-direction
+//                     tangent space { x = tan_theta_min,  y = tan_theta_max,
+//                                     z = tan_phi_min,    w = tan_phi_max }
+// float3 w2o[3]     : rows of the world-to-object (canonical) matrix Σ^{-1/2}R_view^T
+//                     (one float3 per row → 3 rows total per Gaussian)
+// ────────────────────────────────────────────────────────────────────────────
+
+__forceinline__ __device__ bool in_frustum(int idx,
+	const float* orig_points,
+	const float* viewmatrix,
+	bool prefiltered,
+	float3& p_view,
+	float near_threshold = 0.2f)
+{
+	float3 p_orig = { orig_points[3 * idx], orig_points[3 * idx + 1], orig_points[3 * idx + 2] };
+
+	// Bring points to screen space 
+	p_view = transformPoint4x3(p_orig, viewmatrix);
+
+ 	if (p_view.z <= near_threshold)
+	{
+		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

3dgeer/submodules/geer-rasterizer/cuda_rasterizer/backward.cu

@@ -0,0 +1,642 @@
+/*
+ * 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  george.drettakis@inria.fr
+ */
+
+#include "backward.h"
+#include "auxiliary.h"
+#include <cooperative_groups.h>
+#include <cooperative_groups/reduce.h>
+namespace cg = cooperative_groups;
+
+//// IMPLEMENTATION OF THE 3DGEER BACKWARD FUNCTION
+// Backward pass for the conversion of scale and rotation to the inversed Cov3Ds. 
+__device__ void computeWorldToObject(int idx, const glm::vec3 scale, float mod, const glm::vec4 rot, glm::mat3 dL_dMt_inv, glm::vec3* dL_dscales, glm::vec4* dL_drots, float& dL_dhvar, float h_var) {
+	// see details in 3DGEER paper (Eq.C.11-12)
+	// Normalize quaternion to get valid rotation
+	glm::vec4 q = rot;// / glm::length(rot);
+	float r = q.x; //r
+	float x = q.y; //i
+	float y = q.z; //j
+	float z = q.w; //k
+
+	// Compute inv_rotation matrix from quaternion (the transpose of the rotation matrix); column-major
+	glm::mat3 R_inv = glm::mat3(
+		1.f - 2.f * (y * y + z * z), 2.f * (x * y - r * z), 2.f * (x * z + r * y), // column 0
+		2.f * (x * y + r * z), 1.f - 2.f * (x * x + z * z), 2.f * (y * z - r * x), // column 1
+		2.f * (x * z - r * y), 2.f * (y * z + r * x), 1.f - 2.f * (x * x + y * y)  // column 2
+	);
+	glm::mat3 Rt_inv = glm::transpose(R_inv); // to get the row vectors
+
+	// Compute inverse scaling matrix
+	glm::mat3 S_inv = glm::mat3(1.0f);
+	float scaling_inv[3] = { sqrtf(1.f / (sq(scale.x * mod) + h_var)), sqrtf(1.f / (sq(scale.y * mod) + h_var)), sqrtf(1.f / (sq(scale.z * mod) + h_var)) };
+	S_inv[0][0] *= scaling_inv[0];
+	S_inv[1][1] *= scaling_inv[1];
+	S_inv[2][2] *= scaling_inv[2];
+	
+	// Compute gradients of loss w.r.t. scale
+	glm::vec3* dL_dscale = dL_dscales + idx;
+	float dL_dhscale_x = glm::dot(Rt_inv[0], dL_dMt_inv[0]) * (-S_inv[0][0] * S_inv[0][0]);
+	dL_dscale->x = dL_dhscale_x * (S_inv[0][0] * (scale.x * mod));
+	float dL_dhscale_y = glm::dot(Rt_inv[1], dL_dMt_inv[1]) * (-S_inv[1][1] * S_inv[1][1]);
+	dL_dscale->y = dL_dhscale_y * (S_inv[1][1] * (scale.y * mod));
+	float dL_dhscale_z = glm::dot(Rt_inv[2], dL_dMt_inv[2]) * (-S_inv[2][2] * S_inv[2][2]);
+	dL_dscale->z = dL_dhscale_z * (S_inv[2][2] * (scale.z * mod));
+
+	// Scale the loss gradient w.r.t. inv(RS)
+	dL_dMt_inv[0] *= S_inv[0][0];
+	dL_dMt_inv[1] *= S_inv[1][1];
+	dL_dMt_inv[2] *= S_inv[2][2];
+	
+	// Gradients of loss w.r.t. normalized quaternion
+	glm::vec4 dL_dq;
+	dL_dq.x = 2 * z * (dL_dMt_inv[0][1] - dL_dMt_inv[1][0]) + 2 * y * (dL_dMt_inv[2][0] - dL_dMt_inv[0][2]) + 2 * x * (dL_dMt_inv[1][2] - dL_dMt_inv[2][1]); //wrt r,r
+	dL_dq.y = 2 * y * (dL_dMt_inv[1][0] + dL_dMt_inv[0][1]) + 2 * z * (dL_dMt_inv[2][0] + dL_dMt_inv[0][2]) + 2 * r * (dL_dMt_inv[1][2] - dL_dMt_inv[2][1]) - 4 * x * (dL_dMt_inv[2][2] + dL_dMt_inv[1][1]); //wrt i,x
+	dL_dq.z = 2 * x * (dL_dMt_inv[1][0] + dL_dMt_inv[0][1]) + 2 * r * (dL_dMt_inv[2][0] - dL_dMt_inv[0][2]) + 2 * z * (dL_dMt_inv[1][2] + dL_dMt_inv[2][1]) - 4 * y * (dL_dMt_inv[2][2] + dL_dMt_inv[0][0]); //wrt j,y
+	dL_dq.w = 2 * r * (dL_dMt_inv[0][1] - dL_dMt_inv[1][0]) + 2 * x * (dL_dMt_inv[2][0] + dL_dMt_inv[0][2]) + 2 * y * (dL_dMt_inv[1][2] + dL_dMt_inv[2][1]) - 4 * z * (dL_dMt_inv[1][1] + dL_dMt_inv[0][0]); //wrt k,z
+
+	// Gradients of loss w.r.t. unnormalized quaternion
+	float4* dL_drot = reinterpret_cast<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 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);
+}
+
+
+template<int C>
+__global__ void preprocessCUDA_mah(
+	int P, int D, int M,
+	const float3* means,
+	const float3* means3D_view, 
+	const float* depths,
+	const int* radii,
+	const float2* h_opacity,
+	const float3* w2o,
+	const float* viewmatrix, 
+	const float* shs,
+	const bool* clamped,
+	const glm::vec3* scales,
+	const glm::vec4* rotations,
+	const float scale_modifier,
+	const glm::vec3* campos,
+	const float tan_fovx, float tan_fovy,
+	const float focal_x, float focal_y,
+	glm::vec3* dL_dmeans,
+	glm::vec3* dL_dmean2D,
+	float* dL_dcolor,
+	float* dL_dsh,
+	glm::vec3* dL_dscale,
+	glm::vec4* dL_drot,
+	const glm::vec3* dL_dsigmaInv,
+	float* dL_dopacity)
+{
+	auto idx = cg::this_grid().thread_rank();
+	if (idx >= P || !(radii[idx] > 0))
+		return;
+
+	const glm::mat3 Wt = glm::mat3(
+		viewmatrix[0], viewmatrix[4], viewmatrix[8],
+		viewmatrix[1], viewmatrix[5], viewmatrix[9],
+		viewmatrix[2], viewmatrix[6], viewmatrix[10]);
+
+	float3 p_view = means3D_view[idx];
+	float h_var = h_opacity[idx].x;
+
+	// Compute gradient updates due to computing covariance from scale/rotation
+	float dL_dhvar = 0.0f;
+	const glm::vec3* dL_dsigma_inv = dL_dsigmaInv + 3 * idx;
+	// see 3DGEER paper: https://openreview.net/pdf?id=4voMNlRWI7 (Eq.9)
+	glm::vec3 dL_dw2o[3];
+	dL_dw2o[0] = glm::vec3( dL_dmeans[idx].x * p_view.x + dL_dsigma_inv[0].x, 
+							dL_dmeans[idx].x * p_view.y + dL_dsigma_inv[0].y,
+							dL_dmeans[idx].x * p_view.z + dL_dsigma_inv[0].z );
+
+	dL_dw2o[1] = glm::vec3( dL_dmeans[idx].y * p_view.x + dL_dsigma_inv[1].x, 
+							dL_dmeans[idx].y * p_view.y + dL_dsigma_inv[1].y,
+							dL_dmeans[idx].y * p_view.z + dL_dsigma_inv[1].z );
+
+	dL_dw2o[2] = glm::vec3( dL_dmeans[idx].z * p_view.x + dL_dsigma_inv[2].x, 
+							dL_dmeans[idx].z * p_view.y + dL_dsigma_inv[2].y,
+							dL_dmeans[idx].z * p_view.z + dL_dsigma_inv[2].z );
+
+	glm::mat3 dL_dMt_inv = {
+		Wt * dL_dw2o[0],
+		Wt * dL_dw2o[1],
+		Wt * dL_dw2o[2]
+	};
+
+	if (scales)
+		// see 3DGEER paper: https://openreview.net/pdf?id=4voMNlRWI7 (Eq.10-12)
+		computeWorldToObject(idx, scales[idx], scale_modifier, rotations[idx], dL_dMt_inv, dL_dscale, dL_drot, dL_dhvar, h_var);
+
+	// Compute gradient updates to means in the view space
+	glm::vec3 dL_dmean_view = glm::vec3( 
+		dL_dmeans[idx].x * w2o[idx * 3].x + dL_dmeans[idx].y * w2o[idx * 3 + 1].x + dL_dmeans[idx].z * w2o[idx * 3 + 2].x,
+		dL_dmeans[idx].x * w2o[idx * 3].y + dL_dmeans[idx].y * w2o[idx * 3 + 1].y + dL_dmeans[idx].z * w2o[idx * 3 + 2].y,
+		dL_dmeans[idx].x * w2o[idx * 3].z + dL_dmeans[idx].y * w2o[idx * 3 + 1].z + dL_dmeans[idx].z * w2o[idx * 3 + 2].z );
+	
+	float h_cov_scaling = (scales[idx].x * scale_modifier) / sqrtf((sq(scales[idx].x * scale_modifier) + h_var)) * (scales[idx].y * scale_modifier) / sqrtf((sq(scales[idx].y * scale_modifier) + h_var)) * (scales[idx].z * scale_modifier) / sqrtf((sq(scales[idx].z * scale_modifier) + h_var));
+	dL_dopacity[idx] *= fmaxf(h_cov_scaling, 5e-3f);
+
+	// Compute gradient updates to means in the object space
+	// see 3DGEER paper: https://openreview.net/pdf?id=4voMNlRWI7 (Eq.13)
+	dL_dmeans[idx] = Wt * dL_dmean_view;
+
+	// For densification
+	dL_dmean2D[idx] = glm::vec3( 
+		dL_dmean2D[idx].x * w2o[idx * 3].x + dL_dmean2D[idx].y * w2o[idx * 3 + 1].x + dL_dmean2D[idx].z * w2o[idx * 3 + 2].x,
+		dL_dmean2D[idx].x * w2o[idx * 3].y + dL_dmean2D[idx].y * w2o[idx * 3 + 1].y + dL_dmean2D[idx].z * w2o[idx * 3 + 2].y,
+		dL_dmean2D[idx].x * w2o[idx * 3].z + dL_dmean2D[idx].y * w2o[idx * 3 + 1].z + dL_dmean2D[idx].z * w2o[idx * 3 + 2].z ) * (sq(depths[idx]) + 1.f) * 3e-1f;
+
+	// 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);
+}
+
+// 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* tan_theta,
+	const float* tan_phi,
+	const float* __restrict__ raymap,
+	const float focal_x,
+	const float focal_y,
+	const int mode,
+	const float* __restrict__ bg_color,
+	const float3* __restrict__ points_xyz_view,
+	const float2* __restrict__ h_opacity,
+	const float3* __restrict__ w2o, 
+	const float* __restrict__ colors,
+	const float* __restrict__ depths,
+	const float* __restrict__ final_Ts,
+	const uint32_t* __restrict__ n_contrib,
+	const float* __restrict__ dL_dpixels,
+	const float* __restrict__ dL_invdepths,
+	float3* __restrict__ dL_dmean2D,
+	glm::vec3* __restrict__ dL_dmeans,
+	float* __restrict__ dL_dopacity,
+	float* __restrict__ dL_dcolors,
+	float* __restrict__ dL_dinvdepths,
+	glm::vec3* __restrict__ dL_dsigmaInv
+)
+{
+	// 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 = { pix_min.x + block.thread_index().x, pix_min.y + block.thread_index().y };
+	const uint32_t pix_id = W * pix.y + pix.x;
+
+	// Compute per-pixel ray direction matching the forward pass mode logic.
+	float3 rayf;
+	if (mode == 0) {
+		// BEAP mode: look up ray direction in the sorted reference arrays.
+		// In BEAP mode W == len(tan_theta) and H == len(tan_phi), so the
+		// clamped indices are always in bounds.
+		rayf = {(float)tan_theta[min(pix.x, W-1)], (float)tan_phi[min(pix.y, H-1)], 1.f};
+	} else if (mode == 1) {
+		// KB / EQ mode: per-pixel ray directions stored in the raymap [H, W, 3].
+		// Guard against out-of-bounds threads at tile edges.
+		const uint32_t safe_id = min(pix_id, (uint32_t)(W * H - 1));
+		rayf = make_float3(raymap[safe_id * 3], raymap[safe_id * 3 + 1], raymap[safe_id * 3 + 2]);
+	} else {
+		// PH mode (and any future pinhole-like mode): compute ray direction
+		// analytically from focal lengths, matching the forward kernel formula.
+		rayf = { ((float)pix.x + 0.5f) / focal_x - W / (2.0f * focal_x),
+		         ((float)pix.y + 0.5f) / focal_y - H / (2.0f * focal_y),
+		         1.0f };
+	}
+
+	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__ float3 collected_xyz[BLOCK_SIZE];
+	__shared__ float2 collected_h_opacity[BLOCK_SIZE];
+	__shared__ float3 collected_w2o[BLOCK_SIZE * 3];
+	__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 ? final_Ts[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 dL_invdepth;
+	float accum_invdepth_rec = 0;
+	if (inside)
+	{
+		for (int i = 0; i < C; i++)
+			dL_dpixel[i] = dL_dpixels[i * H * W + pix_id];
+		if(dL_invdepths)
+		dL_invdepth = dL_invdepths[pix_id];
+	}
+
+	float last_alpha = 0;
+	float last_color[C] = { 0 };
+	float last_invdepth = 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];
+			int thread_idx = block.thread_rank();
+
+			collected_id[thread_idx] = coll_id;
+			collected_xyz[thread_idx] = points_xyz_view[coll_id];  
+
+			collected_h_opacity[thread_idx] = h_opacity[coll_id];
+			for (int j = 0; j < 3; j++) {
+				collected_w2o[thread_idx * 3 + j] = w2o[coll_id * 3 + j];  
+			}
+
+			for (int i = 0; i < C; i++)
+				collected_colors[i * BLOCK_SIZE + thread_idx] = colors[coll_id * C + i];
+
+			if(dL_invdepths)
+			collected_depths[thread_idx] = 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 float3 xyz = collected_xyz[j];
+			const float2 h_o = collected_h_opacity[j];
+			float3* w2o_rows = collected_w2o + j * 3; 
+			
+			// see 3DGEER paper: https://openreview.net/pdf?id=4voMNlRWI7 (Eq. 5, Sec.C)
+			// Transform Gaussian centre and ray direction into the canonical/object frame
+			// using the packed world-to-object matrix rows w2o_rows[0..2].
+			const float3 p_obj = { dot(xyz, w2o_rows[0]), dot(xyz, w2o_rows[1]), dot(xyz, w2o_rows[2]) };
+			const float3 d_obj = { dot(rayf, w2o_rows[0]), dot(rayf, w2o_rows[1]), dot(rayf, w2o_rows[2]) };  
+			const float3 normal = cross(d_obj, p_obj);
+			const float dobj_norm_sq = dot(d_obj, d_obj);
+			const float D2 = dot(normal, normal) / dobj_norm_sq;
+			const float power_mah = -0.5f * D2;
+
+			if (power_mah > 0.0f)
+				continue;
+
+			const float G = exp(power_mah);
+			const float alpha = min(0.99f, h_o.y * G);
+			if (alpha < 1.0f / 255.0f)
+				continue;
+
+			T = T / (1.f - alpha);
+			const float dchannel_dcolor = alpha * T;
+
+			// Propagate gradients to per-Gaussian colors and keep
+			// gradients w.r.t. alpha (blending factor for a Gaussian/pixel
+			// pair).
+			float dL_dalpha = 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_dalpha += (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 inverse depth to alphaas and
+			// per Gaussian inverse depths
+			if (dL_dinvdepths)
+			{
+				const float invd = 1.f / collected_depths[j];
+				accum_invdepth_rec = last_alpha * last_invdepth + (1.f - last_alpha) * accum_invdepth_rec;
+				last_invdepth = invd;
+				dL_dalpha += (invd - accum_invdepth_rec) * dL_invdepth;
+				atomicAdd(&(dL_dinvdepths[global_id]), dchannel_dcolor * dL_invdepth);
+			}
+
+			dL_dalpha *= 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_dalpha += (-T_final / (1.f - alpha)) * bg_dot_dpixel;
+
+
+			// Helpful reusable temporary variables
+			const float dL_dG = h_o.y * dL_dalpha;
+
+			const float dL_dD2 = -0.5f * dL_dG * G;  
+			const float3 dL_dnormal = { 2.f * dL_dD2 * normal.x / dobj_norm_sq, 2.f * dL_dD2 * normal.y / dobj_norm_sq, 2.f * dL_dD2 * normal.z / dobj_norm_sq };  
+			const float dL_ddenom = dL_dG * G * (-power_mah / dobj_norm_sq);  
+			float3 dL_dpobj;
+			dL_dpobj.x = dL_dnormal.y * d_obj.z - dL_dnormal.z * d_obj.y;
+			dL_dpobj.y = dL_dnormal.z * d_obj.x - dL_dnormal.x * d_obj.z;
+			dL_dpobj.z = dL_dnormal.x * d_obj.y - dL_dnormal.y * d_obj.x;
+
+			atomicAdd(&dL_dmeans[global_id].x, dL_dpobj.x);
+			atomicAdd(&dL_dmeans[global_id].y, dL_dpobj.y);
+			atomicAdd(&dL_dmeans[global_id].z, dL_dpobj.z);
+
+			atomicAdd(&dL_dmean2D[global_id].x, fabsf(dL_dpobj.x));
+			atomicAdd(&dL_dmean2D[global_id].y, fabsf(dL_dpobj.y));
+			atomicAdd(&dL_dmean2D[global_id].z, fabsf(dL_dpobj.z));
+
+			// see 3DGEER: https://openreview.net/pdf?id=4voMNlRWI7 (Eq.C.6-8)
+			float dL_ddobj[3];
+			dL_ddobj[0] = 2.f * dL_ddenom * d_obj.x - dL_dnormal.y * p_obj.z + dL_dnormal.z * p_obj.y;
+			dL_ddobj[1] = 2.f * dL_ddenom * d_obj.y - dL_dnormal.z * p_obj.x + dL_dnormal.x * p_obj.z;
+			dL_ddobj[2] = 2.f * dL_ddenom * d_obj.z - dL_dnormal.x * p_obj.y + dL_dnormal.y * p_obj.x;
+			// Atomic addition component-wise
+			#pragma unroll
+			for (int i = 0; i < 3; i++) {
+				atomicAdd(&dL_dsigmaInv[global_id * 3 + i].x, dL_ddobj[i] * rayf.x);
+				atomicAdd(&dL_dsigmaInv[global_id * 3 + i].y, dL_ddobj[i] * rayf.y);
+				atomicAdd(&dL_dsigmaInv[global_id * 3 + i].z, dL_ddobj[i] * rayf.z);
+			}
+
+			// Update gradients w.r.t. opacity of the Gaussian
+			atomicAdd(&(dL_dopacity[global_id]), G * dL_dalpha);
+		}
+	}
+}
+
+void BACKWARD::preprocess(
+	int P, int D, int M,
+	const float3* means3D,
+	const float3* means3D_view,  
+	const float* depths,
+	const int* radii,
+	const float* shs,
+	const bool* clamped,
+	const float* opacities,
+	const glm::vec3* scales,
+	const glm::vec4* rotations,
+	const float scale_modifier, 
+	const float2* h_opacity,
+	const float3* w2o,  
+	const float* viewmatrix,
+	const float focal_x, float focal_y,
+	const float tan_fovx, float tan_fovy,
+	const glm::vec3* campos,
+	float3* dL_dmean2D,
+	const float* dL_dinvdepth,
+	float* dL_dopacity,
+	glm::vec3* dL_dmean3D,
+	float* dL_dcolor,
+	float* dL_dsh,
+	glm::vec3* dL_dscale,
+	glm::vec4* dL_drot,
+	const glm::vec3* dL_dsigmaInv,
+	bool antialiasing)
+{
+	// 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.	
+	preprocessCUDA_mah<NUM_CHANNELS> << < (P + 255) / 256, 256 >> > (
+		P, D, M,
+		(float3*)means3D,
+		(float3*)means3D_view,  
+		depths,
+		radii,
+		h_opacity,
+		w2o,
+		viewmatrix,
+		shs,
+		clamped,
+		(glm::vec3*)scales,
+		(glm::vec4*)rotations,
+		scale_modifier,
+		campos,
+		tan_fovx, tan_fovy,
+		focal_x, focal_y,
+		(glm::vec3*)dL_dmean3D,
+		(glm::vec3*)dL_dmean2D,
+		dL_dcolor,
+		dL_dsh,
+		dL_dscale,
+		dL_drot,
+		(glm::vec3*)dL_dsigmaInv,
+		dL_dopacity);
+}
+
+void BACKWARD::render(
+	const dim3 grid, const dim3 block,
+	const uint2* ranges,
+	const uint32_t* point_list,
+	int W, int H,
+	const float* tan_theta,  
+	const float* tan_phi,
+	const float* raymap,
+	const float focal_x, const float focal_y,
+	const int mode,
+	const float* bg_color,
+	const float3* means3D_view,
+	const float2* h_opacity,
+	const float3* w2o, 
+	const float* colors,
+	const float* depths,
+	const float* final_Ts,
+	const uint32_t* n_contrib,
+	const float* dL_dpixels,
+	const float* dL_invdepths,
+	float3* dL_dmean2D,
+	glm::vec3* dL_dmean3D,  
+	float* dL_dopacity,
+	float* dL_dcolors,
+	float* dL_dinvdepths,
+	glm::vec3* dL_dsigmaInv)
+{
+	renderCUDA<NUM_CHANNELS> << <grid, block >> >(
+		ranges,
+		point_list,
+		W, H,
+		tan_theta, tan_phi,
+		raymap,
+		focal_x, focal_y,
+		mode,
+		bg_color,
+		means3D_view,  
+		h_opacity,
+		w2o,
+		colors,
+		depths,
+		final_Ts,
+		n_contrib,
+		dL_dpixels,
+		dL_invdepths,
+		dL_dmean2D,
+		dL_dmean3D, 
+		dL_dopacity,
+		dL_dcolors,
+		dL_dinvdepths,
+		dL_dsigmaInv);
+}

3dgeer/submodules/geer-rasterizer/cuda_rasterizer/backward.h

@@ -0,0 +1,80 @@
+/*
+ * 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  george.drettakis@inria.fr
+ */
+
+#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* tan_theta,
+		const float* tan_phi,
+		const float* raymap,
+		const float focal_x, float focal_y,
+		int mode,
+		const float* bg_color,
+		const float3* means3D_view,
+		const float2* h_opacity,
+		const float3* w2o,
+		const float* colors,
+		const float* depths,
+		const float* final_Ts,
+		const uint32_t* n_contrib,
+		const float* dL_dpixels,
+		const float* dL_invdepths,
+		float3* dL_dmean2D,
+		glm::vec3* dL_dmeans,
+		float* dL_dopacity,
+		float* dL_dcolors,
+		float* dL_dinvdepths,
+		glm::vec3* dL_dsigmaInv);
+
+	void preprocess(
+		int P, int D, int M,
+		const float3* means,
+		const float3* means3D_view,
+		const float* depths,
+		const int* radii,
+		const float* shs,
+		const bool* clamped,
+		const float* opacities,
+		const glm::vec3* scales,
+		const glm::vec4* rotations,
+		const float scale_modifier,
+		const float2* h_opacity,
+		const float3* w2o,
+		const float* view,
+		const float focal_x, float focal_y,
+		const float tan_fovx, float tan_fovy,
+		const glm::vec3* campos,
+		float3* dL_dmean2D,
+		const float* dL_dinvdepth,
+		float* dL_dopacity,
+		glm::vec3* dL_dmeans,
+		float* dL_dcolor,
+		float* dL_dsh,
+		glm::vec3* dL_dscale,
+		glm::vec4* dL_drot,
+		const glm::vec3* dL_dsigmaInv,
+		bool antialiasing);
+}
+
+#endif

3dgeer/submodules/geer-rasterizer/cuda_rasterizer/config.h

@@ -0,0 +1,19 @@
+/*
+ * Copyright (C) 2023, Inria
+ * GRAPHDECO research group, https://team.inria.fr/graphdeco
+ * All rights reserved.
+ *
+ * This software is free for non-commercial, research and evaluation use 
+ * under the terms of the LICENSE.md file.
+ *
+ * For inquiries contact  george.drettakis@inria.fr
+ */
+
+#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

3dgeer/submodules/geer-rasterizer/cuda_rasterizer/forward.cu

@@ -0,0 +1,1249 @@
+/*
+ * 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  george.drettakis@inria.fr
+ */
+
+#include "forward.h"
+#include "auxiliary.h"
+#include <thrust/sort.h>
+#include <thrust/binary_search.h>
+#include <cooperative_groups.h>
+#include <cooperative_groups/reduce.h>
+namespace cg = cooperative_groups;
+
+__device__ glm::mat3 computeRotationMatrix(const glm::vec4 rot, const float* viewmatrix)
+{
+	// 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)
+	);
+
+	// viewmatrix float* has been the column-major, 0,1,2 is the column; 
+	glm::mat3 W = glm::mat3(
+		viewmatrix[0], viewmatrix[1], viewmatrix[2],
+		viewmatrix[4], viewmatrix[5], viewmatrix[6],
+		viewmatrix[8], viewmatrix[9], viewmatrix[10]);
+
+	glm::mat3 R_view = W * R;
+	return R_view;
+}
+
+__device__ bool computeCov3D(const glm::vec3 scale, const float mod, const glm::mat3 R_view, float* cov3D, const float h_var)
+{
+	glm::mat3 R_scaled = glm::mat3(
+        R_view[0] * (sq(scale.x * mod) + h_var),
+        R_view[1] * (sq(scale.y * mod) + h_var),
+        R_view[2] * (sq(scale.z * mod) + h_var)
+	);
+
+	glm::mat3 Cov3D_mat = R_scaled * glm::transpose(R_view);
+
+	// Covariance is symmetric, only store upper right
+	cov3D[0] = Cov3D_mat[0][0];
+	cov3D[1] = Cov3D_mat[0][1];
+	cov3D[2] = Cov3D_mat[0][2];
+	cov3D[3] = Cov3D_mat[1][1];
+	cov3D[4] = Cov3D_mat[1][2];
+	cov3D[5] = Cov3D_mat[2][2];
+
+	const float det_cov_plus_h_cov = cov3D[0] * cov3D[3] * cov3D[5] + 2.f * cov3D[1] * cov3D[2] * cov3D[4] - cov3D[0] * cov3D[4] * cov3D[4] - cov3D[3] * cov3D[2] * cov3D[2] - cov3D[5] * cov3D[1] * cov3D[1];
+
+	if (det_cov_plus_h_cov == 0.0f)
+		return false;
+
+	return true;
+}
+
+__forceinline__ __device__ void searchsorted_pbf(
+    const float* ref_u, int u_span,
+    const float* ref_v, int v_span,
+    const float* uv_values,
+    int* u_indices, int* v_indices) {
+    thrust::lower_bound(thrust::device, ref_u, ref_u + u_span, uv_values, uv_values + 2, u_indices);
+    thrust::lower_bound(thrust::device, ref_v, ref_v + v_span, uv_values + 2, uv_values + 4, v_indices);
+}
+
+__forceinline__ __device__ void invinterpolated_pbf(
+	const int W, int H,
+	const float focal_x, float focal_y, 
+	const float principal_x, float principal_y, 
+	const float4 dist_coeff, 
+	const float4 tan_xxyy,
+    int* u_indices, int* v_indices) {
+	if ((tan_xxyy.y < 0.0f && tan_xxyy.z > 0.0f) || (tan_xxyy.x > 0.0f && tan_xxyy.w < 0.0f)) {
+		float2 _left_bottom = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, tan_xxyy.x, tan_xxyy.z);
+		float2 _right_top = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, tan_xxyy.y, tan_xxyy.w);
+		u_indices[0] = (int)floor(_left_bottom.x);
+		u_indices[1] = (int)floor(_right_top.x);
+		v_indices[0] = (int)floor(_left_bottom.y);
+		v_indices[1] = (int)floor(_right_top.y);
+	} else if ((tan_xxyy.y < 0.0f && tan_xxyy.w < 0.0f) || (tan_xxyy.x > 0.0f && tan_xxyy.z > 0.0f)) {
+		float2 _left_top = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, tan_xxyy.x, tan_xxyy.w);
+		float2 _right_bottom = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, tan_xxyy.y, tan_xxyy.z);
+		u_indices[0] = (int)floor(_left_top.x);
+		u_indices[1] = (int)floor(_right_bottom.x);
+		v_indices[0] = (int)floor(_right_bottom.y);
+		v_indices[1] = (int)floor(_left_top.y);
+	} else if ((tan_xxyy.x < 0.0f && tan_xxyy.y > 0.0f) && tan_xxyy.z > 0.0f) {
+		float2 _left_bottom = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, tan_xxyy.x, tan_xxyy.z);
+		float2 _right_bottom = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, tan_xxyy.y, tan_xxyy.z);
+		float2 _mid_top = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, 0.0f, tan_xxyy.w);
+		u_indices[0] = (int)floor(_left_bottom.x);
+		u_indices[1] = (int)floor(_right_bottom.x);
+		v_indices[0] = (int)floor(fminf(_left_bottom.y, _right_bottom.y));
+		v_indices[1] = (int)floor(_mid_top.y);
+	} else if ((tan_xxyy.x < 0.0f && tan_xxyy.y > 0.0f) && tan_xxyy.w < 0.0f) {
+		float2 _right_top = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, tan_xxyy.y, tan_xxyy.w);
+		float2 _left_top = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, tan_xxyy.x, tan_xxyy.w);
+		float2 _mid_bottom = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, 0.0f, tan_xxyy.z);
+		u_indices[0] = (int)floor(_left_top.x);
+		u_indices[1] = (int)floor(_right_top.x);
+		v_indices[0] = (int)floor(_mid_bottom.y);
+		v_indices[1] = (int)floor(fmaxf(_left_top.y, _right_top.y));
+	} else if ((tan_xxyy.z < 0.0f && tan_xxyy.w > 0.0f) && tan_xxyy.y < 0.0f) {
+		float2 _right_top = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, tan_xxyy.y, tan_xxyy.w);
+		float2 _right_bottom = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, tan_xxyy.y, tan_xxyy.z);
+		float2 _left_mid = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, tan_xxyy.x, 0.0f);
+		u_indices[0] = (int)floor(_left_mid.x);
+		u_indices[1] = (int)floor(fmaxf(_right_bottom.x, _right_top.x));
+		v_indices[0] = (int)floor(_right_bottom.y);
+		v_indices[1] = (int)floor(_right_top.y);
+	} else if ((tan_xxyy.z < 0.0f && tan_xxyy.w > 0.0f) && tan_xxyy.x > 0.0f) {
+		float2 _left_bottom = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, tan_xxyy.x, tan_xxyy.z);
+		float2 _left_top = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, tan_xxyy.x, tan_xxyy.w);
+		float2 _right_mid = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, tan_xxyy.y, 0.0f);
+		u_indices[0] = (int)floor(fminf(_left_bottom.x, _left_top.x));
+		u_indices[1] = (int)floor(_right_mid.x);
+		v_indices[0] = (int)floor(_left_bottom.y);
+		v_indices[1] = (int)floor(_left_top.y);
+	} else {
+		float2 _mid_top = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, 0.0f, tan_xxyy.w);
+		float2 _mid_bottom = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, 0.0f, tan_xxyy.z);
+		float2 _left_mid = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, tan_xxyy.x, 0.0f);
+		float2 _right_mid = invinterpolated_uv(focal_x, focal_y, principal_x, principal_y, dist_coeff, tan_xxyy.y, 0.0f);
+		u_indices[0] = (int)floor(_left_mid.x);
+		u_indices[1] = (int)floor(_right_mid.x);
+		v_indices[0] = (int)floor(_mid_bottom.y);
+		v_indices[1] = (int)floor(_mid_top.y);
+	}
+	u_indices[0] = fminf(fmaxf((int)0, u_indices[0]), (int)(W-1));
+	u_indices[1] = fminf(fmaxf((int)0, u_indices[1]), (int)(W-1));
+	v_indices[0] = fminf(fmaxf((int)0, v_indices[0]), (int)(H-1));
+	v_indices[1] = fminf(fmaxf((int)0, v_indices[1]), (int)(H-1));
+}
+
+// Compute antialiasing variance (h_var) and pack into h_opacity:
+//   h_opacity->x = h_var  (small isotropic variance added to each axis for anti-aliasing)
+//   h_opacity->y = antialiasing-scaled Gaussian opacity
+// Returns false if the resulting opacity falls below the visibility threshold.
+__device__ bool omni_hvar(const glm::vec3 scale, const float mod, const float opacity, float2* h_opacity, bool antialiasing)
+{
+	float h_var = 1e-7f;
+	
+	float h_cov_scaling = 1.0f;
+	if (antialiasing) {
+		h_cov_scaling = (scale.x * mod) * (scale.y * mod) * (scale.z * mod) / sqrtf((sq(scale.x * mod) + h_var) * (sq(scale.y * mod) + h_var) * (sq(scale.z * mod) + h_var));
+	}
+
+	h_opacity->x = h_var;
+	h_opacity->y = h_cov_scaling * opacity;
+
+	if (h_opacity->y < 1.0f / 255.0f)
+		return false;
+
+	return true;
+}
+
+__device__ void mirror_transform_pbf(const float4& m, const float xi, float* result) {
+	float _m0 = xi * sqrtf(1 + m.x * m.x);
+	float _m1 = xi * sqrtf(1 + m.y * m.y);
+	float _m2 = xi * sqrtf(1 + m.z * m.z);
+	float _m3 = xi * sqrtf(1 + m.w * m.w);
+	result[0] = m.x / (1 + _m0);
+	result[1] = m.x / (1 - _m0);
+	result[2] = m.y / (1 + _m1);
+	result[3] = m.y / (1 - _m1);
+	result[4] = m.z / (1 + _m2);
+	result[5] = m.z / (1 - _m2);
+	result[6] = m.w / (1 + _m3);
+	result[7] = m.w / (1 - _m3);
+}
+
+__device__ void mirror_transform_fov(const float tan_fovx, const float tan_fovy, const float xi, float* result) {
+	float _tan_fovx = xi * sqrtf(1 + tan_fovx * tan_fovx);
+	float _tan_fovy = xi * sqrtf(1 + tan_fovy * tan_fovy);
+	result[0] = tan_fovx / (1 + _tan_fovx);
+	result[1] = -result[0];
+	result[2] = tan_fovy / (1 + _tan_fovy);
+	result[3] = -result[2];
+}
+
+__forceinline__ __device__ float mirror_transform_tan(const float m, const float z, const float xi) {
+    if (xi == 0.0f) {
+        return m;
+    }
+	return m / (1 + xi * (z / fabsf(z)) * sqrtf(1 + m * m));
+}
+
+// Compute the Particle Bounding Frustum (PBF) for a 3D Gaussian in ray-direction
+// tangent space.  The PBF is a tight axis-aligned bounding box (AABB) on the set
+// of rays that intersect the Gaussian's λ-sigma ellipsoid.  It is defined as
+//   pbf = {tan_theta_min, tan_theta_max, tan_phi_min, tan_phi_max}
+// and maps directly to pixel ranges via the BEAP reference arrays or the KB grid.
+// See 3DGEER paper (https://openreview.net/pdf?id=4voMNlRWI7), Sec. D / Eq. 10.
+// Returns false if the Gaussian is degenerate or entirely outside the frustum.
+__device__ bool computePBF(
+    const glm::vec3 scale, const float mod, const glm::mat3 R_view, const float3 p_view, const float lambda, float4& pbf, const float tan_fovx, const float tan_fovy, float h_var)
+{
+    float lambda_sq = sq(lambda);
+	float cov3d[6];
+	if (!computeCov3D(scale, mod, R_view, cov3d, h_var))
+		return false;
+	
+	float Tc_22 = lambda_sq * cov3d[5] - p_view.z * p_view.z;
+	if (Tc_22 == 0.0f)
+		return false;
+
+	float Tc_00 = lambda_sq * cov3d[0] - p_view.x * p_view.x;
+    float Tc_02 = lambda_sq * cov3d[2] - p_view.x * p_view.z;
+    float Tc_11 = lambda_sq * cov3d[3] - p_view.y * p_view.y;
+    float Tc_12 = lambda_sq * cov3d[4] - p_view.y * p_view.z;
+
+    float center[2];
+    center[0] = Tc_02 / Tc_22;
+    center[1]= Tc_12 / Tc_22;
+
+    float half_extend[2];
+    half_extend[0] = sqrtf(Tc_02 * Tc_02 - Tc_22 * Tc_00) / fabsf(Tc_22);
+    half_extend[1] = sqrtf(Tc_12 * Tc_12 - Tc_22 * Tc_11) / fabsf(Tc_22);
+
+	bool neg = false;
+	if (isnan(half_extend[0]))
+	{ 
+		half_extend[0] = fmaxf(fabsf(center[0] - tan_fovx), fabsf(center[0] + tan_fovx));
+		neg = true; 
+	}
+	if (isnan(half_extend[1]))
+	{ 
+		half_extend[1] = fmaxf(fabsf(center[1] - tan_fovy), fabsf(center[1] + tan_fovy));
+		neg = true;
+	}
+	float _left = center[0] - half_extend[0];
+	float _right = center[0] + half_extend[0];
+	float _bottom = center[1] - half_extend[1];
+	float _upper = center[1] + half_extend[1];
+
+    pbf.x = _left;
+    pbf.y = _right;
+	pbf.z = _bottom;
+    pbf.w = _upper;
+
+	// If half-extend is negative, return and do not compute the omni
+	if (neg) return false;
+
+	// Omni mapping for AABB
+	float xi = 1.0;
+    float mirror_transformed_pbf[8];
+	mirror_transform_pbf(pbf, xi, mirror_transformed_pbf);
+
+    const float eps = 1e-6f;
+    float depth = p_view.z;
+    depth = (fabsf(depth) < eps) ? eps : depth; // Prevent division by zero
+    float gaus_center_omni[2] = {
+        mirror_transform_tan(p_view.x / depth, depth, xi),
+        mirror_transform_tan(p_view.y / depth, depth, xi)
+    };
+
+    float fov_omni[4];
+    mirror_transform_fov(tan_fovx, tan_fovy, xi, fov_omni);
+
+    float aa_omni[4] = { mirror_transformed_pbf[0], mirror_transformed_pbf[1], mirror_transformed_pbf[2], mirror_transformed_pbf[3] };
+	float bb_omni[4] = { mirror_transformed_pbf[4], mirror_transformed_pbf[5], mirror_transformed_pbf[6], mirror_transformed_pbf[7] };
+	float a_min = -INFINITY;
+	float a_max = INFINITY;
+	float b_min = -INFINITY;
+	float b_max = INFINITY;
+
+    int a_min_idx = -1;
+	int a_max_idx = -1;
+	int b_min_idx = -1;
+	int b_max_idx = -1;
+
+	for (int i = 0; i < 4; i++) {
+        if (aa_omni[i] < gaus_center_omni[0] && aa_omni[i] >= a_min){
+            a_min = aa_omni[i];
+            a_min_idx = i;
+        }
+        if (aa_omni[i] > gaus_center_omni[0] && aa_omni[i] <= a_max){ 
+            a_max = aa_omni[i];
+            a_max_idx = i;
+        }
+		if (bb_omni[i] < gaus_center_omni[1] && bb_omni[i] >= b_min){
+            b_min = bb_omni[i];
+            b_min_idx = i;
+        }
+        if (bb_omni[i] > gaus_center_omni[1] && bb_omni[i] <= b_max){
+            b_max = bb_omni[i];
+            b_max_idx = i;
+        }
+    }
+    if (a_min < fov_omni[1]) a_min_idx = 4;
+    if (a_min > fov_omni[0]) a_min_idx = 5;
+
+    if (a_max < fov_omni[1]) a_max_idx = 4;
+    if (a_max > fov_omni[0]) a_max_idx = 5;
+
+    if (b_min < fov_omni[3]) b_min_idx = 4;
+    if (b_min > fov_omni[2]) b_min_idx = 5;
+
+    if (b_max < fov_omni[3]) b_max_idx = 4;
+    if (b_max > fov_omni[2]) b_max_idx = 5;
+
+    if (a_min_idx == 4) pbf.x = -tan_fovx;
+    else if (a_min_idx == 5) pbf.x = tan_fovx;
+    else if (a_min_idx == 0) pbf.x = _left;
+    else if (a_min_idx == 1) pbf.x = _left;
+    else if (a_min_idx == 2) pbf.x = _right;
+    else if (a_min_idx == 3) pbf.x = _right;
+    
+    if (a_max_idx == 5) pbf.y = tan_fovx;
+    else if (a_max_idx == 4) pbf.y = -tan_fovx;
+    else if (a_max_idx == 0) pbf.y = _left;
+    else if (a_max_idx == 1) pbf.y = _left;
+    else if (a_max_idx == 2) pbf.y = _right;
+    else if (a_max_idx == 3) pbf.y = _right;
+
+    if (b_min_idx == 4) pbf.z = -tan_fovy;
+    else if (b_min_idx == 5) pbf.z = tan_fovy;
+    else if (b_min_idx == 0) pbf.z = _bottom;
+    else if (b_min_idx == 1) pbf.z = _bottom;
+    else if (b_min_idx == 2) pbf.z = _upper;
+    else if (b_min_idx == 3) pbf.z = _upper;
+
+    if (b_max_idx == 5) pbf.w = tan_fovy;
+    else if (b_max_idx == 4) pbf.w = -tan_fovy;
+    else if (b_max_idx == 0) pbf.w = _bottom;
+    else if (b_max_idx == 1) pbf.w = _bottom;
+    else if (b_max_idx == 2) pbf.w = _upper;
+    else if (b_max_idx == 3) pbf.w = _upper;
+
+    return true;
+}
+
+// For runtime ablation: PBF vs. UT vs. EWA
+
+__device__ void sample_ut(const glm::vec3 scale, const float mod, const glm::mat3 R_view, const float3 p_view, float2& p_ut, float3& cov_ut){
+	float ut_sqrt = sqrtf(ut_lambda + 3.f);
+	float2 x_[7];
+	glm::vec3 p_view_vec(p_view.x, p_view.y, p_view.z);
+	x_[0] = atan(divide_z(p_view_vec));
+	x_[1] = atan(divide_z(p_view_vec + (ut_sqrt * R_view[0] * scale.x * mod)));
+	x_[2] = atan(divide_z(p_view_vec + (ut_sqrt * R_view[1] * scale.y * mod)));
+	x_[3] = atan(divide_z(p_view_vec + (ut_sqrt * R_view[2] * scale.z * mod)));
+	x_[4] = atan(divide_z(p_view_vec - (ut_sqrt * R_view[0] * scale.x * mod)));
+	x_[5] = atan(divide_z(p_view_vec - (ut_sqrt * R_view[1] * scale.y * mod)));
+	x_[6] = atan(divide_z(p_view_vec - (ut_sqrt * R_view[2] * scale.z * mod)));
+
+	float l1 = ut_lambda / (ut_lambda + 3.0f);
+	float l2 = 0.5f / (ut_lambda + 3.0f);
+
+	p_ut.x = (l1) * x_[0].x + (l2) * (x_[1].x + x_[2].x + x_[3].x + x_[4].x + x_[5].x + x_[6].x);
+	p_ut.y = (l1) * x_[0].y + (l2) * (x_[1].y + x_[2].y + x_[3].y + x_[4].y + x_[5].y + x_[6].y);
+
+	cov_ut.x = (l1 + 1.f - sq(ut_alpha) + ut_beta) * sq(x_[0].x - p_ut.x) + (l2) * (sq(x_[1].x - p_ut.x) + sq(x_[2].x - p_ut.x) + sq(x_[3].x - p_ut.x) + sq(x_[4].x - p_ut.x) + sq(x_[5].x - p_ut.x) + sq(x_[6].x - p_ut.x));
+
+	cov_ut.y = (l1 + 1.f - sq(ut_alpha) + ut_beta) * (x_[0].x - p_ut.x) * (x_[0].y - p_ut.y) + (l2) * ((x_[1].x - p_ut.x) * (x_[1].y - p_ut.y) + (x_[2].x - p_ut.x) * (x_[2].y - p_ut.y) + (x_[3].x - p_ut.x) * (x_[3].y - p_ut.y) + (x_[4].x - p_ut.x) * (x_[4].y - p_ut.y) + (x_[5].x - p_ut.x) * (x_[5].y - p_ut.y) + (x_[6].x - p_ut.x) * (x_[6].y - p_ut.y));
+
+	cov_ut.z = (l1 + 1.f - sq(ut_alpha) + ut_beta) * sq(x_[0].y - p_ut.y) + (l2) * (sq(x_[1].y - p_ut.y) + sq(x_[2].y - p_ut.y) + sq(x_[3].y - p_ut.y) + sq(x_[4].y - p_ut.y) + sq(x_[5].y - p_ut.y) + sq(x_[6].y - p_ut.y));
+}
+
+
+__device__ float2 computeEllipseIntersection(
+	const float3 con_o, const float disc, const float t, const float2 p,
+	const bool isY, const float coord)
+{
+	float p_u = isY ? p.y : p.x;
+	float p_v = isY ? p.x : p.y;
+	float coeff = isY ? con_o.x : con_o.z;
+
+	float h = coord - p_u;  // h = y - p.y for y, x - p.x for x
+	float sqrt_term = sqrt(disc * h * h + t * coeff);
+
+	return {
+	  (-con_o.y * h - sqrt_term) / coeff + p_v,
+	  (-con_o.y * h + sqrt_term) / coeff + p_v
+	};
+}
+
+__device__ bool computeAABB_UT(
+    const glm::vec3 scale, const float mod, const glm::mat3 R_view, const float3 p_view, const float lambda, float4& aabb, const float tan_fovx, const float tan_fovy, float h_var, bool tighten)
+{
+	float3 cov;
+	float2 p;
+	sample_ut(scale, mod, R_view, p_view, p, cov); // https://arxiv.org/abs/2412.12507
+	const float det = cov.x * cov.z - cov.y * cov.y;
+	if (det == 0.0f)
+		return false;
+	float det_inv = 1.f / det;
+
+	float center_angle[2];
+	center_angle[0] = p.x;
+    center_angle[1]= p.y;
+
+	float half_extend_angle[2];
+	if (tighten)
+	{
+		// tighten the AABB https://arxiv.org/pdf/2412.00578
+		float3 conic = { cov.z * det_inv, -cov.y * det_inv, cov.x * det_inv };
+		float denom = sq(conic.y) - conic.x * conic.z;
+		if (conic.x <= 0 || conic.z <= 0 || denom >= 0) {
+			return false;
+		}
+
+		float x_term = lambda * sqrt(-sq(conic.y) / (denom * conic.x));
+		x_term = (conic.y < 0) ? x_term : -x_term;
+		float y_term = lambda * sqrt(-sq(conic.y) / (denom * conic.z));
+		y_term = (conic.y < 0) ? y_term : -y_term;
+		float2 bbox_argmin = { p.y - y_term, p.x - x_term };
+		float2 bbox_argmax = { p.y + y_term, p.x + x_term };
+		float2 bbox_min = {
+			computeEllipseIntersection(conic, denom, sq(lambda), p, true, bbox_argmin.x).x,
+			computeEllipseIntersection(conic, denom, sq(lambda), p, false, bbox_argmin.y).x
+		};
+		float2 bbox_max = {
+		computeEllipseIntersection(conic, denom, sq(lambda), p, true, bbox_argmax.x).y,
+		computeEllipseIntersection(conic, denom, sq(lambda), p, false, bbox_argmax.y).y
+		};
+		half_extend_angle[0] = (bbox_max.x - bbox_min.x) / 2.f;
+		half_extend_angle[1] = (bbox_max.y - bbox_min.y) / 2.f;
+	}
+	else
+	{
+		// loosen the AABB
+		float mid = 0.5f * (cov.x + cov.z);
+		float lambda1 = mid + sqrt(max(0.0f, mid * mid - det));
+		float lambda2 = mid - sqrt(max(0.0f, mid * mid - det));
+		// float my_radius = ceil(3.f * sqrt(max(lambda1, lambda2)));
+		float my_radius = (lambda * sqrt(max(lambda1, lambda2)));
+		half_extend_angle[0] = my_radius; // my_radius / focal_x;
+		half_extend_angle[1] = my_radius; // my_radius / focal_y;
+	}
+
+	float center[2];
+	float half_extend[2];
+	center[0] = (tan(center_angle[0] + half_extend_angle[0]) + tan(center_angle[0] - half_extend_angle[0])) / 2.f;
+	center[1] = (tan(center_angle[1] + half_extend_angle[1]) + tan(center_angle[1] - half_extend_angle[1])) / 2.f;
+	half_extend[0] = (tan(center_angle[0] + half_extend_angle[0]) - tan(center_angle[0] - half_extend_angle[0])) / 2.f;
+	half_extend[1] = (tan(center_angle[1] + half_extend_angle[1]) - tan(center_angle[1] - half_extend_angle[1])) / 2.f;
+
+	float neg = false;
+
+	if (isnan(half_extend[0]))
+	{ 
+		half_extend[0] = fmaxf(fabsf(center[0] - tan_fovx), fabsf(center[0] + tan_fovx));
+		neg = true; 
+	}
+	if (isnan(half_extend[1]))
+	{ 
+		half_extend[1] = fmaxf(fabsf(center[1] - tan_fovy), fabsf(center[1] + tan_fovy));
+		neg = true;
+	}
+	float _left = center[0] - half_extend[0];
+	float _right = center[0] + half_extend[0];
+	float _bottom = center[1] - half_extend[1];
+	float _upper = center[1] + half_extend[1];
+
+    aabb.x = _left;
+    aabb.y = _right;
+	aabb.z = _bottom;
+    aabb.w = _upper;
+
+	// If half-extend is negative, return and do not compute the omni
+	if (neg) return false;
+
+	// Omni mapping for AABB
+	float xi = 1.0;
+    float aabb_omni[8];
+	mirror_transform_pbf(aabb, xi, aabb_omni);
+
+    const float eps = 1e-6f;
+    float depth = p_view.z;
+    depth = (fabsf(depth) < eps) ? eps : depth; // Prevent division by zero
+    float gaus_center_omni[2] = {
+        mirror_transform_tan(p_view.x / depth, depth, xi),
+        mirror_transform_tan(p_view.y / depth, depth, xi)
+    };
+
+    float fov_omni[4];
+    mirror_transform_fov(tan_fovx, tan_fovy, xi, fov_omni);
+
+    float aa_omni[4] = { aabb_omni[0], aabb_omni[1], aabb_omni[2], aabb_omni[3] };
+	float bb_omni[4] = { aabb_omni[4], aabb_omni[5], aabb_omni[6], aabb_omni[7] };
+	float a_min = -INFINITY;
+	float a_max = INFINITY;
+	float b_min = -INFINITY;
+	float b_max = INFINITY;
+
+    int a_min_idx = -1;
+	int a_max_idx = -1;
+	int b_min_idx = -1;
+	int b_max_idx = -1;
+
+	for (int i = 0; i < 4; i++) {
+        if (aa_omni[i] < gaus_center_omni[0] && aa_omni[i] >= a_min){
+            a_min = aa_omni[i];
+            a_min_idx = i;
+        }
+        if (aa_omni[i] > gaus_center_omni[0] && aa_omni[i] <= a_max){ 
+            a_max = aa_omni[i];
+            a_max_idx = i;
+        }
+		if (bb_omni[i] < gaus_center_omni[1] && bb_omni[i] >= b_min){
+            b_min = bb_omni[i];
+            b_min_idx = i;
+        }
+        if (bb_omni[i] > gaus_center_omni[1] && bb_omni[i] <= b_max){
+            b_max = bb_omni[i];
+            b_max_idx = i;
+        }
+    }
+    if (a_min < fov_omni[1]) a_min_idx = 4;
+    if (a_min > fov_omni[0]) a_min_idx = 5;
+
+    if (a_max < fov_omni[1]) a_max_idx = 4;
+    if (a_max > fov_omni[0]) a_max_idx = 5;
+
+    if (b_min < fov_omni[3]) b_min_idx = 4;
+    if (b_min > fov_omni[2]) b_min_idx = 5;
+
+    if (b_max < fov_omni[3]) b_max_idx = 4;
+    if (b_max > fov_omni[2]) b_max_idx = 5;
+
+    if (a_min_idx == 4) aabb.x = -tan_fovx;
+    else if (a_min_idx == 5) aabb.x = tan_fovx;
+    else if (a_min_idx == 0) aabb.x = _left;
+    else if (a_min_idx == 1) aabb.x = _left;
+    else if (a_min_idx == 2) aabb.x = _right;
+    else if (a_min_idx == 3) aabb.x = _right;
+    
+    if (a_max_idx == 5) aabb.y = tan_fovx;
+    else if (a_max_idx == 4) aabb.y = -tan_fovx;
+    else if (a_max_idx == 0) aabb.y = _left;
+    else if (a_max_idx == 1) aabb.y = _left;
+    else if (a_max_idx == 2) aabb.y = _right;
+    else if (a_max_idx == 3) aabb.y = _right;
+
+    if (b_min_idx == 4) aabb.z = -tan_fovy;
+    else if (b_min_idx == 5) aabb.z = tan_fovy;
+    else if (b_min_idx == 0) aabb.z = _bottom;
+    else if (b_min_idx == 1) aabb.z = _bottom;
+    else if (b_min_idx == 2) aabb.z = _upper;
+    else if (b_min_idx == 3) aabb.z = _upper;
+
+    if (b_max_idx == 5) aabb.w = tan_fovy;
+    else if (b_max_idx == 4) aabb.w = -tan_fovy;
+    else if (b_max_idx == 0) aabb.w = _bottom;
+    else if (b_max_idx == 1) aabb.w = _bottom;
+    else if (b_max_idx == 2) aabb.w = _upper;
+    else if (b_max_idx == 3) aabb.w = _upper;
+
+    return true;
+}
+
+__device__ bool computeAABB_EWA(
+    const glm::vec3 scale, const float mod, const glm::mat3 R_view, const float3 p_view, const float lambda, float4& aabb, const float tan_fovx, const float tan_fovy, float h_var, bool tighten)
+{
+    float lambda_sq = sq(lambda);
+	float cov3d[6];
+	if (!computeCov3D(scale, mod, R_view, cov3d, h_var))
+		return false;
+
+	float3 t = p_view;
+	const float txtz = t.x / t.z;
+	const float tytz = t.y / 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 J = glm::mat3(
+		1.f / t.z, 0.0f, -t.x / (t.z * t.z),
+			0.0f, 1.f / t.z, -t.y / (t.z * t.z),
+			0, 0, 0);
+	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 cov2d = glm::transpose(J) * glm::transpose(Vrk) * J;
+	float3 cov = { float(cov2d[0][0]), float(cov2d[0][1]), float(cov2d[1][1]) };
+	const float det = cov.x * cov.z - cov.y * cov.y;
+	if (det == 0.0f)
+		return false;
+	float det_inv = 1.f / det;
+
+	// float3 cov_ut;
+	// float2 p_ut;
+	// sample_ut(scale, mod, R_view, p_view, p_ut, cov_ut);
+	// printf("cov2d: %f %f %f\n cov_ut: %f %f %f\n p2d: %f %f\n p_ut: %f %f\n", cov.x, cov.y, cov.z, cov_ut.x, cov_ut.y, cov_ut.z, txtz, tytz, p_ut.x, p_ut.y);
+
+	// float mid = 0.5f * (cov.x + cov.z);
+	// float lambda1 = mid + sqrt(max(0.0f, mid * mid - det));
+	// float lambda2 = mid - sqrt(max(0.0f, mid * mid - det));
+	// // float my_radius = ceil(3.f * sqrt(max(lambda1, lambda2)));
+	// float my_radius = (lambda * sqrt(max(lambda1, lambda2)));
+
+	float center[2];
+	center[0] = txtz;
+    center[1] = tytz;
+
+	float half_extend[2];
+	if (tighten)
+	{
+		// tighten the AABB https://arxiv.org/pdf/2412.00578
+		float3 conic = { cov.z * det_inv, -cov.y * det_inv, cov.x * det_inv };
+		float denom = sq(conic.y) - conic.x * conic.z;
+		float2 p = { center[0], center[1] };
+		if (conic.x <= 0 || conic.z <= 0 || denom >= 0) {
+			return false;
+		}
+
+		float x_term = lambda * sqrt(-sq(conic.y) / (denom * conic.x));
+		x_term = (conic.y < 0) ? x_term : -x_term;
+		float y_term = lambda * sqrt(-sq(conic.y) / (denom * conic.z));
+		y_term = (conic.y < 0) ? y_term : -y_term;
+		float2 bbox_argmin = { p.y - y_term, p.x - x_term };
+		float2 bbox_argmax = { p.y + y_term, p.x + x_term };
+		float2 bbox_min = {
+			computeEllipseIntersection(conic, denom, sq(lambda), p, true, bbox_argmin.x).x,
+			computeEllipseIntersection(conic, denom, sq(lambda), p, false, bbox_argmin.y).x
+		};
+		float2 bbox_max = {
+		computeEllipseIntersection(conic, denom, sq(lambda), p, true, bbox_argmax.x).y,
+		computeEllipseIntersection(conic, denom, sq(lambda), p, false, bbox_argmax.y).y
+		};
+		half_extend[0] = (bbox_max.x - bbox_min.x) / 2.f;
+		half_extend[1] = (bbox_max.y - bbox_min.y) / 2.f;
+	}
+	else
+	{
+		// loosen the AABB
+		float mid = 0.5f * (cov.x + cov.z);
+		float lambda1 = mid + sqrt(max(0.0f, mid * mid - det));
+		float lambda2 = mid - sqrt(max(0.0f, mid * mid - det));
+		// float my_radius = ceil(3.f * sqrt(max(lambda1, lambda2)));
+		float my_radius = (lambda * sqrt(max(lambda1, lambda2)));
+		half_extend[0] = my_radius; // my_radius / focal_x;
+		half_extend[1] = my_radius; // my_radius / focal_y;
+	}
+
+	float neg = false;
+
+	if (isnan(half_extend[0]))
+	{ 
+		half_extend[0] = fmaxf(fabsf(center[0] - tan_fovx), fabsf(center[0] + tan_fovx));
+		neg = true; 
+	}
+	if (isnan(half_extend[1]))
+	{ 
+		half_extend[1] = fmaxf(fabsf(center[1] - tan_fovy), fabsf(center[1] + tan_fovy));
+		neg = true;
+	}
+	float _left = center[0] - half_extend[0];
+	float _right = center[0] + half_extend[0];
+	float _bottom = center[1] - half_extend[1];
+	float _upper = center[1] + half_extend[1];
+
+    aabb.x = _left;
+    aabb.y = _right;
+	aabb.z = _bottom;
+    aabb.w = _upper;
+
+	// If half-extend is negative, return and do not compute the omni
+	if (neg) return;
+
+	// Omni mapping for AABB
+	float xi = 1.0;
+    float aabb_omni[8];
+	mirror_transform_pbf(aabb, xi, aabb_omni);
+
+    const float eps = 1e-6f;
+    float depth = p_view.z;
+    depth = (fabsf(depth) < eps) ? eps : depth; // Prevent division by zero
+    float gaus_center_omni[2] = {
+        mirror_transform_tan(p_view.x / depth, depth, xi),
+        mirror_transform_tan(p_view.y / depth, depth, xi)
+    };
+
+    float fov_omni[4];
+    mirror_transform_fov(tan_fovx, tan_fovy, xi, fov_omni);
+
+    float aa_omni[4] = { aabb_omni[0], aabb_omni[1], aabb_omni[2], aabb_omni[3] };
+	float bb_omni[4] = { aabb_omni[4], aabb_omni[5], aabb_omni[6], aabb_omni[7] };
+	float a_min = -INFINITY;
+	float a_max = INFINITY;
+	float b_min = -INFINITY;
+	float b_max = INFINITY;
+
+    int a_min_idx = -1;
+	int a_max_idx = -1;
+	int b_min_idx = -1;
+	int b_max_idx = -1;
+
+	for (int i = 0; i < 4; i++) {
+        if (aa_omni[i] < gaus_center_omni[0] && aa_omni[i] >= a_min){
+            a_min = aa_omni[i];
+            a_min_idx = i;
+        }
+        if (aa_omni[i] > gaus_center_omni[0] && aa_omni[i] <= a_max){ 
+            a_max = aa_omni[i];
+            a_max_idx = i;
+        }
+		if (bb_omni[i] < gaus_center_omni[1] && bb_omni[i] >= b_min){
+            b_min = bb_omni[i];
+            b_min_idx = i;
+        }
+        if (bb_omni[i] > gaus_center_omni[1] && bb_omni[i] <= b_max){
+            b_max = bb_omni[i];
+            b_max_idx = i;
+        }
+    }
+    if (a_min < fov_omni[1]) a_min_idx = 4;
+    if (a_min > fov_omni[0]) a_min_idx = 5;
+
+    if (a_max < fov_omni[1]) a_max_idx = 4;
+    if (a_max > fov_omni[0]) a_max_idx = 5;
+
+    if (b_min < fov_omni[3]) b_min_idx = 4;
+    if (b_min > fov_omni[2]) b_min_idx = 5;
+
+    if (b_max < fov_omni[3]) b_max_idx = 4;
+    if (b_max > fov_omni[2]) b_max_idx = 5;
+
+    if (a_min_idx == 4) aabb.x = -tan_fovx;
+    else if (a_min_idx == 5) aabb.x = tan_fovx;
+    else if (a_min_idx == 0) aabb.x = _left;
+    else if (a_min_idx == 1) aabb.x = _left;
+    else if (a_min_idx == 2) aabb.x = _right;
+    else if (a_min_idx == 3) aabb.x = _right;
+    
+    if (a_max_idx == 5) aabb.y = tan_fovx;
+    else if (a_max_idx == 4) aabb.y = -tan_fovx;
+    else if (a_max_idx == 0) aabb.y = _left;
+    else if (a_max_idx == 1) aabb.y = _left;
+    else if (a_max_idx == 2) aabb.y = _right;
+    else if (a_max_idx == 3) aabb.y = _right;
+
+    if (b_min_idx == 4) aabb.z = -tan_fovy;
+    else if (b_min_idx == 5) aabb.z = tan_fovy;
+    else if (b_min_idx == 0) aabb.z = _bottom;
+    else if (b_min_idx == 1) aabb.z = _bottom;
+    else if (b_min_idx == 2) aabb.z = _upper;
+    else if (b_min_idx == 3) aabb.z = _upper;
+
+    if (b_max_idx == 5) aabb.w = tan_fovy;
+    else if (b_max_idx == 4) aabb.w = -tan_fovy;
+    else if (b_max_idx == 0) aabb.w = _bottom;
+    else if (b_max_idx == 1) aabb.w = _bottom;
+    else if (b_max_idx == 2) aabb.w = _upper;
+    else if (b_max_idx == 3) aabb.w = _upper;
+
+    return true;
+}
+
+// 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);
+}
+
+
+// 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* colors_precomp,
+	const float* viewmatrix,
+	const float* mirror_transformed_tan_x, // tan_theta of mirror transformed PBF 
+	const float* mirror_transformed_tan_y, // tan_phi of mirror transformed PBF 
+	const glm::vec3* cam_pos,
+	const int W, int H,
+	const float tan_fovx, float tan_fovy,
+	const float focal_x, float focal_y,
+	const float principal_x, float principal_y,
+	const float* distortion_coeffs, // KB fisheye distortion coefficients (k1,k2,k3,k4 in polynomial angle model)
+	int* radii,
+	int* pbf_id,
+	float4* pbf_tan,
+	const float* xmap, 
+	const float* ymap, 
+	float3* points_xyz_view,
+	float* depths,
+	float* rgb,
+	float2* h_opacity,
+	float3* w2o, 
+	const dim3 grid,
+	uint32_t* tiles_touched,
+	bool prefiltered,
+	bool antialiasing,
+	int mode,
+	float near_threshold,
+	int asso_mode)
+{
+	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;
+	pbf_id[idx * 4] = 0; 
+	pbf_id[idx * 4 + 1] = 0;
+	pbf_id[idx * 4 + 2] = 0; 
+	pbf_id[idx * 4 + 3] = 0; 
+
+	tiles_touched[idx] = 0;
+
+	// Perform near culling, quit if outside.
+	float3 p_view;
+	if (!in_frustum(idx, orig_points, viewmatrix, prefiltered, p_view, near_threshold))
+		return;
+
+	glm::mat3 R_view = computeRotationMatrix(rotations[idx], viewmatrix);
+	float cutoff = 3.0f;
+	float3 p_view_identity = {orig_points[3 * idx] + viewmatrix[12], orig_points[3 * idx + 1] + viewmatrix[13], orig_points[3 * idx + 2] + viewmatrix[14]};
+	if (!omni_hvar(scales[idx], scale_modifier, opacities[idx], h_opacity + idx, true)) return;
+
+	// Prepare world-to-canonical transformation maxtrix for exact ray-Gaussian integral
+	// see details in 3DGEER https://openreview.net/pdf?id=4voMNlRWI7, Eq.3 
+	w2o[idx * 3 + 0] = toFloat3(R_view[0] / (sqrtf(sq(scales[idx].x) + h_opacity[idx].x) * scale_modifier));
+	w2o[idx * 3 + 1] = toFloat3(R_view[1] / (sqrtf(sq(scales[idx].y) + h_opacity[idx].x) * scale_modifier));
+	w2o[idx * 3 + 2] = toFloat3(R_view[2] / (sqrtf(sq(scales[idx].z) + h_opacity[idx].x) * scale_modifier));
+
+	points_xyz_view[idx] = p_view;
+
+	// Compute bounding region for this Gaussian using the selected association mode:
+	//   asso_mode == 0: Particle Bounding Frustum (PBF) - exact and tight (default)
+	//   asso_mode == 1: AABB via Elliptical Weighted Average (EWA)
+	//   asso_mode == 2: AABB via Unscented Transform (UT)
+	// Any value outside [0, 2] falls back to PBF.
+	float4 tan_xxyy; // clamped tan value in x / y dir, i.e., tan_theta, tan_phi
+	bool tighten = false;
+	if (asso_mode == 1) {
+		if (!computeAABB_EWA(scales[idx], scale_modifier, R_view, p_view, cutoff, tan_xxyy, tan_fovx, tan_fovy, h_opacity[idx].x, tighten)) return;
+	} else if (asso_mode == 2) {
+		if (!computeAABB_UT(scales[idx], scale_modifier, R_view, p_view, cutoff, tan_xxyy, tan_fovx, tan_fovy, h_opacity[idx].x, tighten)) return;
+	} else {
+		// Default: asso_mode == 0, use PBF
+		// see details in 3DGEER paper: https://openreview.net/pdf?id=4voMNlRWI7, Eq.10 (mathmatical proof in Sec.D.1)
+		if (!computePBF(scales[idx], scale_modifier, R_view, p_view, cutoff, tan_xxyy, tan_fovx, tan_fovy, h_opacity[idx].x)) return;
+	}
+
+	if ((tan_xxyy.y - tan_xxyy.x) * (tan_xxyy.w - tan_xxyy.z) == 0)
+		return;
+
+	int _aa[2];
+	int _bb[2];
+	if (mode == 0)
+	{
+		// Convert PBF into BEAP space;
+		searchsorted_pbf(mirror_transformed_tan_x, W, mirror_transformed_tan_y, H, (float*)(&tan_xxyy), _aa, _bb);
+	} else if (mode == 1) {
+		// Bound PBF into KB imaging space;
+		const float4* kb_params4 = reinterpret_cast<const float4*>(distortion_coeffs);
+		const float4 kb_params = kb_params4[0];
+		invinterpolated_pbf(W, H, focal_x, focal_y, principal_x, principal_y, kb_params, tan_xxyy, _aa, _bb);
+	} else {
+		_aa[0] = (int)fmaxf(-(float)W, fminf(2.0f * W, floorf(focal_x * tan_xxyy.x + W / 2.0f - 1.0f)));
+		_aa[1] = (int)fmaxf(-(float)W, fminf(2.0f * W, ceilf( focal_x * tan_xxyy.y + W / 2.0f + 1.0f)));
+		_bb[0] = (int)fmaxf(-(float)H, fminf(2.0f * H, floorf(focal_y * tan_xxyy.z + H / 2.0f - 1.0f)));
+		_bb[1] = (int)fmaxf(-(float)H, fminf(2.0f * H, ceilf( focal_y * tan_xxyy.w + H / 2.0f + 1.0f)));
+	}
+	int4 _pbf = {_aa[0], _aa[1], _bb[0], _bb[1]};
+	if ((_pbf.y - _pbf.x) * (_pbf.w - _pbf.z) == 0)
+		return;
+
+	int4 screen_grid_aligned_pbf = _pbf;
+	float2 point_image = { (screen_grid_aligned_pbf.y + screen_grid_aligned_pbf.x)/2.f, (screen_grid_aligned_pbf.w + screen_grid_aligned_pbf.z)/2.f };
+
+	uint2 rect_min, rect_max;
+	getRect2(screen_grid_aligned_pbf, rect_min, rect_max, grid);
+	if ((rect_max.x - rect_min.x) * (rect_max.y - rect_min.y) == 0)
+		return;
+	int my_radius = max(rect_max.x - rect_min.x, rect_max.y - rect_min.y);
+
+	// 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] = sqrtf((p_view.z * p_view.z) + (p_view.x * p_view.x) + (p_view.y * p_view.y));
+	radii[idx] = my_radius;
+	
+	pbf_id[idx * 4] = screen_grid_aligned_pbf.x; 
+	pbf_id[idx * 4 + 1] = screen_grid_aligned_pbf.y;
+	pbf_id[idx * 4 + 2] = screen_grid_aligned_pbf.z;
+	pbf_id[idx * 4 + 3] = screen_grid_aligned_pbf.w;
+
+	pbf_tan[idx] = tan_xxyy;
+	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 int mode,
+	const float focal_x, float focal_y,
+	const float* tan_theta, 
+	const float* tan_phi, 
+	const float* raymap, 
+	const float4* __restrict__ pbf_tan,
+	const float3* __restrict__ points_xyz_view,
+	const float* __restrict__ features,
+	const float2* __restrict__ h_opacity,
+	const float3* __restrict__ w2o_mat,
+	float* __restrict__ final_T,
+	uint32_t* __restrict__ n_contrib,
+	const float* __restrict__ bg_color,
+	float* __restrict__ out_color,
+	const float* __restrict__ depths,
+	float* __restrict__ invdepth
+)
+{
+	// 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 = { pix_min.x + block.thread_index().x, pix_min.y + block.thread_index().y };
+	uint32_t pix_id = W * pix.y + pix.x;
+	bool inside = pix.x < W && pix.y < H;
+	float3 rayf;
+	// if (raymap == nullptr) {
+	// 	rayf = make_float3((float)tan_theta[min(pix.x, W-1)], (float)tan_phi[min(pix.y, H-1)], 1.f);
+	// } else {
+	// 	rayf = make_float3((float)raymap[pix_id * 3], (float)raymap[pix_id * 3 + 1],(float)raymap[pix_id * 3 + 2]);
+	// }
+	if (mode == 0) {
+		rayf = make_float3((float)tan_theta[min(pix.x, W-1)], (float)tan_phi[min(pix.y, H-1)], 1.f);
+	} else if (mode == 1) {
+		rayf = inside
+			? make_float3((float)raymap[pix_id * 3], (float)raymap[pix_id * 3 + 1], (float)raymap[pix_id * 3 + 2])
+			: make_float3(0.0f, 0.0f, 1.0f);
+	} else {
+		rayf = { ((float)pix.x + 0.5f) / focal_x - W / (2.0f * focal_x), ((float)pix.y + 0.5f) / focal_y - H / (2.0f * focal_y), 1.0f };
+	}
+
+	// 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__ float3 collected_xyz[BLOCK_SIZE];
+	__shared__ float2 collected_h_opacity[BLOCK_SIZE];
+	__shared__ float3 collected_w2o[BLOCK_SIZE * 3]; 
+	__shared__ float4 collected_pbf_tan[BLOCK_SIZE * 4];
+
+	// Initialize helper variables
+	float T = 1.0f;
+	uint32_t contributor = 0;
+	uint32_t last_contributor = 0;
+	float C[CHANNELS] = { 0 };
+
+	float expected_invdepth = 0.0f;
+
+	// 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];
+			int thread_idx = block.thread_rank();
+
+			collected_id[thread_idx] = coll_id;
+			collected_xyz[thread_idx] = points_xyz_view[coll_id];
+			collected_pbf_tan[thread_idx] = pbf_tan[coll_id];
+
+			for (int j = 0; j < 3; j++) {
+				collected_w2o[thread_idx * 3 + j] = w2o_mat[coll_id * 3 + j];
+			}
+			collected_h_opacity[thread_idx] = h_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++;
+
+			// if (rayf not in pbf_tan) continue;
+			float4 b_xxyy = collected_pbf_tan[j];
+
+			if (mode==1) {
+				if (((rayf.x / rayf.z) < b_xxyy.x) || ((rayf.x / rayf.z) > b_xxyy.y))
+					continue;
+				if (((rayf.y / rayf.z) < b_xxyy.z) || ((rayf.y / rayf.z) > b_xxyy.w))
+					continue;
+			}
+
+			float3 xyz = collected_xyz[j];
+			float2 h_o = collected_h_opacity[j];
+			float3* w2o = collected_w2o + j * 3; 
+			
+			// see 3DGEER paper: https://openreview.net/pdf?id=4voMNlRWI7 (Eq. 5, mathmatical proof in Sec.B)
+			float3 p_obj = { dot(xyz, w2o[0]), dot(xyz, w2o[1]), dot(xyz, w2o[2]) }; 
+			float3 d_obj = { dot(rayf, w2o[0]), dot(rayf, w2o[1]), dot(rayf, w2o[2]) }; 
+			float3 normal = cross(d_obj, p_obj); // check Sec.C.7
+			float power_mah = -0.5f * dot(normal, normal) / dot(d_obj, d_obj);
+
+			if (power_mah > 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, h_o.y * exp(power_mah)); // For ray-splatting
+			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;
+
+			if(invdepth)
+			expected_invdepth += (1 / 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)
+	{
+		final_T[pix_id] = T;
+		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];
+
+		if (invdepth)
+		invdepth[pix_id] = expected_invdepth;// 1. / (expected_depth + T * 1e3);
+	}
+}
+
+void FORWARD::render(
+	const dim3 grid, dim3 block,
+	const uint2* ranges,
+	const uint32_t* point_list,
+	int W, int H,
+	int mode,
+	float focal_x, float focal_y,
+	const float* tan_theta, 
+	const float* tan_phi,
+	const float* raymap, 
+	const float4* pbf_tan,
+	const float3* means3D_view, 
+	const float* colors,
+	const float2* h_opacity,
+	const float3* w2o,
+	float* final_T,
+	uint32_t* n_contrib,
+	const float* bg_color,
+	float* out_color,
+	float* depths,
+	float* depth)
+{
+	renderCUDA<NUM_CHANNELS> << <grid, block >> > (
+		ranges,
+		point_list,
+		W, H,
+		mode,
+		focal_x, focal_y,
+		tan_theta, tan_phi,
+		raymap,
+		pbf_tan,
+		means3D_view,
+		colors,
+		h_opacity,
+		w2o,
+		final_T,
+		n_contrib,
+		bg_color,
+		out_color,
+		depths, 
+		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* colors_precomp,
+	const float* viewmatrix,
+	const float* mirror_transformed_tan_x,
+	const float* mirror_transformed_tan_y, 
+	const glm::vec3* cam_pos,
+	const int W, int H,
+	const float focal_x, float focal_y,
+	const float principal_x, float principal_y,
+	const float* distortion_coeffs,
+	const float tan_fovx, float tan_fovy,
+	int* radii,
+	int* pbf,
+	float4* pbf_tan,
+	const float* xmap,
+	const float* ymap,
+	float3* means3D_view,
+	float* depths,
+	float* rgb,
+	float2* h_opacity,
+	float3* w2o, 
+	const dim3 grid,
+	uint32_t* tiles_touched,
+	bool prefiltered,
+	bool antialiasing,
+	int mode,
+	float near_threshold,
+	int asso_mode)
+{
+	preprocessCUDA<NUM_CHANNELS> << <(P + 255) / 256, 256 >> > (
+		P, D, M,
+		means3D,
+		scales,
+		scale_modifier,
+		rotations,
+		opacities,
+		shs,
+		clamped,
+		colors_precomp,
+		viewmatrix, 
+		mirror_transformed_tan_x, mirror_transformed_tan_y,
+		cam_pos,
+		W, H,
+		tan_fovx, tan_fovy,
+		focal_x, focal_y,
+		principal_x, principal_y,
+		distortion_coeffs,
+		radii,
+		pbf, pbf_tan,
+		xmap, ymap,
+		means3D_view, 
+		depths,
+		rgb, h_opacity,
+		w2o,
+		grid,
+		tiles_touched,
+		prefiltered,
+		antialiasing,
+		mode,
+		near_threshold,
+		asso_mode
+		);
+}

3dgeer/submodules/geer-rasterizer/cuda_rasterizer/forward.h

@@ -0,0 +1,84 @@
+/*
+ * 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  george.drettakis@inria.fr
+ */
+
+#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* colors_precomp,
+		const float* viewmatrix,
+		const float* mirror_transformed_tan_theta, 
+		const float* mirror_transformed_tan_phi,
+		const glm::vec3* cam_pos,
+		const int W, int H,
+		const float focal_x, float focal_y,
+		const float principal_x, float principal_y,
+		const float* distortion_coeffs,
+		const float tan_fovx, float tan_fovy,
+		int* radii,
+		int* pbf_id,
+		float4* pbf_tan,
+		const float* xmap, 
+		const float* ymap,
+		float3* points_xyz_view, 
+		float* depths,
+		float* colors,
+		float2* h_opacity,
+		float3* w2o,
+		const dim3 grid,
+		uint32_t* tiles_touched,
+		bool prefiltered,
+		bool antialiasing,
+		int mode,
+		float near_threshold = 0.2f,
+		int asso_mode = 0);
+
+	// Main rasterization method.
+	void render(
+		const dim3 grid, dim3 block,
+		const uint2* ranges,
+		const uint32_t* point_list,
+		int W, int H,
+		int mode,
+		float focal_x, float focal_y,
+		const float* tan_theta,
+		const float* tan_phi,
+		const float* raymap,
+		const float4* pbf_tan,
+		const float3* points_xyz_view,
+		const float* features,
+		const float2* h_opacity,
+		const float3* w2o,
+		float* final_T,
+		uint32_t* n_contrib,
+		const float* bg_color,
+		float* out_color,
+		float* depths,
+		float* depth);
+}
+
+#endif

3dgeer/submodules/geer-rasterizer/cuda_rasterizer/rasterizer.h

@@ -0,0 +1,107 @@
+/*
+ * 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  george.drettakis@inria.fr
+ */
+
+#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,
+			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* viewmatrix,
+			const float* mirror_transformed_tan_theta,
+			const float* mirror_transformed_tan_phi,
+			const float* tan_theta,
+			const float* tan_phi,
+			const float* cam_pos,
+			const float focal_x, float focal_y, 
+			const float principal_x, float principal_y,
+			const float* distortion_coeffs,
+			const float* raymap,
+			float* xmap,
+			float* ymap,
+			const float tan_fovx, float tan_fovy,
+			const bool prefiltered,
+			float* kernel_times,
+			float* out_color,
+			float* depth,
+			bool antialiasing,
+			int mode,
+			int* radii = nullptr,
+			int* ranges = nullptr,
+			float near_threshold = 0.2f,
+			bool debug = false,
+			int asso_mode = 0);
+
+		static void backward(
+			const int P, int D, int M, int R,
+			const float* background,
+			const int width, int height,
+			const float* tan_theta,
+			const float* tan_phi,
+			const float* raymap,
+			const int mode,
+			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* viewmatrix,
+			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_invdepths,
+			float* dL_dmean2D,
+			float* dL_dopacity,
+			float* dL_dcolor,
+			float* dL_dinvdepth,
+			float* dL_dmean3D,
+			float* dL_dsh,
+			float* dL_dscale,
+			float* dL_drot,
+			float* dL_dsigmaInv,
+			bool antialiasing,
+			bool debug);
+	};
+};
+
+#endif

3dgeer/submodules/geer-rasterizer/cuda_rasterizer/rasterizer_impl.cu

@@ -0,0 +1,616 @@
+/*
+ * 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  george.drettakis@inria.fr
+ */
+
+#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,
+	bool* present)
+{
+	auto idx = cg::this_grid().thread_rank();
+	if (idx >= P)
+		return;
+
+	float3 p_view;
+	present[idx] = in_frustum(idx, orig_points, viewmatrix, false, p_view);
+}
+
+__global__ void extractRaymapChannel(const float* raymap,
+	int W, int H,
+	float* channelmap, int c, 
+	int N) 
+{
+	auto idx = cg::this_grid().thread_rank();
+	if (idx >= N || raymap == nullptr)
+		return;
+	int ray_idx = idx;
+	if (c == 1) {
+		int x = int(idx / H);
+		int y = idx - H * x;
+		ray_idx = y * W + x;
+	}
+	
+	channelmap[idx] = raymap[3 * ray_idx + c] / raymap[3 * ray_idx + 2];
+}
+
+// Generates one key/value pair for all Gaussian / tile overlaps. 
+// Run once per Gaussian (1:N mapping).
+__global__ void duplicateWithKeys(
+	int P,
+	const float3* points_xyz,
+	const float3* w2o,
+	const float2* h_opacity,
+	const float* depths,
+	const uint32_t* offsets,
+	uint64_t* gaussian_keys_unsorted,
+	uint32_t* gaussian_values_unsorted,
+	int* radii,
+	const int4* pbf,
+	const float4* pbf_tan,
+	const float* xmap,
+	const float* ymap,
+	const int W, int H,
+	uint32_t* tiles_touched,
+	dim3 grid,
+	int mode)
+{
+	auto idx = cg::this_grid().thread_rank();
+	if (idx >= P)
+		return;
+
+	// Generate no key/value pair for invisible Gaussians
+	if ((radii[idx] > 0) && (tiles_touched[idx] > 0))
+	{
+		const bool use_kb_sorted_tile_culling = false;
+
+		// Find this Gaussian's offset in buffer for writing keys/values.
+		uint32_t off = (idx == 0) ? 0 : offsets[idx - 1];
+
+		// Update unsorted arrays with Gaussian idx for every tile that Gaussian touches
+
+		// 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. 
+		if ((xmap == nullptr) || (mode != 1) || !use_kb_sorted_tile_culling) {
+			uint2 rect_min, rect_max;
+			getRect2(pbf[idx], rect_min, rect_max, grid);
+	
+			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++;
+				}
+			}
+		} else {
+			tiles_touched[idx] = duplicateToTilesTouched(
+				points_xyz[idx], w2o + 3 * idx, h_opacity[idx].y,
+				pbf[idx], pbf_tan[idx], grid,
+				W, H,
+				idx, off, depths[idx],
+				gaussian_keys_unsorted,
+				gaussian_values_unsorted,
+				xmap, ymap);
+		}
+	}
+}
+
+// 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;
+}
+
+// ranges for each tile: Compute the length of each tile's range in the full sorted list
+__global__ void computeRangeLengths(const uint2* ranges, int* range_len, int N)
+{
+	auto idx = cg::this_grid().thread_rank();
+	if (idx >= N)
+		return;
+	range_len[idx] = ranges[idx].y - ranges[idx].x;
+}
+
+// Mark Gaussians as visible/invisible, based on view frustum testing
+void CudaRasterizer::Rasterizer::markVisible(
+	int P,
+	float* means3D,
+	float* viewmatrix,
+	bool* present)
+{
+	checkFrustum << <(P + 255) / 256, 256 >> > (
+		P,
+		means3D,
+		viewmatrix,
+		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.means3D_view, P, 128);
+	obtain(chunk, geom.h_opacity, P, 128);
+	obtain(chunk, geom.w2o, P * 3, 128);
+	obtain(chunk, geom.pbf, P * 4, 128); 
+	obtain(chunk, geom.pbf_tan, 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.accum_alpha, N, 128);
+	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* viewmatrix,
+	const float* mirror_transformed_tan_theta, const float* mirror_transformed_tan_phi, 
+	const float* tan_theta, const float* tan_phi,
+	const float* cam_pos,
+	const float focal_x, float focal_y, 
+	const float principal_x, float principal_y,
+	const float* distortion_coeffs,
+	const float* raymap, 
+	float* xmap, float* ymap,
+	const float tan_fovx, float tan_fovy,
+	const bool prefiltered,
+	float* kernel_times,
+	float* out_color,
+	float* depth,
+	bool antialiasing,
+	const int mode,
+	int* radii,
+	int* range_len,
+	float near_threshold,
+	bool debug,
+	int asso_mode)
+{
+	cudaEvent_t overallStart, overallStop;
+	cudaEvent_t preprocessStart, preprocessStop;
+	cudaEvent_t duplicateStart, duplicateStop;
+	cudaEvent_t sortStart, sortStop;
+	cudaEvent_t renderStart, renderStop;
+	cudaEventCreate(&overallStart);
+	cudaEventCreate(&overallStop);
+	cudaEventCreate(&preprocessStart);
+	cudaEventCreate(&preprocessStop);
+	cudaEventCreate(&duplicateStart);
+	cudaEventCreate(&duplicateStop);
+	cudaEventCreate(&sortStart);
+	cudaEventCreate(&sortStop);
+	cudaEventCreate(&renderStart);
+	cudaEventCreate(&renderStop);
+	float milliseconds_overall, milliseconds_preprocess, milliseconds_duplicate, milliseconds_sort, milliseconds_render;
+
+	cudaEventRecord(overallStart, 0);
+
+	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!");
+	}
+
+	if ((mode == 1) && (raymap != nullptr)) {
+		extractRaymapChannel << <(width * height + 255) / 256, 256 >> > (
+			raymap,
+			width, height,
+			xmap, 0,
+			width * height);
+		CHECK_CUDA(, debug);
+	
+		extractRaymapChannel << <(width * height + 255) / 256, 256 >> > (
+			raymap,
+			width, height,
+			ymap, 1,
+			width * height);
+		CHECK_CUDA(, debug);
+	}
+
+	// Run preprocessing per-Gaussian (transformation, bounding, conversion of SHs to RGB)
+	cudaEventRecord(preprocessStart, 0);
+	CHECK_CUDA(FORWARD::preprocess(
+		P, D, M,
+		means3D,
+		(glm::vec3*)scales,
+		scale_modifier,
+		(glm::vec4*)rotations,
+		opacities,
+		shs,
+		geomState.clamped,
+		colors_precomp,
+		viewmatrix, 
+		mirror_transformed_tan_theta, 
+		mirror_transformed_tan_phi,
+		(glm::vec3*)cam_pos,
+		width, height,
+		focal_x, focal_y,
+	    principal_x, principal_y,
+	    distortion_coeffs,
+		tan_fovx, tan_fovy,
+		radii,
+		geomState.pbf,
+		geomState.pbf_tan,
+		xmap, ymap,
+		geomState.means3D_view,
+		geomState.depths,
+		geomState.rgb,
+		geomState.h_opacity,
+		geomState.w2o,
+		tile_grid,
+		geomState.tiles_touched,
+		prefiltered,
+		antialiasing,
+		mode,
+		near_threshold,
+		asso_mode
+	), debug)
+
+	cudaEventRecord(preprocessStop, 0);
+	cudaEventSynchronize(preprocessStop);
+	cudaEventElapsedTime(&milliseconds_preprocess, preprocessStart, preprocessStop);
+
+	// 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
+	cudaEventRecord(duplicateStart, 0);
+	duplicateWithKeys << <(P + 255) / 256, 256 >> > (
+		P,
+		geomState.means3D_view,
+		geomState.w2o,
+		geomState.h_opacity,
+		geomState.depths,
+		geomState.point_offsets,
+		binningState.point_list_keys_unsorted,
+		binningState.point_list_unsorted,
+		radii,
+		(int4*) geomState.pbf,
+		geomState.pbf_tan,
+		xmap, ymap,
+		width, height,
+		geomState.tiles_touched,
+		tile_grid,
+		mode)
+	CHECK_CUDA(, debug)
+	cudaEventRecord(duplicateStop, 0);
+	cudaEventSynchronize(duplicateStop);
+	cudaEventElapsedTime(&milliseconds_duplicate, duplicateStart, duplicateStop);
+	
+	int bit = getHigherMsb(tile_grid.x * tile_grid.y);
+
+	// Sort complete list of (duplicated) Gaussian indices by keys
+	cudaEventRecord(sortStart, 0);
+	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)
+	cudaEventRecord(sortStop, 0);
+	cudaEventSynchronize(sortStop);
+	cudaEventElapsedTime(&milliseconds_sort, sortStart, sortStop);
+
+	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)
+
+	// ranges for each tile
+	computeRangeLengths << <(tile_grid.x * tile_grid.y + 255) / 256, 256 >> > (
+		imgState.ranges,
+		range_len, // ranges for each tile
+		tile_grid.x * tile_grid.y);
+	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;
+	cudaEventRecord(renderStart, 0);
+	CHECK_CUDA(FORWARD::render(
+		tile_grid, block,
+		imgState.ranges,
+		binningState.point_list,
+		width, height,
+		mode,
+		focal_x, focal_y,
+		tan_theta, tan_phi, 
+		raymap, 
+		geomState.pbf_tan, 
+		geomState.means3D_view, 
+		feature_ptr,
+		geomState.h_opacity,
+		geomState.w2o,  
+		imgState.accum_alpha,
+		imgState.n_contrib,
+		background,
+		out_color,
+		geomState.depths,
+		depth), debug)
+
+	cudaEventRecord(overallStop, 0);
+	cudaEventSynchronize(overallStop);
+
+	cudaEventElapsedTime(&milliseconds_render, renderStart, overallStop);
+	cudaEventElapsedTime(&milliseconds_overall, overallStart, overallStop);
+	kernel_times[0] = milliseconds_overall;
+	kernel_times[1] = milliseconds_preprocess;
+	kernel_times[2] = milliseconds_duplicate;
+	kernel_times[3] = milliseconds_sort;
+	kernel_times[4] = milliseconds_render;
+
+	cudaEventDestroy(overallStart);
+	cudaEventDestroy(overallStop);
+
+	cudaEventDestroy(preprocessStart);
+	cudaEventDestroy(preprocessStop);
+
+	cudaEventDestroy(duplicateStart);
+	cudaEventDestroy(duplicateStop);
+
+	cudaEventDestroy(sortStart);
+	cudaEventDestroy(sortStop);
+
+	cudaEventDestroy(renderStart);
+	cudaEventDestroy(renderStop);
+	
+	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* tan_theta, 
+	const float* tan_phi, 
+	const float* raymap,
+	const int mode,
+	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* viewmatrix,
+	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_invdepths,
+	float* dL_dmean2D,
+	float* dL_dopacity,
+	float* dL_dcolor,
+	float* dL_dinvdepth,
+	float* dL_dmean3D,
+	float* dL_dsh,
+	float* dL_dscale,
+	float* dL_drot,
+	float* dL_dsigmaInv,
+	bool antialiasing,
+	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;
+	CHECK_CUDA(BACKWARD::render(
+		tile_grid,
+		block,
+		imgState.ranges,
+		binningState.point_list,
+		width, height,
+		tan_theta, tan_phi,
+		raymap,
+		focal_x, focal_y,
+		mode,
+		background,
+		geomState.means3D_view, 
+		geomState.h_opacity,
+		geomState.w2o,
+		color_ptr,
+		geomState.depths,
+		imgState.accum_alpha,
+		imgState.n_contrib,
+		dL_dpix,
+		dL_invdepths,
+		(float3*)dL_dmean2D,
+		(glm::vec3*)dL_dmean3D,
+		dL_dopacity,
+		dL_dcolor,
+		dL_dinvdepth,
+		(glm::vec3*)dL_dsigmaInv), debug);
+
+	CHECK_CUDA(BACKWARD::preprocess(P, D, M,
+		(float3*)means3D,
+		geomState.means3D_view,
+		geomState.depths,
+		radii,
+		shs,
+		geomState.clamped,
+		opacities,
+		(glm::vec3*)scales,
+		(glm::vec4*)rotations,
+		scale_modifier,
+		geomState.h_opacity,
+		geomState.w2o,
+		viewmatrix,
+		focal_x, focal_y,
+		tan_fovx, tan_fovy,
+		(glm::vec3*)campos,
+		(float3*)dL_dmean2D,
+		dL_dinvdepth,
+		dL_dopacity,
+		(glm::vec3*)dL_dmean3D,
+		dL_dcolor,
+		dL_dsh,
+		(glm::vec3*)dL_dscale,
+		(glm::vec4*)dL_drot,
+		(glm::vec3*)dL_dsigmaInv,
+		antialiasing), debug);
+}

3dgeer/submodules/geer-rasterizer/cuda_rasterizer/rasterizer_impl.h

@@ -0,0 +1,76 @@
+/*
+ * 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  george.drettakis@inria.fr
+ */
+
+#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;          // Euclidean distance from camera to each Gaussian centre (used for depth-sorted blending)
+		char* scanning_space;
+		bool* clamped;          // Per-channel SH clamping flags (for backward pass)
+		int* pbf;               // Pixel-space PBF of each Gaussian: [x_min, x_max, y_min, y_max]
+		float4* pbf_tan;        // PBF (Particle Bounding Frustum) in ray-direction tangent space {tan_theta_min, tan_theta_max, tan_phi_min, tan_phi_max}
+		int* internal_radii;
+		float3* means3D_view;   // Gaussian centre positions in view/camera space
+		float2* h_opacity;      // Packed {x=antialiasing variance h_var, y=antialiasing-scaled opacity}
+		float3* w2o;            // World-to-object (canonical) matrix rows: 3 float3 per Gaussian = Σ^{-1/2}R_view^T
+		float* rgb;             // Pre-computed RGB colors (from SH evaluation)
+		uint32_t* point_offsets;
+		uint32_t* tiles_touched;
+
+		static GeometryState fromChunk(char*& chunk, size_t P);
+	};
+
+	struct ImageState
+	{
+		uint2* ranges;          // Per-tile [start, end) range in the sorted Gaussian list
+		uint32_t* n_contrib;    // Per-pixel: index of the last contributing Gaussian (for backward)
+		float* accum_alpha;     // Per-pixel accumulated transmittance T (= product of (1-alpha) terms)
+
+		static ImageState fromChunk(char*& chunk, size_t N);
+	};
+
+	struct BinningState
+	{
+		size_t sorting_size;
+		uint64_t* point_list_keys_unsorted;  // Unsorted keys: upper 32 bits = tile ID, lower 32 bits = depth bits
+		uint64_t* point_list_keys;           // Sorted keys
+		uint32_t* point_list_unsorted;       // Unsorted Gaussian indices
+		uint32_t* point_list;               // Sorted Gaussian indices (tile-then-depth order)
+		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;
+	}
+};

3dgeer/submodules/geer-rasterizer/diff_gaussian_rasterization/__init__.py

@@ -0,0 +1,239 @@
+#
+# 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  george.drettakis@inria.fr
+#
+
+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,
+    raster_settings,
+):
+    return _RasterizeGaussians.apply(
+        means3D,
+        means2D,
+        sh,
+        colors_precomp,
+        opacities,
+        scales,
+        rotations,
+        raster_settings,
+    )
+
+class _RasterizeGaussians(torch.autograd.Function):
+    @staticmethod
+    def forward(
+        ctx,
+        means3D,
+        means2D,
+        sh,
+        colors_precomp,
+        opacities,
+        scales,
+        rotations,
+        raster_settings,
+    ):
+        """Forward pass: rasterize 3D Gaussians into an image using the GEER algorithm.
+
+        Returns (color [C,H,W], radii [P], invdepth [1,H,W], kernel_times [5], tile_ranges [T]).
+        """
+
+        # Restructure arguments the way that the C++ lib expects them
+        args = (
+            raster_settings.bg, 
+            means3D,
+            colors_precomp,
+            opacities,
+            scales,
+            rotations,
+            raster_settings.scale_modifier,
+            raster_settings.viewmatrix,
+            raster_settings.mirror_transformed_tan_theta,
+            raster_settings.mirror_transformed_tan_phi,
+            raster_settings.tan_theta,
+            raster_settings.tan_phi,
+            raster_settings.focal_x, raster_settings.focal_y, 
+            raster_settings.principal_x, raster_settings.principal_y,
+            raster_settings.distortion_coeffs,
+            raster_settings.raymap,
+            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.antialiasing,
+            raster_settings.render_mode,
+            raster_settings.near_threshold,
+            raster_settings.debug,
+            raster_settings.asso_mode
+        )
+
+        # Invoke C++/CUDA rasterizer
+        num_rendered, color, radii, kernel_times, ranges, geomBuffer, binningBuffer, imgBuffer, invdepths = _C.rasterize_gaussians(*args) # ranges for each tile
+
+        # Keep relevant tensors for backward
+        ctx.raster_settings = raster_settings
+        ctx.num_rendered = num_rendered
+        ctx.save_for_backward(colors_precomp, means3D, scales, rotations, radii, sh, opacities, geomBuffer, binningBuffer, imgBuffer)
+        return color, radii, invdepths, kernel_times, ranges
+
+    @staticmethod
+    def backward(ctx, grad_out_color, grad_radii, grad_out_depth, grad_kernel_times, grad_ranges):
+        """Backward pass: propagate gradients from pixel loss to Gaussian parameters.
+
+        Inputs grad_out_color [C,H,W] and grad_out_depth [1,H,W]; grad_radii,
+        grad_kernel_times, and grad_ranges are unused (non-differentiable outputs).
+        Returns gradients for (means3D, means2D, sh, colors_precomp, opacities, scales, rotations, None).
+        """
+
+        # Restore necessary values from context
+        num_rendered = ctx.num_rendered
+        raster_settings = ctx.raster_settings
+        colors_precomp, means3D, scales, rotations, radii, sh, opacities, geomBuffer, binningBuffer, imgBuffer = ctx.saved_tensors
+
+        # Restructure args as C++ method expects them
+        args = (raster_settings.bg,
+                means3D, 
+                radii, 
+                colors_precomp, 
+                opacities,
+                scales, 
+                rotations, 
+                raster_settings.scale_modifier, 
+                raster_settings.viewmatrix, 
+                raster_settings.tan_theta,
+                raster_settings.tan_phi,
+                raster_settings.raymap,
+                raster_settings.render_mode,
+                raster_settings.tanfovx, 
+                raster_settings.tanfovy, 
+                grad_out_color,
+                grad_out_depth, 
+                sh, 
+                raster_settings.sh_degree, 
+                raster_settings.campos,
+                geomBuffer,
+                num_rendered,
+                binningBuffer,
+                imgBuffer,
+                raster_settings.antialiasing,
+                raster_settings.debug)
+
+        # Compute gradients for relevant tensors by invoking backward method
+        grad_means2D, grad_colors_precomp, grad_opacities, grad_means3D, grad_sh, grad_scales, grad_rotations = _C.rasterize_gaussians_backward(*args)        
+
+        grads = (
+            grad_means3D,
+            grad_means2D,
+            grad_sh,
+            grad_colors_precomp,
+            grad_opacities,
+            grad_scales,
+            grad_rotations,
+            None,
+        )
+
+        return grads
+
+class GaussianRasterizationSettings(NamedTuple):
+    """
+        Settings passed to the CUDA rasterizer for each forward/backward call.
+    """
+    image_height: int
+    image_width: int
+    tanfovx: float        
+    tanfovy: float       
+    bg: torch.Tensor       
+    scale_modifier: float   
+    viewmatrix: torch.Tensor  
+    # BEAP ray-direction reference arrays (sorted, used for PBF→pixel mapping in BEAP mode)
+    mirror_transformed_tan_theta: torch.Tensor  # 1-D tensor of tan(θ) values along the horizontal axis
+    mirror_transformed_tan_phi: torch.Tensor    # 1-D tensor of tan(φ) values along the vertical axis
+    # Per-pixel ray direction tangents (BEAP mode: 1-D sorted grids; KB mode: unused)
+    tan_theta: torch.Tensor  # Horizontal ray tangents
+    tan_phi: torch.Tensor    # Vertical ray tangents
+    # KB / EQ fisheye intrinsics (only used when render_model==1)
+    focal_x: float          # Horizontal focal length (pixels)
+    focal_y: float          # Vertical focal length (pixels)
+    principal_x: float      # Horizontal principal point (pixels)
+    principal_y: float      # Vertical principal point (pixels)
+    distortion_coeffs: torch.Tensor  # KB polynomial distortion coefficients [k1, k2, k3, k4]
+    raymap: torch.Tensor    # [H, W, 3] per-pixel ray direction map (used in KB/EQ mode)
+    sh_degree: int          
+    campos: torch.Tensor    # Camera centre in world space [3]
+    prefiltered: bool       
+    debug: bool            
+    antialiasing: bool   
+    render_mode: int
+    near_threshold: float
+    asso_mode: int
+
+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)
+            
+        return visible
+
+    def forward(self, means3D, means2D, opacities, shs = None, colors_precomp = None, scales = None, rotations = None, cov3D_precomp = 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([])
+
+        # Invoke C++/CUDA rasterization routine
+        return rasterize_gaussians(
+            means3D,
+            means2D,
+            shs,
+            colors_precomp,
+            opacities,
+            scales, 
+            rotations,
+            raster_settings, 
+        )
+

3dgeer/submodules/geer-rasterizer/ext.cpp

@@ -0,0 +1,19 @@
+/*
+ * Copyright (C) 2023, Inria
+ * GRAPHDECO research group, https://team.inria.fr/graphdeco
+ * All rights reserved.
+ *
+ * This software is free for non-commercial, research and evaluation use 
+ * under the terms of the LICENSE.md file.
+ *
+ * For inquiries contact  george.drettakis@inria.fr
+ */
+
+#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);
+}

3dgeer/submodules/geer-rasterizer/rasterize_points.cu

@@ -0,0 +1,274 @@
+/*
+ * 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  george.drettakis@inria.fr
+ */
+
+#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, 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& viewmatrix,
+	const torch::Tensor& mirror_transformed_tan_theta, 
+	const torch::Tensor& mirror_transformed_tan_phi, 
+	const torch::Tensor& tan_theta, 
+	const torch::Tensor& tan_phi, 
+	const float focal_x, float focal_y, 
+	const float principal_x, float principal_y,
+	const torch::Tensor& distortion_coeffs,
+	const torch::Tensor& raymap,
+	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 antialiasing,
+	const int mode,
+	const float near_threshold,
+	const bool debug,
+	const int asso_mode)
+{
+  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 kernel_times = torch::full({5}, 0.0, float_opts.device(torch::kCPU));
+  torch::Tensor out_color = torch::full({NUM_CHANNELS, H, W}, 0.0, float_opts);
+  torch::Tensor out_invdepth = torch::full({0, H, W}, 0.0, float_opts);
+  float* out_invdepthptr = nullptr;
+
+  out_invdepth = torch::full({1, H, W}, 0.0, float_opts).contiguous();
+  out_invdepthptr = out_invdepth.data<float>();
+
+  torch::Tensor radii = torch::full({P}, 0, means3D.options().dtype(torch::kInt32));
+
+  // ranges for each tile
+  dim3 tile_grid((image_width + BLOCK_X - 1) / BLOCK_X, (image_height + BLOCK_Y - 1) / BLOCK_Y, 1);
+  torch::Tensor range_len = torch::empty({tile_grid.x * tile_grid.y}, means3D.options().dtype(torch::kInt32));
+
+  torch::Tensor xmap = torch::empty({image_width * image_height}, raymap.options().dtype(torch::kFloat32));
+  torch::Tensor ymap = torch::empty({image_width * image_height}, raymap.options().dtype(torch::kFloat32));
+
+  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>(),
+		viewmatrix.contiguous().data<float>(), 
+		mirror_transformed_tan_theta.contiguous().data<float>(),
+		mirror_transformed_tan_phi.contiguous().data<float>(),
+		tan_theta.contiguous().data<float>(), 
+		tan_phi.contiguous().data<float>(),
+		campos.contiguous().data<float>(),
+		focal_x, focal_y, 
+		principal_x, principal_y,
+		distortion_coeffs.contiguous().data<float>(),
+		raymap.contiguous().data<float>(),
+		xmap.contiguous().data<float>(),
+		ymap.contiguous().data<float>(),
+		tan_fovx,
+		tan_fovy,
+		prefiltered,
+		kernel_times.contiguous().data<float>(),
+		out_color.contiguous().data<float>(),
+		out_invdepthptr,
+		antialiasing,
+		mode,
+		radii.contiguous().data<int>(),
+		range_len.contiguous().data<int>(), // ranges for each tile
+		near_threshold,
+		debug,
+		asso_mode);
+  }
+	return std::make_tuple(rendered, out_color, radii, kernel_times, range_len, geomBuffer, binningBuffer, imgBuffer, out_invdepth);
+}
+
+std::tuple<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& opacities,
+	const torch::Tensor& scales,
+	const torch::Tensor& rotations,
+	const float scale_modifier,
+	const torch::Tensor& viewmatrix,
+	const torch::Tensor& tan_theta, 
+	const torch::Tensor& tan_phi,
+	const torch::Tensor& raymap,
+	const int mode,
+	const float tan_fovx,
+	const float tan_fovy,
+    const torch::Tensor& dL_dout_color,
+	const torch::Tensor& dL_dout_invdepth,
+	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 bool antialiasing,
+	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_dopacity = torch::zeros({P, 1}, 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());
+  torch::Tensor dL_dinvdepths = torch::zeros({0, 1}, means3D.options());
+  torch::Tensor dL_dsigmaInv = torch::zeros({P, 3, 3}, means3D.options());
+  
+  float* dL_dinvdepthsptr = nullptr;
+  float* dL_dout_invdepthptr = nullptr;
+  if(dL_dout_invdepth.size(0) != 0)
+  {
+	dL_dinvdepths = torch::zeros({P, 1}, means3D.options());
+	dL_dinvdepths = dL_dinvdepths.contiguous();
+	dL_dinvdepthsptr = dL_dinvdepths.data<float>();
+	dL_dout_invdepthptr = dL_dout_invdepth.data<float>();
+  }
+
+  if(P != 0)
+  {  
+	  CudaRasterizer::Rasterizer::backward(P, degree, M, R,
+	  background.contiguous().data<float>(),
+	  W, H,
+	  tan_theta.contiguous().data<float>(),
+	  tan_phi.contiguous().data<float>(),
+	  raymap.numel() > 0 ? raymap.contiguous().data<float>() : nullptr,
+	  mode,
+	  means3D.contiguous().data<float>(),
+	  sh.contiguous().data<float>(),
+	  colors.contiguous().data<float>(),
+	  opacities.contiguous().data<float>(),
+	  scales.data_ptr<float>(),
+	  scale_modifier,
+	  rotations.data_ptr<float>(),
+	  viewmatrix.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_invdepthptr,
+	  dL_dmeans2D.contiguous().data<float>(),
+	  dL_dopacity.contiguous().data<float>(),
+	  dL_dcolors.contiguous().data<float>(),
+	  dL_dinvdepthsptr,
+	  dL_dmeans3D.contiguous().data<float>(),
+	  dL_dsh.contiguous().data<float>(),
+	  dL_dscales.contiguous().data<float>(),
+	  dL_drotations.contiguous().data<float>(),
+	  dL_dsigmaInv.contiguous().data<float>(), 
+	  antialiasing,
+	  debug);
+  }
+
+  return std::make_tuple(dL_dmeans2D, dL_dcolors, dL_dopacity, dL_dmeans3D, dL_dsh, dL_dscales, dL_drotations);
+}
+
+torch::Tensor markVisible(
+		torch::Tensor& means3D,
+		torch::Tensor& viewmatrix)
+{ 
+  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>(),
+		present.contiguous().data<bool>());
+  }
+  
+  return present;
+}

3dgeer/submodules/geer-rasterizer/rasterize_points.h

@@ -0,0 +1,81 @@
+/*
+ * 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  george.drettakis@inria.fr
+ */
+
+#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, 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& viewmatrix,
+	const torch::Tensor& mirror_transformed_tan_theta, 
+	const torch::Tensor& mirror_transformed_tan_phi, 
+	const torch::Tensor& tan_theta, 
+	const torch::Tensor& tan_phi, 
+	const float focal_x, float focal_y,
+	const float principal_x, float principal_y,
+	const torch::Tensor& distortion_coeffs,
+	const torch::Tensor& raymap, 
+	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 antialiasing,
+	const int mode,
+	const float near_threshold,
+	const bool debug,
+	const int asso_mode = 0);
+
+std::tuple<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& opacities,
+	const torch::Tensor& rotations,
+	const float scale_modifier,
+	const torch::Tensor& viewmatrix,
+	const torch::Tensor& tan_theta, 
+	const torch::Tensor& tan_phi,
+	const torch::Tensor& raymap,
+	const int mode,
+	const float tan_fovx, 
+	const float tan_fovy,
+    const torch::Tensor& dL_dout_color,
+	const torch::Tensor& dL_dout_invdepth,
+	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 bool antialiasing,
+	const bool debug);
+		
+torch::Tensor markVisible(
+		torch::Tensor& means3D,
+		torch::Tensor& viewmatrix);

3dgeer/submodules/geer-rasterizer/setup.py

@@ -0,0 +1,34 @@
+#
+# Copyright (C) 2023, Inria
+# GRAPHDECO research group, https://team.inria.fr/graphdeco
+# All rights reserved.
+#
+# This software is free for non-commercial, research and evaluation use 
+# under the terms of the LICENSE.md file.
+#
+# For inquiries contact  george.drettakis@inria.fr
+#
+
+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
+    }
+)

3dgeer/submodules/geer-rasterizer/third_party/glm/.appveyor.yml

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

3dgeer/submodules/geer-rasterizer/third_party/glm/.gitignore

@@ -0,0 +1,61 @@
+# Compiled Object files
+*.slo
+*.lo
+*.o
+*.obj
+
+# Precompiled Headers
+*.gch
+*.pch
+
+# Compiled Dynamic libraries
+*.so
+*.dylib
+*.dll
+
+# Fortran module files
+*.mod
+
+# Compiled Static libraries
+*.lai
+*.la
+*.a
+*.lib
+
+# Executables
+*.exe
+*.out
+*.app
+
+# CMake
+CMakeCache.txt
+CMakeFiles
+cmake_install.cmake
+install_manifest.txt
+*.cmake
+!glmConfig.cmake
+!glmConfig-version.cmake
+# ^ May need to add future .cmake files as exceptions
+
+# Test logs
+Testing/*
+
+# Test input
+test/gtc/*.dds
+
+# Project Files
+Makefile
+*.cbp
+*.user
+
+# Misc.
+*.log
+
+# local build(s)
+build*
+
+/.vs
+/.vscode
+/CMakeSettings.json
+.DS_Store
+*.swp

3dgeer/submodules/geer-rasterizer/third_party/glm/.travis.yml

@@ -0,0 +1,388 @@
+language: cpp
+
+branches:
+  only:
+    - master
+    - stable
+
+jobs:
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+      os: osx
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+      env:
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+
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+      os: osx
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+      env:
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+
+    - name: "Xcode 7.3 C++98 ms release"
+      os: osx
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+      env:
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+
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+
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+
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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_17=ON -DGLM_TEST_FORCE_PURE=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+    - name: "Clang C++17 pure release"
+      os: linux
+      dist: focal
+      env:
+        - MATRIX_EVAL="CC=clang && CXX=clang++"
+        - CMAKE_BUILD_ENV="-DCMAKE_BUILD_TYPE=Release -DGLM_TEST_ENABLE=ON -DGLM_TEST_ENABLE_CXX_17=ON -DGLM_TEST_FORCE_PURE=ON"
+        - CTEST_ENV="--parallel 4 --output-on-failure"
+        - CMAKE_ENV="--parallel"
+
+before_script:
+    - cmake --version
+    - eval "${MATRIX_EVAL}"
+
+script:
+  - ${CC} --version
+  - mkdir ./build
+  - cd ./build
+  - cmake -DCMAKE_INSTALL_PREFIX=$TRAVIS_BUILD_DIR/install -DCMAKE_CXX_COMPILER=$COMPILER ${CMAKE_BUILD_ENV} ..
+  - cmake --build . ${CMAKE_ENV}
+  - ctest ${CTEST_ENV}
+  - cmake --build . --target install ${CMAKE_ENV}
+  - cd $TRAVIS_BUILD_DIR
+  - mkdir ./build_test_cmake
+  - cd ./build_test_cmake
+  - cmake -DCMAKE_CXX_COMPILER=$COMPILER $TRAVIS_BUILD_DIR/test/cmake/ -DCMAKE_PREFIX_PATH=$TRAVIS_BUILD_DIR/install
+  - cmake --build .
+
+

3dgeer/submodules/geer-rasterizer/third_party/glm/CMakeLists.txt

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

3dgeer/submodules/geer-rasterizer/third_party/glm/cmake/cmake_uninstall.cmake.in

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

3dgeer/submodules/geer-rasterizer/third_party/glm/copying.txt

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

3dgeer/submodules/geer-rasterizer/third_party/glm/doc/api/a00001_source.html

@@ -0,0 +1,493 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml">
+<head>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta http-equiv="X-UA-Compatible" content="IE=9"/>
+<meta name="generator" content="Doxygen 1.8.10"/>
+<title>0.9.9 API documentation: _features.hpp Source File</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="jquery.js"></script>
+<script type="text/javascript" src="dynsections.js"></script>
+<link href="search/search.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="search/searchdata.js"></script>
+<script type="text/javascript" src="search/search.js"></script>
+<script type="text/javascript">
+  $(document).ready(function() { init_search(); });
+</script>
+<link href="doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
+<table cellspacing="0" cellpadding="0">
+ <tbody>
+ <tr style="height: 56px;">
+  <td id="projectlogo"><img alt="Logo" src="logo-mini.png"/></td>
+  <td id="projectalign" style="padding-left: 0.5em;">
+   <div id="projectname">0.9.9 API documentation
+   </div>
+  </td>
+ </tr>
+ </tbody>
+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.10 -->
+<script type="text/javascript">
+var searchBox = new SearchBox("searchBox", "search",false,'Search');
+</script>
+  <div id="navrow1" class="tabs">
+    <ul class="tablist">
+      <li><a href="index.html"><span>Main&#160;Page</span></a></li>
+      <li><a href="modules.html"><span>Modules</span></a></li>
+      <li class="current"><a href="files.html"><span>Files</span></a></li>
+      <li>
+        <div id="MSearchBox" class="MSearchBoxInactive">
+        <span class="left">
+          <img id="MSearchSelect" src="search/mag_sel.png"
+               onmouseover="return searchBox.OnSearchSelectShow()"
+               onmouseout="return searchBox.OnSearchSelectHide()"
+               alt=""/>
+          <input type="text" id="MSearchField" value="Search" accesskey="S"
+               onfocus="searchBox.OnSearchFieldFocus(true)" 
+               onblur="searchBox.OnSearchFieldFocus(false)" 
+               onkeyup="searchBox.OnSearchFieldChange(event)"/>
+          </span><span class="right">
+            <a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.png" alt=""/></a>
+          </span>
+        </div>
+      </li>
+    </ul>
+  </div>
+  <div id="navrow2" class="tabs2">
+    <ul class="tablist">
+      <li><a href="files.html"><span>File&#160;List</span></a></li>
+    </ul>
+  </div>
+<!-- window showing the filter options -->
+<div id="MSearchSelectWindow"
+     onmouseover="return searchBox.OnSearchSelectShow()"
+     onmouseout="return searchBox.OnSearchSelectHide()"
+     onkeydown="return searchBox.OnSearchSelectKey(event)">
+</div>
+
+<!-- iframe showing the search results (closed by default) -->
+<div id="MSearchResultsWindow">
+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div id="nav-path" class="navpath">
+  <ul>
+<li class="navelem"><a class="el" href="dir_3a581ba30d25676e4b797b1f96d53b45.html">F:</a></li><li class="navelem"><a class="el" href="dir_9e5fe034a00e89334fd5186c3e7db156.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_d9496f0844b48bc7e53b5af8c99b9ab2.html">Source</a></li><li class="navelem"><a class="el" href="dir_a8bee7be44182a33f3820393ae0b105d.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_44e5e654415abd9ca6fdeaddaff8565e.html">glm</a></li><li class="navelem"><a class="el" href="dir_cef2d71d502cb69a9252bca2297d9549.html">glm</a></li><li class="navelem"><a class="el" href="dir_033f5edb0915b828d2c46ed4804e5503.html">detail</a></li>  </ul>
+</div>
+</div><!-- top -->
+<div class="header">
+  <div class="headertitle">
+<div class="title">_features.hpp</div>  </div>
+</div><!--header-->
+<div class="contents">
+<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#pragma once</span></div>
+<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;</div>
+<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">// #define GLM_CXX98_EXCEPTIONS</span></div>
+<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// #define GLM_CXX98_RTTI</span></div>
+<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;</div>
+<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// #define GLM_CXX11_RVALUE_REFERENCES</span></div>
+<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Rvalue references - GCC 4.3</span></div>
+<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n2118.html</span></div>
+<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;</div>
+<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">// GLM_CXX11_TRAILING_RETURN</span></div>
+<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">// Rvalue references for *this - GCC not supported</span></div>
+<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2439.htm</span></div>
+<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;</div>
+<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment">// GLM_CXX11_NONSTATIC_MEMBER_INIT</span></div>
+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">// Initialization of class objects by rvalues - GCC any</span></div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2004/n1610.html</span></div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;</div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment">// GLM_CXX11_NONSTATIC_MEMBER_INIT</span></div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment">// Non-static data member initializers - GCC 4.7</span></div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="comment">// http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2008/n2756.htm</span></div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;</div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="comment">// #define GLM_CXX11_VARIADIC_TEMPLATE</span></div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="comment">// Variadic templates - GCC 4.3</span></div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2242.pdf</span></div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="comment">// Extending variadic template template parameters - GCC 4.4</span></div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2555.pdf</span></div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="comment">// #define GLM_CXX11_GENERALIZED_INITIALIZERS</span></div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="comment">// Initializer lists - GCC 4.4</span></div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2672.htm</span></div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="comment">// #define GLM_CXX11_STATIC_ASSERT</span></div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="comment">// Static assertions - GCC 4.3</span></div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2004/n1720.html</span></div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="comment">// #define GLM_CXX11_AUTO_TYPE</span></div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="comment">// auto-typed variables - GCC 4.4</span></div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n1984.pdf</span></div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="comment">// #define GLM_CXX11_AUTO_TYPE</span></div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="comment">// Multi-declarator auto - GCC 4.4</span></div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2004/n1737.pdf</span></div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;<span class="comment">// #define GLM_CXX11_AUTO_TYPE</span></div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;<span class="comment">// Removal of auto as a storage-class specifier - GCC 4.4</span></div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2546.htm</span></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">   50</span>&#160;<span class="comment">// #define GLM_CXX11_AUTO_TYPE</span></div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;<span class="comment">// New function declarator syntax - GCC 4.4</span></div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2541.htm</span></div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;<span class="comment">// #define GLM_CXX11_LAMBDAS</span></div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;<span class="comment">// New wording for C++0x lambdas - GCC 4.5</span></div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;<span class="comment">// http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2009/n2927.pdf</span></div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;<span class="comment">// #define GLM_CXX11_DECLTYPE</span></div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;<span class="comment">// Declared type of an expression - GCC 4.3</span></div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2343.pdf</span></div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;<span class="comment">// Right angle brackets - GCC 4.3</span></div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1757.html</span></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">   66</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;<span class="comment">// Default template arguments for function templates    DR226   GCC 4.3</span></div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/cwg_defects.html#226</span></div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;<span class="comment">// Solving the SFINAE problem for expressions   DR339   GCC 4.4</span></div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2634.html</span></div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;</div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;<span class="comment">// #define GLM_CXX11_ALIAS_TEMPLATE</span></div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;<span class="comment">// Template aliases     N2258   GCC 4.7</span></div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2258.pdf</span></div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;<span class="comment">// Extern templates     N1987   Yes</span></div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n1987.htm</span></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">   82</span>&#160;<span class="comment">// #define GLM_CXX11_NULLPTR</span></div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;<span class="comment">// Null pointer constant        N2431   GCC 4.6</span></div>
+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2431.pdf</span></div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;</div>
+<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;<span class="comment">// #define GLM_CXX11_STRONG_ENUMS</span></div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;<span class="comment">// Strongly-typed enums N2347   GCC 4.4</span></div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2347.pdf</span></div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;</div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;<span class="comment">// Forward declarations for enums       N2764   GCC 4.6</span></div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2764.pdf</span></div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;<span class="comment">// Generalized attributes       N2761   GCC 4.8</span></div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2761.pdf</span></div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;</div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;<span class="comment">// Generalized constant expressions     N2235   GCC 4.6</span></div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2235.pdf</span></div>
+<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;</div>
+<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;<span class="comment">// Alignment support    N2341   GCC 4.8</span></div>
+<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2341.pdf</span></div>
+<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;</div>
+<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;<span class="comment">// #define GLM_CXX11_DELEGATING_CONSTRUCTORS</span></div>
+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;<span class="comment">// Delegating constructors      N1986   GCC 4.7</span></div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n1986.pdf</span></div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;</div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;<span class="comment">// Inheriting constructors      N2540   GCC 4.8</span></div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2540.htm</span></div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;</div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;<span class="comment">// #define GLM_CXX11_EXPLICIT_CONVERSIONS</span></div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;<span class="comment">// Explicit conversion operators        N2437   GCC 4.5</span></div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2437.pdf</span></div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;</div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;<span class="comment">// New character types  N2249   GCC 4.4</span></div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2249.html</span></div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;<span class="comment">// Unicode string literals      N2442   GCC 4.5</span></div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2442.htm</span></div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;</div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;<span class="comment">// Raw string literals  N2442   GCC 4.5</span></div>
+<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2442.htm</span></div>
+<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;</div>
+<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;<span class="comment">// Universal character name literals    N2170   GCC 4.5</span></div>
+<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2170.html</span></div>
+<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;</div>
+<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;<span class="comment">// #define GLM_CXX11_USER_LITERALS</span></div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;<span class="comment">// User-defined literals                N2765   GCC 4.7</span></div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2765.pdf</span></div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;</div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;<span class="comment">// Standard Layout Types        N2342   GCC 4.5</span></div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2342.htm</span></div>
+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;</div>
+<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;<span class="comment">// #define GLM_CXX11_DEFAULTED_FUNCTIONS</span></div>
+<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;<span class="comment">// #define GLM_CXX11_DELETED_FUNCTIONS</span></div>
+<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;<span class="comment">// Defaulted and deleted functions      N2346   GCC 4.4</span></div>
+<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2346.htm</span></div>
+<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;</div>
+<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;<span class="comment">// Extended friend declarations N1791   GCC 4.7</span></div>
+<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1791.pdf</span></div>
+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;</div>
+<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;<span class="comment">// Extending sizeof     N2253   GCC 4.4</span></div>
+<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2253.html</span></div>
+<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;</div>
+<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;<span class="comment">// #define GLM_CXX11_INLINE_NAMESPACES</span></div>
+<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;<span class="comment">// Inline namespaces    N2535   GCC 4.4</span></div>
+<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2535.htm</span></div>
+<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;</div>
+<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;<span class="comment">// #define GLM_CXX11_UNRESTRICTED_UNIONS</span></div>
+<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;<span class="comment">// Unrestricted unions  N2544   GCC 4.6</span></div>
+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2544.pdf</span></div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;</div>
+<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;<span class="comment">// #define GLM_CXX11_LOCAL_TYPE_TEMPLATE_ARGS</span></div>
+<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;<span class="comment">// Local and unnamed types as template arguments        N2657   GCC 4.5</span></div>
+<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2657.htm</span></div>
+<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;</div>
+<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;<span class="comment">// #define GLM_CXX11_RANGE_FOR</span></div>
+<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;<span class="comment">// Range-based for      N2930   GCC 4.6</span></div>
+<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;<span class="comment">// http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2009/n2930.html</span></div>
+<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;</div>
+<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;<span class="comment">// #define GLM_CXX11_OVERRIDE_CONTROL</span></div>
+<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;<span class="comment">// Explicit virtual overrides   N2928 N3206 N3272       GCC 4.7</span></div>
+<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;<span class="comment">// http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2009/n2928.htm</span></div>
+<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2010/n3206.htm</span></div>
+<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2011/n3272.htm</span></div>
+<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;</div>
+<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;<span class="comment">// Minimal support for garbage collection and reachability-based leak detection N2670   No</span></div>
+<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2670.htm</span></div>
+<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;</div>
+<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;<span class="comment">// #define GLM_CXX11_NOEXCEPT</span></div>
+<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;<span class="comment">// Allowing move constructors to throw [noexcept]       N3050   GCC 4.6 (core language only)</span></div>
+<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2010/n3050.html</span></div>
+<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;</div>
+<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;<span class="comment">// Defining move special member functions       N3053   GCC 4.6</span></div>
+<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2010/n3053.html</span></div>
+<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;</div>
+<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;<span class="comment">// Sequence points      N2239   Yes</span></div>
+<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2239.html</span></div>
+<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;</div>
+<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;<span class="comment">// Atomic operations    N2427   GCC 4.4</span></div>
+<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2239.html</span></div>
+<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;</div>
+<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;<span class="comment">// Strong Compare and Exchange  N2748   GCC 4.5</span></div>
+<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2427.html</span></div>
+<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;</div>
+<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;<span class="comment">// Bidirectional Fences N2752   GCC 4.8</span></div>
+<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2752.htm</span></div>
+<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;</div>
+<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;<span class="comment">// Memory model N2429   GCC 4.8</span></div>
+<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2429.htm</span></div>
+<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;</div>
+<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;<span class="comment">// Data-dependency ordering: atomics and memory model   N2664   GCC 4.4</span></div>
+<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2664.htm</span></div>
+<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;</div>
+<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;<span class="comment">// Propagating exceptions       N2179   GCC 4.4</span></div>
+<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2179.html</span></div>
+<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;</div>
+<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;<span class="comment">// Abandoning a process and at_quick_exit       N2440   GCC 4.8</span></div>
+<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2440.htm</span></div>
+<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;</div>
+<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;<span class="comment">// Allow atomics use in signal handlers N2547   Yes</span></div>
+<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2547.htm</span></div>
+<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;</div>
+<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;<span class="comment">// Thread-local storage N2659   GCC 4.8</span></div>
+<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2659.htm</span></div>
+<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;</div>
+<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;<span class="comment">// Dynamic initialization and destruction with concurrency      N2660   GCC 4.3</span></div>
+<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2660.htm</span></div>
+<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;</div>
+<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;<span class="comment">// __func__ predefined identifier       N2340   GCC 4.3</span></div>
+<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2340.htm</span></div>
+<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;</div>
+<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;<span class="comment">// C99 preprocessor     N1653   GCC 4.3</span></div>
+<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2004/n1653.htm</span></div>
+<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;</div>
+<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;<span class="comment">// long long    N1811   GCC 4.3</span></div>
+<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1811.pdf</span></div>
+<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;</div>
+<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;<span class="comment">//</span></div>
+<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;<span class="comment">// Extended integral types      N1988   Yes</span></div>
+<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;<span class="comment">// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n1988.pdf</span></div>
+<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;</div>
+<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;<span class="preprocessor">#if(GLM_COMPILER &amp; GLM_COMPILER_GCC)</span></div>
+<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;</div>
+<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;<span class="preprocessor">#       define GLM_CXX11_STATIC_ASSERT</span></div>
+<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;</div>
+<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;<span class="preprocessor">#elif(GLM_COMPILER &amp; GLM_COMPILER_CLANG)</span></div>
+<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_exceptions))</span></div>
+<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;<span class="preprocessor">#               define GLM_CXX98_EXCEPTIONS</span></div>
+<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;</div>
+<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_rtti))</span></div>
+<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;<span class="preprocessor">#               define GLM_CXX98_RTTI</span></div>
+<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;</div>
+<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_access_control_sfinae))</span></div>
+<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;<span class="preprocessor">#               define GLM_CXX11_ACCESS_CONTROL_SFINAE</span></div>
+<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;</div>
+<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_alias_templates))</span></div>
+<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;<span class="preprocessor">#               define GLM_CXX11_ALIAS_TEMPLATE</span></div>
+<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;</div>
+<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_alignas))</span></div>
+<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;<span class="preprocessor">#               define GLM_CXX11_ALIGNAS</span></div>
+<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;</div>
+<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_attributes))</span></div>
+<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;<span class="preprocessor">#               define GLM_CXX11_ATTRIBUTES</span></div>
+<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;</div>
+<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_constexpr))</span></div>
+<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;<span class="preprocessor">#               define GLM_CXX11_CONSTEXPR</span></div>
+<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;</div>
+<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_decltype))</span></div>
+<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;<span class="preprocessor">#               define GLM_CXX11_DECLTYPE</span></div>
+<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;</div>
+<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_default_function_template_args))</span></div>
+<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;<span class="preprocessor">#               define GLM_CXX11_DEFAULT_FUNCTION_TEMPLATE_ARGS</span></div>
+<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;</div>
+<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_defaulted_functions))</span></div>
+<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;<span class="preprocessor">#               define GLM_CXX11_DEFAULTED_FUNCTIONS</span></div>
+<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;</div>
+<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_delegating_constructors))</span></div>
+<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;<span class="preprocessor">#               define GLM_CXX11_DELEGATING_CONSTRUCTORS</span></div>
+<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;</div>
+<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_deleted_functions))</span></div>
+<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;<span class="preprocessor">#               define GLM_CXX11_DELETED_FUNCTIONS</span></div>
+<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;</div>
+<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_explicit_conversions))</span></div>
+<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;<span class="preprocessor">#               define GLM_CXX11_EXPLICIT_CONVERSIONS</span></div>
+<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;</div>
+<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_generalized_initializers))</span></div>
+<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;<span class="preprocessor">#               define GLM_CXX11_GENERALIZED_INITIALIZERS</span></div>
+<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;</div>
+<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_implicit_moves))</span></div>
+<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;<span class="preprocessor">#               define GLM_CXX11_IMPLICIT_MOVES</span></div>
+<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;</div>
+<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_inheriting_constructors))</span></div>
+<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;<span class="preprocessor">#               define GLM_CXX11_INHERITING_CONSTRUCTORS</span></div>
+<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;</div>
+<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_inline_namespaces))</span></div>
+<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;<span class="preprocessor">#               define GLM_CXX11_INLINE_NAMESPACES</span></div>
+<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;</div>
+<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_lambdas))</span></div>
+<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;<span class="preprocessor">#               define GLM_CXX11_LAMBDAS</span></div>
+<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;</div>
+<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_local_type_template_args))</span></div>
+<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;<span class="preprocessor">#               define GLM_CXX11_LOCAL_TYPE_TEMPLATE_ARGS</span></div>
+<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;</div>
+<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_noexcept))</span></div>
+<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;<span class="preprocessor">#               define GLM_CXX11_NOEXCEPT</span></div>
+<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;</div>
+<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_nonstatic_member_init))</span></div>
+<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;<span class="preprocessor">#               define GLM_CXX11_NONSTATIC_MEMBER_INIT</span></div>
+<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;</div>
+<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_nullptr))</span></div>
+<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;<span class="preprocessor">#               define GLM_CXX11_NULLPTR</span></div>
+<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;</div>
+<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_override_control))</span></div>
+<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;<span class="preprocessor">#               define GLM_CXX11_OVERRIDE_CONTROL</span></div>
+<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;</div>
+<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_reference_qualified_functions))</span></div>
+<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;<span class="preprocessor">#               define GLM_CXX11_REFERENCE_QUALIFIED_FUNCTIONS</span></div>
+<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;</div>
+<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_range_for))</span></div>
+<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;<span class="preprocessor">#               define GLM_CXX11_RANGE_FOR</span></div>
+<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;</div>
+<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_raw_string_literals))</span></div>
+<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;<span class="preprocessor">#               define GLM_CXX11_RAW_STRING_LITERALS</span></div>
+<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;</div>
+<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_rvalue_references))</span></div>
+<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;<span class="preprocessor">#               define GLM_CXX11_RVALUE_REFERENCES</span></div>
+<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;</div>
+<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_static_assert))</span></div>
+<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;<span class="preprocessor">#               define GLM_CXX11_STATIC_ASSERT</span></div>
+<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;</div>
+<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_auto_type))</span></div>
+<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;<span class="preprocessor">#               define GLM_CXX11_AUTO_TYPE</span></div>
+<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;</div>
+<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_strong_enums))</span></div>
+<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;<span class="preprocessor">#               define GLM_CXX11_STRONG_ENUMS</span></div>
+<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;</div>
+<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_trailing_return))</span></div>
+<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;<span class="preprocessor">#               define GLM_CXX11_TRAILING_RETURN</span></div>
+<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;</div>
+<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_unicode_literals))</span></div>
+<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;<span class="preprocessor">#               define GLM_CXX11_UNICODE_LITERALS</span></div>
+<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;</div>
+<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_unrestricted_unions))</span></div>
+<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;<span class="preprocessor">#               define GLM_CXX11_UNRESTRICTED_UNIONS</span></div>
+<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;<span class="preprocessor">#       endif</span></div>
+<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;</div>
+<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;<span class="preprocessor">#       if(__has_feature(cxx_user_literals))</span></div>
+<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;<span class="preprocessor">#               define GLM_CXX11_USER_LITERALS</span></div>
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+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;        {</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;                <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(1.79284291400159) - <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(0.85373472095314) * r;</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;        }</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;</div>
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+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;        GLM_FUNC_QUALIFIER vec&lt;2, T, Q&gt; fade(vec&lt;2, T, Q&gt; <span class="keyword">const</span>&amp; t)</div>
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+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt;</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        GLM_FUNC_QUALIFIER vec&lt;3, T, Q&gt; fade(vec&lt;3, T, Q&gt; <span class="keyword">const</span>&amp; t)</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">   71</span>&#160;                <span class="keywordflow">return</span> (t * t * t) * (t * (t * <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(6) - static_cast&lt;T&gt;(15)) + static_cast&lt;T&gt;(10));</div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;        }</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;</div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt;</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;        GLM_FUNC_QUALIFIER vec&lt;4, T, Q&gt; fade(vec&lt;4, T, Q&gt; <span class="keyword">const</span>&amp; t)</div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        {</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;                <span class="keywordflow">return</span> (t * t * t) * (t * (t * <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(6) - static_cast&lt;T&gt;(15)) + static_cast&lt;T&gt;(10));</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        }</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;}<span class="comment">//namespace detail</span></div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;}<span class="comment">//namespace glm</span></div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;</div>
+<div class="ttc" id="a00241_html_gaa9d0742639e85b29c7c5de11cfd6840d"><div class="ttname"><a href="a00241.html#gaa9d0742639e85b29c7c5de11cfd6840d">glm::floor</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, T, Q &gt; floor(vec&lt; L, T, Q &gt; const &amp;x)</div><div class="ttdoc">Returns a value equal to the nearest integer that is less then or equal to x. </div></div>
+<div class="ttc" id="a00236_html"><div class="ttname"><a href="a00236.html">glm</a></div><div class="ttdef"><b>Definition:</b> <a href="a00015_source.html#l00020">common.hpp:20</a></div></div>
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+<li class="navelem"><a class="el" href="dir_3a581ba30d25676e4b797b1f96d53b45.html">F:</a></li><li class="navelem"><a class="el" href="dir_9e5fe034a00e89334fd5186c3e7db156.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_d9496f0844b48bc7e53b5af8c99b9ab2.html">Source</a></li><li class="navelem"><a class="el" href="dir_a8bee7be44182a33f3820393ae0b105d.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_44e5e654415abd9ca6fdeaddaff8565e.html">glm</a></li><li class="navelem"><a class="el" href="dir_cef2d71d502cb69a9252bca2297d9549.html">glm</a></li><li class="navelem"><a class="el" href="dir_033f5edb0915b828d2c46ed4804e5503.html">detail</a></li>  </ul>
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+<div class="title">_vectorize.hpp</div>  </div>
+</div><!--header-->
+<div class="contents">
+<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#pragma once</span></div>
+<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;</div>
+<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="keyword">namespace </span><a class="code" href="a00236.html">glm</a>{</div>
+<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="keyword">namespace </span>detail</div>
+<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;{</div>
+<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">template</span>&lt;length_t L, <span class="keyword">typename</span> T, qualifier Q&gt; <span class="keyword">class </span>vec, length_t L, <span class="keyword">typename</span> R, <span class="keyword">typename</span> T, qualifier Q&gt;</div>
+<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;        <span class="keyword">struct </span>functor1{};</div>
+<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;</div>
+<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">template</span>&lt;length_t L, <span class="keyword">typename</span> T, qualifier Q&gt; <span class="keyword">class </span>vec, <span class="keyword">typename</span> R, <span class="keyword">typename</span> T, qualifier Q&gt;</div>
+<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;        <span class="keyword">struct </span>functor1&lt;vec, 1, R, T, Q&gt;</div>
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+<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;                GLM_FUNC_QUALIFIER GLM_CONSTEXPR <span class="keyword">static</span> vec&lt;1, R, Q&gt; call(R (*Func) (T x), vec&lt;1, T, Q&gt; <span class="keyword">const</span>&amp; v)</div>
+<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;                {</div>
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+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">template</span>&lt;length_t L, <span class="keyword">typename</span> T, qualifier Q&gt; <span class="keyword">class </span>vec, <span class="keyword">typename</span> R, <span class="keyword">typename</span> T, qualifier Q&gt;</div>
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+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;                GLM_FUNC_QUALIFIER GLM_CONSTEXPR <span class="keyword">static</span> vec&lt;2, R, Q&gt; call(R (*Func) (T x), vec&lt;2, T, Q&gt; <span class="keyword">const</span>&amp; v)</div>
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+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">template</span>&lt;length_t L, <span class="keyword">typename</span> T, qualifier Q&gt; <span class="keyword">class </span>vec, <span class="keyword">typename</span> R, <span class="keyword">typename</span> T, qualifier Q&gt;</div>
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+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;                GLM_FUNC_QUALIFIER GLM_CONSTEXPR <span class="keyword">static</span> vec&lt;3, R, Q&gt; call(R (*Func) (T x), vec&lt;3, T, Q&gt; <span class="keyword">const</span>&amp; v)</div>
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+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;        };</div>
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+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;        <span class="keyword">struct </span>functor2{};</div>
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+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">template</span>&lt;length_t L, <span class="keyword">typename</span> T, qualifier Q&gt; <span class="keyword">class </span>vec, <span class="keyword">typename</span> T, qualifier Q&gt;</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;        <span class="keyword">struct </span>functor2&lt;vec, 1, T, Q&gt;</div>
+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;        {</div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;                GLM_FUNC_QUALIFIER <span class="keyword">static</span> vec&lt;1, T, Q&gt; call(T (*Func) (T x, T y), vec&lt;1, T, Q&gt; <span class="keyword">const</span>&amp; a, vec&lt;1, T, Q&gt; <span class="keyword">const</span>&amp; b)</div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;                {</div>
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+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">template</span>&lt;length_t L, <span class="keyword">typename</span> T, qualifier Q&gt; <span class="keyword">class </span>vec, <span class="keyword">typename</span> T, qualifier Q&gt;</div>
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+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;                GLM_FUNC_QUALIFIER <span class="keyword">static</span> vec&lt;3, T, Q&gt; call(T (*Func) (T x, T y), vec&lt;3, T, Q&gt; <span class="keyword">const</span>&amp; a, vec&lt;3, T, Q&gt; <span class="keyword">const</span>&amp; b)</div>
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+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;                }</div>
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+<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, qualifier Q&gt;</div>
+<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;        <span class="keyword">struct </span>functor2_vec_int&lt;4, T, Q&gt;</div>
+<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;        {</div>
+<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;                GLM_FUNC_QUALIFIER <span class="keyword">static</span> vec&lt;4, int, Q&gt; call(<span class="keywordtype">int</span> (*Func) (T x, <span class="keywordtype">int</span> y), vec&lt;4, T, Q&gt; <span class="keyword">const</span>&amp; a, vec&lt;4, int, Q&gt; <span class="keyword">const</span>&amp; b)</div>
+<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;                {</div>
+<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;                        <span class="keywordflow">return</span> vec&lt;4, int, Q&gt;(Func(a.x, b.x), Func(a.y, b.y), Func(a.z, b.z), Func(a.w, b.w));</div>
+<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;                }</div>
+<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;        };</div>
+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;}<span class="comment">//namespace detail</span></div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;}<span class="comment">//namespace glm</span></div>
+<div class="ttc" id="a00236_html"><div class="ttname"><a href="a00236.html">glm</a></div><div class="ttdef"><b>Definition:</b> <a href="a00015_source.html#l00020">common.hpp:20</a></div></div>
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+<li class="navelem"><a class="el" href="dir_3a581ba30d25676e4b797b1f96d53b45.html">F:</a></li><li class="navelem"><a class="el" href="dir_9e5fe034a00e89334fd5186c3e7db156.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_d9496f0844b48bc7e53b5af8c99b9ab2.html">Source</a></li><li class="navelem"><a class="el" href="dir_a8bee7be44182a33f3820393ae0b105d.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_44e5e654415abd9ca6fdeaddaff8565e.html">glm</a></li><li class="navelem"><a class="el" href="dir_cef2d71d502cb69a9252bca2297d9549.html">glm</a></li><li class="navelem"><a class="el" href="dir_f35778ec600a1b9bbc4524e62e226aa2.html">gtx</a></li>  </ul>
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+<a href="#func-members">Functions</a>  </div>
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+<div class="title">associated_min_max.hpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a class="el" href="a00308.html">GLM_GTX_associated_min_max</a>  
+<a href="#details">More...</a></p>
+
+<p><a href="a00007_source.html">Go to the source code of this file.</a></p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ga7d9c8785230c8db60f72ec8975f1ba45"><td class="memTemplParams" colspan="2">template&lt;typename T , typename U &gt; </td></tr>
+<tr class="memitem:ga7d9c8785230c8db60f72ec8975f1ba45"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL U&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#ga7d9c8785230c8db60f72ec8975f1ba45">associatedMax</a> (T x, U a, T y, U b)</td></tr>
+<tr class="memdesc:ga7d9c8785230c8db60f72ec8975f1ba45"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maximum comparison between 2 variables and returns 2 associated variable values.  <a href="a00308.html#ga7d9c8785230c8db60f72ec8975f1ba45">More...</a><br /></td></tr>
+<tr class="separator:ga7d9c8785230c8db60f72ec8975f1ba45"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga5c6758bc50aa7fbe700f87123a045aad"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , typename U , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga5c6758bc50aa7fbe700f87123a045aad"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; 2, U, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#ga5c6758bc50aa7fbe700f87123a045aad">associatedMax</a> (vec&lt; L, T, Q &gt; const &amp;x, vec&lt; L, U, Q &gt; const &amp;a, vec&lt; L, T, Q &gt; const &amp;y, vec&lt; L, U, Q &gt; const &amp;b)</td></tr>
+<tr class="memdesc:ga5c6758bc50aa7fbe700f87123a045aad"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maximum comparison between 2 variables and returns 2 associated variable values.  <a href="a00308.html#ga5c6758bc50aa7fbe700f87123a045aad">More...</a><br /></td></tr>
+<tr class="separator:ga5c6758bc50aa7fbe700f87123a045aad"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga0d169d6ce26b03248df175f39005d77f"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , typename U , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga0d169d6ce26b03248df175f39005d77f"><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="a00308.html#ga0d169d6ce26b03248df175f39005d77f">associatedMax</a> (T x, vec&lt; L, U, Q &gt; const &amp;a, T y, vec&lt; L, U, Q &gt; const &amp;b)</td></tr>
+<tr class="memdesc:ga0d169d6ce26b03248df175f39005d77f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maximum comparison between 2 variables and returns 2 associated variable values.  <a href="a00308.html#ga0d169d6ce26b03248df175f39005d77f">More...</a><br /></td></tr>
+<tr class="separator:ga0d169d6ce26b03248df175f39005d77f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga4086269afabcb81dd7ded33cb3448653"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , typename U , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga4086269afabcb81dd7ded33cb3448653"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, U, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#ga4086269afabcb81dd7ded33cb3448653">associatedMax</a> (vec&lt; L, T, Q &gt; const &amp;x, U a, vec&lt; L, T, Q &gt; const &amp;y, U b)</td></tr>
+<tr class="memdesc:ga4086269afabcb81dd7ded33cb3448653"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maximum comparison between 2 variables and returns 2 associated variable values.  <a href="a00308.html#ga4086269afabcb81dd7ded33cb3448653">More...</a><br /></td></tr>
+<tr class="separator:ga4086269afabcb81dd7ded33cb3448653"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaec891e363d91abbf3a4443cf2f652209"><td class="memTemplParams" colspan="2">template&lt;typename T , typename U &gt; </td></tr>
+<tr class="memitem:gaec891e363d91abbf3a4443cf2f652209"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL U&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#gaec891e363d91abbf3a4443cf2f652209">associatedMax</a> (T x, U a, T y, U b, T z, U c)</td></tr>
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+<tr class="separator:gaec891e363d91abbf3a4443cf2f652209"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gab84fdc35016a31e8cd0cbb8296bddf7c"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , typename U , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:gab84fdc35016a31e8cd0cbb8296bddf7c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maximum comparison between 3 variables and returns 3 associated variable values.  <a href="a00308.html#gab84fdc35016a31e8cd0cbb8296bddf7c">More...</a><br /></td></tr>
+<tr class="separator:gab84fdc35016a31e8cd0cbb8296bddf7c"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gadd2a2002f4f2144bbc39eb2336dd2fba"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , typename U , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:gadd2a2002f4f2144bbc39eb2336dd2fba"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maximum comparison between 3 variables and returns 3 associated variable values.  <a href="a00308.html#gadd2a2002f4f2144bbc39eb2336dd2fba">More...</a><br /></td></tr>
+<tr class="separator:gadd2a2002f4f2144bbc39eb2336dd2fba"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga19f59d1141a51a3b2108a9807af78f7f"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , typename U , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga19f59d1141a51a3b2108a9807af78f7f"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, U, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#ga19f59d1141a51a3b2108a9807af78f7f">associatedMax</a> (vec&lt; L, T, Q &gt; const &amp;x, U a, vec&lt; L, T, Q &gt; const &amp;y, U b, vec&lt; L, T, Q &gt; const &amp;z, U c)</td></tr>
+<tr class="memdesc:ga19f59d1141a51a3b2108a9807af78f7f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maximum comparison between 3 variables and returns 3 associated variable values.  <a href="a00308.html#ga19f59d1141a51a3b2108a9807af78f7f">More...</a><br /></td></tr>
+<tr class="separator:ga19f59d1141a51a3b2108a9807af78f7f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga3038ffcb43eaa6af75897a99a5047ccc"><td class="memTemplParams" colspan="2">template&lt;typename T , typename U &gt; </td></tr>
+<tr class="memitem:ga3038ffcb43eaa6af75897a99a5047ccc"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL U&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#ga3038ffcb43eaa6af75897a99a5047ccc">associatedMax</a> (T x, U a, T y, U b, T z, U c, T w, U d)</td></tr>
+<tr class="memdesc:ga3038ffcb43eaa6af75897a99a5047ccc"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maximum comparison between 4 variables and returns 4 associated variable values.  <a href="a00308.html#ga3038ffcb43eaa6af75897a99a5047ccc">More...</a><br /></td></tr>
+<tr class="separator:ga3038ffcb43eaa6af75897a99a5047ccc"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaf5ab0c428f8d1cd9e3b45fcfbf6423a6"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , typename U , qualifier Q&gt; </td></tr>
+<tr class="memitem:gaf5ab0c428f8d1cd9e3b45fcfbf6423a6"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, U, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#gaf5ab0c428f8d1cd9e3b45fcfbf6423a6">associatedMax</a> (vec&lt; L, T, Q &gt; const &amp;x, vec&lt; L, U, Q &gt; const &amp;a, vec&lt; L, T, Q &gt; const &amp;y, vec&lt; L, U, Q &gt; const &amp;b, vec&lt; L, T, Q &gt; const &amp;z, vec&lt; L, U, Q &gt; const &amp;c, vec&lt; L, T, Q &gt; const &amp;w, vec&lt; L, U, Q &gt; const &amp;d)</td></tr>
+<tr class="memdesc:gaf5ab0c428f8d1cd9e3b45fcfbf6423a6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maximum comparison between 4 variables and returns 4 associated variable values.  <a href="a00308.html#gaf5ab0c428f8d1cd9e3b45fcfbf6423a6">More...</a><br /></td></tr>
+<tr class="separator:gaf5ab0c428f8d1cd9e3b45fcfbf6423a6"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga11477c2c4b5b0bfd1b72b29df3725a9d"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , typename U , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga11477c2c4b5b0bfd1b72b29df3725a9d"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, U, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#ga11477c2c4b5b0bfd1b72b29df3725a9d">associatedMax</a> (T x, vec&lt; L, U, Q &gt; const &amp;a, T y, vec&lt; L, U, Q &gt; const &amp;b, T z, vec&lt; L, U, Q &gt; const &amp;c, T w, vec&lt; L, U, Q &gt; const &amp;d)</td></tr>
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+<tr class="separator:ga11477c2c4b5b0bfd1b72b29df3725a9d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gab9c3dd74cac899d2c625b5767ea3b3fb"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , typename U , qualifier Q&gt; </td></tr>
+<tr class="memitem:gab9c3dd74cac899d2c625b5767ea3b3fb"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, U, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#gab9c3dd74cac899d2c625b5767ea3b3fb">associatedMax</a> (vec&lt; L, T, Q &gt; const &amp;x, U a, vec&lt; L, T, Q &gt; const &amp;y, U b, vec&lt; L, T, Q &gt; const &amp;z, U c, vec&lt; L, T, Q &gt; const &amp;w, U d)</td></tr>
+<tr class="memdesc:gab9c3dd74cac899d2c625b5767ea3b3fb"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maximum comparison between 4 variables and returns 4 associated variable values.  <a href="a00308.html#gab9c3dd74cac899d2c625b5767ea3b3fb">More...</a><br /></td></tr>
+<tr class="separator:gab9c3dd74cac899d2c625b5767ea3b3fb"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gacc01bd272359572fc28437ae214a02df"><td class="memTemplParams" colspan="2">template&lt;typename T , typename U , qualifier Q&gt; </td></tr>
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+<tr class="separator:gacc01bd272359572fc28437ae214a02df"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gac2f0dff90948f2e44386a5eafd941d1c"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , typename U , qualifier Q&gt; </td></tr>
+<tr class="memitem:gac2f0dff90948f2e44386a5eafd941d1c"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; 2, U, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#gac2f0dff90948f2e44386a5eafd941d1c">associatedMin</a> (vec&lt; L, T, Q &gt; const &amp;x, vec&lt; L, U, Q &gt; const &amp;a, vec&lt; L, T, Q &gt; const &amp;y, vec&lt; L, U, Q &gt; const &amp;b)</td></tr>
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+<tr class="separator:gac2f0dff90948f2e44386a5eafd941d1c"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gacfec519c820331d023ef53a511749319"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , typename U , qualifier Q&gt; </td></tr>
+<tr class="memitem:gacfec519c820331d023ef53a511749319"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, U, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#gacfec519c820331d023ef53a511749319">associatedMin</a> (T x, const vec&lt; L, U, Q &gt; &amp;a, T y, const vec&lt; L, U, Q &gt; &amp;b)</td></tr>
+<tr class="memdesc:gacfec519c820331d023ef53a511749319"><td class="mdescLeft">&#160;</td><td class="mdescRight">Minimum comparison between 2 variables and returns 2 associated variable values.  <a href="a00308.html#gacfec519c820331d023ef53a511749319">More...</a><br /></td></tr>
+<tr class="separator:gacfec519c820331d023ef53a511749319"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga4757c7cab2d809124a8525d0a9deeb37"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , typename U , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga4757c7cab2d809124a8525d0a9deeb37"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, U, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#ga4757c7cab2d809124a8525d0a9deeb37">associatedMin</a> (vec&lt; L, T, Q &gt; const &amp;x, U a, vec&lt; L, T, Q &gt; const &amp;y, U b)</td></tr>
+<tr class="memdesc:ga4757c7cab2d809124a8525d0a9deeb37"><td class="mdescLeft">&#160;</td><td class="mdescRight">Minimum comparison between 2 variables and returns 2 associated variable values.  <a href="a00308.html#ga4757c7cab2d809124a8525d0a9deeb37">More...</a><br /></td></tr>
+<tr class="separator:ga4757c7cab2d809124a8525d0a9deeb37"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gad0aa8f86259a26d839d34a3577a923fc"><td class="memTemplParams" colspan="2">template&lt;typename T , typename U &gt; </td></tr>
+<tr class="memitem:gad0aa8f86259a26d839d34a3577a923fc"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL U&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#gad0aa8f86259a26d839d34a3577a923fc">associatedMin</a> (T x, U a, T y, U b, T z, U c)</td></tr>
+<tr class="memdesc:gad0aa8f86259a26d839d34a3577a923fc"><td class="mdescLeft">&#160;</td><td class="mdescRight">Minimum comparison between 3 variables and returns 3 associated variable values.  <a href="a00308.html#gad0aa8f86259a26d839d34a3577a923fc">More...</a><br /></td></tr>
+<tr class="separator:gad0aa8f86259a26d839d34a3577a923fc"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga723e5411cebc7ffbd5c81ffeec61127d"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , typename U , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga723e5411cebc7ffbd5c81ffeec61127d"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, U, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#ga723e5411cebc7ffbd5c81ffeec61127d">associatedMin</a> (vec&lt; L, T, Q &gt; const &amp;x, vec&lt; L, U, Q &gt; const &amp;a, vec&lt; L, T, Q &gt; const &amp;y, vec&lt; L, U, Q &gt; const &amp;b, vec&lt; L, T, Q &gt; const &amp;z, vec&lt; L, U, Q &gt; const &amp;c)</td></tr>
+<tr class="memdesc:ga723e5411cebc7ffbd5c81ffeec61127d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Minimum comparison between 3 variables and returns 3 associated variable values.  <a href="a00308.html#ga723e5411cebc7ffbd5c81ffeec61127d">More...</a><br /></td></tr>
+<tr class="separator:ga723e5411cebc7ffbd5c81ffeec61127d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga432224ebe2085eaa2b63a077ecbbbff6"><td class="memTemplParams" colspan="2">template&lt;typename T , typename U &gt; </td></tr>
+<tr class="memitem:ga432224ebe2085eaa2b63a077ecbbbff6"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL U&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#ga432224ebe2085eaa2b63a077ecbbbff6">associatedMin</a> (T x, U a, T y, U b, T z, U c, T w, U d)</td></tr>
+<tr class="memdesc:ga432224ebe2085eaa2b63a077ecbbbff6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Minimum comparison between 4 variables and returns 4 associated variable values.  <a href="a00308.html#ga432224ebe2085eaa2b63a077ecbbbff6">More...</a><br /></td></tr>
+<tr class="separator:ga432224ebe2085eaa2b63a077ecbbbff6"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga66b08118bc88f0494bcacb7cdb940556"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , typename U , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:ga66b08118bc88f0494bcacb7cdb940556"><td class="mdescLeft">&#160;</td><td class="mdescRight">Minimum comparison between 4 variables and returns 4 associated variable values.  <a href="a00308.html#ga66b08118bc88f0494bcacb7cdb940556">More...</a><br /></td></tr>
+<tr class="separator:ga66b08118bc88f0494bcacb7cdb940556"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga78c28fde1a7080fb7420bd88e68c6c68"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , typename U , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga78c28fde1a7080fb7420bd88e68c6c68"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, U, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#ga78c28fde1a7080fb7420bd88e68c6c68">associatedMin</a> (T x, vec&lt; L, U, Q &gt; const &amp;a, T y, vec&lt; L, U, Q &gt; const &amp;b, T z, vec&lt; L, U, Q &gt; const &amp;c, T w, vec&lt; L, U, Q &gt; const &amp;d)</td></tr>
+<tr class="memdesc:ga78c28fde1a7080fb7420bd88e68c6c68"><td class="mdescLeft">&#160;</td><td class="mdescRight">Minimum comparison between 4 variables and returns 4 associated variable values.  <a href="a00308.html#ga78c28fde1a7080fb7420bd88e68c6c68">More...</a><br /></td></tr>
+<tr class="separator:ga78c28fde1a7080fb7420bd88e68c6c68"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga2db7e351994baee78540a562d4bb6d3b"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , typename U , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga2db7e351994baee78540a562d4bb6d3b"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, U, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00308.html#ga2db7e351994baee78540a562d4bb6d3b">associatedMin</a> (vec&lt; L, T, Q &gt; const &amp;x, U a, vec&lt; L, T, Q &gt; const &amp;y, U b, vec&lt; L, T, Q &gt; const &amp;z, U c, vec&lt; L, T, Q &gt; const &amp;w, U d)</td></tr>
+<tr class="memdesc:ga2db7e351994baee78540a562d4bb6d3b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Minimum comparison between 4 variables and returns 4 associated variable values.  <a href="a00308.html#ga2db7e351994baee78540a562d4bb6d3b">More...</a><br /></td></tr>
+<tr class="separator:ga2db7e351994baee78540a562d4bb6d3b"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a class="el" href="a00308.html">GLM_GTX_associated_min_max</a> </p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00280.html" title="Features that implement in C++ the GLSL specification as closely as possible. ">Core features</a> (dependence) </dd>
+<dd>
+gtx_extented_min_max (dependence) </dd></dl>
+
+<p>Definition in file <a class="el" href="a00007_source.html">associated_min_max.hpp</a>.</p>
+</div></div><!-- contents -->
+<!-- start footer part -->
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3dgeer/submodules/geer-rasterizer/third_party/glm/doc/api/a00007_source.html

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+<li class="navelem"><a class="el" href="dir_3a581ba30d25676e4b797b1f96d53b45.html">F:</a></li><li class="navelem"><a class="el" href="dir_9e5fe034a00e89334fd5186c3e7db156.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_d9496f0844b48bc7e53b5af8c99b9ab2.html">Source</a></li><li class="navelem"><a class="el" href="dir_a8bee7be44182a33f3820393ae0b105d.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_44e5e654415abd9ca6fdeaddaff8565e.html">glm</a></li><li class="navelem"><a class="el" href="dir_cef2d71d502cb69a9252bca2297d9549.html">glm</a></li><li class="navelem"><a class="el" href="dir_f35778ec600a1b9bbc4524e62e226aa2.html">gtx</a></li>  </ul>
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+<div class="title">associated_min_max.hpp</div>  </div>
+</div><!--header-->
+<div class="contents">
+<a href="a00007.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>
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+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment">// Dependency:</span></div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="preprocessor">#include &quot;../glm.hpp&quot;</span></div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;</div>
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+<div class="ttc" id="a00308_html_gab9c3dd74cac899d2c625b5767ea3b3fb"><div class="ttname"><a href="a00308.html#gab9c3dd74cac899d2c625b5767ea3b3fb">glm::associatedMax</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, U, Q &gt; associatedMax(vec&lt; L, T, Q &gt; const &amp;x, U a, vec&lt; L, T, Q &gt; const &amp;y, U b, vec&lt; L, T, Q &gt; const &amp;z, U c, vec&lt; L, T, Q &gt; const &amp;w, U d)</div><div class="ttdoc">Maximum comparison between 4 variables and returns 4 associated variable values. </div></div>
+<div class="ttc" id="a00308_html_ga2db7e351994baee78540a562d4bb6d3b"><div class="ttname"><a href="a00308.html#ga2db7e351994baee78540a562d4bb6d3b">glm::associatedMin</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, U, Q &gt; associatedMin(vec&lt; L, T, Q &gt; const &amp;x, U a, vec&lt; L, T, Q &gt; const &amp;y, U b, vec&lt; L, T, Q &gt; const &amp;z, U c, vec&lt; L, T, Q &gt; const &amp;w, U d)</div><div class="ttdoc">Minimum comparison between 4 variables and returns 4 associated variable values. </div></div>
+<div class="ttc" id="a00236_html"><div class="ttname"><a href="a00236.html">glm</a></div><div class="ttdef"><b>Definition:</b> <a href="a00015_source.html#l00020">common.hpp:20</a></div></div>
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+<li class="navelem"><a class="el" href="dir_3a581ba30d25676e4b797b1f96d53b45.html">F:</a></li><li class="navelem"><a class="el" href="dir_9e5fe034a00e89334fd5186c3e7db156.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_d9496f0844b48bc7e53b5af8c99b9ab2.html">Source</a></li><li class="navelem"><a class="el" href="dir_a8bee7be44182a33f3820393ae0b105d.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_44e5e654415abd9ca6fdeaddaff8565e.html">glm</a></li><li class="navelem"><a class="el" href="dir_cef2d71d502cb69a9252bca2297d9549.html">glm</a></li><li class="navelem"><a class="el" href="dir_f35778ec600a1b9bbc4524e62e226aa2.html">gtx</a></li>  </ul>
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+<a href="#func-members">Functions</a>  </div>
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+<div class="title">bit.hpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a class="el" href="a00309.html">GLM_GTX_bit</a>  
+<a href="#details">More...</a></p>
+
+<p><a href="a00008_source.html">Go to the source code of this file.</a></p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ga0dcc8fe7c3d3ad60dea409281efa3d05"><td class="memTemplParams" colspan="2">template&lt;typename genIUType &gt; </td></tr>
+<tr class="memitem:ga0dcc8fe7c3d3ad60dea409281efa3d05"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genIUType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00309.html#ga0dcc8fe7c3d3ad60dea409281efa3d05">highestBitValue</a> (genIUType Value)</td></tr>
+<tr class="separator:ga0dcc8fe7c3d3ad60dea409281efa3d05"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga898ef075ccf809a1e480faab48fe96bf"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga898ef075ccf809a1e480faab48fe96bf"><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="a00309.html#ga898ef075ccf809a1e480faab48fe96bf">highestBitValue</a> (vec&lt; L, T, Q &gt; const &amp;value)</td></tr>
+<tr class="memdesc:ga898ef075ccf809a1e480faab48fe96bf"><td class="mdescLeft">&#160;</td><td class="mdescRight">Find the highest bit set to 1 in a integer variable and return its value.  <a href="a00309.html#ga898ef075ccf809a1e480faab48fe96bf">More...</a><br /></td></tr>
+<tr class="separator:ga898ef075ccf809a1e480faab48fe96bf"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga2ff6568089f3a9b67f5c30918855fc6f"><td class="memTemplParams" colspan="2">template&lt;typename genIUType &gt; </td></tr>
+<tr class="memitem:ga2ff6568089f3a9b67f5c30918855fc6f"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genIUType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00309.html#ga2ff6568089f3a9b67f5c30918855fc6f">lowestBitValue</a> (genIUType Value)</td></tr>
+<tr class="separator:ga2ff6568089f3a9b67f5c30918855fc6f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga8cda2459871f574a0aecbe702ac93291"><td class="memTemplParams" colspan="2">template&lt;typename genIUType &gt; </td></tr>
+<tr class="memitem:ga8cda2459871f574a0aecbe702ac93291"><td class="memTemplItemLeft" align="right" valign="top">GLM_DEPRECATED GLM_FUNC_DECL genIUType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00309.html#ga8cda2459871f574a0aecbe702ac93291">powerOfTwoAbove</a> (genIUType Value)</td></tr>
+<tr class="memdesc:ga8cda2459871f574a0aecbe702ac93291"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return the power of two number which value is just higher the input value.  <a href="a00309.html#ga8cda2459871f574a0aecbe702ac93291">More...</a><br /></td></tr>
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+<tr class="memdesc:ga3de7df63c589325101a2817a56f8e29d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return the power of two number which value is just lower the input value.  <a href="a00309.html#ga3de7df63c589325101a2817a56f8e29d">More...</a><br /></td></tr>
+<tr class="separator:ga3de7df63c589325101a2817a56f8e29d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaf78ddcc4152c051b2a21e68fecb10980"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:gaf78ddcc4152c051b2a21e68fecb10980"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return the power of two number which value is just lower the input value.  <a href="a00309.html#gaf78ddcc4152c051b2a21e68fecb10980">More...</a><br /></td></tr>
+<tr class="separator:gaf78ddcc4152c051b2a21e68fecb10980"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga5f65973a5d2ea38c719e6a663149ead9"><td class="memTemplParams" colspan="2">template&lt;typename genIUType &gt; </td></tr>
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+<tr class="memdesc:ga5f65973a5d2ea38c719e6a663149ead9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return the power of two number which value is the closet to the input value.  <a href="a00309.html#ga5f65973a5d2ea38c719e6a663149ead9">More...</a><br /></td></tr>
+<tr class="separator:ga5f65973a5d2ea38c719e6a663149ead9"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gac87e65d11e16c3d6b91c3bcfaef7da0b"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:gac87e65d11e16c3d6b91c3bcfaef7da0b"><td class="memTemplItemLeft" align="right" valign="top">GLM_DEPRECATED GLM_FUNC_DECL vec&lt; L, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00309.html#gac87e65d11e16c3d6b91c3bcfaef7da0b">powerOfTwoNearest</a> (vec&lt; L, T, Q &gt; const &amp;value)</td></tr>
+<tr class="memdesc:gac87e65d11e16c3d6b91c3bcfaef7da0b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return the power of two number which value is the closet to the input value.  <a href="a00309.html#gac87e65d11e16c3d6b91c3bcfaef7da0b">More...</a><br /></td></tr>
+<tr class="separator:gac87e65d11e16c3d6b91c3bcfaef7da0b"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a class="el" href="a00309.html">GLM_GTX_bit</a> </p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00280.html" title="Features that implement in C++ the GLSL specification as closely as possible. ">Core features</a> (dependence) </dd></dl>
+
+<p>Definition in file <a class="el" href="a00008_source.html">bit.hpp</a>.</p>
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+<li class="navelem"><a class="el" href="dir_3a581ba30d25676e4b797b1f96d53b45.html">F:</a></li><li class="navelem"><a class="el" href="dir_9e5fe034a00e89334fd5186c3e7db156.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_d9496f0844b48bc7e53b5af8c99b9ab2.html">Source</a></li><li class="navelem"><a class="el" href="dir_a8bee7be44182a33f3820393ae0b105d.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_44e5e654415abd9ca6fdeaddaff8565e.html">glm</a></li><li class="navelem"><a class="el" href="dir_cef2d71d502cb69a9252bca2297d9549.html">glm</a></li><li class="navelem"><a class="el" href="dir_f35778ec600a1b9bbc4524e62e226aa2.html">gtx</a></li>  </ul>
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+</div><!--header-->
+<div class="contents">
+<a href="a00008.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;</div>
+<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#pragma once</span></div>
+<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;</div>
+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">// Dependencies</span></div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#include &quot;../gtc/bitfield.hpp&quot;</span></div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;</div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="preprocessor">#if GLM_MESSAGES == GLM_ENABLE &amp;&amp; !defined(GLM_EXT_INCLUDED)</span></div>
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+<div class="ttc" id="a00236_html"><div class="ttname"><a href="a00236.html">glm</a></div><div class="ttdef"><b>Definition:</b> <a href="a00015_source.html#l00020">common.hpp:20</a></div></div>
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+<a href="#func-members">Functions</a>  </div>
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+<div class="title">bitfield.hpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a class="el" href="a00288.html">GLM_GTC_bitfield</a>  
+<a href="#details">More...</a></p>
+
+<p><a href="a00009_source.html">Go to the source code of this file.</a></p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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+<tr class="separator:ga091d934233a2e121df91b8c7230357c8"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga7d1cc24dfbcdd932c3a2abbb76235f98"><td class="memItemLeft" align="right" valign="top">GLM_FUNC_DECL <a class="el" href="a00304.html#ga2a78447eb9d66a114b193f4a25899c16">glm::u16vec2</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00288.html#ga7d1cc24dfbcdd932c3a2abbb76235f98">bitfieldDeinterleave</a> (<a class="el" href="a00263.html#ga1134b580f8da4de94ca6b1de4d37975e">glm::uint32</a> x)</td></tr>
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+<tr class="separator:ga8a44ae22f5c953b296c42d067dccbe6d"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="separator:ga14bb274d54a3c26f4919dd7ed0dd0c36"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="separator:ga180a63161e1319fbd5a53c84d0429c7a"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gafca8768671a14c8016facccb66a89f26"><td class="memItemLeft" align="right" valign="top">GLM_FUNC_DECL uint64&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00288.html#gafca8768671a14c8016facccb66a89f26">bitfieldInterleave</a> (uint16 x, uint16 y, uint16 z, uint16 w)</td></tr>
+<tr class="memdesc:gafca8768671a14c8016facccb66a89f26"><td class="mdescLeft">&#160;</td><td class="mdescRight">Interleaves the bits of x, y, z and w.  <a href="a00288.html#gafca8768671a14c8016facccb66a89f26">More...</a><br /></td></tr>
+<tr class="separator:gafca8768671a14c8016facccb66a89f26"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga2eb49678a344ce1495bdb5586d9896b9"><td class="memTemplParams" colspan="2">template&lt;typename genIUType &gt; </td></tr>
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+<tr class="memdesc:ga2eb49678a344ce1495bdb5586d9896b9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Rotate all bits to the left.  <a href="a00288.html#ga2eb49678a344ce1495bdb5586d9896b9">More...</a><br /></td></tr>
+<tr class="separator:ga2eb49678a344ce1495bdb5586d9896b9"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gae186317091b1a39214ebf79008d44a1e"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:gae186317091b1a39214ebf79008d44a1e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Rotate all bits to the left.  <a href="a00288.html#gae186317091b1a39214ebf79008d44a1e">More...</a><br /></td></tr>
+<tr class="separator:gae186317091b1a39214ebf79008d44a1e"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga1c33d075c5fb8bd8dbfd5092bfc851ca"><td class="memTemplParams" colspan="2">template&lt;typename genIUType &gt; </td></tr>
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+<tr class="memdesc:ga1c33d075c5fb8bd8dbfd5092bfc851ca"><td class="mdescLeft">&#160;</td><td class="mdescRight">Rotate all bits to the right.  <a href="a00288.html#ga1c33d075c5fb8bd8dbfd5092bfc851ca">More...</a><br /></td></tr>
+<tr class="separator:ga1c33d075c5fb8bd8dbfd5092bfc851ca"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga590488e1fc00a6cfe5d3bcaf93fbfe88"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga590488e1fc00a6cfe5d3bcaf93fbfe88"><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="a00288.html#ga590488e1fc00a6cfe5d3bcaf93fbfe88">bitfieldRotateRight</a> (vec&lt; L, T, Q &gt; const &amp;In, int Shift)</td></tr>
+<tr class="memdesc:ga590488e1fc00a6cfe5d3bcaf93fbfe88"><td class="mdescLeft">&#160;</td><td class="mdescRight">Rotate all bits to the right.  <a href="a00288.html#ga590488e1fc00a6cfe5d3bcaf93fbfe88">More...</a><br /></td></tr>
+<tr class="separator:ga590488e1fc00a6cfe5d3bcaf93fbfe88"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gad7eba518a0b71662114571ee76939f8a"><td class="memTemplParams" colspan="2">template&lt;typename genIUType &gt; </td></tr>
+<tr class="memitem:gad7eba518a0b71662114571ee76939f8a"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genIUType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00288.html#gad7eba518a0b71662114571ee76939f8a">mask</a> (genIUType Bits)</td></tr>
+<tr class="memdesc:gad7eba518a0b71662114571ee76939f8a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Build a mask of 'count' bits.  <a href="a00288.html#gad7eba518a0b71662114571ee76939f8a">More...</a><br /></td></tr>
+<tr class="separator:gad7eba518a0b71662114571ee76939f8a"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga2e64e3b922a296033b825311e7f5fff1"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga2e64e3b922a296033b825311e7f5fff1"><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="a00288.html#ga2e64e3b922a296033b825311e7f5fff1">mask</a> (vec&lt; L, T, Q &gt; const &amp;v)</td></tr>
+<tr class="memdesc:ga2e64e3b922a296033b825311e7f5fff1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Build a mask of 'count' bits.  <a href="a00288.html#ga2e64e3b922a296033b825311e7f5fff1">More...</a><br /></td></tr>
+<tr class="separator:ga2e64e3b922a296033b825311e7f5fff1"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a class="el" href="a00288.html">GLM_GTC_bitfield</a> </p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00280.html" title="Features that implement in C++ the GLSL specification as closely as possible. ">Core features</a> (dependence) </dd>
+<dd>
+<a class="el" href="a00288.html" title="Include <glm/gtc/bitfield.hpp> to use the features of this extension. ">GLM_GTC_bitfield</a> (dependence) </dd></dl>
+
+<p>Definition in file <a class="el" href="a00009_source.html">bitfield.hpp</a>.</p>
+</div></div><!-- contents -->
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+<li class="navelem"><a class="el" href="dir_3a581ba30d25676e4b797b1f96d53b45.html">F:</a></li><li class="navelem"><a class="el" href="dir_9e5fe034a00e89334fd5186c3e7db156.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_d9496f0844b48bc7e53b5af8c99b9ab2.html">Source</a></li><li class="navelem"><a class="el" href="dir_a8bee7be44182a33f3820393ae0b105d.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_44e5e654415abd9ca6fdeaddaff8565e.html">glm</a></li><li class="navelem"><a class="el" href="dir_cef2d71d502cb69a9252bca2297d9549.html">glm</a></li><li class="navelem"><a class="el" href="dir_4c6bd29c73fa4e5a2509e1c15f846751.html">gtc</a></li>  </ul>
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+<div class="title">bitfield.hpp</div>  </div>
+</div><!--header-->
+<div class="contents">
+<a href="a00009.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;</div>
+<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &quot;../detail/setup.hpp&quot;</span></div>
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+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment">// Dependencies</span></div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="preprocessor">#include &quot;../ext/scalar_int_sized.hpp&quot;</span></div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="preprocessor">#include &quot;../ext/scalar_uint_sized.hpp&quot;</span></div>
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+<div class="ttc" id="a00288_html_gafca8768671a14c8016facccb66a89f26"><div class="ttname"><a href="a00288.html#gafca8768671a14c8016facccb66a89f26">glm::bitfieldInterleave</a></div><div class="ttdeci">GLM_FUNC_DECL uint64 bitfieldInterleave(uint16 x, uint16 y, uint16 z, uint16 w)</div><div class="ttdoc">Interleaves the bits of x, y, z and w. </div></div>
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+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">closest_point.hpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a class="el" href="a00310.html">GLM_GTX_closest_point</a>  
+<a href="#details">More...</a></p>
+
+<p><a href="a00010_source.html">Go to the source code of this file.</a></p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ga36529c278ef716986151d58d151d697d"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga36529c278ef716986151d58d151d697d"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; 3, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00310.html#ga36529c278ef716986151d58d151d697d">closestPointOnLine</a> (vec&lt; 3, T, Q &gt; const &amp;point, vec&lt; 3, T, Q &gt; const &amp;a, vec&lt; 3, T, Q &gt; const &amp;b)</td></tr>
+<tr class="memdesc:ga36529c278ef716986151d58d151d697d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Find the point on a straight line which is the closet of a point.  <a href="a00310.html#ga36529c278ef716986151d58d151d697d">More...</a><br /></td></tr>
+<tr class="separator:ga36529c278ef716986151d58d151d697d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga55bcbcc5fc06cb7ff7bc7a6e0e155eb0"><td class="memTemplParams" colspan="2"><a class="anchor" id="ga55bcbcc5fc06cb7ff7bc7a6e0e155eb0"></a>
+template&lt;typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga55bcbcc5fc06cb7ff7bc7a6e0e155eb0"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; 2, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00310.html#ga55bcbcc5fc06cb7ff7bc7a6e0e155eb0">closestPointOnLine</a> (vec&lt; 2, T, Q &gt; const &amp;point, vec&lt; 2, T, Q &gt; const &amp;a, vec&lt; 2, T, Q &gt; const &amp;b)</td></tr>
+<tr class="memdesc:ga55bcbcc5fc06cb7ff7bc7a6e0e155eb0"><td class="mdescLeft">&#160;</td><td class="mdescRight">2d lines work as well <br /></td></tr>
+<tr class="separator:ga55bcbcc5fc06cb7ff7bc7a6e0e155eb0"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a class="el" href="a00310.html">GLM_GTX_closest_point</a> </p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00280.html" title="Features that implement in C++ the GLSL specification as closely as possible. ">Core features</a> (dependence) </dd></dl>
+
+<p>Definition in file <a class="el" href="a00010_source.html">closest_point.hpp</a>.</p>
+</div></div><!-- contents -->
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3dgeer/submodules/geer-rasterizer/third_party/glm/doc/api/a00010_source.html

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+</div><!--header-->
+<div class="contents">
+<a href="a00010.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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+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;}<span class="comment">// namespace glm</span></div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;<span class="preprocessor">#include &quot;closest_point.inl&quot;</span></div>
+<div class="ttc" id="a00310_html_ga55bcbcc5fc06cb7ff7bc7a6e0e155eb0"><div class="ttname"><a href="a00310.html#ga55bcbcc5fc06cb7ff7bc7a6e0e155eb0">glm::closestPointOnLine</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; 2, T, Q &gt; closestPointOnLine(vec&lt; 2, T, Q &gt; const &amp;point, vec&lt; 2, T, Q &gt; const &amp;a, vec&lt; 2, T, Q &gt; const &amp;b)</div><div class="ttdoc">2d lines work as well </div></div>
+<div class="ttc" id="a00236_html"><div class="ttname"><a href="a00236.html">glm</a></div><div class="ttdef"><b>Definition:</b> <a href="a00015_source.html#l00020">common.hpp:20</a></div></div>
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+<p><a class="el" href="a00311.html">GLM_GTX_color_encoding</a>  
+<a href="#details">More...</a></p>
+
+<p><a href="a00011_source.html">Go to the source code of this file.</a></p>
+<table class="memberdecls">
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+Functions</h2></td></tr>
+<tr class="memitem:gad12f4f65022b2c80e33fcba2ced0dc48"><td class="memTemplParams" colspan="2"><a class="anchor" id="gad12f4f65022b2c80e33fcba2ced0dc48"></a>
+template&lt;typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:gad12f4f65022b2c80e33fcba2ced0dc48"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; 3, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00311.html#gad12f4f65022b2c80e33fcba2ced0dc48">convertD65XYZToD50XYZ</a> (vec&lt; 3, T, Q &gt; const &amp;ColorD65XYZ)</td></tr>
+<tr class="memdesc:gad12f4f65022b2c80e33fcba2ced0dc48"><td class="mdescLeft">&#160;</td><td class="mdescRight">Convert a D65 YUV color to D50 YUV. <br /></td></tr>
+<tr class="separator:gad12f4f65022b2c80e33fcba2ced0dc48"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga5265386fc3ac29e4c580d37ed470859c"><td class="memTemplParams" colspan="2"><a class="anchor" id="ga5265386fc3ac29e4c580d37ed470859c"></a>
+template&lt;typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga5265386fc3ac29e4c580d37ed470859c"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; 3, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00311.html#ga5265386fc3ac29e4c580d37ed470859c">convertD65XYZToLinearSRGB</a> (vec&lt; 3, T, Q &gt; const &amp;ColorD65XYZ)</td></tr>
+<tr class="memdesc:ga5265386fc3ac29e4c580d37ed470859c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Convert a D65 YUV color to linear sRGB. <br /></td></tr>
+<tr class="separator:ga5265386fc3ac29e4c580d37ed470859c"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+template&lt;typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga1522ba180e3d83d554a734056da031f9"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; 3, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00311.html#ga1522ba180e3d83d554a734056da031f9">convertLinearSRGBToD50XYZ</a> (vec&lt; 3, T, Q &gt; const &amp;ColorLinearSRGB)</td></tr>
+<tr class="memdesc:ga1522ba180e3d83d554a734056da031f9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Convert a linear sRGB color to D50 YUV. <br /></td></tr>
+<tr class="separator:ga1522ba180e3d83d554a734056da031f9"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+template&lt;typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:gaf9e130d9d4ccf51cc99317de7449f369"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; 3, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00311.html#gaf9e130d9d4ccf51cc99317de7449f369">convertLinearSRGBToD65XYZ</a> (vec&lt; 3, T, Q &gt; const &amp;ColorLinearSRGB)</td></tr>
+<tr class="memdesc:gaf9e130d9d4ccf51cc99317de7449f369"><td class="mdescLeft">&#160;</td><td class="mdescRight">Convert a linear sRGB color to D65 YUV. <br /></td></tr>
+<tr class="separator:gaf9e130d9d4ccf51cc99317de7449f369"><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="a00311.html">GLM_GTX_color_encoding</a> </p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00280.html" title="Features that implement in C++ the GLSL specification as closely as possible. ">Core features</a> (dependence) </dd>
+<dd>
+<a class="el" href="a00311.html" title="Include <glm/gtx/color_encoding.hpp> to use the features of this extension. ">GLM_GTX_color_encoding</a> (dependence) </dd></dl>
+
+<p>Definition in file <a class="el" href="a00011_source.html">color_encoding.hpp</a>.</p>
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+<div class="title">color_encoding.hpp</div>  </div>
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+<a href="a00011.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>
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+<div class="ttc" id="a00236_html"><div class="ttname"><a href="a00236.html">glm</a></div><div class="ttdef"><b>Definition:</b> <a href="a00015_source.html#l00020">common.hpp:20</a></div></div>
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3dgeer/submodules/geer-rasterizer/third_party/glm/doc/api/a00012.html

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+<div class="title">gtc/color_space.hpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a class="el" href="a00289.html">GLM_GTC_color_space</a>  
+<a href="#details">More...</a></p>
+
+<p><a href="a00012_source.html">Go to the source code of this file.</a></p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ga42239e7b3da900f7ef37cec7e2476579"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:ga42239e7b3da900f7ef37cec7e2476579"><td class="mdescLeft">&#160;</td><td class="mdescRight">Convert a linear color to sRGB color using a standard gamma correction.  <a href="a00289.html#ga42239e7b3da900f7ef37cec7e2476579">More...</a><br /></td></tr>
+<tr class="separator:ga42239e7b3da900f7ef37cec7e2476579"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaace0a21167d13d26116c283009af57f6"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:gaace0a21167d13d26116c283009af57f6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Convert a linear color to sRGB color using a custom gamma correction.  <a href="a00289.html#gaace0a21167d13d26116c283009af57f6">More...</a><br /></td></tr>
+<tr class="separator:gaace0a21167d13d26116c283009af57f6"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga16c798b7a226b2c3079dedc55083d187"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:ga16c798b7a226b2c3079dedc55083d187"><td class="mdescLeft">&#160;</td><td class="mdescRight">Convert a sRGB color to linear color using a standard gamma correction.  <a href="a00289.html#ga16c798b7a226b2c3079dedc55083d187">More...</a><br /></td></tr>
+<tr class="separator:ga16c798b7a226b2c3079dedc55083d187"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:gad1b91f27a9726c9cb403f9fee6e2e200"><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="a00289.html#gad1b91f27a9726c9cb403f9fee6e2e200">convertSRGBToLinear</a> (vec&lt; L, T, Q &gt; const &amp;ColorSRGB, T Gamma)</td></tr>
+<tr class="memdesc:gad1b91f27a9726c9cb403f9fee6e2e200"><td class="mdescLeft">&#160;</td><td class="mdescRight">Convert a sRGB color to linear color using a custom gamma correction. <br /></td></tr>
+<tr class="separator:gad1b91f27a9726c9cb403f9fee6e2e200"><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="a00289.html">GLM_GTC_color_space</a> </p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00280.html" title="Features that implement in C++ the GLSL specification as closely as possible. ">Core features</a> (dependence) </dd>
+<dd>
+<a class="el" href="a00289.html" title="Include <glm/gtc/color_space.hpp> to use the features of this extension. ">GLM_GTC_color_space</a> (dependence) </dd></dl>
+
+<p>Definition in file <a class="el" href="a00012_source.html">gtc/color_space.hpp</a>.</p>
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+</div><!--header-->
+<div class="contents">
+<a href="a00012.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>
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+<div class="ttc" id="a00236_html"><div class="ttname"><a href="a00236.html">glm</a></div><div class="ttdef"><b>Definition:</b> <a href="a00015_source.html#l00020">common.hpp:20</a></div></div>
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+<div class="title">gtx/color_space.hpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a class="el" href="a00312.html">GLM_GTX_color_space</a>  
+<a href="#details">More...</a></p>
+
+<p><a href="a00013_source.html">Go to the source code of this file.</a></p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ga789802bec2d4fe0f9741c731b4a8a7d8"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga789802bec2d4fe0f9741c731b4a8a7d8"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; 3, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00312.html#ga789802bec2d4fe0f9741c731b4a8a7d8">hsvColor</a> (vec&lt; 3, T, Q &gt; const &amp;rgbValue)</td></tr>
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+<tr class="memdesc:gad028e0a4f1a9c812b39439b746295b34"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute color luminosity associating ratios (0.33, 0.59, 0.11) to RGB canals.  <a href="a00312.html#gad028e0a4f1a9c812b39439b746295b34">More...</a><br /></td></tr>
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+<tr class="memitem:ga5f9193be46f45f0655c05a0cdca006db"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:ga5f9193be46f45f0655c05a0cdca006db"><td class="mdescLeft">&#160;</td><td class="mdescRight">Converts a color from HSV color space to its color in RGB color space.  <a href="a00312.html#ga5f9193be46f45f0655c05a0cdca006db">More...</a><br /></td></tr>
+<tr class="separator:ga5f9193be46f45f0655c05a0cdca006db"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga01a97152b44e1550edcac60bd849e884"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
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+<tr class="memdesc:ga01a97152b44e1550edcac60bd849e884"><td class="mdescLeft">&#160;</td><td class="mdescRight">Build a saturation matrix.  <a href="a00312.html#ga01a97152b44e1550edcac60bd849e884">More...</a><br /></td></tr>
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+<tr class="memdesc:ga2156cea600e90148ece5bc96fd6db43a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modify the saturation of a color.  <a href="a00312.html#ga2156cea600e90148ece5bc96fd6db43a">More...</a><br /></td></tr>
+<tr class="separator:ga2156cea600e90148ece5bc96fd6db43a"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaba0eacee0736dae860e9371cc1ae4785"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:gaba0eacee0736dae860e9371cc1ae4785"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; 4, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00312.html#gaba0eacee0736dae860e9371cc1ae4785">saturation</a> (T const s, vec&lt; 4, T, Q &gt; const &amp;color)</td></tr>
+<tr class="memdesc:gaba0eacee0736dae860e9371cc1ae4785"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modify the saturation of a color.  <a href="a00312.html#gaba0eacee0736dae860e9371cc1ae4785">More...</a><br /></td></tr>
+<tr class="separator:gaba0eacee0736dae860e9371cc1ae4785"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a class="el" href="a00312.html">GLM_GTX_color_space</a> </p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00280.html" title="Features that implement in C++ the GLSL specification as closely as possible. ">Core features</a> (dependence) </dd></dl>
+
+<p>Definition in file <a class="el" href="a00013_source.html">gtx/color_space.hpp</a>.</p>
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+<div class="title">gtx/color_space.hpp</div>  </div>
+</div><!--header-->
+<div class="contents">
+<a href="a00013.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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+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">// Dependency:</span></div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#include &quot;../glm.hpp&quot;</span></div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;</div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="preprocessor">#if GLM_MESSAGES == GLM_ENABLE &amp;&amp; !defined(GLM_EXT_INCLUDED)</span></div>
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+<div class="ttc" id="a00236_html"><div class="ttname"><a href="a00236.html">glm</a></div><div class="ttdef"><b>Definition:</b> <a href="a00015_source.html#l00020">common.hpp:20</a></div></div>
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+<div class="title">color_space_YCoCg.hpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a class="el" href="a00313.html">GLM_GTX_color_space_YCoCg</a>  
+<a href="#details">More...</a></p>
+
+<p><a href="a00014_source.html">Go to the source code of this file.</a></p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ga0606353ec2a9b9eaa84f1b02ec391bc5"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga0606353ec2a9b9eaa84f1b02ec391bc5"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; 3, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00313.html#ga0606353ec2a9b9eaa84f1b02ec391bc5">rgb2YCoCg</a> (vec&lt; 3, T, Q &gt; const &amp;rgbColor)</td></tr>
+<tr class="memdesc:ga0606353ec2a9b9eaa84f1b02ec391bc5"><td class="mdescLeft">&#160;</td><td class="mdescRight">Convert a color from RGB color space to YCoCg color space.  <a href="a00313.html#ga0606353ec2a9b9eaa84f1b02ec391bc5">More...</a><br /></td></tr>
+<tr class="separator:ga0606353ec2a9b9eaa84f1b02ec391bc5"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga0389772e44ca0fd2ba4a79bdd8efe898"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga0389772e44ca0fd2ba4a79bdd8efe898"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; 3, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00313.html#ga0389772e44ca0fd2ba4a79bdd8efe898">rgb2YCoCgR</a> (vec&lt; 3, T, Q &gt; const &amp;rgbColor)</td></tr>
+<tr class="memdesc:ga0389772e44ca0fd2ba4a79bdd8efe898"><td class="mdescLeft">&#160;</td><td class="mdescRight">Convert a color from RGB color space to YCoCgR color space.  <a href="a00313.html#ga0389772e44ca0fd2ba4a79bdd8efe898">More...</a><br /></td></tr>
+<tr class="separator:ga0389772e44ca0fd2ba4a79bdd8efe898"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga163596b804c7241810b2534a99eb1343"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:ga163596b804c7241810b2534a99eb1343"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; 3, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00313.html#ga163596b804c7241810b2534a99eb1343">YCoCg2rgb</a> (vec&lt; 3, T, Q &gt; const &amp;YCoCgColor)</td></tr>
+<tr class="memdesc:ga163596b804c7241810b2534a99eb1343"><td class="mdescLeft">&#160;</td><td class="mdescRight">Convert a color from YCoCg color space to RGB color space.  <a href="a00313.html#ga163596b804c7241810b2534a99eb1343">More...</a><br /></td></tr>
+<tr class="separator:ga163596b804c7241810b2534a99eb1343"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaf8d30574c8576838097d8e20c295384a"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:gaf8d30574c8576838097d8e20c295384a"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; 3, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00313.html#gaf8d30574c8576838097d8e20c295384a">YCoCgR2rgb</a> (vec&lt; 3, T, Q &gt; const &amp;YCoCgColor)</td></tr>
+<tr class="memdesc:gaf8d30574c8576838097d8e20c295384a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Convert a color from YCoCgR color space to RGB color space.  <a href="a00313.html#gaf8d30574c8576838097d8e20c295384a">More...</a><br /></td></tr>
+<tr class="separator:gaf8d30574c8576838097d8e20c295384a"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a class="el" href="a00313.html">GLM_GTX_color_space_YCoCg</a> </p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="a00280.html" title="Features that implement in C++ the GLSL specification as closely as possible. ">Core features</a> (dependence) </dd></dl>
+
+<p>Definition in file <a class="el" href="a00014_source.html">color_space_YCoCg.hpp</a>.</p>
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+<div class="title">color_space_YCoCg.hpp</div>  </div>
+</div><!--header-->
+<div class="contents">
+<a href="a00014.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;</div>
+<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#pragma once</span></div>
+<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;</div>
+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">// Dependency:</span></div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#include &quot;../glm.hpp&quot;</span></div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;</div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="preprocessor">#if GLM_MESSAGES == GLM_ENABLE &amp;&amp; !defined(GLM_EXT_INCLUDED)</span></div>
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+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;                vec&lt;3, T, Q&gt; <span class="keyword">const</span>&amp; <a class="code" href="a00312.html#ga5f9193be46f45f0655c05a0cdca006db">rgbColor</a>);</div>
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+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;}<span class="comment">//namespace glm</span></div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;</div>
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+<div class="ttc" id="a00313_html_gaf8d30574c8576838097d8e20c295384a"><div class="ttname"><a href="a00313.html#gaf8d30574c8576838097d8e20c295384a">glm::YCoCgR2rgb</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; 3, T, Q &gt; YCoCgR2rgb(vec&lt; 3, T, Q &gt; const &amp;YCoCgColor)</div><div class="ttdoc">Convert a color from YCoCgR color space to RGB color space. </div></div>
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+<div class="ttc" id="a00312_html_ga5f9193be46f45f0655c05a0cdca006db"><div class="ttname"><a href="a00312.html#ga5f9193be46f45f0655c05a0cdca006db">glm::rgbColor</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; 3, T, Q &gt; rgbColor(vec&lt; 3, T, Q &gt; const &amp;hsvValue)</div><div class="ttdoc">Converts a color from HSV color space to its color in RGB color space. </div></div>
+<div class="ttc" id="a00313_html_ga0606353ec2a9b9eaa84f1b02ec391bc5"><div class="ttname"><a href="a00313.html#ga0606353ec2a9b9eaa84f1b02ec391bc5">glm::rgb2YCoCg</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; 3, T, Q &gt; rgb2YCoCg(vec&lt; 3, T, Q &gt; const &amp;rgbColor)</div><div class="ttdoc">Convert a color from RGB color space to YCoCg color space. </div></div>
+<div class="ttc" id="a00313_html_ga0389772e44ca0fd2ba4a79bdd8efe898"><div class="ttname"><a href="a00313.html#ga0389772e44ca0fd2ba4a79bdd8efe898">glm::rgb2YCoCgR</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; 3, T, Q &gt; rgb2YCoCgR(vec&lt; 3, T, Q &gt; const &amp;rgbColor)</div><div class="ttdoc">Convert a color from RGB color space to YCoCgR color space. </div></div>
+<div class="ttc" id="a00236_html"><div class="ttname"><a href="a00236.html">glm</a></div><div class="ttdef"><b>Definition:</b> <a href="a00015_source.html#l00020">common.hpp:20</a></div></div>
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+<a href="#func-members">Functions</a>  </div>
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+<p><a class="el" href="a00280.html">Core features</a>  
+<a href="#details">More...</a></p>
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+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ga439e60a72eadecfeda2df5449c613a64"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
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+<tr class="separator:ga439e60a72eadecfeda2df5449c613a64"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga81d3abddd0ef0c8de579bc541ecadab6"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="separator:ga81d3abddd0ef0c8de579bc541ecadab6"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gafb9d2a645a23aca12d4d6de0104b7657"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="separator:gafb9d2a645a23aca12d4d6de0104b7657"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga7cd77683da6361e297c56443fc70806d"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
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+<tr class="separator:ga7cd77683da6361e297c56443fc70806d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gafba2e0674deb5953878d89483cd6323d"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="separator:gafba2e0674deb5953878d89483cd6323d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaa0f2f12e9108b09e22a3f0b2008a0b5d"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="separator:gaa0f2f12e9108b09e22a3f0b2008a0b5d"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="separator:ga1425c1c3160ec51214b03a0469a3013d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga99f7d62f78ac5ea3b49bae715c9488ed"><td class="memTemplParams" colspan="2">template&lt;length_t L, qualifier Q&gt; </td></tr>
+<tr class="memitem:ga99f7d62f78ac5ea3b49bae715c9488ed"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, int, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga99f7d62f78ac5ea3b49bae715c9488ed">floatBitsToInt</a> (vec&lt; L, float, Q &gt; const &amp;v)</td></tr>
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+<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>
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+<tr class="separator:ga29ef934c00306490de837b4746b4e14d"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="separator:gac3010e0a0c35a1b514540f2fb579c58c"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="separator:gae02d42887fc5570451f880e3c624b9ac"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="separator:gac1fec0c3303b572a6d4697a637213870"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga6cf8098827054a270ee36b18e30d471d"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
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+<tr class="separator:ga6cf8098827054a270ee36b18e30d471d"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="separator:gaa7d015eba1f9f48519251f4abe69b14d"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="separator:ga31f49ef9e7d1beb003160c5e009b0c48"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga8e93f374aae27d1a88b921860351f8d4"><td class="memTemplParams" colspan="2">template&lt;typename genTypeT , typename genTypeU &gt; </td></tr>
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+<tr class="separator:ga8e93f374aae27d1a88b921860351f8d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga9b197a452cd52db3c5c18bac72bd7798"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:ga9b197a452cd52db3c5c18bac72bd7798"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modulus.  <a href="a00241.html#ga9b197a452cd52db3c5c18bac72bd7798">More...</a><br /></td></tr>
+<tr class="separator:ga9b197a452cd52db3c5c18bac72bd7798"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga85e33f139b8db1b39b590a5713b9e679"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
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+<tr class="separator:ga85e33f139b8db1b39b590a5713b9e679"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gafa03aca8c4713e1cc892aa92ca135a7e"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:gafa03aca8c4713e1cc892aa92ca135a7e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a value equal to the nearest integer to x.  <a href="a00241.html#gafa03aca8c4713e1cc892aa92ca135a7e">More...</a><br /></td></tr>
+<tr class="separator:gafa03aca8c4713e1cc892aa92ca135a7e"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga76b81785045a057989a84d99aeeb1578"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="separator:ga76b81785045a057989a84d99aeeb1578"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="separator:ga1e2e5cfff800056540e32f6c9b604b28"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga562edf7eca082cc5b7a0aaf180436daf"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
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+<tr class="separator:ga562edf7eca082cc5b7a0aaf180436daf"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga015a1261ff23e12650211aa872863cce"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
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+<tr class="memdesc:ga015a1261ff23e12650211aa872863cce"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns 0.0 if x &lt; edge, otherwise it returns 1.0 for each component of a genType.  <a href="a00241.html#ga015a1261ff23e12650211aa872863cce">More...</a><br /></td></tr>
+<tr class="separator:ga015a1261ff23e12650211aa872863cce"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga8f9a911a48ef244b51654eaefc81c551"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="separator:ga8f9a911a48ef244b51654eaefc81c551"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaf4a5fc81619c7d3e8b22f53d4a098c7f"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:gaf4a5fc81619c7d3e8b22f53d4a098c7f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns 0.0 if x &lt; edge, otherwise it returns 1.0.  <a href="a00241.html#gaf4a5fc81619c7d3e8b22f53d4a098c7f">More...</a><br /></td></tr>
+<tr class="separator:gaf4a5fc81619c7d3e8b22f53d4a098c7f"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="memdesc:gaf9375e3e06173271d49e6ffa3a334259"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a value equal to the nearest integer to x whose absolute value is not larger than the absolute value of x.  <a href="a00241.html#gaf9375e3e06173271d49e6ffa3a334259">More...</a><br /></td></tr>
+<tr class="separator:gaf9375e3e06173271d49e6ffa3a334259"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gab2bae0d15dcdca6093f88f76b3975d97"><td class="memItemLeft" align="right" valign="top">GLM_FUNC_DECL float&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00241.html#gab2bae0d15dcdca6093f88f76b3975d97">uintBitsToFloat</a> (uint const &amp;v)</td></tr>
+<tr class="memdesc:gab2bae0d15dcdca6093f88f76b3975d97"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a floating-point value corresponding to a unsigned integer encoding of a floating-point value.  <a href="a00241.html#gab2bae0d15dcdca6093f88f76b3975d97">More...</a><br /></td></tr>
+<tr class="separator:gab2bae0d15dcdca6093f88f76b3975d97"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga97f46b5f7b42fe44482e13356eb394ae"><td class="memTemplParams" colspan="2">template&lt;length_t L, qualifier Q&gt; </td></tr>
+<tr class="memitem:ga97f46b5f7b42fe44482e13356eb394ae"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, float, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00241.html#ga97f46b5f7b42fe44482e13356eb394ae">uintBitsToFloat</a> (vec&lt; L, uint, Q &gt; const &amp;v)</td></tr>
+<tr class="memdesc:ga97f46b5f7b42fe44482e13356eb394ae"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a floating-point value corresponding to a unsigned integer encoding of a floating-point value.  <a href="a00241.html#ga97f46b5f7b42fe44482e13356eb394ae">More...</a><br /></td></tr>
+<tr class="separator:ga97f46b5f7b42fe44482e13356eb394ae"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a class="el" href="a00280.html">Core features</a> </p>
+<dl class="section see"><dt>See also</dt><dd><a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> </dd></dl>
+
+<p>Definition in file <a class="el" href="a00015_source.html">common.hpp</a>.</p>
+</div></div><!-- contents -->
+<!-- start footer part -->
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+Generated by &#160;<a href="http://www.doxygen.org/index.html">
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3dgeer/submodules/geer-rasterizer/third_party/glm/doc/api/a00015_source.html

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+<li class="navelem"><a class="el" href="dir_3a581ba30d25676e4b797b1f96d53b45.html">F:</a></li><li class="navelem"><a class="el" href="dir_9e5fe034a00e89334fd5186c3e7db156.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_d9496f0844b48bc7e53b5af8c99b9ab2.html">Source</a></li><li class="navelem"><a class="el" href="dir_a8bee7be44182a33f3820393ae0b105d.html">G-Truc</a></li><li class="navelem"><a class="el" href="dir_44e5e654415abd9ca6fdeaddaff8565e.html">glm</a></li><li class="navelem"><a class="el" href="dir_cef2d71d502cb69a9252bca2297d9549.html">glm</a></li>  </ul>
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+<div class="title">common.hpp</div>  </div>
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+<div class="contents">
+<a href="a00015.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="l00015"></a><span class="lineno">   15</span>&#160;<span class="preprocessor">#pragma once</span></div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;</div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="preprocessor">#include &quot;detail/qualifier.hpp&quot;</span></div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="preprocessor">#include &quot;detail/_fixes.hpp&quot;</span></div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;</div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="keyword">namespace </span><a class="code" href="a00236.html">glm</a></div>
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+<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> genType&gt;</div>
+<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;        GLM_FUNC_DECL genType <a class="code" href="a00241.html#ga562edf7eca082cc5b7a0aaf180436daf">smoothstep</a>(genType edge0, genType edge1, genType x);</div>
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+<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;        <span class="keyword">template</span>&lt;length_t L, <span class="keyword">typename</span> T, qualifier Q&gt;</div>
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+<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;        <span class="keyword">template</span>&lt;length_t L, <span class="keyword">typename</span> T, qualifier Q&gt;</div>
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+<div class="ttc" id="a00241_html_gaa9d0742639e85b29c7c5de11cfd6840d"><div class="ttname"><a href="a00241.html#gaa9d0742639e85b29c7c5de11cfd6840d">glm::floor</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, T, Q &gt; floor(vec&lt; L, T, Q &gt; const &amp;x)</div><div class="ttdoc">Returns a value equal to the nearest integer that is less then or equal to x. </div></div>
+<div class="ttc" id="a00241_html_gad0f444d4b81cc53c3b6edf5aa25078c2"><div class="ttname"><a href="a00241.html#gad0f444d4b81cc53c3b6edf5aa25078c2">glm::fma</a></div><div class="ttdeci">GLM_FUNC_DECL genType fma(genType const &amp;a, genType const &amp;b, genType const &amp;c)</div><div class="ttdoc">Computes and returns a * b + c. </div></div>
+<div class="ttc" id="a00241_html_gaf9375e3e06173271d49e6ffa3a334259"><div class="ttname"><a href="a00241.html#gaf9375e3e06173271d49e6ffa3a334259">glm::trunc</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, T, Q &gt; trunc(vec&lt; L, T, Q &gt; const &amp;x)</div><div class="ttdoc">Returns a value equal to the nearest integer to x whose absolute value is not larger than the absolut...</div></div>
+<div class="ttc" id="a00241_html_ga9b197a452cd52db3c5c18bac72bd7798"><div class="ttname"><a href="a00241.html#ga9b197a452cd52db3c5c18bac72bd7798">glm::mod</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, T, Q &gt; mod(vec&lt; L, T, Q &gt; const &amp;x, vec&lt; L, T, Q &gt; const &amp;y)</div><div class="ttdoc">Modulus. </div></div>
+<div class="ttc" id="a00241_html_gaa0f2f12e9108b09e22a3f0b2008a0b5d"><div class="ttname"><a href="a00241.html#gaa0f2f12e9108b09e22a3f0b2008a0b5d">glm::clamp</a></div><div class="ttdeci">GLM_FUNC_DECL GLM_CONSTEXPR vec&lt; L, T, Q &gt; clamp(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)</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="a00241_html_gafa03aca8c4713e1cc892aa92ca135a7e"><div class="ttname"><a href="a00241.html#gafa03aca8c4713e1cc892aa92ca135a7e">glm::round</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, T, Q &gt; round(vec&lt; L, T, Q &gt; const &amp;x)</div><div class="ttdoc">Returns a value equal to the nearest integer to x. </div></div>
+<div class="ttc" id="a00241_html_ga97f46b5f7b42fe44482e13356eb394ae"><div class="ttname"><a href="a00241.html#ga97f46b5f7b42fe44482e13356eb394ae">glm::uintBitsToFloat</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, float, Q &gt; uintBitsToFloat(vec&lt; L, uint, Q &gt; const &amp;v)</div><div class="ttdoc">Returns a floating-point value corresponding to a unsigned integer encoding of a floating-point value...</div></div>
+<div class="ttc" id="a00241_html_ga1e2e5cfff800056540e32f6c9b604b28"><div class="ttname"><a href="a00241.html#ga1e2e5cfff800056540e32f6c9b604b28">glm::sign</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, T, Q &gt; sign(vec&lt; L, T, Q &gt; const &amp;x)</div><div class="ttdoc">Returns 1.0 if x > 0, 0.0 if x == 0, or -1.0 if x < 0. </div></div>
+<div class="ttc" id="a00241_html_ga2885587c23a106301f20443896365b62"><div class="ttname"><a href="a00241.html#ga2885587c23a106301f20443896365b62">glm::isinf</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, bool, Q &gt; isinf(vec&lt; L, T, Q &gt; const &amp;x)</div><div class="ttdoc">Returns true if x holds a positive infinity or negative infinity representation in the underlying imp...</div></div>
+<div class="ttc" id="a00241_html_ga76b81785045a057989a84d99aeeb1578"><div class="ttname"><a href="a00241.html#ga76b81785045a057989a84d99aeeb1578">glm::roundEven</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, T, Q &gt; roundEven(vec&lt; L, T, Q &gt; const &amp;x)</div><div class="ttdoc">Returns a value equal to the nearest integer to x. </div></div>
+<div class="ttc" id="a00241_html_ga85e33f139b8db1b39b590a5713b9e679"><div class="ttname"><a href="a00241.html#ga85e33f139b8db1b39b590a5713b9e679">glm::modf</a></div><div class="ttdeci">GLM_FUNC_DECL genType modf(genType x, genType &amp;i)</div><div class="ttdoc">Returns the fractional part of x and sets i to the integer part (as a whole number floating point val...</div></div>
+<div class="ttc" id="a00241_html_gafb9d2a645a23aca12d4d6de0104b7657"><div class="ttname"><a href="a00241.html#gafb9d2a645a23aca12d4d6de0104b7657">glm::ceil</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, T, Q &gt; ceil(vec&lt; L, T, Q &gt; const &amp;x)</div><div class="ttdoc">Returns a value equal to the nearest integer that is greater than or equal to x. </div></div>
+<div class="ttc" id="a00241_html_ga31f49ef9e7d1beb003160c5e009b0c48"><div class="ttname"><a href="a00241.html#ga31f49ef9e7d1beb003160c5e009b0c48">glm::min</a></div><div class="ttdeci">GLM_FUNC_DECL GLM_CONSTEXPR vec&lt; L, T, Q &gt; min(vec&lt; L, T, Q &gt; const &amp;x, vec&lt; L, T, Q &gt; const &amp;y)</div><div class="ttdoc">Returns y if y < x; otherwise, it returns x. </div></div>
+<div class="ttc" id="a00241_html_ga7a0a8291a1cf3e1c2aee33030a1bd7b0"><div class="ttname"><a href="a00241.html#ga7a0a8291a1cf3e1c2aee33030a1bd7b0">glm::intBitsToFloat</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, float, Q &gt; intBitsToFloat(vec&lt; L, int, Q &gt; const &amp;v)</div><div class="ttdoc">Returns a floating-point value corresponding to a signed integer encoding of a floating-point value...</div></div>
+<div class="ttc" id="a00241_html_ga29ef934c00306490de837b4746b4e14d"><div class="ttname"><a href="a00241.html#ga29ef934c00306490de837b4746b4e14d">glm::isnan</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, bool, Q &gt; isnan(vec&lt; L, T, Q &gt; const &amp;x)</div><div class="ttdoc">Returns true if x holds a NaN (not a number) representation in the underlying implementation&#39;s set of...</div></div>
+<div class="ttc" id="a00242_html_ga071566cadc7505455e611f2a0353f4d4"><div class="ttname"><a href="a00242.html#ga071566cadc7505455e611f2a0353f4d4">glm::exp</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, T, Q &gt; exp(vec&lt; L, T, Q &gt; const &amp;v)</div><div class="ttdoc">Returns the natural exponentiation of x, i.e., e^x. </div></div>
+<div class="ttc" id="a00241_html_ga49418ba4c8a60fbbb5d57b705f3e26db"><div class="ttname"><a href="a00241.html#ga49418ba4c8a60fbbb5d57b705f3e26db">glm::floatBitsToUint</a></div><div class="ttdeci">GLM_FUNC_DECL vec&lt; L, uint, Q &gt; floatBitsToUint(vec&lt; L, float, Q &gt; const &amp;v)</div><div class="ttdoc">Returns a unsigned integer value representing the encoding of a floating-point value. </div></div>
+<div class="ttc" id="a00241_html_ga562edf7eca082cc5b7a0aaf180436daf"><div class="ttname"><a href="a00241.html#ga562edf7eca082cc5b7a0aaf180436daf">glm::smoothstep</a></div><div class="ttdeci">GLM_FUNC_DECL genType smoothstep(genType edge0, genType edge1, genType x)</div><div class="ttdoc">Returns 0.0 if x <= edge0 and 1.0 if x >= edge1 and performs smooth Hermite interpolation between 0 a...</div></div>
+<div class="ttc" id="a00241_html_ga81d3abddd0ef0c8de579bc541ecadab6"><div class="ttname"><a href="a00241.html#ga81d3abddd0ef0c8de579bc541ecadab6">glm::abs</a></div><div class="ttdeci">GLM_FUNC_DECL GLM_CONSTEXPR vec&lt; L, T, Q &gt; abs(vec&lt; L, T, Q &gt; const &amp;x)</div><div class="ttdoc">Returns x if x >= 0; otherwise, it returns -x. </div></div>
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+<div class="ttc" id="a00236_html"><div class="ttname"><a href="a00236.html">glm</a></div><div class="ttdef"><b>Definition:</b> <a href="a00015_source.html#l00020">common.hpp:20</a></div></div>
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+<p><a class="el" href="a00314.html">GLM_GTX_common</a>  
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+<p><a href="a00016_source.html">Go to the source code of this file.</a></p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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+<tr class="memitem:gab7d89c14c48ad01f720fb5daf8813161"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
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+<tr class="memdesc:gab7d89c14c48ad01f720fb5daf8813161"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns whether vector components values are within an interval.  <a href="a00314.html#gab7d89c14c48ad01f720fb5daf8813161">More...</a><br /></td></tr>
+<tr class="separator:gab7d89c14c48ad01f720fb5daf8813161"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gae5e80425df9833164ad469e83b475fb4"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:gae5e80425df9833164ad469e83b475fb4"><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="a00314.html#gae5e80425df9833164ad469e83b475fb4">fmod</a> (vec&lt; L, T, Q &gt; const &amp;v)</td></tr>
+<tr class="memdesc:gae5e80425df9833164ad469e83b475fb4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Similar to 'mod' but with a different rounding and integer support.  <a href="a00314.html#gae5e80425df9833164ad469e83b475fb4">More...</a><br /></td></tr>
+<tr class="separator:gae5e80425df9833164ad469e83b475fb4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga74aa7c7462245d83bd5a9edf9c6c2d91"><td class="memTemplParams" colspan="2">template&lt;typename genType &gt; </td></tr>
+<tr class="memitem:ga74aa7c7462245d83bd5a9edf9c6c2d91"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL genType::bool_type&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00314.html#ga74aa7c7462245d83bd5a9edf9c6c2d91">isdenormal</a> (genType const &amp;x)</td></tr>
+<tr class="memdesc:ga74aa7c7462245d83bd5a9edf9c6c2d91"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns true if x is a denormalized number Numbers whose absolute value is too small to be represented in the normal format are represented in an alternate, denormalized format.  <a href="a00314.html#ga74aa7c7462245d83bd5a9edf9c6c2d91">More...</a><br /></td></tr>
+<tr class="separator:ga74aa7c7462245d83bd5a9edf9c6c2d91"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gafd303042ba2ba695bf53b2315f53f93f"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
+<tr class="memitem:gafd303042ba2ba695bf53b2315f53f93f"><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="a00314.html#gafd303042ba2ba695bf53b2315f53f93f">openBounded</a> (vec&lt; L, T, Q &gt; const &amp;Value, vec&lt; L, T, Q &gt; const &amp;Min, vec&lt; L, T, Q &gt; const &amp;Max)</td></tr>
+<tr class="memdesc:gafd303042ba2ba695bf53b2315f53f93f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns whether vector components values are within an interval.  <a href="a00314.html#gafd303042ba2ba695bf53b2315f53f93f">More...</a><br /></td></tr>
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+<p>Definition in file <a class="el" href="a00016_source.html">gtx/common.hpp</a>.</p>
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