1f9ad8a790398513a845d486f58566854f7eceee4David Li/* 2f9ad8a790398513a845d486f58566854f7eceee4David Li * Mesa 3-D graphics library 3f9ad8a790398513a845d486f58566854f7eceee4David Li * Version: 6.3 4f9ad8a790398513a845d486f58566854f7eceee4David Li * 5f9ad8a790398513a845d486f58566854f7eceee4David Li * Copyright (C) 1999-2005 Brian Paul All Rights Reserved. 6f9ad8a790398513a845d486f58566854f7eceee4David Li * 7f9ad8a790398513a845d486f58566854f7eceee4David Li * Permission is hereby granted, free of charge, to any person obtaining a 8f9ad8a790398513a845d486f58566854f7eceee4David Li * copy of this software and associated documentation files (the "Software"), 9f9ad8a790398513a845d486f58566854f7eceee4David Li * to deal in the Software without restriction, including without limitation 10f9ad8a790398513a845d486f58566854f7eceee4David Li * the rights to use, copy, modify, merge, publish, distribute, sublicense, 11f9ad8a790398513a845d486f58566854f7eceee4David Li * and/or sell copies of the Software, and to permit persons to whom the 12f9ad8a790398513a845d486f58566854f7eceee4David Li * Software is furnished to do so, subject to the following conditions: 13f9ad8a790398513a845d486f58566854f7eceee4David Li * 14f9ad8a790398513a845d486f58566854f7eceee4David Li * The above copyright notice and this permission notice shall be included 15f9ad8a790398513a845d486f58566854f7eceee4David Li * in all copies or substantial portions of the Software. 16f9ad8a790398513a845d486f58566854f7eceee4David Li * 17f9ad8a790398513a845d486f58566854f7eceee4David Li * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 18f9ad8a790398513a845d486f58566854f7eceee4David Li * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 19f9ad8a790398513a845d486f58566854f7eceee4David Li * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 20f9ad8a790398513a845d486f58566854f7eceee4David Li * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN 21f9ad8a790398513a845d486f58566854f7eceee4David Li * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN 22f9ad8a790398513a845d486f58566854f7eceee4David Li * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 23f9ad8a790398513a845d486f58566854f7eceee4David Li */ 24f9ad8a790398513a845d486f58566854f7eceee4David Li 25f9ad8a790398513a845d486f58566854f7eceee4David Li 26f9ad8a790398513a845d486f58566854f7eceee4David Li/** 27f9ad8a790398513a845d486f58566854f7eceee4David Li * \file m_matrix.c 28f9ad8a790398513a845d486f58566854f7eceee4David Li * Matrix operations. 29f9ad8a790398513a845d486f58566854f7eceee4David Li * 30f9ad8a790398513a845d486f58566854f7eceee4David Li * \note 31f9ad8a790398513a845d486f58566854f7eceee4David Li * -# 4x4 transformation matrices are stored in memory in column major order. 32f9ad8a790398513a845d486f58566854f7eceee4David Li * -# Points/vertices are to be thought of as column vectors. 33f9ad8a790398513a845d486f58566854f7eceee4David Li * -# Transformation of a point p by a matrix M is: p' = M * p 34f9ad8a790398513a845d486f58566854f7eceee4David Li */ 35f9ad8a790398513a845d486f58566854f7eceee4David Li 36f9ad8a790398513a845d486f58566854f7eceee4David Li#include <GLES2/gl2.h> 37f9ad8a790398513a845d486f58566854f7eceee4David Li#include <stdio.h> 38f9ad8a790398513a845d486f58566854f7eceee4David Li#include <math.h> 39f9ad8a790398513a845d486f58566854f7eceee4David Li#include <assert.h> 40f9ad8a790398513a845d486f58566854f7eceee4David Li#include <string.h> 41f9ad8a790398513a845d486f58566854f7eceee4David Li 42f9ad8a790398513a845d486f58566854f7eceee4David Li#include "../src/mesa/main/macros.h" 43f9ad8a790398513a845d486f58566854f7eceee4David Li 44f9ad8a790398513a845d486f58566854f7eceee4David Li#include "m_matrix.h" 45f9ad8a790398513a845d486f58566854f7eceee4David Li 46f9ad8a790398513a845d486f58566854f7eceee4David Li#define _mesa_debug(...) 47f9ad8a790398513a845d486f58566854f7eceee4David Li/** 48f9ad8a790398513a845d486f58566854f7eceee4David Li * \defgroup MatFlags MAT_FLAG_XXX-flags 49f9ad8a790398513a845d486f58566854f7eceee4David Li * 50f9ad8a790398513a845d486f58566854f7eceee4David Li * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags 51f9ad8a790398513a845d486f58566854f7eceee4David Li * It would be nice to make all these flags private to m_matrix.c 52f9ad8a790398513a845d486f58566854f7eceee4David Li */ 53f9ad8a790398513a845d486f58566854f7eceee4David Li/*@{*/ 54f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_FLAG_IDENTITY 0 /**< is an identity matrix flag. 55f9ad8a790398513a845d486f58566854f7eceee4David Li* (Not actually used - the identity 56f9ad8a790398513a845d486f58566854f7eceee4David Li* matrix is identified by the absense 57f9ad8a790398513a845d486f58566854f7eceee4David Li* of all other flags.) 58f9ad8a790398513a845d486f58566854f7eceee4David Li*/ 59f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_FLAG_GENERAL 0x1 /**< is a general matrix flag */ 60f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_FLAG_ROTATION 0x2 /**< is a rotation matrix flag */ 61f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_FLAG_TRANSLATION 0x4 /**< is a translation matrix flag */ 62f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_FLAG_UNIFORM_SCALE 0x8 /**< is an uniform scaling matrix flag */ 63f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_FLAG_GENERAL_SCALE 0x10 /**< is a general scaling matrix flag */ 64f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_FLAG_GENERAL_3D 0x20 /**< general 3D matrix flag */ 65f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_FLAG_PERSPECTIVE 0x40 /**< is a perspective proj matrix flag */ 66f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_FLAG_SINGULAR 0x80 /**< is a singular matrix flag */ 67f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_DIRTY_TYPE 0x100 /**< matrix type is dirty */ 68f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_DIRTY_FLAGS 0x200 /**< matrix flags are dirty */ 69f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_DIRTY_INVERSE 0x400 /**< matrix inverse is dirty */ 70f9ad8a790398513a845d486f58566854f7eceee4David Li 71f9ad8a790398513a845d486f58566854f7eceee4David Li/** angle preserving matrix flags mask */ 72f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \ 73f9ad8a790398513a845d486f58566854f7eceee4David LiMAT_FLAG_TRANSLATION | \ 74f9ad8a790398513a845d486f58566854f7eceee4David LiMAT_FLAG_UNIFORM_SCALE) 75f9ad8a790398513a845d486f58566854f7eceee4David Li 76f9ad8a790398513a845d486f58566854f7eceee4David Li/** geometry related matrix flags mask */ 77f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \ 78f9ad8a790398513a845d486f58566854f7eceee4David LiMAT_FLAG_ROTATION | \ 79f9ad8a790398513a845d486f58566854f7eceee4David LiMAT_FLAG_TRANSLATION | \ 80f9ad8a790398513a845d486f58566854f7eceee4David LiMAT_FLAG_UNIFORM_SCALE | \ 81f9ad8a790398513a845d486f58566854f7eceee4David LiMAT_FLAG_GENERAL_SCALE | \ 82f9ad8a790398513a845d486f58566854f7eceee4David LiMAT_FLAG_GENERAL_3D | \ 83f9ad8a790398513a845d486f58566854f7eceee4David LiMAT_FLAG_PERSPECTIVE | \ 84f9ad8a790398513a845d486f58566854f7eceee4David LiMAT_FLAG_SINGULAR) 85f9ad8a790398513a845d486f58566854f7eceee4David Li 86f9ad8a790398513a845d486f58566854f7eceee4David Li/** length preserving matrix flags mask */ 87f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \ 88f9ad8a790398513a845d486f58566854f7eceee4David LiMAT_FLAG_TRANSLATION) 89f9ad8a790398513a845d486f58566854f7eceee4David Li 90f9ad8a790398513a845d486f58566854f7eceee4David Li 91f9ad8a790398513a845d486f58566854f7eceee4David Li/** 3D (non-perspective) matrix flags mask */ 92f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \ 93f9ad8a790398513a845d486f58566854f7eceee4David LiMAT_FLAG_TRANSLATION | \ 94f9ad8a790398513a845d486f58566854f7eceee4David LiMAT_FLAG_UNIFORM_SCALE | \ 95f9ad8a790398513a845d486f58566854f7eceee4David LiMAT_FLAG_GENERAL_SCALE | \ 96f9ad8a790398513a845d486f58566854f7eceee4David LiMAT_FLAG_GENERAL_3D) 97f9ad8a790398513a845d486f58566854f7eceee4David Li 98f9ad8a790398513a845d486f58566854f7eceee4David Li/** dirty matrix flags mask */ 99f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT_DIRTY (MAT_DIRTY_TYPE | \ 100f9ad8a790398513a845d486f58566854f7eceee4David LiMAT_DIRTY_FLAGS | \ 101f9ad8a790398513a845d486f58566854f7eceee4David LiMAT_DIRTY_INVERSE) 102f9ad8a790398513a845d486f58566854f7eceee4David Li 103f9ad8a790398513a845d486f58566854f7eceee4David Li/*@}*/ 104f9ad8a790398513a845d486f58566854f7eceee4David Li 105f9ad8a790398513a845d486f58566854f7eceee4David Li 106f9ad8a790398513a845d486f58566854f7eceee4David Li/** 107f9ad8a790398513a845d486f58566854f7eceee4David Li * Test geometry related matrix flags. 108f9ad8a790398513a845d486f58566854f7eceee4David Li * 109f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat a pointer to a GLmatrix structure. 110f9ad8a790398513a845d486f58566854f7eceee4David Li * \param a flags mask. 111f9ad8a790398513a845d486f58566854f7eceee4David Li * 112f9ad8a790398513a845d486f58566854f7eceee4David Li * \returns non-zero if all geometry related matrix flags are contained within 113f9ad8a790398513a845d486f58566854f7eceee4David Li * the mask, or zero otherwise. 114f9ad8a790398513a845d486f58566854f7eceee4David Li */ 115f9ad8a790398513a845d486f58566854f7eceee4David Li#define TEST_MAT_FLAGS(mat, a) \ 116f9ad8a790398513a845d486f58566854f7eceee4David Li((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0) 117f9ad8a790398513a845d486f58566854f7eceee4David Li 118f9ad8a790398513a845d486f58566854f7eceee4David Li 119f9ad8a790398513a845d486f58566854f7eceee4David Li 120f9ad8a790398513a845d486f58566854f7eceee4David Li/** 121f9ad8a790398513a845d486f58566854f7eceee4David Li * Names of the corresponding GLmatrixtype values. 122f9ad8a790398513a845d486f58566854f7eceee4David Li */ 123f9ad8a790398513a845d486f58566854f7eceee4David Listatic const char *types[] = { 124f9ad8a790398513a845d486f58566854f7eceee4David Li"MATRIX_GENERAL", 125f9ad8a790398513a845d486f58566854f7eceee4David Li"MATRIX_IDENTITY", 126f9ad8a790398513a845d486f58566854f7eceee4David Li"MATRIX_3D_NO_ROT", 127f9ad8a790398513a845d486f58566854f7eceee4David Li"MATRIX_PERSPECTIVE", 128f9ad8a790398513a845d486f58566854f7eceee4David Li"MATRIX_2D", 129f9ad8a790398513a845d486f58566854f7eceee4David Li"MATRIX_2D_NO_ROT", 130f9ad8a790398513a845d486f58566854f7eceee4David Li"MATRIX_3D" 131f9ad8a790398513a845d486f58566854f7eceee4David Li}; 132f9ad8a790398513a845d486f58566854f7eceee4David Li 133f9ad8a790398513a845d486f58566854f7eceee4David Li 134f9ad8a790398513a845d486f58566854f7eceee4David Li/** 135f9ad8a790398513a845d486f58566854f7eceee4David Li * Identity matrix. 136f9ad8a790398513a845d486f58566854f7eceee4David Li */ 137f9ad8a790398513a845d486f58566854f7eceee4David Listatic GLfloat Identity[16] = { 138f9ad8a790398513a845d486f58566854f7eceee4David Li1.0, 0.0, 0.0, 0.0, 139f9ad8a790398513a845d486f58566854f7eceee4David Li0.0, 1.0, 0.0, 0.0, 140f9ad8a790398513a845d486f58566854f7eceee4David Li0.0, 0.0, 1.0, 0.0, 141f9ad8a790398513a845d486f58566854f7eceee4David Li0.0, 0.0, 0.0, 1.0 142f9ad8a790398513a845d486f58566854f7eceee4David Li}; 143f9ad8a790398513a845d486f58566854f7eceee4David Li 144f9ad8a790398513a845d486f58566854f7eceee4David Li 145f9ad8a790398513a845d486f58566854f7eceee4David Li 146f9ad8a790398513a845d486f58566854f7eceee4David Li/**********************************************************************/ 147f9ad8a790398513a845d486f58566854f7eceee4David Li/** \name Matrix multiplication */ 148f9ad8a790398513a845d486f58566854f7eceee4David Li/*@{*/ 149f9ad8a790398513a845d486f58566854f7eceee4David Li 150f9ad8a790398513a845d486f58566854f7eceee4David Li#define A(row,col) a[(col<<2)+row] 151f9ad8a790398513a845d486f58566854f7eceee4David Li#define B(row,col) b[(col<<2)+row] 152f9ad8a790398513a845d486f58566854f7eceee4David Li#define P(row,col) product[(col<<2)+row] 153f9ad8a790398513a845d486f58566854f7eceee4David Li 154f9ad8a790398513a845d486f58566854f7eceee4David Li/** 155f9ad8a790398513a845d486f58566854f7eceee4David Li * Perform a full 4x4 matrix multiplication. 156f9ad8a790398513a845d486f58566854f7eceee4David Li * 157f9ad8a790398513a845d486f58566854f7eceee4David Li * \param a matrix. 158f9ad8a790398513a845d486f58566854f7eceee4David Li * \param b matrix. 159f9ad8a790398513a845d486f58566854f7eceee4David Li * \param product will receive the product of \p a and \p b. 160f9ad8a790398513a845d486f58566854f7eceee4David Li * 161f9ad8a790398513a845d486f58566854f7eceee4David Li * \warning Is assumed that \p product != \p b. \p product == \p a is allowed. 162f9ad8a790398513a845d486f58566854f7eceee4David Li * 163f9ad8a790398513a845d486f58566854f7eceee4David Li * \note KW: 4*16 = 64 multiplications 164f9ad8a790398513a845d486f58566854f7eceee4David Li * 165f9ad8a790398513a845d486f58566854f7eceee4David Li * \author This \c matmul was contributed by Thomas Malik 166f9ad8a790398513a845d486f58566854f7eceee4David Li */ 167f9ad8a790398513a845d486f58566854f7eceee4David Listatic void matmul4( GLfloat *product, const GLfloat *a, const GLfloat *b ) 168f9ad8a790398513a845d486f58566854f7eceee4David Li{ 169f9ad8a790398513a845d486f58566854f7eceee4David Li assert(product != b); 170f9ad8a790398513a845d486f58566854f7eceee4David Li GLint i; 171f9ad8a790398513a845d486f58566854f7eceee4David Li for (i = 0; i < 4; i++) { 172f9ad8a790398513a845d486f58566854f7eceee4David Li const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3); 173f9ad8a790398513a845d486f58566854f7eceee4David Li P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0); 174f9ad8a790398513a845d486f58566854f7eceee4David Li P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1); 175f9ad8a790398513a845d486f58566854f7eceee4David Li P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2); 176f9ad8a790398513a845d486f58566854f7eceee4David Li P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3); 177f9ad8a790398513a845d486f58566854f7eceee4David Li } 178f9ad8a790398513a845d486f58566854f7eceee4David Li} 179f9ad8a790398513a845d486f58566854f7eceee4David Li 180f9ad8a790398513a845d486f58566854f7eceee4David Li/** 181f9ad8a790398513a845d486f58566854f7eceee4David Li * Multiply two matrices known to occupy only the top three rows, such 182f9ad8a790398513a845d486f58566854f7eceee4David Li * as typical model matrices, and orthogonal matrices. 183f9ad8a790398513a845d486f58566854f7eceee4David Li * 184f9ad8a790398513a845d486f58566854f7eceee4David Li * \param a matrix. 185f9ad8a790398513a845d486f58566854f7eceee4David Li * \param b matrix. 186f9ad8a790398513a845d486f58566854f7eceee4David Li * \param product will receive the product of \p a and \p b. 187f9ad8a790398513a845d486f58566854f7eceee4David Li */ 188f9ad8a790398513a845d486f58566854f7eceee4David Listatic void matmul34( GLfloat *product, const GLfloat *a, const GLfloat *b ) 189f9ad8a790398513a845d486f58566854f7eceee4David Li{ 190f9ad8a790398513a845d486f58566854f7eceee4David Li GLint i; 191f9ad8a790398513a845d486f58566854f7eceee4David Li for (i = 0; i < 3; i++) { 192f9ad8a790398513a845d486f58566854f7eceee4David Li const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3); 193f9ad8a790398513a845d486f58566854f7eceee4David Li P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0); 194f9ad8a790398513a845d486f58566854f7eceee4David Li P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1); 195f9ad8a790398513a845d486f58566854f7eceee4David Li P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2); 196f9ad8a790398513a845d486f58566854f7eceee4David Li P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3; 197f9ad8a790398513a845d486f58566854f7eceee4David Li } 198f9ad8a790398513a845d486f58566854f7eceee4David Li P(3,0) = 0; 199f9ad8a790398513a845d486f58566854f7eceee4David Li P(3,1) = 0; 200f9ad8a790398513a845d486f58566854f7eceee4David Li P(3,2) = 0; 201f9ad8a790398513a845d486f58566854f7eceee4David Li P(3,3) = 1; 202f9ad8a790398513a845d486f58566854f7eceee4David Li} 203f9ad8a790398513a845d486f58566854f7eceee4David Li 204f9ad8a790398513a845d486f58566854f7eceee4David Li#undef A 205f9ad8a790398513a845d486f58566854f7eceee4David Li#undef B 206f9ad8a790398513a845d486f58566854f7eceee4David Li#undef P 207f9ad8a790398513a845d486f58566854f7eceee4David Li 208f9ad8a790398513a845d486f58566854f7eceee4David Li/** 209f9ad8a790398513a845d486f58566854f7eceee4David Li * Multiply a matrix by an array of floats with known properties. 210f9ad8a790398513a845d486f58566854f7eceee4David Li * 211f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat pointer to a GLmatrix structure containing the left multiplication 212f9ad8a790398513a845d486f58566854f7eceee4David Li * matrix, and that will receive the product result. 213f9ad8a790398513a845d486f58566854f7eceee4David Li * \param m right multiplication matrix array. 214f9ad8a790398513a845d486f58566854f7eceee4David Li * \param flags flags of the matrix \p m. 215f9ad8a790398513a845d486f58566854f7eceee4David Li * 216f9ad8a790398513a845d486f58566854f7eceee4David Li * Joins both flags and marks the type and inverse as dirty. Calls matmul34() 217f9ad8a790398513a845d486f58566854f7eceee4David Li * if both matrices are 3D, or matmul4() otherwise. 218f9ad8a790398513a845d486f58566854f7eceee4David Li */ 219f9ad8a790398513a845d486f58566854f7eceee4David Listatic void matrix_multf( GLmatrix *mat, const GLfloat *m, GLuint flags ) 220f9ad8a790398513a845d486f58566854f7eceee4David Li{ 221f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= (flags | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE); 222f9ad8a790398513a845d486f58566854f7eceee4David Li 223f9ad8a790398513a845d486f58566854f7eceee4David Li if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) 224f9ad8a790398513a845d486f58566854f7eceee4David Li matmul34( mat->m, mat->m, m ); 225f9ad8a790398513a845d486f58566854f7eceee4David Li else 226f9ad8a790398513a845d486f58566854f7eceee4David Li matmul4( mat->m, mat->m, m ); 227f9ad8a790398513a845d486f58566854f7eceee4David Li} 228f9ad8a790398513a845d486f58566854f7eceee4David Li 229f9ad8a790398513a845d486f58566854f7eceee4David Li/** 230f9ad8a790398513a845d486f58566854f7eceee4David Li * Matrix multiplication. 231f9ad8a790398513a845d486f58566854f7eceee4David Li * 232f9ad8a790398513a845d486f58566854f7eceee4David Li * \param dest destination matrix. 233f9ad8a790398513a845d486f58566854f7eceee4David Li * \param a left matrix. 234f9ad8a790398513a845d486f58566854f7eceee4David Li * \param b right matrix. 235f9ad8a790398513a845d486f58566854f7eceee4David Li * 236f9ad8a790398513a845d486f58566854f7eceee4David Li * Joins both flags and marks the type and inverse as dirty. Calls matmul34() 237f9ad8a790398513a845d486f58566854f7eceee4David Li * if both matrices are 3D, or matmul4() otherwise. 238f9ad8a790398513a845d486f58566854f7eceee4David Li */ 239f9ad8a790398513a845d486f58566854f7eceee4David Livoid 240f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_mul_matrix( GLmatrix *dest, const GLmatrix *a, const GLmatrix *b ) 241f9ad8a790398513a845d486f58566854f7eceee4David Li{ 242f9ad8a790398513a845d486f58566854f7eceee4David Li dest->flags = (a->flags | 243f9ad8a790398513a845d486f58566854f7eceee4David Li b->flags | 244f9ad8a790398513a845d486f58566854f7eceee4David Li MAT_DIRTY_TYPE | 245f9ad8a790398513a845d486f58566854f7eceee4David Li MAT_DIRTY_INVERSE); 246f9ad8a790398513a845d486f58566854f7eceee4David Li 247f9ad8a790398513a845d486f58566854f7eceee4David Li if (TEST_MAT_FLAGS(dest, MAT_FLAGS_3D)) 248f9ad8a790398513a845d486f58566854f7eceee4David Li matmul34( dest->m, a->m, b->m ); 249f9ad8a790398513a845d486f58566854f7eceee4David Li else 250f9ad8a790398513a845d486f58566854f7eceee4David Li matmul4( dest->m, a->m, b->m ); 251f9ad8a790398513a845d486f58566854f7eceee4David Li} 252f9ad8a790398513a845d486f58566854f7eceee4David Li 253f9ad8a790398513a845d486f58566854f7eceee4David Li/** 254f9ad8a790398513a845d486f58566854f7eceee4David Li * Matrix multiplication. 255f9ad8a790398513a845d486f58566854f7eceee4David Li * 256f9ad8a790398513a845d486f58566854f7eceee4David Li * \param dest left and destination matrix. 257f9ad8a790398513a845d486f58566854f7eceee4David Li * \param m right matrix array. 258f9ad8a790398513a845d486f58566854f7eceee4David Li * 259f9ad8a790398513a845d486f58566854f7eceee4David Li * Marks the matrix flags with general flag, and type and inverse dirty flags. 260f9ad8a790398513a845d486f58566854f7eceee4David Li * Calls matmul4() for the multiplication. 261f9ad8a790398513a845d486f58566854f7eceee4David Li */ 262f9ad8a790398513a845d486f58566854f7eceee4David Livoid 263f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m ) 264f9ad8a790398513a845d486f58566854f7eceee4David Li{ 265f9ad8a790398513a845d486f58566854f7eceee4David Li dest->flags |= (MAT_FLAG_GENERAL | 266f9ad8a790398513a845d486f58566854f7eceee4David Li MAT_DIRTY_TYPE | 267f9ad8a790398513a845d486f58566854f7eceee4David Li MAT_DIRTY_INVERSE | 268f9ad8a790398513a845d486f58566854f7eceee4David Li MAT_DIRTY_FLAGS); 269f9ad8a790398513a845d486f58566854f7eceee4David Li 270f9ad8a790398513a845d486f58566854f7eceee4David Li matmul4( dest->m, dest->m, m ); 271f9ad8a790398513a845d486f58566854f7eceee4David Li} 272f9ad8a790398513a845d486f58566854f7eceee4David Li 273f9ad8a790398513a845d486f58566854f7eceee4David Li/*@}*/ 274f9ad8a790398513a845d486f58566854f7eceee4David Li 275f9ad8a790398513a845d486f58566854f7eceee4David Li 276f9ad8a790398513a845d486f58566854f7eceee4David Li/**********************************************************************/ 277f9ad8a790398513a845d486f58566854f7eceee4David Li/** \name Matrix output */ 278f9ad8a790398513a845d486f58566854f7eceee4David Li/*@{*/ 279f9ad8a790398513a845d486f58566854f7eceee4David Li 280f9ad8a790398513a845d486f58566854f7eceee4David Li/** 281f9ad8a790398513a845d486f58566854f7eceee4David Li * Print a matrix array. 282f9ad8a790398513a845d486f58566854f7eceee4David Li * 283f9ad8a790398513a845d486f58566854f7eceee4David Li * \param m matrix array. 284f9ad8a790398513a845d486f58566854f7eceee4David Li * 285f9ad8a790398513a845d486f58566854f7eceee4David Li * Called by _math_matrix_print() to print a matrix or its inverse. 286f9ad8a790398513a845d486f58566854f7eceee4David Li */ 287f9ad8a790398513a845d486f58566854f7eceee4David Listatic void print_matrix_floats( const GLfloat m[16] ) 288f9ad8a790398513a845d486f58566854f7eceee4David Li{ 289f9ad8a790398513a845d486f58566854f7eceee4David Li int i; 290f9ad8a790398513a845d486f58566854f7eceee4David Li for (i=0;i<4;i++) { 291f9ad8a790398513a845d486f58566854f7eceee4David Li _mesa_debug(NULL,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] ); 292f9ad8a790398513a845d486f58566854f7eceee4David Li } 293f9ad8a790398513a845d486f58566854f7eceee4David Li} 294f9ad8a790398513a845d486f58566854f7eceee4David Li 295f9ad8a790398513a845d486f58566854f7eceee4David Li/** 296f9ad8a790398513a845d486f58566854f7eceee4David Li * Dumps the contents of a GLmatrix structure. 297f9ad8a790398513a845d486f58566854f7eceee4David Li * 298f9ad8a790398513a845d486f58566854f7eceee4David Li * \param m pointer to the GLmatrix structure. 299f9ad8a790398513a845d486f58566854f7eceee4David Li */ 300f9ad8a790398513a845d486f58566854f7eceee4David Livoid 301f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_print( const GLmatrix *m ) 302f9ad8a790398513a845d486f58566854f7eceee4David Li{ 303f9ad8a790398513a845d486f58566854f7eceee4David Li _mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags); 304f9ad8a790398513a845d486f58566854f7eceee4David Li print_matrix_floats(m->m); 305f9ad8a790398513a845d486f58566854f7eceee4David Li _mesa_debug(NULL, "Inverse: \n"); 306f9ad8a790398513a845d486f58566854f7eceee4David Li if (m->inv) { 307f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat prod[16]; 308f9ad8a790398513a845d486f58566854f7eceee4David Li print_matrix_floats(m->inv); 309f9ad8a790398513a845d486f58566854f7eceee4David Li matmul4(prod, m->m, m->inv); 310f9ad8a790398513a845d486f58566854f7eceee4David Li _mesa_debug(NULL, "Mat * Inverse:\n"); 311f9ad8a790398513a845d486f58566854f7eceee4David Li print_matrix_floats(prod); 312f9ad8a790398513a845d486f58566854f7eceee4David Li } 313f9ad8a790398513a845d486f58566854f7eceee4David Li else { 314f9ad8a790398513a845d486f58566854f7eceee4David Li _mesa_debug(NULL, " - not available\n"); 315f9ad8a790398513a845d486f58566854f7eceee4David Li } 316f9ad8a790398513a845d486f58566854f7eceee4David Li} 317f9ad8a790398513a845d486f58566854f7eceee4David Li 318f9ad8a790398513a845d486f58566854f7eceee4David Li/*@}*/ 319f9ad8a790398513a845d486f58566854f7eceee4David Li 320f9ad8a790398513a845d486f58566854f7eceee4David Li 321f9ad8a790398513a845d486f58566854f7eceee4David Li/** 322f9ad8a790398513a845d486f58566854f7eceee4David Li * References an element of 4x4 matrix. 323f9ad8a790398513a845d486f58566854f7eceee4David Li * 324f9ad8a790398513a845d486f58566854f7eceee4David Li * \param m matrix array. 325f9ad8a790398513a845d486f58566854f7eceee4David Li * \param c column of the desired element. 326f9ad8a790398513a845d486f58566854f7eceee4David Li * \param r row of the desired element. 327f9ad8a790398513a845d486f58566854f7eceee4David Li * 328f9ad8a790398513a845d486f58566854f7eceee4David Li * \return value of the desired element. 329f9ad8a790398513a845d486f58566854f7eceee4David Li * 330f9ad8a790398513a845d486f58566854f7eceee4David Li * Calculate the linear storage index of the element and references it. 331f9ad8a790398513a845d486f58566854f7eceee4David Li */ 332f9ad8a790398513a845d486f58566854f7eceee4David Li#define MAT(m,r,c) (m)[(c)*4+(r)] 333f9ad8a790398513a845d486f58566854f7eceee4David Li 334f9ad8a790398513a845d486f58566854f7eceee4David Li 335f9ad8a790398513a845d486f58566854f7eceee4David Li/**********************************************************************/ 336f9ad8a790398513a845d486f58566854f7eceee4David Li/** \name Matrix inversion */ 337f9ad8a790398513a845d486f58566854f7eceee4David Li/*@{*/ 338f9ad8a790398513a845d486f58566854f7eceee4David Li 339f9ad8a790398513a845d486f58566854f7eceee4David Li/** 340f9ad8a790398513a845d486f58566854f7eceee4David Li * Swaps the values of two floating pointer variables. 341f9ad8a790398513a845d486f58566854f7eceee4David Li * 342f9ad8a790398513a845d486f58566854f7eceee4David Li * Used by invert_matrix_general() to swap the row pointers. 343f9ad8a790398513a845d486f58566854f7eceee4David Li */ 344f9ad8a790398513a845d486f58566854f7eceee4David Li#define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; } 345f9ad8a790398513a845d486f58566854f7eceee4David Li 346f9ad8a790398513a845d486f58566854f7eceee4David Li/** 347f9ad8a790398513a845d486f58566854f7eceee4David Li * Compute inverse of 4x4 transformation matrix. 348f9ad8a790398513a845d486f58566854f7eceee4David Li * 349f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat pointer to a GLmatrix structure. The matrix inverse will be 350f9ad8a790398513a845d486f58566854f7eceee4David Li * stored in the GLmatrix::inv attribute. 351f9ad8a790398513a845d486f58566854f7eceee4David Li * 352f9ad8a790398513a845d486f58566854f7eceee4David Li * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 353f9ad8a790398513a845d486f58566854f7eceee4David Li * 354f9ad8a790398513a845d486f58566854f7eceee4David Li * \author 355f9ad8a790398513a845d486f58566854f7eceee4David Li * Code contributed by Jacques Leroy jle@star.be 356f9ad8a790398513a845d486f58566854f7eceee4David Li * 357f9ad8a790398513a845d486f58566854f7eceee4David Li * Calculates the inverse matrix by performing the gaussian matrix reduction 358f9ad8a790398513a845d486f58566854f7eceee4David Li * with partial pivoting followed by back/substitution with the loops manually 359f9ad8a790398513a845d486f58566854f7eceee4David Li * unrolled. 360f9ad8a790398513a845d486f58566854f7eceee4David Li */ 361f9ad8a790398513a845d486f58566854f7eceee4David Listatic GLboolean invert_matrix_general( GLmatrix *mat ) 362f9ad8a790398513a845d486f58566854f7eceee4David Li{ 363f9ad8a790398513a845d486f58566854f7eceee4David Li const GLfloat *m = mat->m; 364f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat *out = mat->inv; 365f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat wtmp[4][8]; 366f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat m0, m1, m2, m3, s; 367f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat *r0, *r1, *r2, *r3; 368f9ad8a790398513a845d486f58566854f7eceee4David Li 369f9ad8a790398513a845d486f58566854f7eceee4David Li r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3]; 370f9ad8a790398513a845d486f58566854f7eceee4David Li 371f9ad8a790398513a845d486f58566854f7eceee4David Li r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1), 372f9ad8a790398513a845d486f58566854f7eceee4David Li r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3), 373f9ad8a790398513a845d486f58566854f7eceee4David Li r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0, 374f9ad8a790398513a845d486f58566854f7eceee4David Li 375f9ad8a790398513a845d486f58566854f7eceee4David Li r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1), 376f9ad8a790398513a845d486f58566854f7eceee4David Li r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3), 377f9ad8a790398513a845d486f58566854f7eceee4David Li r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0, 378f9ad8a790398513a845d486f58566854f7eceee4David Li 379f9ad8a790398513a845d486f58566854f7eceee4David Li r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1), 380f9ad8a790398513a845d486f58566854f7eceee4David Li r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3), 381f9ad8a790398513a845d486f58566854f7eceee4David Li r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0, 382f9ad8a790398513a845d486f58566854f7eceee4David Li 383f9ad8a790398513a845d486f58566854f7eceee4David Li r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1), 384f9ad8a790398513a845d486f58566854f7eceee4David Li r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3), 385f9ad8a790398513a845d486f58566854f7eceee4David Li r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0; 386f9ad8a790398513a845d486f58566854f7eceee4David Li 387f9ad8a790398513a845d486f58566854f7eceee4David Li /* choose pivot - or die */ 388f9ad8a790398513a845d486f58566854f7eceee4David Li if (FABSF(r3[0])>FABSF(r2[0])) SWAP_ROWS(r3, r2); 389f9ad8a790398513a845d486f58566854f7eceee4David Li if (FABSF(r2[0])>FABSF(r1[0])) SWAP_ROWS(r2, r1); 390f9ad8a790398513a845d486f58566854f7eceee4David Li if (FABSF(r1[0])>FABSF(r0[0])) SWAP_ROWS(r1, r0); 391f9ad8a790398513a845d486f58566854f7eceee4David Li if (0.0 == r0[0]) return GL_FALSE; 392f9ad8a790398513a845d486f58566854f7eceee4David Li 393f9ad8a790398513a845d486f58566854f7eceee4David Li /* eliminate first variable */ 394f9ad8a790398513a845d486f58566854f7eceee4David Li m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0]; 395f9ad8a790398513a845d486f58566854f7eceee4David Li s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s; 396f9ad8a790398513a845d486f58566854f7eceee4David Li s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s; 397f9ad8a790398513a845d486f58566854f7eceee4David Li s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s; 398f9ad8a790398513a845d486f58566854f7eceee4David Li s = r0[4]; 399f9ad8a790398513a845d486f58566854f7eceee4David Li if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; } 400f9ad8a790398513a845d486f58566854f7eceee4David Li s = r0[5]; 401f9ad8a790398513a845d486f58566854f7eceee4David Li if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; } 402f9ad8a790398513a845d486f58566854f7eceee4David Li s = r0[6]; 403f9ad8a790398513a845d486f58566854f7eceee4David Li if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; } 404f9ad8a790398513a845d486f58566854f7eceee4David Li s = r0[7]; 405f9ad8a790398513a845d486f58566854f7eceee4David Li if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; } 406f9ad8a790398513a845d486f58566854f7eceee4David Li 407f9ad8a790398513a845d486f58566854f7eceee4David Li /* choose pivot - or die */ 408f9ad8a790398513a845d486f58566854f7eceee4David Li if (FABSF(r3[1])>FABSF(r2[1])) SWAP_ROWS(r3, r2); 409f9ad8a790398513a845d486f58566854f7eceee4David Li if (FABSF(r2[1])>FABSF(r1[1])) SWAP_ROWS(r2, r1); 410f9ad8a790398513a845d486f58566854f7eceee4David Li if (0.0 == r1[1]) return GL_FALSE; 411f9ad8a790398513a845d486f58566854f7eceee4David Li 412f9ad8a790398513a845d486f58566854f7eceee4David Li /* eliminate second variable */ 413f9ad8a790398513a845d486f58566854f7eceee4David Li m2 = r2[1]/r1[1]; m3 = r3[1]/r1[1]; 414f9ad8a790398513a845d486f58566854f7eceee4David Li r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2]; 415f9ad8a790398513a845d486f58566854f7eceee4David Li r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3]; 416f9ad8a790398513a845d486f58566854f7eceee4David Li s = r1[4]; if (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; } 417f9ad8a790398513a845d486f58566854f7eceee4David Li s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; } 418f9ad8a790398513a845d486f58566854f7eceee4David Li s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; } 419f9ad8a790398513a845d486f58566854f7eceee4David Li s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; } 420f9ad8a790398513a845d486f58566854f7eceee4David Li 421f9ad8a790398513a845d486f58566854f7eceee4David Li /* choose pivot - or die */ 422f9ad8a790398513a845d486f58566854f7eceee4David Li if (FABSF(r3[2])>FABSF(r2[2])) SWAP_ROWS(r3, r2); 423f9ad8a790398513a845d486f58566854f7eceee4David Li if (0.0 == r2[2]) return GL_FALSE; 424f9ad8a790398513a845d486f58566854f7eceee4David Li 425f9ad8a790398513a845d486f58566854f7eceee4David Li /* eliminate third variable */ 426f9ad8a790398513a845d486f58566854f7eceee4David Li m3 = r3[2]/r2[2]; 427f9ad8a790398513a845d486f58566854f7eceee4David Li r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4], 428f9ad8a790398513a845d486f58566854f7eceee4David Li r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], 429f9ad8a790398513a845d486f58566854f7eceee4David Li r3[7] -= m3 * r2[7]; 430f9ad8a790398513a845d486f58566854f7eceee4David Li 431f9ad8a790398513a845d486f58566854f7eceee4David Li /* last check */ 432f9ad8a790398513a845d486f58566854f7eceee4David Li if (0.0 == r3[3]) return GL_FALSE; 433f9ad8a790398513a845d486f58566854f7eceee4David Li 434f9ad8a790398513a845d486f58566854f7eceee4David Li s = 1.0F/r3[3]; /* now back substitute row 3 */ 435f9ad8a790398513a845d486f58566854f7eceee4David Li r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s; 436f9ad8a790398513a845d486f58566854f7eceee4David Li 437f9ad8a790398513a845d486f58566854f7eceee4David Li m2 = r2[3]; /* now back substitute row 2 */ 438f9ad8a790398513a845d486f58566854f7eceee4David Li s = 1.0F/r2[2]; 439f9ad8a790398513a845d486f58566854f7eceee4David Li r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2), 440f9ad8a790398513a845d486f58566854f7eceee4David Li r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2); 441f9ad8a790398513a845d486f58566854f7eceee4David Li m1 = r1[3]; 442f9ad8a790398513a845d486f58566854f7eceee4David Li r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1, 443f9ad8a790398513a845d486f58566854f7eceee4David Li r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1; 444f9ad8a790398513a845d486f58566854f7eceee4David Li m0 = r0[3]; 445f9ad8a790398513a845d486f58566854f7eceee4David Li r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0, 446f9ad8a790398513a845d486f58566854f7eceee4David Li r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0; 447f9ad8a790398513a845d486f58566854f7eceee4David Li 448f9ad8a790398513a845d486f58566854f7eceee4David Li m1 = r1[2]; /* now back substitute row 1 */ 449f9ad8a790398513a845d486f58566854f7eceee4David Li s = 1.0F/r1[1]; 450f9ad8a790398513a845d486f58566854f7eceee4David Li r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1), 451f9ad8a790398513a845d486f58566854f7eceee4David Li r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1); 452f9ad8a790398513a845d486f58566854f7eceee4David Li m0 = r0[2]; 453f9ad8a790398513a845d486f58566854f7eceee4David Li r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0, 454f9ad8a790398513a845d486f58566854f7eceee4David Li r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0; 455f9ad8a790398513a845d486f58566854f7eceee4David Li 456f9ad8a790398513a845d486f58566854f7eceee4David Li m0 = r0[1]; /* now back substitute row 0 */ 457f9ad8a790398513a845d486f58566854f7eceee4David Li s = 1.0F/r0[0]; 458f9ad8a790398513a845d486f58566854f7eceee4David Li r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0), 459f9ad8a790398513a845d486f58566854f7eceee4David Li r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0); 460f9ad8a790398513a845d486f58566854f7eceee4David Li 461f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,0) = r0[4]; MAT(out,0,1) = r0[5], 462f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,2) = r0[6]; MAT(out,0,3) = r0[7], 463f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,0) = r1[4]; MAT(out,1,1) = r1[5], 464f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,2) = r1[6]; MAT(out,1,3) = r1[7], 465f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,0) = r2[4]; MAT(out,2,1) = r2[5], 466f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,2) = r2[6]; MAT(out,2,3) = r2[7], 467f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,3,0) = r3[4]; MAT(out,3,1) = r3[5], 468f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,3,2) = r3[6]; MAT(out,3,3) = r3[7]; 469f9ad8a790398513a845d486f58566854f7eceee4David Li 470f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_TRUE; 471f9ad8a790398513a845d486f58566854f7eceee4David Li} 472f9ad8a790398513a845d486f58566854f7eceee4David Li#undef SWAP_ROWS 473f9ad8a790398513a845d486f58566854f7eceee4David Li 474f9ad8a790398513a845d486f58566854f7eceee4David Li/** 475f9ad8a790398513a845d486f58566854f7eceee4David Li * Compute inverse of a general 3d transformation matrix. 476f9ad8a790398513a845d486f58566854f7eceee4David Li * 477f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat pointer to a GLmatrix structure. The matrix inverse will be 478f9ad8a790398513a845d486f58566854f7eceee4David Li * stored in the GLmatrix::inv attribute. 479f9ad8a790398513a845d486f58566854f7eceee4David Li * 480f9ad8a790398513a845d486f58566854f7eceee4David Li * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 481f9ad8a790398513a845d486f58566854f7eceee4David Li * 482f9ad8a790398513a845d486f58566854f7eceee4David Li * \author Adapted from graphics gems II. 483f9ad8a790398513a845d486f58566854f7eceee4David Li * 484f9ad8a790398513a845d486f58566854f7eceee4David Li * Calculates the inverse of the upper left by first calculating its 485f9ad8a790398513a845d486f58566854f7eceee4David Li * determinant and multiplying it to the symmetric adjust matrix of each 486f9ad8a790398513a845d486f58566854f7eceee4David Li * element. Finally deals with the translation part by transforming the 487f9ad8a790398513a845d486f58566854f7eceee4David Li * original translation vector using by the calculated submatrix inverse. 488f9ad8a790398513a845d486f58566854f7eceee4David Li */ 489f9ad8a790398513a845d486f58566854f7eceee4David Listatic GLboolean invert_matrix_3d_general( GLmatrix *mat ) 490f9ad8a790398513a845d486f58566854f7eceee4David Li{ 491f9ad8a790398513a845d486f58566854f7eceee4David Li const GLfloat *in = mat->m; 492f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat *out = mat->inv; 493f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat pos, neg, t; 494f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat det; 495f9ad8a790398513a845d486f58566854f7eceee4David Li 496f9ad8a790398513a845d486f58566854f7eceee4David Li /* Calculate the determinant of upper left 3x3 submatrix and 497f9ad8a790398513a845d486f58566854f7eceee4David Li * determine if the matrix is singular. 498f9ad8a790398513a845d486f58566854f7eceee4David Li */ 499f9ad8a790398513a845d486f58566854f7eceee4David Li pos = neg = 0.0; 500f9ad8a790398513a845d486f58566854f7eceee4David Li t = MAT(in,0,0) * MAT(in,1,1) * MAT(in,2,2); 501f9ad8a790398513a845d486f58566854f7eceee4David Li if (t >= 0.0) pos += t; else neg += t; 502f9ad8a790398513a845d486f58566854f7eceee4David Li 503f9ad8a790398513a845d486f58566854f7eceee4David Li t = MAT(in,1,0) * MAT(in,2,1) * MAT(in,0,2); 504f9ad8a790398513a845d486f58566854f7eceee4David Li if (t >= 0.0) pos += t; else neg += t; 505f9ad8a790398513a845d486f58566854f7eceee4David Li 506f9ad8a790398513a845d486f58566854f7eceee4David Li t = MAT(in,2,0) * MAT(in,0,1) * MAT(in,1,2); 507f9ad8a790398513a845d486f58566854f7eceee4David Li if (t >= 0.0) pos += t; else neg += t; 508f9ad8a790398513a845d486f58566854f7eceee4David Li 509f9ad8a790398513a845d486f58566854f7eceee4David Li t = -MAT(in,2,0) * MAT(in,1,1) * MAT(in,0,2); 510f9ad8a790398513a845d486f58566854f7eceee4David Li if (t >= 0.0) pos += t; else neg += t; 511f9ad8a790398513a845d486f58566854f7eceee4David Li 512f9ad8a790398513a845d486f58566854f7eceee4David Li t = -MAT(in,1,0) * MAT(in,0,1) * MAT(in,2,2); 513f9ad8a790398513a845d486f58566854f7eceee4David Li if (t >= 0.0) pos += t; else neg += t; 514f9ad8a790398513a845d486f58566854f7eceee4David Li 515f9ad8a790398513a845d486f58566854f7eceee4David Li t = -MAT(in,0,0) * MAT(in,2,1) * MAT(in,1,2); 516f9ad8a790398513a845d486f58566854f7eceee4David Li if (t >= 0.0) pos += t; else neg += t; 517f9ad8a790398513a845d486f58566854f7eceee4David Li 518f9ad8a790398513a845d486f58566854f7eceee4David Li det = pos + neg; 519f9ad8a790398513a845d486f58566854f7eceee4David Li 520f9ad8a790398513a845d486f58566854f7eceee4David Li if (det*det < 1e-25) 521f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_FALSE; 522f9ad8a790398513a845d486f58566854f7eceee4David Li 523f9ad8a790398513a845d486f58566854f7eceee4David Li det = 1.0F / det; 524f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,0) = ( (MAT(in,1,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,1,2) )*det); 525f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,1) = (- (MAT(in,0,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,0,2) )*det); 526f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,2) = ( (MAT(in,0,1)*MAT(in,1,2) - MAT(in,1,1)*MAT(in,0,2) )*det); 527f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,0) = (- (MAT(in,1,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,1,2) )*det); 528f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,1) = ( (MAT(in,0,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,0,2) )*det); 529f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,2) = (- (MAT(in,0,0)*MAT(in,1,2) - MAT(in,1,0)*MAT(in,0,2) )*det); 530f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,0) = ( (MAT(in,1,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,1,1) )*det); 531f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,1) = (- (MAT(in,0,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,0,1) )*det); 532f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,2) = ( (MAT(in,0,0)*MAT(in,1,1) - MAT(in,1,0)*MAT(in,0,1) )*det); 533f9ad8a790398513a845d486f58566854f7eceee4David Li 534f9ad8a790398513a845d486f58566854f7eceee4David Li /* Do the translation part */ 535f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) + 536f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(in,1,3) * MAT(out,0,1) + 537f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(in,2,3) * MAT(out,0,2) ); 538f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) + 539f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(in,1,3) * MAT(out,1,1) + 540f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(in,2,3) * MAT(out,1,2) ); 541f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) + 542f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(in,1,3) * MAT(out,2,1) + 543f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(in,2,3) * MAT(out,2,2) ); 544f9ad8a790398513a845d486f58566854f7eceee4David Li 545f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_TRUE; 546f9ad8a790398513a845d486f58566854f7eceee4David Li} 547f9ad8a790398513a845d486f58566854f7eceee4David Li 548f9ad8a790398513a845d486f58566854f7eceee4David Li/** 549f9ad8a790398513a845d486f58566854f7eceee4David Li * Compute inverse of a 3d transformation matrix. 550f9ad8a790398513a845d486f58566854f7eceee4David Li * 551f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat pointer to a GLmatrix structure. The matrix inverse will be 552f9ad8a790398513a845d486f58566854f7eceee4David Li * stored in the GLmatrix::inv attribute. 553f9ad8a790398513a845d486f58566854f7eceee4David Li * 554f9ad8a790398513a845d486f58566854f7eceee4David Li * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 555f9ad8a790398513a845d486f58566854f7eceee4David Li * 556f9ad8a790398513a845d486f58566854f7eceee4David Li * If the matrix is not an angle preserving matrix then calls 557f9ad8a790398513a845d486f58566854f7eceee4David Li * invert_matrix_3d_general for the actual calculation. Otherwise calculates 558f9ad8a790398513a845d486f58566854f7eceee4David Li * the inverse matrix analyzing and inverting each of the scaling, rotation and 559f9ad8a790398513a845d486f58566854f7eceee4David Li * translation parts. 560f9ad8a790398513a845d486f58566854f7eceee4David Li */ 561f9ad8a790398513a845d486f58566854f7eceee4David Listatic GLboolean invert_matrix_3d( GLmatrix *mat ) 562f9ad8a790398513a845d486f58566854f7eceee4David Li{ 563f9ad8a790398513a845d486f58566854f7eceee4David Li const GLfloat *in = mat->m; 564f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat *out = mat->inv; 565f9ad8a790398513a845d486f58566854f7eceee4David Li 566f9ad8a790398513a845d486f58566854f7eceee4David Li if (!TEST_MAT_FLAGS(mat, MAT_FLAGS_ANGLE_PRESERVING)) { 567f9ad8a790398513a845d486f58566854f7eceee4David Li return invert_matrix_3d_general( mat ); 568f9ad8a790398513a845d486f58566854f7eceee4David Li } 569f9ad8a790398513a845d486f58566854f7eceee4David Li 570f9ad8a790398513a845d486f58566854f7eceee4David Li if (mat->flags & MAT_FLAG_UNIFORM_SCALE) { 571f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat scale = (MAT(in,0,0) * MAT(in,0,0) + 572f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(in,0,1) * MAT(in,0,1) + 573f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(in,0,2) * MAT(in,0,2)); 574f9ad8a790398513a845d486f58566854f7eceee4David Li 575f9ad8a790398513a845d486f58566854f7eceee4David Li if (scale == 0.0) 576f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_FALSE; 577f9ad8a790398513a845d486f58566854f7eceee4David Li 578f9ad8a790398513a845d486f58566854f7eceee4David Li scale = 1.0F / scale; 579f9ad8a790398513a845d486f58566854f7eceee4David Li 580f9ad8a790398513a845d486f58566854f7eceee4David Li /* Transpose and scale the 3 by 3 upper-left submatrix. */ 581f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,0) = scale * MAT(in,0,0); 582f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,0) = scale * MAT(in,0,1); 583f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,0) = scale * MAT(in,0,2); 584f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,1) = scale * MAT(in,1,0); 585f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,1) = scale * MAT(in,1,1); 586f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,1) = scale * MAT(in,1,2); 587f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,2) = scale * MAT(in,2,0); 588f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,2) = scale * MAT(in,2,1); 589f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,2) = scale * MAT(in,2,2); 590f9ad8a790398513a845d486f58566854f7eceee4David Li } 591f9ad8a790398513a845d486f58566854f7eceee4David Li else if (mat->flags & MAT_FLAG_ROTATION) { 592f9ad8a790398513a845d486f58566854f7eceee4David Li /* Transpose the 3 by 3 upper-left submatrix. */ 593f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,0) = MAT(in,0,0); 594f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,0) = MAT(in,0,1); 595f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,0) = MAT(in,0,2); 596f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,1) = MAT(in,1,0); 597f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,1) = MAT(in,1,1); 598f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,1) = MAT(in,1,2); 599f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,2) = MAT(in,2,0); 600f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,2) = MAT(in,2,1); 601f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,2) = MAT(in,2,2); 602f9ad8a790398513a845d486f58566854f7eceee4David Li } 603f9ad8a790398513a845d486f58566854f7eceee4David Li else { 604f9ad8a790398513a845d486f58566854f7eceee4David Li /* pure translation */ 605f9ad8a790398513a845d486f58566854f7eceee4David Li memcpy( out, Identity, sizeof(Identity) ); 606f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,3) = - MAT(in,0,3); 607f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,3) = - MAT(in,1,3); 608f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,3) = - MAT(in,2,3); 609f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_TRUE; 610f9ad8a790398513a845d486f58566854f7eceee4David Li } 611f9ad8a790398513a845d486f58566854f7eceee4David Li 612f9ad8a790398513a845d486f58566854f7eceee4David Li if (mat->flags & MAT_FLAG_TRANSLATION) { 613f9ad8a790398513a845d486f58566854f7eceee4David Li /* Do the translation part */ 614f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) + 615f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(in,1,3) * MAT(out,0,1) + 616f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(in,2,3) * MAT(out,0,2) ); 617f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) + 618f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(in,1,3) * MAT(out,1,1) + 619f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(in,2,3) * MAT(out,1,2) ); 620f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) + 621f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(in,1,3) * MAT(out,2,1) + 622f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(in,2,3) * MAT(out,2,2) ); 623f9ad8a790398513a845d486f58566854f7eceee4David Li } 624f9ad8a790398513a845d486f58566854f7eceee4David Li else { 625f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,3) = MAT(out,1,3) = MAT(out,2,3) = 0.0; 626f9ad8a790398513a845d486f58566854f7eceee4David Li } 627f9ad8a790398513a845d486f58566854f7eceee4David Li 628f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_TRUE; 629f9ad8a790398513a845d486f58566854f7eceee4David Li} 630f9ad8a790398513a845d486f58566854f7eceee4David Li 631f9ad8a790398513a845d486f58566854f7eceee4David Li/** 632f9ad8a790398513a845d486f58566854f7eceee4David Li * Compute inverse of an identity transformation matrix. 633f9ad8a790398513a845d486f58566854f7eceee4David Li * 634f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat pointer to a GLmatrix structure. The matrix inverse will be 635f9ad8a790398513a845d486f58566854f7eceee4David Li * stored in the GLmatrix::inv attribute. 636f9ad8a790398513a845d486f58566854f7eceee4David Li * 637f9ad8a790398513a845d486f58566854f7eceee4David Li * \return always GL_TRUE. 638f9ad8a790398513a845d486f58566854f7eceee4David Li * 639f9ad8a790398513a845d486f58566854f7eceee4David Li * Simply copies Identity into GLmatrix::inv. 640f9ad8a790398513a845d486f58566854f7eceee4David Li */ 641f9ad8a790398513a845d486f58566854f7eceee4David Listatic GLboolean invert_matrix_identity( GLmatrix *mat ) 642f9ad8a790398513a845d486f58566854f7eceee4David Li{ 643f9ad8a790398513a845d486f58566854f7eceee4David Li memcpy( mat->inv, Identity, sizeof(Identity) ); 644f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_TRUE; 645f9ad8a790398513a845d486f58566854f7eceee4David Li} 646f9ad8a790398513a845d486f58566854f7eceee4David Li 647f9ad8a790398513a845d486f58566854f7eceee4David Li/** 648f9ad8a790398513a845d486f58566854f7eceee4David Li * Compute inverse of a no-rotation 3d transformation matrix. 649f9ad8a790398513a845d486f58566854f7eceee4David Li * 650f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat pointer to a GLmatrix structure. The matrix inverse will be 651f9ad8a790398513a845d486f58566854f7eceee4David Li * stored in the GLmatrix::inv attribute. 652f9ad8a790398513a845d486f58566854f7eceee4David Li * 653f9ad8a790398513a845d486f58566854f7eceee4David Li * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 654f9ad8a790398513a845d486f58566854f7eceee4David Li * 655f9ad8a790398513a845d486f58566854f7eceee4David Li * Calculates the 656f9ad8a790398513a845d486f58566854f7eceee4David Li */ 657f9ad8a790398513a845d486f58566854f7eceee4David Listatic GLboolean invert_matrix_3d_no_rot( GLmatrix *mat ) 658f9ad8a790398513a845d486f58566854f7eceee4David Li{ 659f9ad8a790398513a845d486f58566854f7eceee4David Li const GLfloat *in = mat->m; 660f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat *out = mat->inv; 661f9ad8a790398513a845d486f58566854f7eceee4David Li 662f9ad8a790398513a845d486f58566854f7eceee4David Li if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0 || MAT(in,2,2) == 0 ) 663f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_FALSE; 664f9ad8a790398513a845d486f58566854f7eceee4David Li 665f9ad8a790398513a845d486f58566854f7eceee4David Li memcpy( out, Identity, 16 * sizeof(GLfloat) ); 666f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,0) = 1.0F / MAT(in,0,0); 667f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,1) = 1.0F / MAT(in,1,1); 668f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,2) = 1.0F / MAT(in,2,2); 669f9ad8a790398513a845d486f58566854f7eceee4David Li 670f9ad8a790398513a845d486f58566854f7eceee4David Li if (mat->flags & MAT_FLAG_TRANSLATION) { 671f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0)); 672f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1)); 673f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,3) = - (MAT(in,2,3) * MAT(out,2,2)); 674f9ad8a790398513a845d486f58566854f7eceee4David Li } 675f9ad8a790398513a845d486f58566854f7eceee4David Li 676f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_TRUE; 677f9ad8a790398513a845d486f58566854f7eceee4David Li} 678f9ad8a790398513a845d486f58566854f7eceee4David Li 679f9ad8a790398513a845d486f58566854f7eceee4David Li/** 680f9ad8a790398513a845d486f58566854f7eceee4David Li * Compute inverse of a no-rotation 2d transformation matrix. 681f9ad8a790398513a845d486f58566854f7eceee4David Li * 682f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat pointer to a GLmatrix structure. The matrix inverse will be 683f9ad8a790398513a845d486f58566854f7eceee4David Li * stored in the GLmatrix::inv attribute. 684f9ad8a790398513a845d486f58566854f7eceee4David Li * 685f9ad8a790398513a845d486f58566854f7eceee4David Li * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 686f9ad8a790398513a845d486f58566854f7eceee4David Li * 687f9ad8a790398513a845d486f58566854f7eceee4David Li * Calculates the inverse matrix by applying the inverse scaling and 688f9ad8a790398513a845d486f58566854f7eceee4David Li * translation to the identity matrix. 689f9ad8a790398513a845d486f58566854f7eceee4David Li */ 690f9ad8a790398513a845d486f58566854f7eceee4David Listatic GLboolean invert_matrix_2d_no_rot( GLmatrix *mat ) 691f9ad8a790398513a845d486f58566854f7eceee4David Li{ 692f9ad8a790398513a845d486f58566854f7eceee4David Li const GLfloat *in = mat->m; 693f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat *out = mat->inv; 694f9ad8a790398513a845d486f58566854f7eceee4David Li 695f9ad8a790398513a845d486f58566854f7eceee4David Li if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0) 696f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_FALSE; 697f9ad8a790398513a845d486f58566854f7eceee4David Li 698f9ad8a790398513a845d486f58566854f7eceee4David Li memcpy( out, Identity, 16 * sizeof(GLfloat) ); 699f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,0) = 1.0F / MAT(in,0,0); 700f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,1) = 1.0F / MAT(in,1,1); 701f9ad8a790398513a845d486f58566854f7eceee4David Li 702f9ad8a790398513a845d486f58566854f7eceee4David Li if (mat->flags & MAT_FLAG_TRANSLATION) { 703f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0)); 704f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1)); 705f9ad8a790398513a845d486f58566854f7eceee4David Li } 706f9ad8a790398513a845d486f58566854f7eceee4David Li 707f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_TRUE; 708f9ad8a790398513a845d486f58566854f7eceee4David Li} 709f9ad8a790398513a845d486f58566854f7eceee4David Li 710f9ad8a790398513a845d486f58566854f7eceee4David Li#if 0 711f9ad8a790398513a845d486f58566854f7eceee4David Li/* broken */ 712f9ad8a790398513a845d486f58566854f7eceee4David Listatic GLboolean invert_matrix_perspective( GLmatrix *mat ) 713f9ad8a790398513a845d486f58566854f7eceee4David Li{ 714f9ad8a790398513a845d486f58566854f7eceee4David Li const GLfloat *in = mat->m; 715f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat *out = mat->inv; 716f9ad8a790398513a845d486f58566854f7eceee4David Li 717f9ad8a790398513a845d486f58566854f7eceee4David Li if (MAT(in,2,3) == 0) 718f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_FALSE; 719f9ad8a790398513a845d486f58566854f7eceee4David Li 720f9ad8a790398513a845d486f58566854f7eceee4David Li memcpy( out, Identity, 16 * sizeof(GLfloat) ); 721f9ad8a790398513a845d486f58566854f7eceee4David Li 722f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,0) = 1.0F / MAT(in,0,0); 723f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,1) = 1.0F / MAT(in,1,1); 724f9ad8a790398513a845d486f58566854f7eceee4David Li 725f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,0,3) = MAT(in,0,2); 726f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,1,3) = MAT(in,1,2); 727f9ad8a790398513a845d486f58566854f7eceee4David Li 728f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,2) = 0; 729f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,2,3) = -1; 730f9ad8a790398513a845d486f58566854f7eceee4David Li 731f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,3,2) = 1.0F / MAT(in,2,3); 732f9ad8a790398513a845d486f58566854f7eceee4David Li MAT(out,3,3) = MAT(in,2,2) * MAT(out,3,2); 733f9ad8a790398513a845d486f58566854f7eceee4David Li 734f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_TRUE; 735f9ad8a790398513a845d486f58566854f7eceee4David Li} 736f9ad8a790398513a845d486f58566854f7eceee4David Li#endif 737f9ad8a790398513a845d486f58566854f7eceee4David Li 738f9ad8a790398513a845d486f58566854f7eceee4David Li/** 739f9ad8a790398513a845d486f58566854f7eceee4David Li * Matrix inversion function pointer type. 740f9ad8a790398513a845d486f58566854f7eceee4David Li */ 741f9ad8a790398513a845d486f58566854f7eceee4David Litypedef GLboolean (*inv_mat_func)( GLmatrix *mat ); 742f9ad8a790398513a845d486f58566854f7eceee4David Li 743f9ad8a790398513a845d486f58566854f7eceee4David Li/** 744f9ad8a790398513a845d486f58566854f7eceee4David Li * Table of the matrix inversion functions according to the matrix type. 745f9ad8a790398513a845d486f58566854f7eceee4David Li */ 746f9ad8a790398513a845d486f58566854f7eceee4David Listatic inv_mat_func inv_mat_tab[7] = { 747f9ad8a790398513a845d486f58566854f7eceee4David Liinvert_matrix_general, 748f9ad8a790398513a845d486f58566854f7eceee4David Liinvert_matrix_identity, 749f9ad8a790398513a845d486f58566854f7eceee4David Liinvert_matrix_3d_no_rot, 750f9ad8a790398513a845d486f58566854f7eceee4David Li#if 0 751f9ad8a790398513a845d486f58566854f7eceee4David Li/* Don't use this function for now - it fails when the projection matrix 752f9ad8a790398513a845d486f58566854f7eceee4David Li * is premultiplied by a translation (ala Chromium's tilesort SPU). 753f9ad8a790398513a845d486f58566854f7eceee4David Li */ 754f9ad8a790398513a845d486f58566854f7eceee4David Liinvert_matrix_perspective, 755f9ad8a790398513a845d486f58566854f7eceee4David Li#else 756f9ad8a790398513a845d486f58566854f7eceee4David Liinvert_matrix_general, 757f9ad8a790398513a845d486f58566854f7eceee4David Li#endif 758f9ad8a790398513a845d486f58566854f7eceee4David Liinvert_matrix_3d, /* lazy! */ 759f9ad8a790398513a845d486f58566854f7eceee4David Liinvert_matrix_2d_no_rot, 760f9ad8a790398513a845d486f58566854f7eceee4David Liinvert_matrix_3d 761f9ad8a790398513a845d486f58566854f7eceee4David Li}; 762f9ad8a790398513a845d486f58566854f7eceee4David Li 763f9ad8a790398513a845d486f58566854f7eceee4David Li/** 764f9ad8a790398513a845d486f58566854f7eceee4David Li * Compute inverse of a transformation matrix. 765f9ad8a790398513a845d486f58566854f7eceee4David Li * 766f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat pointer to a GLmatrix structure. The matrix inverse will be 767f9ad8a790398513a845d486f58566854f7eceee4David Li * stored in the GLmatrix::inv attribute. 768f9ad8a790398513a845d486f58566854f7eceee4David Li * 769f9ad8a790398513a845d486f58566854f7eceee4David Li * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 770f9ad8a790398513a845d486f58566854f7eceee4David Li * 771f9ad8a790398513a845d486f58566854f7eceee4David Li * Calls the matrix inversion function in inv_mat_tab corresponding to the 772f9ad8a790398513a845d486f58566854f7eceee4David Li * given matrix type. In case of failure, updates the MAT_FLAG_SINGULAR flag, 773f9ad8a790398513a845d486f58566854f7eceee4David Li * and copies the identity matrix into GLmatrix::inv. 774f9ad8a790398513a845d486f58566854f7eceee4David Li */ 775f9ad8a790398513a845d486f58566854f7eceee4David Listatic GLboolean matrix_invert( GLmatrix *mat ) 776f9ad8a790398513a845d486f58566854f7eceee4David Li{ 777f9ad8a790398513a845d486f58566854f7eceee4David Li if (inv_mat_tab[mat->type](mat)) { 778f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags &= ~MAT_FLAG_SINGULAR; 779f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_TRUE; 780f9ad8a790398513a845d486f58566854f7eceee4David Li } else { 781f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_SINGULAR; 782f9ad8a790398513a845d486f58566854f7eceee4David Li memcpy( mat->inv, Identity, sizeof(Identity) ); 783f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_FALSE; 784f9ad8a790398513a845d486f58566854f7eceee4David Li } 785f9ad8a790398513a845d486f58566854f7eceee4David Li} 786f9ad8a790398513a845d486f58566854f7eceee4David Li 787f9ad8a790398513a845d486f58566854f7eceee4David Li/*@}*/ 788f9ad8a790398513a845d486f58566854f7eceee4David Li 789f9ad8a790398513a845d486f58566854f7eceee4David Li 790f9ad8a790398513a845d486f58566854f7eceee4David Li/**********************************************************************/ 791f9ad8a790398513a845d486f58566854f7eceee4David Li/** \name Matrix generation */ 792f9ad8a790398513a845d486f58566854f7eceee4David Li/*@{*/ 793f9ad8a790398513a845d486f58566854f7eceee4David Li 794f9ad8a790398513a845d486f58566854f7eceee4David Li/** 795f9ad8a790398513a845d486f58566854f7eceee4David Li * Generate a 4x4 transformation matrix from glRotate parameters, and 796f9ad8a790398513a845d486f58566854f7eceee4David Li * post-multiply the input matrix by it. 797f9ad8a790398513a845d486f58566854f7eceee4David Li * 798f9ad8a790398513a845d486f58566854f7eceee4David Li * \author 799f9ad8a790398513a845d486f58566854f7eceee4David Li * This function was contributed by Erich Boleyn (erich@uruk.org). 800f9ad8a790398513a845d486f58566854f7eceee4David Li * Optimizations contributed by Rudolf Opalla (rudi@khm.de). 801f9ad8a790398513a845d486f58566854f7eceee4David Li */ 802f9ad8a790398513a845d486f58566854f7eceee4David Livoid 803f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_rotate( GLmatrix *mat, 804f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat angle, GLfloat x, GLfloat y, GLfloat z ) 805f9ad8a790398513a845d486f58566854f7eceee4David Li{ 806f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c; 807f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat m[16]; 808f9ad8a790398513a845d486f58566854f7eceee4David Li GLboolean optimized; 809f9ad8a790398513a845d486f58566854f7eceee4David Li 810f9ad8a790398513a845d486f58566854f7eceee4David Li s = (GLfloat) sinf( angle * (M_PI / 180.0f) ); 811f9ad8a790398513a845d486f58566854f7eceee4David Li c = (GLfloat) cosf( angle * (M_PI / 180.0f) ); 812f9ad8a790398513a845d486f58566854f7eceee4David Li 813f9ad8a790398513a845d486f58566854f7eceee4David Li memcpy(m, Identity, sizeof(GLfloat)*16); 814f9ad8a790398513a845d486f58566854f7eceee4David Li optimized = GL_FALSE; 815f9ad8a790398513a845d486f58566854f7eceee4David Li 816f9ad8a790398513a845d486f58566854f7eceee4David Li#define M(row,col) m[col*4+row] 817f9ad8a790398513a845d486f58566854f7eceee4David Li 818f9ad8a790398513a845d486f58566854f7eceee4David Li if (x == 0.0F) { 819f9ad8a790398513a845d486f58566854f7eceee4David Li if (y == 0.0F) { 820f9ad8a790398513a845d486f58566854f7eceee4David Li if (z != 0.0F) { 821f9ad8a790398513a845d486f58566854f7eceee4David Li optimized = GL_TRUE; 822f9ad8a790398513a845d486f58566854f7eceee4David Li /* rotate only around z-axis */ 823f9ad8a790398513a845d486f58566854f7eceee4David Li M(0,0) = c; 824f9ad8a790398513a845d486f58566854f7eceee4David Li M(1,1) = c; 825f9ad8a790398513a845d486f58566854f7eceee4David Li if (z < 0.0F) { 826f9ad8a790398513a845d486f58566854f7eceee4David Li M(0,1) = s; 827f9ad8a790398513a845d486f58566854f7eceee4David Li M(1,0) = -s; 828f9ad8a790398513a845d486f58566854f7eceee4David Li } 829f9ad8a790398513a845d486f58566854f7eceee4David Li else { 830f9ad8a790398513a845d486f58566854f7eceee4David Li M(0,1) = -s; 831f9ad8a790398513a845d486f58566854f7eceee4David Li M(1,0) = s; 832f9ad8a790398513a845d486f58566854f7eceee4David Li } 833f9ad8a790398513a845d486f58566854f7eceee4David Li } 834f9ad8a790398513a845d486f58566854f7eceee4David Li } 835f9ad8a790398513a845d486f58566854f7eceee4David Li else if (z == 0.0F) { 836f9ad8a790398513a845d486f58566854f7eceee4David Li optimized = GL_TRUE; 837f9ad8a790398513a845d486f58566854f7eceee4David Li /* rotate only around y-axis */ 838f9ad8a790398513a845d486f58566854f7eceee4David Li M(0,0) = c; 839f9ad8a790398513a845d486f58566854f7eceee4David Li M(2,2) = c; 840f9ad8a790398513a845d486f58566854f7eceee4David Li if (y < 0.0F) { 841f9ad8a790398513a845d486f58566854f7eceee4David Li M(0,2) = -s; 842f9ad8a790398513a845d486f58566854f7eceee4David Li M(2,0) = s; 843f9ad8a790398513a845d486f58566854f7eceee4David Li } 844f9ad8a790398513a845d486f58566854f7eceee4David Li else { 845f9ad8a790398513a845d486f58566854f7eceee4David Li M(0,2) = s; 846f9ad8a790398513a845d486f58566854f7eceee4David Li M(2,0) = -s; 847f9ad8a790398513a845d486f58566854f7eceee4David Li } 848f9ad8a790398513a845d486f58566854f7eceee4David Li } 849f9ad8a790398513a845d486f58566854f7eceee4David Li } 850f9ad8a790398513a845d486f58566854f7eceee4David Li else if (y == 0.0F) { 851f9ad8a790398513a845d486f58566854f7eceee4David Li if (z == 0.0F) { 852f9ad8a790398513a845d486f58566854f7eceee4David Li optimized = GL_TRUE; 853f9ad8a790398513a845d486f58566854f7eceee4David Li /* rotate only around x-axis */ 854f9ad8a790398513a845d486f58566854f7eceee4David Li M(1,1) = c; 855f9ad8a790398513a845d486f58566854f7eceee4David Li M(2,2) = c; 856f9ad8a790398513a845d486f58566854f7eceee4David Li if (x < 0.0F) { 857f9ad8a790398513a845d486f58566854f7eceee4David Li M(1,2) = s; 858f9ad8a790398513a845d486f58566854f7eceee4David Li M(2,1) = -s; 859f9ad8a790398513a845d486f58566854f7eceee4David Li } 860f9ad8a790398513a845d486f58566854f7eceee4David Li else { 861f9ad8a790398513a845d486f58566854f7eceee4David Li M(1,2) = -s; 862f9ad8a790398513a845d486f58566854f7eceee4David Li M(2,1) = s; 863f9ad8a790398513a845d486f58566854f7eceee4David Li } 864f9ad8a790398513a845d486f58566854f7eceee4David Li } 865f9ad8a790398513a845d486f58566854f7eceee4David Li } 866f9ad8a790398513a845d486f58566854f7eceee4David Li 867f9ad8a790398513a845d486f58566854f7eceee4David Li if (!optimized) { 868f9ad8a790398513a845d486f58566854f7eceee4David Li const GLfloat mag = SQRTF(x * x + y * y + z * z); 869f9ad8a790398513a845d486f58566854f7eceee4David Li 870f9ad8a790398513a845d486f58566854f7eceee4David Li if (mag <= 1.0e-4) { 871f9ad8a790398513a845d486f58566854f7eceee4David Li /* no rotation, leave mat as-is */ 872f9ad8a790398513a845d486f58566854f7eceee4David Li return; 873f9ad8a790398513a845d486f58566854f7eceee4David Li } 874f9ad8a790398513a845d486f58566854f7eceee4David Li 875f9ad8a790398513a845d486f58566854f7eceee4David Li x /= mag; 876f9ad8a790398513a845d486f58566854f7eceee4David Li y /= mag; 877f9ad8a790398513a845d486f58566854f7eceee4David Li z /= mag; 878f9ad8a790398513a845d486f58566854f7eceee4David Li 879f9ad8a790398513a845d486f58566854f7eceee4David Li 880f9ad8a790398513a845d486f58566854f7eceee4David Li /* 881f9ad8a790398513a845d486f58566854f7eceee4David Li * Arbitrary axis rotation matrix. 882f9ad8a790398513a845d486f58566854f7eceee4David Li * 883f9ad8a790398513a845d486f58566854f7eceee4David Li * This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied 884f9ad8a790398513a845d486f58566854f7eceee4David Li * like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation 885f9ad8a790398513a845d486f58566854f7eceee4David Li * (which is about the X-axis), and the two composite transforms 886f9ad8a790398513a845d486f58566854f7eceee4David Li * Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary 887f9ad8a790398513a845d486f58566854f7eceee4David Li * from the arbitrary axis to the X-axis then back. They are 888f9ad8a790398513a845d486f58566854f7eceee4David Li * all elementary rotations. 889f9ad8a790398513a845d486f58566854f7eceee4David Li * 890f9ad8a790398513a845d486f58566854f7eceee4David Li * Rz' is a rotation about the Z-axis, to bring the axis vector 891f9ad8a790398513a845d486f58566854f7eceee4David Li * into the x-z plane. Then Ry' is applied, rotating about the 892f9ad8a790398513a845d486f58566854f7eceee4David Li * Y-axis to bring the axis vector parallel with the X-axis. The 893f9ad8a790398513a845d486f58566854f7eceee4David Li * rotation about the X-axis is then performed. Ry and Rz are 894f9ad8a790398513a845d486f58566854f7eceee4David Li * simply the respective inverse transforms to bring the arbitrary 895f9ad8a790398513a845d486f58566854f7eceee4David Li * axis back to it's original orientation. The first transforms 896f9ad8a790398513a845d486f58566854f7eceee4David Li * Rz' and Ry' are considered inverses, since the data from the 897f9ad8a790398513a845d486f58566854f7eceee4David Li * arbitrary axis gives you info on how to get to it, not how 898f9ad8a790398513a845d486f58566854f7eceee4David Li * to get away from it, and an inverse must be applied. 899f9ad8a790398513a845d486f58566854f7eceee4David Li * 900f9ad8a790398513a845d486f58566854f7eceee4David Li * The basic calculation used is to recognize that the arbitrary 901f9ad8a790398513a845d486f58566854f7eceee4David Li * axis vector (x, y, z), since it is of unit length, actually 902f9ad8a790398513a845d486f58566854f7eceee4David Li * represents the sines and cosines of the angles to rotate the 903f9ad8a790398513a845d486f58566854f7eceee4David Li * X-axis to the same orientation, with theta being the angle about 904f9ad8a790398513a845d486f58566854f7eceee4David Li * Z and phi the angle about Y (in the order described above) 905f9ad8a790398513a845d486f58566854f7eceee4David Li * as follows: 906f9ad8a790398513a845d486f58566854f7eceee4David Li * 907f9ad8a790398513a845d486f58566854f7eceee4David Li * cos ( theta ) = x / sqrt ( 1 - z^2 ) 908f9ad8a790398513a845d486f58566854f7eceee4David Li * sin ( theta ) = y / sqrt ( 1 - z^2 ) 909f9ad8a790398513a845d486f58566854f7eceee4David Li * 910f9ad8a790398513a845d486f58566854f7eceee4David Li * cos ( phi ) = sqrt ( 1 - z^2 ) 911f9ad8a790398513a845d486f58566854f7eceee4David Li * sin ( phi ) = z 912f9ad8a790398513a845d486f58566854f7eceee4David Li * 913f9ad8a790398513a845d486f58566854f7eceee4David Li * Note that cos ( phi ) can further be inserted to the above 914f9ad8a790398513a845d486f58566854f7eceee4David Li * formulas: 915f9ad8a790398513a845d486f58566854f7eceee4David Li * 916f9ad8a790398513a845d486f58566854f7eceee4David Li * cos ( theta ) = x / cos ( phi ) 917f9ad8a790398513a845d486f58566854f7eceee4David Li * sin ( theta ) = y / sin ( phi ) 918f9ad8a790398513a845d486f58566854f7eceee4David Li * 919f9ad8a790398513a845d486f58566854f7eceee4David Li * ...etc. Because of those relations and the standard trigonometric 920f9ad8a790398513a845d486f58566854f7eceee4David Li * relations, it is pssible to reduce the transforms down to what 921f9ad8a790398513a845d486f58566854f7eceee4David Li * is used below. It may be that any primary axis chosen will give the 922f9ad8a790398513a845d486f58566854f7eceee4David Li * same results (modulo a sign convention) using thie method. 923f9ad8a790398513a845d486f58566854f7eceee4David Li * 924f9ad8a790398513a845d486f58566854f7eceee4David Li * Particularly nice is to notice that all divisions that might 925f9ad8a790398513a845d486f58566854f7eceee4David Li * have caused trouble when parallel to certain planes or 926f9ad8a790398513a845d486f58566854f7eceee4David Li * axis go away with care paid to reducing the expressions. 927f9ad8a790398513a845d486f58566854f7eceee4David Li * After checking, it does perform correctly under all cases, since 928f9ad8a790398513a845d486f58566854f7eceee4David Li * in all the cases of division where the denominator would have 929f9ad8a790398513a845d486f58566854f7eceee4David Li * been zero, the numerator would have been zero as well, giving 930f9ad8a790398513a845d486f58566854f7eceee4David Li * the expected result. 931f9ad8a790398513a845d486f58566854f7eceee4David Li */ 932f9ad8a790398513a845d486f58566854f7eceee4David Li 933f9ad8a790398513a845d486f58566854f7eceee4David Li xx = x * x; 934f9ad8a790398513a845d486f58566854f7eceee4David Li yy = y * y; 935f9ad8a790398513a845d486f58566854f7eceee4David Li zz = z * z; 936f9ad8a790398513a845d486f58566854f7eceee4David Li xy = x * y; 937f9ad8a790398513a845d486f58566854f7eceee4David Li yz = y * z; 938f9ad8a790398513a845d486f58566854f7eceee4David Li zx = z * x; 939f9ad8a790398513a845d486f58566854f7eceee4David Li xs = x * s; 940f9ad8a790398513a845d486f58566854f7eceee4David Li ys = y * s; 941f9ad8a790398513a845d486f58566854f7eceee4David Li zs = z * s; 942f9ad8a790398513a845d486f58566854f7eceee4David Li one_c = 1.0F - c; 943f9ad8a790398513a845d486f58566854f7eceee4David Li 944f9ad8a790398513a845d486f58566854f7eceee4David Li /* We already hold the identity-matrix so we can skip some statements */ 945f9ad8a790398513a845d486f58566854f7eceee4David Li M(0,0) = (one_c * xx) + c; 946f9ad8a790398513a845d486f58566854f7eceee4David Li M(0,1) = (one_c * xy) - zs; 947f9ad8a790398513a845d486f58566854f7eceee4David Li M(0,2) = (one_c * zx) + ys; 948f9ad8a790398513a845d486f58566854f7eceee4David Li /* M(0,3) = 0.0F; */ 949f9ad8a790398513a845d486f58566854f7eceee4David Li 950f9ad8a790398513a845d486f58566854f7eceee4David Li M(1,0) = (one_c * xy) + zs; 951f9ad8a790398513a845d486f58566854f7eceee4David Li M(1,1) = (one_c * yy) + c; 952f9ad8a790398513a845d486f58566854f7eceee4David Li M(1,2) = (one_c * yz) - xs; 953f9ad8a790398513a845d486f58566854f7eceee4David Li /* M(1,3) = 0.0F; */ 954f9ad8a790398513a845d486f58566854f7eceee4David Li 955f9ad8a790398513a845d486f58566854f7eceee4David Li M(2,0) = (one_c * zx) - ys; 956f9ad8a790398513a845d486f58566854f7eceee4David Li M(2,1) = (one_c * yz) + xs; 957f9ad8a790398513a845d486f58566854f7eceee4David Li M(2,2) = (one_c * zz) + c; 958f9ad8a790398513a845d486f58566854f7eceee4David Li /* M(2,3) = 0.0F; */ 959f9ad8a790398513a845d486f58566854f7eceee4David Li 960f9ad8a790398513a845d486f58566854f7eceee4David Li /* 961f9ad8a790398513a845d486f58566854f7eceee4David Li M(3,0) = 0.0F; 962f9ad8a790398513a845d486f58566854f7eceee4David Li M(3,1) = 0.0F; 963f9ad8a790398513a845d486f58566854f7eceee4David Li M(3,2) = 0.0F; 964f9ad8a790398513a845d486f58566854f7eceee4David Li M(3,3) = 1.0F; 965f9ad8a790398513a845d486f58566854f7eceee4David Li */ 966f9ad8a790398513a845d486f58566854f7eceee4David Li } 967f9ad8a790398513a845d486f58566854f7eceee4David Li#undef M 968f9ad8a790398513a845d486f58566854f7eceee4David Li 969f9ad8a790398513a845d486f58566854f7eceee4David Li matrix_multf( mat, m, MAT_FLAG_ROTATION ); 970f9ad8a790398513a845d486f58566854f7eceee4David Li} 971f9ad8a790398513a845d486f58566854f7eceee4David Li 972f9ad8a790398513a845d486f58566854f7eceee4David Li/** 973f9ad8a790398513a845d486f58566854f7eceee4David Li * Apply a perspective projection matrix. 974f9ad8a790398513a845d486f58566854f7eceee4David Li * 975f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat matrix to apply the projection. 976f9ad8a790398513a845d486f58566854f7eceee4David Li * \param left left clipping plane coordinate. 977f9ad8a790398513a845d486f58566854f7eceee4David Li * \param right right clipping plane coordinate. 978f9ad8a790398513a845d486f58566854f7eceee4David Li * \param bottom bottom clipping plane coordinate. 979f9ad8a790398513a845d486f58566854f7eceee4David Li * \param top top clipping plane coordinate. 980f9ad8a790398513a845d486f58566854f7eceee4David Li * \param nearval distance to the near clipping plane. 981f9ad8a790398513a845d486f58566854f7eceee4David Li * \param farval distance to the far clipping plane. 982f9ad8a790398513a845d486f58566854f7eceee4David Li * 983f9ad8a790398513a845d486f58566854f7eceee4David Li * Creates the projection matrix and multiplies it with \p mat, marking the 984f9ad8a790398513a845d486f58566854f7eceee4David Li * MAT_FLAG_PERSPECTIVE flag. 985f9ad8a790398513a845d486f58566854f7eceee4David Li */ 986f9ad8a790398513a845d486f58566854f7eceee4David Livoid 987f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_frustum( GLmatrix *mat, 988f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat left, GLfloat right, 989f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat bottom, GLfloat top, 990f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat nearval, GLfloat farval ) 991f9ad8a790398513a845d486f58566854f7eceee4David Li{ 992f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat x, y, a, b, c, d; 993f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat m[16]; 994f9ad8a790398513a845d486f58566854f7eceee4David Li 995f9ad8a790398513a845d486f58566854f7eceee4David Li x = (2.0F*nearval) / (right-left); 996f9ad8a790398513a845d486f58566854f7eceee4David Li y = (2.0F*nearval) / (top-bottom); 997f9ad8a790398513a845d486f58566854f7eceee4David Li a = (right+left) / (right-left); 998f9ad8a790398513a845d486f58566854f7eceee4David Li b = (top+bottom) / (top-bottom); 999f9ad8a790398513a845d486f58566854f7eceee4David Li c = -(farval+nearval) / ( farval-nearval); 1000f9ad8a790398513a845d486f58566854f7eceee4David Li d = -(2.0F*farval*nearval) / (farval-nearval); /* error? */ 1001f9ad8a790398513a845d486f58566854f7eceee4David Li 1002f9ad8a790398513a845d486f58566854f7eceee4David Li if (0) 1003f9ad8a790398513a845d486f58566854f7eceee4David Li { 1004f9ad8a790398513a845d486f58566854f7eceee4David Li c /= farval; // linearize z in vs by gl_Position.z *= gl_Position.w 1005f9ad8a790398513a845d486f58566854f7eceee4David Li d /= farval; 1006f9ad8a790398513a845d486f58566854f7eceee4David Li } 1007f9ad8a790398513a845d486f58566854f7eceee4David Li 1008f9ad8a790398513a845d486f58566854f7eceee4David Li#define M(row,col) m[col*4+row] 1009f9ad8a790398513a845d486f58566854f7eceee4David Li M(0,0) = x; M(0,1) = 0.0F; M(0,2) = a; M(0,3) = 0.0F; 1010f9ad8a790398513a845d486f58566854f7eceee4David Li M(1,0) = 0.0F; M(1,1) = y; M(1,2) = b; M(1,3) = 0.0F; 1011f9ad8a790398513a845d486f58566854f7eceee4David Li M(2,0) = 0.0F; M(2,1) = 0.0F; M(2,2) = c; M(2,3) = d; 1012f9ad8a790398513a845d486f58566854f7eceee4David Li M(3,0) = 0.0F; M(3,1) = 0.0F; M(3,2) = -1.0F; M(3,3) = 0.0F; 1013f9ad8a790398513a845d486f58566854f7eceee4David Li#undef M 1014f9ad8a790398513a845d486f58566854f7eceee4David Li 1015f9ad8a790398513a845d486f58566854f7eceee4David Li matrix_multf( mat, m, MAT_FLAG_PERSPECTIVE ); 1016f9ad8a790398513a845d486f58566854f7eceee4David Li} 1017f9ad8a790398513a845d486f58566854f7eceee4David Li 1018f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1019f9ad8a790398513a845d486f58566854f7eceee4David Li * Apply an orthographic projection matrix. 1020f9ad8a790398513a845d486f58566854f7eceee4David Li * 1021f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat matrix to apply the projection. 1022f9ad8a790398513a845d486f58566854f7eceee4David Li * \param left left clipping plane coordinate. 1023f9ad8a790398513a845d486f58566854f7eceee4David Li * \param right right clipping plane coordinate. 1024f9ad8a790398513a845d486f58566854f7eceee4David Li * \param bottom bottom clipping plane coordinate. 1025f9ad8a790398513a845d486f58566854f7eceee4David Li * \param top top clipping plane coordinate. 1026f9ad8a790398513a845d486f58566854f7eceee4David Li * \param nearval distance to the near clipping plane. 1027f9ad8a790398513a845d486f58566854f7eceee4David Li * \param farval distance to the far clipping plane. 1028f9ad8a790398513a845d486f58566854f7eceee4David Li * 1029f9ad8a790398513a845d486f58566854f7eceee4David Li * Creates the projection matrix and multiplies it with \p mat, marking the 1030f9ad8a790398513a845d486f58566854f7eceee4David Li * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags. 1031f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1032f9ad8a790398513a845d486f58566854f7eceee4David Livoid 1033f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_ortho( GLmatrix *mat, 1034f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat left, GLfloat right, 1035f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat bottom, GLfloat top, 1036f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat nearval, GLfloat farval ) 1037f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1038f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat m[16]; 1039f9ad8a790398513a845d486f58566854f7eceee4David Li 1040f9ad8a790398513a845d486f58566854f7eceee4David Li#define M(row,col) m[col*4+row] 1041f9ad8a790398513a845d486f58566854f7eceee4David Li M(0,0) = 2.0F / (right-left); 1042f9ad8a790398513a845d486f58566854f7eceee4David Li M(0,1) = 0.0F; 1043f9ad8a790398513a845d486f58566854f7eceee4David Li M(0,2) = 0.0F; 1044f9ad8a790398513a845d486f58566854f7eceee4David Li M(0,3) = -(right+left) / (right-left); 1045f9ad8a790398513a845d486f58566854f7eceee4David Li 1046f9ad8a790398513a845d486f58566854f7eceee4David Li M(1,0) = 0.0F; 1047f9ad8a790398513a845d486f58566854f7eceee4David Li M(1,1) = 2.0F / (top-bottom); 1048f9ad8a790398513a845d486f58566854f7eceee4David Li M(1,2) = 0.0F; 1049f9ad8a790398513a845d486f58566854f7eceee4David Li M(1,3) = -(top+bottom) / (top-bottom); 1050f9ad8a790398513a845d486f58566854f7eceee4David Li 1051f9ad8a790398513a845d486f58566854f7eceee4David Li M(2,0) = 0.0F; 1052f9ad8a790398513a845d486f58566854f7eceee4David Li M(2,1) = 0.0F; 1053f9ad8a790398513a845d486f58566854f7eceee4David Li M(2,2) = -2.0F / (farval-nearval); 1054f9ad8a790398513a845d486f58566854f7eceee4David Li M(2,3) = -(farval+nearval) / (farval-nearval); 1055f9ad8a790398513a845d486f58566854f7eceee4David Li 1056f9ad8a790398513a845d486f58566854f7eceee4David Li M(3,0) = 0.0F; 1057f9ad8a790398513a845d486f58566854f7eceee4David Li M(3,1) = 0.0F; 1058f9ad8a790398513a845d486f58566854f7eceee4David Li M(3,2) = 0.0F; 1059f9ad8a790398513a845d486f58566854f7eceee4David Li M(3,3) = 1.0F; 1060f9ad8a790398513a845d486f58566854f7eceee4David Li#undef M 1061f9ad8a790398513a845d486f58566854f7eceee4David Li 1062f9ad8a790398513a845d486f58566854f7eceee4David Li matrix_multf( mat, m, (MAT_FLAG_GENERAL_SCALE|MAT_FLAG_TRANSLATION)); 1063f9ad8a790398513a845d486f58566854f7eceee4David Li} 1064f9ad8a790398513a845d486f58566854f7eceee4David Li 1065f9ad8a790398513a845d486f58566854f7eceee4David Li// multiplies mat by a perspective transform matrix 1066f9ad8a790398513a845d486f58566854f7eceee4David Livoid _math_matrix_perspective(GLmatrix * mat, GLfloat fovy, GLfloat aspect, 1067f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat zNear, GLfloat zFar) 1068f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1069f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat xmin, xmax, ymin, ymax; 1070f9ad8a790398513a845d486f58566854f7eceee4David Li 1071f9ad8a790398513a845d486f58566854f7eceee4David Li ymax = zNear * tan(fovy * M_PI / 360.0); 1072f9ad8a790398513a845d486f58566854f7eceee4David Li ymin = -ymax; 1073f9ad8a790398513a845d486f58566854f7eceee4David Li xmin = ymin * aspect; 1074f9ad8a790398513a845d486f58566854f7eceee4David Li xmax = ymax * aspect; 1075f9ad8a790398513a845d486f58566854f7eceee4David Li 1076f9ad8a790398513a845d486f58566854f7eceee4David Li _math_matrix_frustum(mat, xmin, xmax, ymin, ymax, zNear, zFar); 1077f9ad8a790398513a845d486f58566854f7eceee4David Li} 1078f9ad8a790398513a845d486f58566854f7eceee4David Li 1079f9ad8a790398513a845d486f58566854f7eceee4David Li// multiplies mat by a look at matrix 1080f9ad8a790398513a845d486f58566854f7eceee4David Livoid _math_matrix_lookat(GLmatrix * mat, GLfloat eyex, GLfloat eyey, GLfloat eyez, 1081f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat centerx, GLfloat centery, GLfloat centerz, 1082f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat upx, GLfloat upy, GLfloat upz) 1083f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1084f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat m[16]; 1085f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat x[3], y[3], z[3]; 1086f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat mag; 1087f9ad8a790398513a845d486f58566854f7eceee4David Li 1088f9ad8a790398513a845d486f58566854f7eceee4David Li /* Make rotation matrix */ 1089f9ad8a790398513a845d486f58566854f7eceee4David Li 1090f9ad8a790398513a845d486f58566854f7eceee4David Li /* Z vector */ 1091f9ad8a790398513a845d486f58566854f7eceee4David Li z[0] = eyex - centerx; 1092f9ad8a790398513a845d486f58566854f7eceee4David Li z[1] = eyey - centery; 1093f9ad8a790398513a845d486f58566854f7eceee4David Li z[2] = eyez - centerz; 1094f9ad8a790398513a845d486f58566854f7eceee4David Li mag = sqrt(z[0] * z[0] + z[1] * z[1] + z[2] * z[2]); 1095f9ad8a790398513a845d486f58566854f7eceee4David Li if (mag) { /* mpichler, 19950515 */ 1096f9ad8a790398513a845d486f58566854f7eceee4David Li z[0] /= mag; 1097f9ad8a790398513a845d486f58566854f7eceee4David Li z[1] /= mag; 1098f9ad8a790398513a845d486f58566854f7eceee4David Li z[2] /= mag; 1099f9ad8a790398513a845d486f58566854f7eceee4David Li } 1100f9ad8a790398513a845d486f58566854f7eceee4David Li 1101f9ad8a790398513a845d486f58566854f7eceee4David Li /* Y vector */ 1102f9ad8a790398513a845d486f58566854f7eceee4David Li y[0] = upx; 1103f9ad8a790398513a845d486f58566854f7eceee4David Li y[1] = upy; 1104f9ad8a790398513a845d486f58566854f7eceee4David Li y[2] = upz; 1105f9ad8a790398513a845d486f58566854f7eceee4David Li 1106f9ad8a790398513a845d486f58566854f7eceee4David Li /* X vector = Y cross Z */ 1107f9ad8a790398513a845d486f58566854f7eceee4David Li x[0] = y[1] * z[2] - y[2] * z[1]; 1108f9ad8a790398513a845d486f58566854f7eceee4David Li x[1] = -y[0] * z[2] + y[2] * z[0]; 1109f9ad8a790398513a845d486f58566854f7eceee4David Li x[2] = y[0] * z[1] - y[1] * z[0]; 1110f9ad8a790398513a845d486f58566854f7eceee4David Li 1111f9ad8a790398513a845d486f58566854f7eceee4David Li /* Recompute Y = Z cross X */ 1112f9ad8a790398513a845d486f58566854f7eceee4David Li y[0] = z[1] * x[2] - z[2] * x[1]; 1113f9ad8a790398513a845d486f58566854f7eceee4David Li y[1] = -z[0] * x[2] + z[2] * x[0]; 1114f9ad8a790398513a845d486f58566854f7eceee4David Li y[2] = z[0] * x[1] - z[1] * x[0]; 1115f9ad8a790398513a845d486f58566854f7eceee4David Li 1116f9ad8a790398513a845d486f58566854f7eceee4David Li /* mpichler, 19950515 */ 1117f9ad8a790398513a845d486f58566854f7eceee4David Li /* cross product gives area of parallelogram, which is < 1.0 for 1118f9ad8a790398513a845d486f58566854f7eceee4David Li * non-perpendicular unit-length vectors; so normalize x, y here 1119f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1120f9ad8a790398513a845d486f58566854f7eceee4David Li 1121f9ad8a790398513a845d486f58566854f7eceee4David Li mag = sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]); 1122f9ad8a790398513a845d486f58566854f7eceee4David Li if (mag) { 1123f9ad8a790398513a845d486f58566854f7eceee4David Li x[0] /= mag; 1124f9ad8a790398513a845d486f58566854f7eceee4David Li x[1] /= mag; 1125f9ad8a790398513a845d486f58566854f7eceee4David Li x[2] /= mag; 1126f9ad8a790398513a845d486f58566854f7eceee4David Li } 1127f9ad8a790398513a845d486f58566854f7eceee4David Li 1128f9ad8a790398513a845d486f58566854f7eceee4David Li mag = sqrt(y[0] * y[0] + y[1] * y[1] + y[2] * y[2]); 1129f9ad8a790398513a845d486f58566854f7eceee4David Li if (mag) { 1130f9ad8a790398513a845d486f58566854f7eceee4David Li y[0] /= mag; 1131f9ad8a790398513a845d486f58566854f7eceee4David Li y[1] /= mag; 1132f9ad8a790398513a845d486f58566854f7eceee4David Li y[2] /= mag; 1133f9ad8a790398513a845d486f58566854f7eceee4David Li } 1134f9ad8a790398513a845d486f58566854f7eceee4David Li 1135f9ad8a790398513a845d486f58566854f7eceee4David Li#define M(row,col) m[col*4+row] 1136f9ad8a790398513a845d486f58566854f7eceee4David Li M(0, 0) = x[0]; 1137f9ad8a790398513a845d486f58566854f7eceee4David Li M(0, 1) = x[1]; 1138f9ad8a790398513a845d486f58566854f7eceee4David Li M(0, 2) = x[2]; 1139f9ad8a790398513a845d486f58566854f7eceee4David Li M(0, 3) = 0.0; 1140f9ad8a790398513a845d486f58566854f7eceee4David Li M(1, 0) = y[0]; 1141f9ad8a790398513a845d486f58566854f7eceee4David Li M(1, 1) = y[1]; 1142f9ad8a790398513a845d486f58566854f7eceee4David Li M(1, 2) = y[2]; 1143f9ad8a790398513a845d486f58566854f7eceee4David Li M(1, 3) = 0.0; 1144f9ad8a790398513a845d486f58566854f7eceee4David Li M(2, 0) = z[0]; 1145f9ad8a790398513a845d486f58566854f7eceee4David Li M(2, 1) = z[1]; 1146f9ad8a790398513a845d486f58566854f7eceee4David Li M(2, 2) = z[2]; 1147f9ad8a790398513a845d486f58566854f7eceee4David Li M(2, 3) = 0.0; 1148f9ad8a790398513a845d486f58566854f7eceee4David Li M(3, 0) = 0.0; 1149f9ad8a790398513a845d486f58566854f7eceee4David Li M(3, 1) = 0.0; 1150f9ad8a790398513a845d486f58566854f7eceee4David Li M(3, 2) = 0.0; 1151f9ad8a790398513a845d486f58566854f7eceee4David Li M(3, 3) = 1.0; 1152f9ad8a790398513a845d486f58566854f7eceee4David Li#undef M 1153f9ad8a790398513a845d486f58566854f7eceee4David Li 1154f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat translate[16] = 1155f9ad8a790398513a845d486f58566854f7eceee4David Li { 1156f9ad8a790398513a845d486f58566854f7eceee4David Li 1, 0, 0, 0, 1157f9ad8a790398513a845d486f58566854f7eceee4David Li 0, 1, 0, 0, 1158f9ad8a790398513a845d486f58566854f7eceee4David Li 0, 0, 1, 0, 1159f9ad8a790398513a845d486f58566854f7eceee4David Li -eyex, -eyey, -eyez, 1, 1160f9ad8a790398513a845d486f58566854f7eceee4David Li }; 1161f9ad8a790398513a845d486f58566854f7eceee4David Li 1162f9ad8a790398513a845d486f58566854f7eceee4David Li _math_matrix_mul_floats(mat, m); 1163f9ad8a790398513a845d486f58566854f7eceee4David Li 1164f9ad8a790398513a845d486f58566854f7eceee4David Li _math_matrix_mul_floats(mat, translate); 1165f9ad8a790398513a845d486f58566854f7eceee4David Li 1166f9ad8a790398513a845d486f58566854f7eceee4David Li /* Translate Eye to Origin */ 1167f9ad8a790398513a845d486f58566854f7eceee4David Li // glTranslated(-eyex, -eyey, -eyez); 1168f9ad8a790398513a845d486f58566854f7eceee4David Li 1169f9ad8a790398513a845d486f58566854f7eceee4David Li} 1170f9ad8a790398513a845d486f58566854f7eceee4David Li 1171f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1172f9ad8a790398513a845d486f58566854f7eceee4David Li * Multiply a matrix with a general scaling matrix. 1173f9ad8a790398513a845d486f58566854f7eceee4David Li * 1174f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat matrix. 1175f9ad8a790398513a845d486f58566854f7eceee4David Li * \param x x axis scale factor. 1176f9ad8a790398513a845d486f58566854f7eceee4David Li * \param y y axis scale factor. 1177f9ad8a790398513a845d486f58566854f7eceee4David Li * \param z z axis scale factor. 1178f9ad8a790398513a845d486f58566854f7eceee4David Li * 1179f9ad8a790398513a845d486f58566854f7eceee4David Li * Multiplies in-place the elements of \p mat by the scale factors. Checks if 1180f9ad8a790398513a845d486f58566854f7eceee4David Li * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE 1181f9ad8a790398513a845d486f58566854f7eceee4David Li * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and 1182f9ad8a790398513a845d486f58566854f7eceee4David Li * MAT_DIRTY_INVERSE dirty flags. 1183f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1184f9ad8a790398513a845d486f58566854f7eceee4David Livoid 1185f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_scale( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z ) 1186f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1187f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat *m = mat->m; 1188f9ad8a790398513a845d486f58566854f7eceee4David Li m[0] *= x; m[4] *= y; m[8] *= z; 1189f9ad8a790398513a845d486f58566854f7eceee4David Li m[1] *= x; m[5] *= y; m[9] *= z; 1190f9ad8a790398513a845d486f58566854f7eceee4David Li m[2] *= x; m[6] *= y; m[10] *= z; 1191f9ad8a790398513a845d486f58566854f7eceee4David Li m[3] *= x; m[7] *= y; m[11] *= z; 1192f9ad8a790398513a845d486f58566854f7eceee4David Li 1193f9ad8a790398513a845d486f58566854f7eceee4David Li if (FABSF(x - y) < 1e-8 && FABSF(x - z) < 1e-8) 1194f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_UNIFORM_SCALE; 1195f9ad8a790398513a845d486f58566854f7eceee4David Li else 1196f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_GENERAL_SCALE; 1197f9ad8a790398513a845d486f58566854f7eceee4David Li 1198f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= (MAT_DIRTY_TYPE | 1199f9ad8a790398513a845d486f58566854f7eceee4David Li MAT_DIRTY_INVERSE); 1200f9ad8a790398513a845d486f58566854f7eceee4David Li} 1201f9ad8a790398513a845d486f58566854f7eceee4David Li 1202f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1203f9ad8a790398513a845d486f58566854f7eceee4David Li * Multiply a matrix with a translation matrix. 1204f9ad8a790398513a845d486f58566854f7eceee4David Li * 1205f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat matrix. 1206f9ad8a790398513a845d486f58566854f7eceee4David Li * \param x translation vector x coordinate. 1207f9ad8a790398513a845d486f58566854f7eceee4David Li * \param y translation vector y coordinate. 1208f9ad8a790398513a845d486f58566854f7eceee4David Li * \param z translation vector z coordinate. 1209f9ad8a790398513a845d486f58566854f7eceee4David Li * 1210f9ad8a790398513a845d486f58566854f7eceee4David Li * Adds the translation coordinates to the elements of \p mat in-place. Marks 1211f9ad8a790398513a845d486f58566854f7eceee4David Li * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE 1212f9ad8a790398513a845d486f58566854f7eceee4David Li * dirty flags. 1213f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1214f9ad8a790398513a845d486f58566854f7eceee4David Livoid 1215f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_translate( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z ) 1216f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1217f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat *m = mat->m; 1218f9ad8a790398513a845d486f58566854f7eceee4David Li m[12] = m[0] * x + m[4] * y + m[8] * z + m[12]; 1219f9ad8a790398513a845d486f58566854f7eceee4David Li m[13] = m[1] * x + m[5] * y + m[9] * z + m[13]; 1220f9ad8a790398513a845d486f58566854f7eceee4David Li m[14] = m[2] * x + m[6] * y + m[10] * z + m[14]; 1221f9ad8a790398513a845d486f58566854f7eceee4David Li m[15] = m[3] * x + m[7] * y + m[11] * z + m[15]; 1222f9ad8a790398513a845d486f58566854f7eceee4David Li 1223f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= (MAT_FLAG_TRANSLATION | 1224f9ad8a790398513a845d486f58566854f7eceee4David Li MAT_DIRTY_TYPE | 1225f9ad8a790398513a845d486f58566854f7eceee4David Li MAT_DIRTY_INVERSE); 1226f9ad8a790398513a845d486f58566854f7eceee4David Li} 1227f9ad8a790398513a845d486f58566854f7eceee4David Li 1228f9ad8a790398513a845d486f58566854f7eceee4David Li 1229f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1230f9ad8a790398513a845d486f58566854f7eceee4David Li * Set matrix to do viewport and depthrange mapping. 1231f9ad8a790398513a845d486f58566854f7eceee4David Li * Transforms Normalized Device Coords to window/Z values. 1232f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1233f9ad8a790398513a845d486f58566854f7eceee4David Livoid 1234f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_viewport(GLmatrix *m, GLint x, GLint y, GLint width, GLint height, 1235f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat zNear, GLfloat zFar, GLfloat depthMax) 1236f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1237f9ad8a790398513a845d486f58566854f7eceee4David Li m->m[MAT_SX] = (GLfloat) width / 2.0F; 1238f9ad8a790398513a845d486f58566854f7eceee4David Li m->m[MAT_TX] = m->m[MAT_SX] + x; 1239f9ad8a790398513a845d486f58566854f7eceee4David Li m->m[MAT_SY] = (GLfloat) height / 2.0F; 1240f9ad8a790398513a845d486f58566854f7eceee4David Li m->m[MAT_TY] = m->m[MAT_SY] + y; 1241f9ad8a790398513a845d486f58566854f7eceee4David Li m->m[MAT_SZ] = depthMax * ((zFar - zNear) / 2.0F); 1242f9ad8a790398513a845d486f58566854f7eceee4David Li m->m[MAT_TZ] = depthMax * ((zFar - zNear) / 2.0F + zNear); 1243f9ad8a790398513a845d486f58566854f7eceee4David Li m->flags = MAT_FLAG_GENERAL_SCALE | MAT_FLAG_TRANSLATION; 1244f9ad8a790398513a845d486f58566854f7eceee4David Li m->type = MATRIX_3D_NO_ROT; 1245f9ad8a790398513a845d486f58566854f7eceee4David Li} 1246f9ad8a790398513a845d486f58566854f7eceee4David Li 1247f9ad8a790398513a845d486f58566854f7eceee4David Li 1248f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1249f9ad8a790398513a845d486f58566854f7eceee4David Li * Set a matrix to the identity matrix. 1250f9ad8a790398513a845d486f58566854f7eceee4David Li * 1251f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat matrix. 1252f9ad8a790398513a845d486f58566854f7eceee4David Li * 1253f9ad8a790398513a845d486f58566854f7eceee4David Li * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL. 1254f9ad8a790398513a845d486f58566854f7eceee4David Li * Sets the matrix type to identity, and clear the dirty flags. 1255f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1256f9ad8a790398513a845d486f58566854f7eceee4David Livoid 1257f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_set_identity( GLmatrix *mat ) 1258f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1259f9ad8a790398513a845d486f58566854f7eceee4David Li memcpy( mat->m, Identity, 16*sizeof(GLfloat) ); 1260f9ad8a790398513a845d486f58566854f7eceee4David Li 1261f9ad8a790398513a845d486f58566854f7eceee4David Li if (mat->inv) 1262f9ad8a790398513a845d486f58566854f7eceee4David Li memcpy( mat->inv, Identity, 16*sizeof(GLfloat) ); 1263f9ad8a790398513a845d486f58566854f7eceee4David Li 1264f9ad8a790398513a845d486f58566854f7eceee4David Li mat->type = MATRIX_IDENTITY; 1265f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags &= ~(MAT_DIRTY_FLAGS| 1266f9ad8a790398513a845d486f58566854f7eceee4David Li MAT_DIRTY_TYPE| 1267f9ad8a790398513a845d486f58566854f7eceee4David Li MAT_DIRTY_INVERSE); 1268f9ad8a790398513a845d486f58566854f7eceee4David Li} 1269f9ad8a790398513a845d486f58566854f7eceee4David Li 1270f9ad8a790398513a845d486f58566854f7eceee4David Li/*@}*/ 1271f9ad8a790398513a845d486f58566854f7eceee4David Li 1272f9ad8a790398513a845d486f58566854f7eceee4David Li 1273f9ad8a790398513a845d486f58566854f7eceee4David Li/**********************************************************************/ 1274f9ad8a790398513a845d486f58566854f7eceee4David Li/** \name Matrix analysis */ 1275f9ad8a790398513a845d486f58566854f7eceee4David Li/*@{*/ 1276f9ad8a790398513a845d486f58566854f7eceee4David Li 1277f9ad8a790398513a845d486f58566854f7eceee4David Li#define ZERO(x) (1<<x) 1278f9ad8a790398513a845d486f58566854f7eceee4David Li#define ONE(x) (1<<(x+16)) 1279f9ad8a790398513a845d486f58566854f7eceee4David Li 1280f9ad8a790398513a845d486f58566854f7eceee4David Li#define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14)) 1281f9ad8a790398513a845d486f58566854f7eceee4David Li#define MASK_NO_2D_SCALE ( ONE(0) | ONE(5)) 1282f9ad8a790398513a845d486f58566854f7eceee4David Li 1283f9ad8a790398513a845d486f58566854f7eceee4David Li#define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\ 1284f9ad8a790398513a845d486f58566854f7eceee4David LiZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\ 1285f9ad8a790398513a845d486f58566854f7eceee4David LiZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ 1286f9ad8a790398513a845d486f58566854f7eceee4David LiZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1287f9ad8a790398513a845d486f58566854f7eceee4David Li 1288f9ad8a790398513a845d486f58566854f7eceee4David Li#define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \ 1289f9ad8a790398513a845d486f58566854f7eceee4David LiZERO(1) | ZERO(9) | \ 1290f9ad8a790398513a845d486f58566854f7eceee4David LiZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ 1291f9ad8a790398513a845d486f58566854f7eceee4David LiZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1292f9ad8a790398513a845d486f58566854f7eceee4David Li 1293f9ad8a790398513a845d486f58566854f7eceee4David Li#define MASK_2D ( ZERO(8) | \ 1294f9ad8a790398513a845d486f58566854f7eceee4David LiZERO(9) | \ 1295f9ad8a790398513a845d486f58566854f7eceee4David LiZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ 1296f9ad8a790398513a845d486f58566854f7eceee4David LiZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1297f9ad8a790398513a845d486f58566854f7eceee4David Li 1298f9ad8a790398513a845d486f58566854f7eceee4David Li 1299f9ad8a790398513a845d486f58566854f7eceee4David Li#define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \ 1300f9ad8a790398513a845d486f58566854f7eceee4David LiZERO(1) | ZERO(9) | \ 1301f9ad8a790398513a845d486f58566854f7eceee4David LiZERO(2) | ZERO(6) | \ 1302f9ad8a790398513a845d486f58566854f7eceee4David LiZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1303f9ad8a790398513a845d486f58566854f7eceee4David Li 1304f9ad8a790398513a845d486f58566854f7eceee4David Li#define MASK_3D ( \ 1305f9ad8a790398513a845d486f58566854f7eceee4David Li\ 1306f9ad8a790398513a845d486f58566854f7eceee4David Li\ 1307f9ad8a790398513a845d486f58566854f7eceee4David LiZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1308f9ad8a790398513a845d486f58566854f7eceee4David Li 1309f9ad8a790398513a845d486f58566854f7eceee4David Li 1310f9ad8a790398513a845d486f58566854f7eceee4David Li#define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\ 1311f9ad8a790398513a845d486f58566854f7eceee4David LiZERO(1) | ZERO(13) |\ 1312f9ad8a790398513a845d486f58566854f7eceee4David LiZERO(2) | ZERO(6) | \ 1313f9ad8a790398513a845d486f58566854f7eceee4David LiZERO(3) | ZERO(7) | ZERO(15) ) 1314f9ad8a790398513a845d486f58566854f7eceee4David Li 1315f9ad8a790398513a845d486f58566854f7eceee4David Li#define SQ(x) ((x)*(x)) 1316f9ad8a790398513a845d486f58566854f7eceee4David Li 1317f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1318f9ad8a790398513a845d486f58566854f7eceee4David Li * Determine type and flags from scratch. 1319f9ad8a790398513a845d486f58566854f7eceee4David Li * 1320f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat matrix. 1321f9ad8a790398513a845d486f58566854f7eceee4David Li * 1322f9ad8a790398513a845d486f58566854f7eceee4David Li * This is expensive enough to only want to do it once. 1323f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1324f9ad8a790398513a845d486f58566854f7eceee4David Listatic void analyse_from_scratch( GLmatrix *mat ) 1325f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1326f9ad8a790398513a845d486f58566854f7eceee4David Li const GLfloat *m = mat->m; 1327f9ad8a790398513a845d486f58566854f7eceee4David Li GLuint mask = 0; 1328f9ad8a790398513a845d486f58566854f7eceee4David Li GLuint i; 1329f9ad8a790398513a845d486f58566854f7eceee4David Li 1330f9ad8a790398513a845d486f58566854f7eceee4David Li for (i = 0 ; i < 16 ; i++) { 1331f9ad8a790398513a845d486f58566854f7eceee4David Li if (m[i] == 0.0) mask |= (1<<i); 1332f9ad8a790398513a845d486f58566854f7eceee4David Li } 1333f9ad8a790398513a845d486f58566854f7eceee4David Li 1334f9ad8a790398513a845d486f58566854f7eceee4David Li if (m[0] == 1.0F) mask |= (1<<16); 1335f9ad8a790398513a845d486f58566854f7eceee4David Li if (m[5] == 1.0F) mask |= (1<<21); 1336f9ad8a790398513a845d486f58566854f7eceee4David Li if (m[10] == 1.0F) mask |= (1<<26); 1337f9ad8a790398513a845d486f58566854f7eceee4David Li if (m[15] == 1.0F) mask |= (1<<31); 1338f9ad8a790398513a845d486f58566854f7eceee4David Li 1339f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags &= ~MAT_FLAGS_GEOMETRY; 1340f9ad8a790398513a845d486f58566854f7eceee4David Li 1341f9ad8a790398513a845d486f58566854f7eceee4David Li /* Check for translation - no-one really cares 1342f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1343f9ad8a790398513a845d486f58566854f7eceee4David Li if ((mask & MASK_NO_TRX) != MASK_NO_TRX) 1344f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_TRANSLATION; 1345f9ad8a790398513a845d486f58566854f7eceee4David Li 1346f9ad8a790398513a845d486f58566854f7eceee4David Li /* Do the real work 1347f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1348f9ad8a790398513a845d486f58566854f7eceee4David Li if (mask == (GLuint) MASK_IDENTITY) { 1349f9ad8a790398513a845d486f58566854f7eceee4David Li mat->type = MATRIX_IDENTITY; 1350f9ad8a790398513a845d486f58566854f7eceee4David Li } 1351f9ad8a790398513a845d486f58566854f7eceee4David Li else if ((mask & MASK_2D_NO_ROT) == (GLuint) MASK_2D_NO_ROT) { 1352f9ad8a790398513a845d486f58566854f7eceee4David Li mat->type = MATRIX_2D_NO_ROT; 1353f9ad8a790398513a845d486f58566854f7eceee4David Li 1354f9ad8a790398513a845d486f58566854f7eceee4David Li if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE) 1355f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_GENERAL_SCALE; 1356f9ad8a790398513a845d486f58566854f7eceee4David Li } 1357f9ad8a790398513a845d486f58566854f7eceee4David Li else if ((mask & MASK_2D) == (GLuint) MASK_2D) { 1358f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat mm = DOT2(m, m); 1359f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat m4m4 = DOT2(m+4,m+4); 1360f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat mm4 = DOT2(m,m+4); 1361f9ad8a790398513a845d486f58566854f7eceee4David Li 1362f9ad8a790398513a845d486f58566854f7eceee4David Li mat->type = MATRIX_2D; 1363f9ad8a790398513a845d486f58566854f7eceee4David Li 1364f9ad8a790398513a845d486f58566854f7eceee4David Li /* Check for scale */ 1365f9ad8a790398513a845d486f58566854f7eceee4David Li if (SQ(mm-1) > SQ(1e-6) || 1366f9ad8a790398513a845d486f58566854f7eceee4David Li SQ(m4m4-1) > SQ(1e-6)) 1367f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_GENERAL_SCALE; 1368f9ad8a790398513a845d486f58566854f7eceee4David Li 1369f9ad8a790398513a845d486f58566854f7eceee4David Li /* Check for rotation */ 1370f9ad8a790398513a845d486f58566854f7eceee4David Li if (SQ(mm4) > SQ(1e-6)) 1371f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_GENERAL_3D; 1372f9ad8a790398513a845d486f58566854f7eceee4David Li else 1373f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_ROTATION; 1374f9ad8a790398513a845d486f58566854f7eceee4David Li 1375f9ad8a790398513a845d486f58566854f7eceee4David Li } 1376f9ad8a790398513a845d486f58566854f7eceee4David Li else if ((mask & MASK_3D_NO_ROT) == (GLuint) MASK_3D_NO_ROT) { 1377f9ad8a790398513a845d486f58566854f7eceee4David Li mat->type = MATRIX_3D_NO_ROT; 1378f9ad8a790398513a845d486f58566854f7eceee4David Li 1379f9ad8a790398513a845d486f58566854f7eceee4David Li /* Check for scale */ 1380f9ad8a790398513a845d486f58566854f7eceee4David Li if (SQ(m[0]-m[5]) < SQ(1e-6) && 1381f9ad8a790398513a845d486f58566854f7eceee4David Li SQ(m[0]-m[10]) < SQ(1e-6)) { 1382f9ad8a790398513a845d486f58566854f7eceee4David Li if (SQ(m[0]-1.0) > SQ(1e-6)) { 1383f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_UNIFORM_SCALE; 1384f9ad8a790398513a845d486f58566854f7eceee4David Li } 1385f9ad8a790398513a845d486f58566854f7eceee4David Li } 1386f9ad8a790398513a845d486f58566854f7eceee4David Li else { 1387f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_GENERAL_SCALE; 1388f9ad8a790398513a845d486f58566854f7eceee4David Li } 1389f9ad8a790398513a845d486f58566854f7eceee4David Li } 1390f9ad8a790398513a845d486f58566854f7eceee4David Li else if ((mask & MASK_3D) == (GLuint) MASK_3D) { 1391f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat c1 = DOT3(m,m); 1392f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat c2 = DOT3(m+4,m+4); 1393f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat c3 = DOT3(m+8,m+8); 1394f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat d1 = DOT3(m, m+4); 1395f9ad8a790398513a845d486f58566854f7eceee4David Li GLfloat cp[3]; 1396f9ad8a790398513a845d486f58566854f7eceee4David Li 1397f9ad8a790398513a845d486f58566854f7eceee4David Li mat->type = MATRIX_3D; 1398f9ad8a790398513a845d486f58566854f7eceee4David Li 1399f9ad8a790398513a845d486f58566854f7eceee4David Li /* Check for scale */ 1400f9ad8a790398513a845d486f58566854f7eceee4David Li if (SQ(c1-c2) < SQ(1e-6) && SQ(c1-c3) < SQ(1e-6)) { 1401f9ad8a790398513a845d486f58566854f7eceee4David Li if (SQ(c1-1.0) > SQ(1e-6)) 1402f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_UNIFORM_SCALE; 1403f9ad8a790398513a845d486f58566854f7eceee4David Li /* else no scale at all */ 1404f9ad8a790398513a845d486f58566854f7eceee4David Li } 1405f9ad8a790398513a845d486f58566854f7eceee4David Li else { 1406f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_GENERAL_SCALE; 1407f9ad8a790398513a845d486f58566854f7eceee4David Li } 1408f9ad8a790398513a845d486f58566854f7eceee4David Li 1409f9ad8a790398513a845d486f58566854f7eceee4David Li /* Check for rotation */ 1410f9ad8a790398513a845d486f58566854f7eceee4David Li if (SQ(d1) < SQ(1e-6)) { 1411f9ad8a790398513a845d486f58566854f7eceee4David Li CROSS3( cp, m, m+4 ); 1412f9ad8a790398513a845d486f58566854f7eceee4David Li SUB_3V( cp, cp, (m+8) ); 1413f9ad8a790398513a845d486f58566854f7eceee4David Li if (LEN_SQUARED_3FV(cp) < SQ(1e-6)) 1414f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_ROTATION; 1415f9ad8a790398513a845d486f58566854f7eceee4David Li else 1416f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_GENERAL_3D; 1417f9ad8a790398513a845d486f58566854f7eceee4David Li } 1418f9ad8a790398513a845d486f58566854f7eceee4David Li else { 1419f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */ 1420f9ad8a790398513a845d486f58566854f7eceee4David Li } 1421f9ad8a790398513a845d486f58566854f7eceee4David Li } 1422f9ad8a790398513a845d486f58566854f7eceee4David Li else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0F) { 1423f9ad8a790398513a845d486f58566854f7eceee4David Li mat->type = MATRIX_PERSPECTIVE; 1424f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_GENERAL; 1425f9ad8a790398513a845d486f58566854f7eceee4David Li } 1426f9ad8a790398513a845d486f58566854f7eceee4David Li else { 1427f9ad8a790398513a845d486f58566854f7eceee4David Li mat->type = MATRIX_GENERAL; 1428f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags |= MAT_FLAG_GENERAL; 1429f9ad8a790398513a845d486f58566854f7eceee4David Li } 1430f9ad8a790398513a845d486f58566854f7eceee4David Li} 1431f9ad8a790398513a845d486f58566854f7eceee4David Li 1432f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1433f9ad8a790398513a845d486f58566854f7eceee4David Li * Analyze a matrix given that its flags are accurate. 1434f9ad8a790398513a845d486f58566854f7eceee4David Li * 1435f9ad8a790398513a845d486f58566854f7eceee4David Li * This is the more common operation, hopefully. 1436f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1437f9ad8a790398513a845d486f58566854f7eceee4David Listatic void analyse_from_flags( GLmatrix *mat ) 1438f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1439f9ad8a790398513a845d486f58566854f7eceee4David Li const GLfloat *m = mat->m; 1440f9ad8a790398513a845d486f58566854f7eceee4David Li 1441f9ad8a790398513a845d486f58566854f7eceee4David Li if (TEST_MAT_FLAGS(mat, 0)) { 1442f9ad8a790398513a845d486f58566854f7eceee4David Li mat->type = MATRIX_IDENTITY; 1443f9ad8a790398513a845d486f58566854f7eceee4David Li } 1444f9ad8a790398513a845d486f58566854f7eceee4David Li else if (TEST_MAT_FLAGS(mat, (MAT_FLAG_TRANSLATION | 1445f9ad8a790398513a845d486f58566854f7eceee4David Li MAT_FLAG_UNIFORM_SCALE | 1446f9ad8a790398513a845d486f58566854f7eceee4David Li MAT_FLAG_GENERAL_SCALE))) { 1447f9ad8a790398513a845d486f58566854f7eceee4David Li if ( m[10]==1.0F && m[14]==0.0F ) { 1448f9ad8a790398513a845d486f58566854f7eceee4David Li mat->type = MATRIX_2D_NO_ROT; 1449f9ad8a790398513a845d486f58566854f7eceee4David Li } 1450f9ad8a790398513a845d486f58566854f7eceee4David Li else { 1451f9ad8a790398513a845d486f58566854f7eceee4David Li mat->type = MATRIX_3D_NO_ROT; 1452f9ad8a790398513a845d486f58566854f7eceee4David Li } 1453f9ad8a790398513a845d486f58566854f7eceee4David Li } 1454f9ad8a790398513a845d486f58566854f7eceee4David Li else if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) { 1455f9ad8a790398513a845d486f58566854f7eceee4David Li if ( m[ 8]==0.0F 1456f9ad8a790398513a845d486f58566854f7eceee4David Li && m[ 9]==0.0F 1457f9ad8a790398513a845d486f58566854f7eceee4David Li && m[2]==0.0F && m[6]==0.0F && m[10]==1.0F && m[14]==0.0F) { 1458f9ad8a790398513a845d486f58566854f7eceee4David Li mat->type = MATRIX_2D; 1459f9ad8a790398513a845d486f58566854f7eceee4David Li } 1460f9ad8a790398513a845d486f58566854f7eceee4David Li else { 1461f9ad8a790398513a845d486f58566854f7eceee4David Li mat->type = MATRIX_3D; 1462f9ad8a790398513a845d486f58566854f7eceee4David Li } 1463f9ad8a790398513a845d486f58566854f7eceee4David Li } 1464f9ad8a790398513a845d486f58566854f7eceee4David Li else if ( m[4]==0.0F && m[12]==0.0F 1465f9ad8a790398513a845d486f58566854f7eceee4David Li && m[1]==0.0F && m[13]==0.0F 1466f9ad8a790398513a845d486f58566854f7eceee4David Li && m[2]==0.0F && m[6]==0.0F 1467f9ad8a790398513a845d486f58566854f7eceee4David Li && m[3]==0.0F && m[7]==0.0F && m[11]==-1.0F && m[15]==0.0F) { 1468f9ad8a790398513a845d486f58566854f7eceee4David Li mat->type = MATRIX_PERSPECTIVE; 1469f9ad8a790398513a845d486f58566854f7eceee4David Li } 1470f9ad8a790398513a845d486f58566854f7eceee4David Li else { 1471f9ad8a790398513a845d486f58566854f7eceee4David Li mat->type = MATRIX_GENERAL; 1472f9ad8a790398513a845d486f58566854f7eceee4David Li } 1473f9ad8a790398513a845d486f58566854f7eceee4David Li} 1474f9ad8a790398513a845d486f58566854f7eceee4David Li 1475f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1476f9ad8a790398513a845d486f58566854f7eceee4David Li * Analyze and update a matrix. 1477f9ad8a790398513a845d486f58566854f7eceee4David Li * 1478f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat matrix. 1479f9ad8a790398513a845d486f58566854f7eceee4David Li * 1480f9ad8a790398513a845d486f58566854f7eceee4David Li * If the matrix type is dirty then calls either analyse_from_scratch() or 1481f9ad8a790398513a845d486f58566854f7eceee4David Li * analyse_from_flags() to determine its type, according to whether the flags 1482f9ad8a790398513a845d486f58566854f7eceee4David Li * are dirty or not, respectively. If the matrix has an inverse and it's dirty 1483f9ad8a790398513a845d486f58566854f7eceee4David Li * then calls matrix_invert(). Finally clears the dirty flags. 1484f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1485f9ad8a790398513a845d486f58566854f7eceee4David Livoid 1486f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_analyse( GLmatrix *mat ) 1487f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1488f9ad8a790398513a845d486f58566854f7eceee4David Li if (mat->flags & MAT_DIRTY_TYPE) { 1489f9ad8a790398513a845d486f58566854f7eceee4David Li if (mat->flags & MAT_DIRTY_FLAGS) 1490f9ad8a790398513a845d486f58566854f7eceee4David Li analyse_from_scratch( mat ); 1491f9ad8a790398513a845d486f58566854f7eceee4David Li else 1492f9ad8a790398513a845d486f58566854f7eceee4David Li analyse_from_flags( mat ); 1493f9ad8a790398513a845d486f58566854f7eceee4David Li } 1494f9ad8a790398513a845d486f58566854f7eceee4David Li 1495f9ad8a790398513a845d486f58566854f7eceee4David Li if (mat->inv && (mat->flags & MAT_DIRTY_INVERSE)) { 1496f9ad8a790398513a845d486f58566854f7eceee4David Li matrix_invert( mat ); 1497f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags &= ~MAT_DIRTY_INVERSE; 1498f9ad8a790398513a845d486f58566854f7eceee4David Li } 1499f9ad8a790398513a845d486f58566854f7eceee4David Li 1500f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags &= ~(MAT_DIRTY_FLAGS | MAT_DIRTY_TYPE); 1501f9ad8a790398513a845d486f58566854f7eceee4David Li} 1502f9ad8a790398513a845d486f58566854f7eceee4David Li 1503f9ad8a790398513a845d486f58566854f7eceee4David Li/*@}*/ 1504f9ad8a790398513a845d486f58566854f7eceee4David Li 1505f9ad8a790398513a845d486f58566854f7eceee4David Li 1506f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1507f9ad8a790398513a845d486f58566854f7eceee4David Li * Test if the given matrix preserves vector lengths. 1508f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1509f9ad8a790398513a845d486f58566854f7eceee4David LiGLboolean 1510f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_is_length_preserving( const GLmatrix *m ) 1511f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1512f9ad8a790398513a845d486f58566854f7eceee4David Li return TEST_MAT_FLAGS( m, MAT_FLAGS_LENGTH_PRESERVING); 1513f9ad8a790398513a845d486f58566854f7eceee4David Li} 1514f9ad8a790398513a845d486f58566854f7eceee4David Li 1515f9ad8a790398513a845d486f58566854f7eceee4David Li 1516f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1517f9ad8a790398513a845d486f58566854f7eceee4David Li * Test if the given matrix does any rotation. 1518f9ad8a790398513a845d486f58566854f7eceee4David Li * (or perhaps if the upper-left 3x3 is non-identity) 1519f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1520f9ad8a790398513a845d486f58566854f7eceee4David LiGLboolean 1521f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_has_rotation( const GLmatrix *m ) 1522f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1523f9ad8a790398513a845d486f58566854f7eceee4David Li if (m->flags & (MAT_FLAG_GENERAL | 1524f9ad8a790398513a845d486f58566854f7eceee4David Li MAT_FLAG_ROTATION | 1525f9ad8a790398513a845d486f58566854f7eceee4David Li MAT_FLAG_GENERAL_3D | 1526f9ad8a790398513a845d486f58566854f7eceee4David Li MAT_FLAG_PERSPECTIVE)) 1527f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_TRUE; 1528f9ad8a790398513a845d486f58566854f7eceee4David Li else 1529f9ad8a790398513a845d486f58566854f7eceee4David Li return GL_FALSE; 1530f9ad8a790398513a845d486f58566854f7eceee4David Li} 1531f9ad8a790398513a845d486f58566854f7eceee4David Li 1532f9ad8a790398513a845d486f58566854f7eceee4David Li 1533f9ad8a790398513a845d486f58566854f7eceee4David LiGLboolean 1534f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_is_general_scale( const GLmatrix *m ) 1535f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1536f9ad8a790398513a845d486f58566854f7eceee4David Li return (m->flags & MAT_FLAG_GENERAL_SCALE) ? GL_TRUE : GL_FALSE; 1537f9ad8a790398513a845d486f58566854f7eceee4David Li} 1538f9ad8a790398513a845d486f58566854f7eceee4David Li 1539f9ad8a790398513a845d486f58566854f7eceee4David Li 1540f9ad8a790398513a845d486f58566854f7eceee4David LiGLboolean 1541f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_is_dirty( const GLmatrix *m ) 1542f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1543f9ad8a790398513a845d486f58566854f7eceee4David Li return (m->flags & MAT_DIRTY) ? GL_TRUE : GL_FALSE; 1544f9ad8a790398513a845d486f58566854f7eceee4David Li} 1545f9ad8a790398513a845d486f58566854f7eceee4David Li 1546f9ad8a790398513a845d486f58566854f7eceee4David Li 1547f9ad8a790398513a845d486f58566854f7eceee4David Li/**********************************************************************/ 1548f9ad8a790398513a845d486f58566854f7eceee4David Li/** \name Matrix setup */ 1549f9ad8a790398513a845d486f58566854f7eceee4David Li/*@{*/ 1550f9ad8a790398513a845d486f58566854f7eceee4David Li 1551f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1552f9ad8a790398513a845d486f58566854f7eceee4David Li * Copy a matrix. 1553f9ad8a790398513a845d486f58566854f7eceee4David Li * 1554f9ad8a790398513a845d486f58566854f7eceee4David Li * \param to destination matrix. 1555f9ad8a790398513a845d486f58566854f7eceee4David Li * \param from source matrix. 1556f9ad8a790398513a845d486f58566854f7eceee4David Li * 1557f9ad8a790398513a845d486f58566854f7eceee4David Li * Copies all fields in GLmatrix, creating an inverse array if necessary. 1558f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1559f9ad8a790398513a845d486f58566854f7eceee4David Livoid 1560f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_copy( GLmatrix *to, const GLmatrix *from ) 1561f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1562f9ad8a790398513a845d486f58566854f7eceee4David Li memcpy( to->m, from->m, sizeof(Identity) ); 1563f9ad8a790398513a845d486f58566854f7eceee4David Li to->flags = from->flags; 1564f9ad8a790398513a845d486f58566854f7eceee4David Li to->type = from->type; 1565f9ad8a790398513a845d486f58566854f7eceee4David Li 1566f9ad8a790398513a845d486f58566854f7eceee4David Li if (to->inv != 0) { 1567f9ad8a790398513a845d486f58566854f7eceee4David Li if (from->inv == 0) { 1568f9ad8a790398513a845d486f58566854f7eceee4David Li matrix_invert( to ); 1569f9ad8a790398513a845d486f58566854f7eceee4David Li } 1570f9ad8a790398513a845d486f58566854f7eceee4David Li else { 1571f9ad8a790398513a845d486f58566854f7eceee4David Li memcpy(to->inv, from->inv, sizeof(GLfloat)*16); 1572f9ad8a790398513a845d486f58566854f7eceee4David Li } 1573f9ad8a790398513a845d486f58566854f7eceee4David Li } 1574f9ad8a790398513a845d486f58566854f7eceee4David Li} 1575f9ad8a790398513a845d486f58566854f7eceee4David Li 1576f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1577f9ad8a790398513a845d486f58566854f7eceee4David Li * Loads a matrix array into GLmatrix. 1578f9ad8a790398513a845d486f58566854f7eceee4David Li * 1579f9ad8a790398513a845d486f58566854f7eceee4David Li * \param m matrix array. 1580f9ad8a790398513a845d486f58566854f7eceee4David Li * \param mat matrix. 1581f9ad8a790398513a845d486f58566854f7eceee4David Li * 1582f9ad8a790398513a845d486f58566854f7eceee4David Li * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY 1583f9ad8a790398513a845d486f58566854f7eceee4David Li * flags. 1584f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1585f9ad8a790398513a845d486f58566854f7eceee4David Livoid 1586f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_loadf( GLmatrix *mat, const GLfloat *m ) 1587f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1588f9ad8a790398513a845d486f58566854f7eceee4David Li memcpy( mat->m, m, 16*sizeof(GLfloat) ); 1589f9ad8a790398513a845d486f58566854f7eceee4David Li mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY); 1590f9ad8a790398513a845d486f58566854f7eceee4David Li} 1591f9ad8a790398513a845d486f58566854f7eceee4David Li 1592f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1593f9ad8a790398513a845d486f58566854f7eceee4David Li * Matrix constructor. 1594f9ad8a790398513a845d486f58566854f7eceee4David Li * 1595f9ad8a790398513a845d486f58566854f7eceee4David Li * \param m matrix. 1596f9ad8a790398513a845d486f58566854f7eceee4David Li * 1597f9ad8a790398513a845d486f58566854f7eceee4David Li * Initialize the GLmatrix fields. 1598f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1599f9ad8a790398513a845d486f58566854f7eceee4David Livoid 1600f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_ctr( GLmatrix *m ) 1601f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1602f9ad8a790398513a845d486f58566854f7eceee4David Li //m->m = (GLfloat *) ALIGN_MALLOC( 16 * sizeof(GLfloat), 16 ); 1603f9ad8a790398513a845d486f58566854f7eceee4David Li if (m->m) 1604f9ad8a790398513a845d486f58566854f7eceee4David Li memcpy( m->m, Identity, sizeof(Identity) ); 1605f9ad8a790398513a845d486f58566854f7eceee4David Li m->inv = NULL; 1606f9ad8a790398513a845d486f58566854f7eceee4David Li m->type = MATRIX_IDENTITY; 1607f9ad8a790398513a845d486f58566854f7eceee4David Li m->flags = 0; 1608f9ad8a790398513a845d486f58566854f7eceee4David Li} 1609f9ad8a790398513a845d486f58566854f7eceee4David Li 1610f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1611f9ad8a790398513a845d486f58566854f7eceee4David Li * Matrix destructor. 1612f9ad8a790398513a845d486f58566854f7eceee4David Li * 1613f9ad8a790398513a845d486f58566854f7eceee4David Li * \param m matrix. 1614f9ad8a790398513a845d486f58566854f7eceee4David Li * 1615f9ad8a790398513a845d486f58566854f7eceee4David Li * Frees the data in a GLmatrix. 1616f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1617f9ad8a790398513a845d486f58566854f7eceee4David Livoid 1618f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_dtr( GLmatrix *m ) 1619f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1620f9ad8a790398513a845d486f58566854f7eceee4David Li if (m->m) { 1621f9ad8a790398513a845d486f58566854f7eceee4David Li //ALIGN_FREE( m->m ); 1622f9ad8a790398513a845d486f58566854f7eceee4David Li //m->m = NULL; 1623f9ad8a790398513a845d486f58566854f7eceee4David Li } 1624f9ad8a790398513a845d486f58566854f7eceee4David Li if (m->inv) { 1625f9ad8a790398513a845d486f58566854f7eceee4David Li free( m->inv ); 1626f9ad8a790398513a845d486f58566854f7eceee4David Li m->inv = NULL; 1627f9ad8a790398513a845d486f58566854f7eceee4David Li } 1628f9ad8a790398513a845d486f58566854f7eceee4David Li} 1629f9ad8a790398513a845d486f58566854f7eceee4David Li 1630f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1631f9ad8a790398513a845d486f58566854f7eceee4David Li * Allocate a matrix inverse. 1632f9ad8a790398513a845d486f58566854f7eceee4David Li * 1633f9ad8a790398513a845d486f58566854f7eceee4David Li * \param m matrix. 1634f9ad8a790398513a845d486f58566854f7eceee4David Li * 1635f9ad8a790398513a845d486f58566854f7eceee4David Li * Allocates the matrix inverse, GLmatrix::inv, and sets it to Identity. 1636f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1637f9ad8a790398513a845d486f58566854f7eceee4David Livoid 1638f9ad8a790398513a845d486f58566854f7eceee4David Li_math_matrix_alloc_inv( GLmatrix *m ) 1639f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1640f9ad8a790398513a845d486f58566854f7eceee4David Li if (!m->inv) { 1641f9ad8a790398513a845d486f58566854f7eceee4David Li m->inv = (GLfloat *) malloc( 16 * sizeof(GLfloat)); 1642f9ad8a790398513a845d486f58566854f7eceee4David Li if (m->inv) 1643f9ad8a790398513a845d486f58566854f7eceee4David Li memcpy( m->inv, Identity, 16 * sizeof(GLfloat) ); 1644f9ad8a790398513a845d486f58566854f7eceee4David Li } 1645f9ad8a790398513a845d486f58566854f7eceee4David Li} 1646f9ad8a790398513a845d486f58566854f7eceee4David Li 1647f9ad8a790398513a845d486f58566854f7eceee4David Li/*@}*/ 1648f9ad8a790398513a845d486f58566854f7eceee4David Li 1649f9ad8a790398513a845d486f58566854f7eceee4David Li 1650f9ad8a790398513a845d486f58566854f7eceee4David Li/**********************************************************************/ 1651f9ad8a790398513a845d486f58566854f7eceee4David Li/** \name Matrix transpose */ 1652f9ad8a790398513a845d486f58566854f7eceee4David Li/*@{*/ 1653f9ad8a790398513a845d486f58566854f7eceee4David Li 1654f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1655f9ad8a790398513a845d486f58566854f7eceee4David Li * Transpose a GLfloat matrix. 1656f9ad8a790398513a845d486f58566854f7eceee4David Li * 1657f9ad8a790398513a845d486f58566854f7eceee4David Li * \param to destination array. 1658f9ad8a790398513a845d486f58566854f7eceee4David Li * \param from source array. 1659f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1660f9ad8a790398513a845d486f58566854f7eceee4David Livoid 1661f9ad8a790398513a845d486f58566854f7eceee4David Li_math_transposef( GLfloat to[16], const GLfloat from[16] ) 1662f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1663f9ad8a790398513a845d486f58566854f7eceee4David Li to[0] = from[0]; 1664f9ad8a790398513a845d486f58566854f7eceee4David Li to[1] = from[4]; 1665f9ad8a790398513a845d486f58566854f7eceee4David Li to[2] = from[8]; 1666f9ad8a790398513a845d486f58566854f7eceee4David Li to[3] = from[12]; 1667f9ad8a790398513a845d486f58566854f7eceee4David Li to[4] = from[1]; 1668f9ad8a790398513a845d486f58566854f7eceee4David Li to[5] = from[5]; 1669f9ad8a790398513a845d486f58566854f7eceee4David Li to[6] = from[9]; 1670f9ad8a790398513a845d486f58566854f7eceee4David Li to[7] = from[13]; 1671f9ad8a790398513a845d486f58566854f7eceee4David Li to[8] = from[2]; 1672f9ad8a790398513a845d486f58566854f7eceee4David Li to[9] = from[6]; 1673f9ad8a790398513a845d486f58566854f7eceee4David Li to[10] = from[10]; 1674f9ad8a790398513a845d486f58566854f7eceee4David Li to[11] = from[14]; 1675f9ad8a790398513a845d486f58566854f7eceee4David Li to[12] = from[3]; 1676f9ad8a790398513a845d486f58566854f7eceee4David Li to[13] = from[7]; 1677f9ad8a790398513a845d486f58566854f7eceee4David Li to[14] = from[11]; 1678f9ad8a790398513a845d486f58566854f7eceee4David Li to[15] = from[15]; 1679f9ad8a790398513a845d486f58566854f7eceee4David Li} 1680f9ad8a790398513a845d486f58566854f7eceee4David Li 1681f9ad8a790398513a845d486f58566854f7eceee4David Li 1682f9ad8a790398513a845d486f58566854f7eceee4David Li/** 1683f9ad8a790398513a845d486f58566854f7eceee4David Li * Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix. This 1684f9ad8a790398513a845d486f58566854f7eceee4David Li * function is used for transforming clipping plane equations and spotlight 1685f9ad8a790398513a845d486f58566854f7eceee4David Li * directions. 1686f9ad8a790398513a845d486f58566854f7eceee4David Li * Mathematically, u = v * m. 1687f9ad8a790398513a845d486f58566854f7eceee4David Li * Input: v - input vector 1688f9ad8a790398513a845d486f58566854f7eceee4David Li * m - transformation matrix 1689f9ad8a790398513a845d486f58566854f7eceee4David Li * Output: u - transformed vector 1690f9ad8a790398513a845d486f58566854f7eceee4David Li */ 1691f9ad8a790398513a845d486f58566854f7eceee4David Livoid 1692f9ad8a790398513a845d486f58566854f7eceee4David Li_mesa_transform_vector( GLfloat u[4], const GLfloat v[4], const GLfloat m[16] ) 1693f9ad8a790398513a845d486f58566854f7eceee4David Li{ 1694f9ad8a790398513a845d486f58566854f7eceee4David Li const GLfloat v0 = v[0], v1 = v[1], v2 = v[2], v3 = v[3]; 1695f9ad8a790398513a845d486f58566854f7eceee4David Li#define M(row,col) m[row + col*4] 1696f9ad8a790398513a845d486f58566854f7eceee4David Li u[0] = v0 * M(0,0) + v1 * M(1,0) + v2 * M(2,0) + v3 * M(3,0); 1697f9ad8a790398513a845d486f58566854f7eceee4David Li u[1] = v0 * M(0,1) + v1 * M(1,1) + v2 * M(2,1) + v3 * M(3,1); 1698f9ad8a790398513a845d486f58566854f7eceee4David Li u[2] = v0 * M(0,2) + v1 * M(1,2) + v2 * M(2,2) + v3 * M(3,2); 1699f9ad8a790398513a845d486f58566854f7eceee4David Li u[3] = v0 * M(0,3) + v1 * M(1,3) + v2 * M(2,3) + v3 * M(3,3); 1700f9ad8a790398513a845d486f58566854f7eceee4David Li#undef M 1701f9ad8a790398513a845d486f58566854f7eceee4David Li} 1702