diff options
Diffstat (limited to 'mesalib/src/mesa/math/m_matrix.c')
| -rw-r--r-- | mesalib/src/mesa/math/m_matrix.c | 3283 |
1 files changed, 1641 insertions, 1642 deletions
diff --git a/mesalib/src/mesa/math/m_matrix.c b/mesalib/src/mesa/math/m_matrix.c index 048b231c4..83eb787c7 100644 --- a/mesalib/src/mesa/math/m_matrix.c +++ b/mesalib/src/mesa/math/m_matrix.c @@ -1,1642 +1,1641 @@ -/* - * Mesa 3-D graphics library - * Version: 6.3 - * - * Copyright (C) 1999-2005 Brian Paul All Rights Reserved. - * - * Permission is hereby granted, free of charge, to any person obtaining a - * copy of this software and associated documentation files (the "Software"), - * to deal in the Software without restriction, including without limitation - * the rights to use, copy, modify, merge, publish, distribute, sublicense, - * and/or sell copies of the Software, and to permit persons to whom the - * Software is furnished to do so, subject to the following conditions: - * - * The above copyright notice and this permission notice shall be included - * in all copies or substantial portions of the Software. - * - * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS - * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, - * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL - * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN - * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN - * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. - */ - - -/** - * \file m_matrix.c - * Matrix operations. - * - * \note - * -# 4x4 transformation matrices are stored in memory in column major order. - * -# Points/vertices are to be thought of as column vectors. - * -# Transformation of a point p by a matrix M is: p' = M * p - */ - - -#include "main/glheader.h" -#include "main/imports.h" -#include "main/macros.h" -#include "main/imports.h" - -#include "m_matrix.h" - - -/** - * \defgroup MatFlags MAT_FLAG_XXX-flags - * - * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags - * It would be nice to make all these flags private to m_matrix.c - */ -/*@{*/ -#define MAT_FLAG_IDENTITY 0 /**< is an identity matrix flag. - * (Not actually used - the identity - * matrix is identified by the absense - * of all other flags.) - */ -#define MAT_FLAG_GENERAL 0x1 /**< is a general matrix flag */ -#define MAT_FLAG_ROTATION 0x2 /**< is a rotation matrix flag */ -#define MAT_FLAG_TRANSLATION 0x4 /**< is a translation matrix flag */ -#define MAT_FLAG_UNIFORM_SCALE 0x8 /**< is an uniform scaling matrix flag */ -#define MAT_FLAG_GENERAL_SCALE 0x10 /**< is a general scaling matrix flag */ -#define MAT_FLAG_GENERAL_3D 0x20 /**< general 3D matrix flag */ -#define MAT_FLAG_PERSPECTIVE 0x40 /**< is a perspective proj matrix flag */ -#define MAT_FLAG_SINGULAR 0x80 /**< is a singular matrix flag */ -#define MAT_DIRTY_TYPE 0x100 /**< matrix type is dirty */ -#define MAT_DIRTY_FLAGS 0x200 /**< matrix flags are dirty */ -#define MAT_DIRTY_INVERSE 0x400 /**< matrix inverse is dirty */ - -/** angle preserving matrix flags mask */ -#define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \ - MAT_FLAG_TRANSLATION | \ - MAT_FLAG_UNIFORM_SCALE) - -/** geometry related matrix flags mask */ -#define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \ - MAT_FLAG_ROTATION | \ - MAT_FLAG_TRANSLATION | \ - MAT_FLAG_UNIFORM_SCALE | \ - MAT_FLAG_GENERAL_SCALE | \ - MAT_FLAG_GENERAL_3D | \ - MAT_FLAG_PERSPECTIVE | \ - MAT_FLAG_SINGULAR) - -/** length preserving matrix flags mask */ -#define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \ - MAT_FLAG_TRANSLATION) - - -/** 3D (non-perspective) matrix flags mask */ -#define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \ - MAT_FLAG_TRANSLATION | \ - MAT_FLAG_UNIFORM_SCALE | \ - MAT_FLAG_GENERAL_SCALE | \ - MAT_FLAG_GENERAL_3D) - -/** dirty matrix flags mask */ -#define MAT_DIRTY (MAT_DIRTY_TYPE | \ - MAT_DIRTY_FLAGS | \ - MAT_DIRTY_INVERSE) - -/*@}*/ - - -/** - * Test geometry related matrix flags. - * - * \param mat a pointer to a GLmatrix structure. - * \param a flags mask. - * - * \returns non-zero if all geometry related matrix flags are contained within - * the mask, or zero otherwise. - */ -#define TEST_MAT_FLAGS(mat, a) \ - ((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0) - - - -/** - * Names of the corresponding GLmatrixtype values. - */ -static const char *types[] = { - "MATRIX_GENERAL", - "MATRIX_IDENTITY", - "MATRIX_3D_NO_ROT", - "MATRIX_PERSPECTIVE", - "MATRIX_2D", - "MATRIX_2D_NO_ROT", - "MATRIX_3D" -}; - - -/** - * Identity matrix. - */ -static GLfloat Identity[16] = { - 1.0, 0.0, 0.0, 0.0, - 0.0, 1.0, 0.0, 0.0, - 0.0, 0.0, 1.0, 0.0, - 0.0, 0.0, 0.0, 1.0 -}; - - - -/**********************************************************************/ -/** \name Matrix multiplication */ -/*@{*/ - -#define A(row,col) a[(col<<2)+row] -#define B(row,col) b[(col<<2)+row] -#define P(row,col) product[(col<<2)+row] - -/** - * Perform a full 4x4 matrix multiplication. - * - * \param a matrix. - * \param b matrix. - * \param product will receive the product of \p a and \p b. - * - * \warning Is assumed that \p product != \p b. \p product == \p a is allowed. - * - * \note KW: 4*16 = 64 multiplications - * - * \author This \c matmul was contributed by Thomas Malik - */ -static void matmul4( GLfloat *product, const GLfloat *a, const GLfloat *b ) -{ - GLint i; - for (i = 0; i < 4; i++) { - const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3); - P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0); - P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1); - P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2); - P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3); - } -} - -/** - * Multiply two matrices known to occupy only the top three rows, such - * as typical model matrices, and orthogonal matrices. - * - * \param a matrix. - * \param b matrix. - * \param product will receive the product of \p a and \p b. - */ -static void matmul34( GLfloat *product, const GLfloat *a, const GLfloat *b ) -{ - GLint i; - for (i = 0; i < 3; i++) { - const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3); - P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0); - P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1); - P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2); - P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3; - } - P(3,0) = 0; - P(3,1) = 0; - P(3,2) = 0; - P(3,3) = 1; -} - -#undef A -#undef B -#undef P - -/** - * Multiply a matrix by an array of floats with known properties. - * - * \param mat pointer to a GLmatrix structure containing the left multiplication - * matrix, and that will receive the product result. - * \param m right multiplication matrix array. - * \param flags flags of the matrix \p m. - * - * Joins both flags and marks the type and inverse as dirty. Calls matmul34() - * if both matrices are 3D, or matmul4() otherwise. - */ -static void matrix_multf( GLmatrix *mat, const GLfloat *m, GLuint flags ) -{ - mat->flags |= (flags | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE); - - if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) - matmul34( mat->m, mat->m, m ); - else - matmul4( mat->m, mat->m, m ); -} - -/** - * Matrix multiplication. - * - * \param dest destination matrix. - * \param a left matrix. - * \param b right matrix. - * - * Joins both flags and marks the type and inverse as dirty. Calls matmul34() - * if both matrices are 3D, or matmul4() otherwise. - */ -void -_math_matrix_mul_matrix( GLmatrix *dest, const GLmatrix *a, const GLmatrix *b ) -{ - dest->flags = (a->flags | - b->flags | - MAT_DIRTY_TYPE | - MAT_DIRTY_INVERSE); - - if (TEST_MAT_FLAGS(dest, MAT_FLAGS_3D)) - matmul34( dest->m, a->m, b->m ); - else - matmul4( dest->m, a->m, b->m ); -} - -/** - * Matrix multiplication. - * - * \param dest left and destination matrix. - * \param m right matrix array. - * - * Marks the matrix flags with general flag, and type and inverse dirty flags. - * Calls matmul4() for the multiplication. - */ -void -_math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m ) -{ - dest->flags |= (MAT_FLAG_GENERAL | - MAT_DIRTY_TYPE | - MAT_DIRTY_INVERSE | - MAT_DIRTY_FLAGS); - - matmul4( dest->m, dest->m, m ); -} - -/*@}*/ - - -/**********************************************************************/ -/** \name Matrix output */ -/*@{*/ - -/** - * Print a matrix array. - * - * \param m matrix array. - * - * Called by _math_matrix_print() to print a matrix or its inverse. - */ -static void print_matrix_floats( const GLfloat m[16] ) -{ - int i; - for (i=0;i<4;i++) { - _mesa_debug(NULL,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] ); - } -} - -/** - * Dumps the contents of a GLmatrix structure. - * - * \param m pointer to the GLmatrix structure. - */ -void -_math_matrix_print( const GLmatrix *m ) -{ - _mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags); - print_matrix_floats(m->m); - _mesa_debug(NULL, "Inverse: \n"); - if (m->inv) { - GLfloat prod[16]; - print_matrix_floats(m->inv); - matmul4(prod, m->m, m->inv); - _mesa_debug(NULL, "Mat * Inverse:\n"); - print_matrix_floats(prod); - } - else { - _mesa_debug(NULL, " - not available\n"); - } -} - -/*@}*/ - - -/** - * References an element of 4x4 matrix. - * - * \param m matrix array. - * \param c column of the desired element. - * \param r row of the desired element. - * - * \return value of the desired element. - * - * Calculate the linear storage index of the element and references it. - */ -#define MAT(m,r,c) (m)[(c)*4+(r)] - - -/**********************************************************************/ -/** \name Matrix inversion */ -/*@{*/ - -/** - * Swaps the values of two floating pointer variables. - * - * Used by invert_matrix_general() to swap the row pointers. - */ -#define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; } - -/** - * Compute inverse of 4x4 transformation matrix. - * - * \param mat pointer to a GLmatrix structure. The matrix inverse will be - * stored in the GLmatrix::inv attribute. - * - * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). - * - * \author - * Code contributed by Jacques Leroy jle@star.be - * - * Calculates the inverse matrix by performing the gaussian matrix reduction - * with partial pivoting followed by back/substitution with the loops manually - * unrolled. - */ -static GLboolean invert_matrix_general( GLmatrix *mat ) -{ - const GLfloat *m = mat->m; - GLfloat *out = mat->inv; - GLfloat wtmp[4][8]; - GLfloat m0, m1, m2, m3, s; - GLfloat *r0, *r1, *r2, *r3; - - r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3]; - - r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1), - r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3), - r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0, - - r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1), - r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3), - r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0, - - r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1), - r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3), - r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0, - - r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1), - r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3), - r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0; - - /* choose pivot - or die */ - if (FABSF(r3[0])>FABSF(r2[0])) SWAP_ROWS(r3, r2); - if (FABSF(r2[0])>FABSF(r1[0])) SWAP_ROWS(r2, r1); - if (FABSF(r1[0])>FABSF(r0[0])) SWAP_ROWS(r1, r0); - if (0.0 == r0[0]) return GL_FALSE; - - /* eliminate first variable */ - m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0]; - s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s; - s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s; - s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s; - s = r0[4]; - if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; } - s = r0[5]; - if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; } - s = r0[6]; - if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; } - s = r0[7]; - if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; } - - /* choose pivot - or die */ - if (FABSF(r3[1])>FABSF(r2[1])) SWAP_ROWS(r3, r2); - if (FABSF(r2[1])>FABSF(r1[1])) SWAP_ROWS(r2, r1); - if (0.0 == r1[1]) return GL_FALSE; - - /* eliminate second variable */ - m2 = r2[1]/r1[1]; m3 = r3[1]/r1[1]; - r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2]; - r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3]; - s = r1[4]; if (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; } - s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; } - s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; } - s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; } - - /* choose pivot - or die */ - if (FABSF(r3[2])>FABSF(r2[2])) SWAP_ROWS(r3, r2); - if (0.0 == r2[2]) return GL_FALSE; - - /* eliminate third variable */ - m3 = r3[2]/r2[2]; - r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4], - r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], - r3[7] -= m3 * r2[7]; - - /* last check */ - if (0.0 == r3[3]) return GL_FALSE; - - s = 1.0F/r3[3]; /* now back substitute row 3 */ - r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s; - - m2 = r2[3]; /* now back substitute row 2 */ - s = 1.0F/r2[2]; - r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2), - r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2); - m1 = r1[3]; - r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1, - r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1; - m0 = r0[3]; - r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0, - r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0; - - m1 = r1[2]; /* now back substitute row 1 */ - s = 1.0F/r1[1]; - r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1), - r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1); - m0 = r0[2]; - r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0, - r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0; - - m0 = r0[1]; /* now back substitute row 0 */ - s = 1.0F/r0[0]; - r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0), - r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0); - - MAT(out,0,0) = r0[4]; MAT(out,0,1) = r0[5], - MAT(out,0,2) = r0[6]; MAT(out,0,3) = r0[7], - MAT(out,1,0) = r1[4]; MAT(out,1,1) = r1[5], - MAT(out,1,2) = r1[6]; MAT(out,1,3) = r1[7], - MAT(out,2,0) = r2[4]; MAT(out,2,1) = r2[5], - MAT(out,2,2) = r2[6]; MAT(out,2,3) = r2[7], - MAT(out,3,0) = r3[4]; MAT(out,3,1) = r3[5], - MAT(out,3,2) = r3[6]; MAT(out,3,3) = r3[7]; - - return GL_TRUE; -} -#undef SWAP_ROWS - -/** - * Compute inverse of a general 3d transformation matrix. - * - * \param mat pointer to a GLmatrix structure. The matrix inverse will be - * stored in the GLmatrix::inv attribute. - * - * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). - * - * \author Adapted from graphics gems II. - * - * Calculates the inverse of the upper left by first calculating its - * determinant and multiplying it to the symmetric adjust matrix of each - * element. Finally deals with the translation part by transforming the - * original translation vector using by the calculated submatrix inverse. - */ -static GLboolean invert_matrix_3d_general( GLmatrix *mat ) -{ - const GLfloat *in = mat->m; - GLfloat *out = mat->inv; - GLfloat pos, neg, t; - GLfloat det; - - /* Calculate the determinant of upper left 3x3 submatrix and - * determine if the matrix is singular. - */ - pos = neg = 0.0; - t = MAT(in,0,0) * MAT(in,1,1) * MAT(in,2,2); - if (t >= 0.0) pos += t; else neg += t; - - t = MAT(in,1,0) * MAT(in,2,1) * MAT(in,0,2); - if (t >= 0.0) pos += t; else neg += t; - - t = MAT(in,2,0) * MAT(in,0,1) * MAT(in,1,2); - if (t >= 0.0) pos += t; else neg += t; - - t = -MAT(in,2,0) * MAT(in,1,1) * MAT(in,0,2); - if (t >= 0.0) pos += t; else neg += t; - - t = -MAT(in,1,0) * MAT(in,0,1) * MAT(in,2,2); - if (t >= 0.0) pos += t; else neg += t; - - t = -MAT(in,0,0) * MAT(in,2,1) * MAT(in,1,2); - if (t >= 0.0) pos += t; else neg += t; - - det = pos + neg; - - if (det*det < 1e-25) - return GL_FALSE; - - det = 1.0F / det; - MAT(out,0,0) = ( (MAT(in,1,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,1,2) )*det); - MAT(out,0,1) = (- (MAT(in,0,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,0,2) )*det); - MAT(out,0,2) = ( (MAT(in,0,1)*MAT(in,1,2) - MAT(in,1,1)*MAT(in,0,2) )*det); - MAT(out,1,0) = (- (MAT(in,1,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,1,2) )*det); - MAT(out,1,1) = ( (MAT(in,0,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,0,2) )*det); - MAT(out,1,2) = (- (MAT(in,0,0)*MAT(in,1,2) - MAT(in,1,0)*MAT(in,0,2) )*det); - MAT(out,2,0) = ( (MAT(in,1,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,1,1) )*det); - MAT(out,2,1) = (- (MAT(in,0,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,0,1) )*det); - MAT(out,2,2) = ( (MAT(in,0,0)*MAT(in,1,1) - MAT(in,1,0)*MAT(in,0,1) )*det); - - /* Do the translation part */ - MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) + - MAT(in,1,3) * MAT(out,0,1) + - MAT(in,2,3) * MAT(out,0,2) ); - MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) + - MAT(in,1,3) * MAT(out,1,1) + - MAT(in,2,3) * MAT(out,1,2) ); - MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) + - MAT(in,1,3) * MAT(out,2,1) + - MAT(in,2,3) * MAT(out,2,2) ); - - return GL_TRUE; -} - -/** - * Compute inverse of a 3d transformation matrix. - * - * \param mat pointer to a GLmatrix structure. The matrix inverse will be - * stored in the GLmatrix::inv attribute. - * - * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). - * - * If the matrix is not an angle preserving matrix then calls - * invert_matrix_3d_general for the actual calculation. Otherwise calculates - * the inverse matrix analyzing and inverting each of the scaling, rotation and - * translation parts. - */ -static GLboolean invert_matrix_3d( GLmatrix *mat ) -{ - const GLfloat *in = mat->m; - GLfloat *out = mat->inv; - - if (!TEST_MAT_FLAGS(mat, MAT_FLAGS_ANGLE_PRESERVING)) { - return invert_matrix_3d_general( mat ); - } - - if (mat->flags & MAT_FLAG_UNIFORM_SCALE) { - GLfloat scale = (MAT(in,0,0) * MAT(in,0,0) + - MAT(in,0,1) * MAT(in,0,1) + - MAT(in,0,2) * MAT(in,0,2)); - - if (scale == 0.0) - return GL_FALSE; - - scale = 1.0F / scale; - - /* Transpose and scale the 3 by 3 upper-left submatrix. */ - MAT(out,0,0) = scale * MAT(in,0,0); - MAT(out,1,0) = scale * MAT(in,0,1); - MAT(out,2,0) = scale * MAT(in,0,2); - MAT(out,0,1) = scale * MAT(in,1,0); - MAT(out,1,1) = scale * MAT(in,1,1); - MAT(out,2,1) = scale * MAT(in,1,2); - MAT(out,0,2) = scale * MAT(in,2,0); - MAT(out,1,2) = scale * MAT(in,2,1); - MAT(out,2,2) = scale * MAT(in,2,2); - } - else if (mat->flags & MAT_FLAG_ROTATION) { - /* Transpose the 3 by 3 upper-left submatrix. */ - MAT(out,0,0) = MAT(in,0,0); - MAT(out,1,0) = MAT(in,0,1); - MAT(out,2,0) = MAT(in,0,2); - MAT(out,0,1) = MAT(in,1,0); - MAT(out,1,1) = MAT(in,1,1); - MAT(out,2,1) = MAT(in,1,2); - MAT(out,0,2) = MAT(in,2,0); - MAT(out,1,2) = MAT(in,2,1); - MAT(out,2,2) = MAT(in,2,2); - } - else { - /* pure translation */ - memcpy( out, Identity, sizeof(Identity) ); - MAT(out,0,3) = - MAT(in,0,3); - MAT(out,1,3) = - MAT(in,1,3); - MAT(out,2,3) = - MAT(in,2,3); - return GL_TRUE; - } - - if (mat->flags & MAT_FLAG_TRANSLATION) { - /* Do the translation part */ - MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) + - MAT(in,1,3) * MAT(out,0,1) + - MAT(in,2,3) * MAT(out,0,2) ); - MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) + - MAT(in,1,3) * MAT(out,1,1) + - MAT(in,2,3) * MAT(out,1,2) ); - MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) + - MAT(in,1,3) * MAT(out,2,1) + - MAT(in,2,3) * MAT(out,2,2) ); - } - else { - MAT(out,0,3) = MAT(out,1,3) = MAT(out,2,3) = 0.0; - } - - return GL_TRUE; -} - -/** - * Compute inverse of an identity transformation matrix. - * - * \param mat pointer to a GLmatrix structure. The matrix inverse will be - * stored in the GLmatrix::inv attribute. - * - * \return always GL_TRUE. - * - * Simply copies Identity into GLmatrix::inv. - */ -static GLboolean invert_matrix_identity( GLmatrix *mat ) -{ - memcpy( mat->inv, Identity, sizeof(Identity) ); - return GL_TRUE; -} - -/** - * Compute inverse of a no-rotation 3d transformation matrix. - * - * \param mat pointer to a GLmatrix structure. The matrix inverse will be - * stored in the GLmatrix::inv attribute. - * - * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). - * - * Calculates the - */ -static GLboolean invert_matrix_3d_no_rot( GLmatrix *mat ) -{ - const GLfloat *in = mat->m; - GLfloat *out = mat->inv; - - if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0 || MAT(in,2,2) == 0 ) - return GL_FALSE; - - memcpy( out, Identity, 16 * sizeof(GLfloat) ); - MAT(out,0,0) = 1.0F / MAT(in,0,0); - MAT(out,1,1) = 1.0F / MAT(in,1,1); - MAT(out,2,2) = 1.0F / MAT(in,2,2); - - if (mat->flags & MAT_FLAG_TRANSLATION) { - MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0)); - MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1)); - MAT(out,2,3) = - (MAT(in,2,3) * MAT(out,2,2)); - } - - return GL_TRUE; -} - -/** - * Compute inverse of a no-rotation 2d transformation matrix. - * - * \param mat pointer to a GLmatrix structure. The matrix inverse will be - * stored in the GLmatrix::inv attribute. - * - * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). - * - * Calculates the inverse matrix by applying the inverse scaling and - * translation to the identity matrix. - */ -static GLboolean invert_matrix_2d_no_rot( GLmatrix *mat ) -{ - const GLfloat *in = mat->m; - GLfloat *out = mat->inv; - - if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0) - return GL_FALSE; - - memcpy( out, Identity, 16 * sizeof(GLfloat) ); - MAT(out,0,0) = 1.0F / MAT(in,0,0); - MAT(out,1,1) = 1.0F / MAT(in,1,1); - - if (mat->flags & MAT_FLAG_TRANSLATION) { - MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0)); - MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1)); - } - - return GL_TRUE; -} - -#if 0 -/* broken */ -static GLboolean invert_matrix_perspective( GLmatrix *mat ) -{ - const GLfloat *in = mat->m; - GLfloat *out = mat->inv; - - if (MAT(in,2,3) == 0) - return GL_FALSE; - - memcpy( out, Identity, 16 * sizeof(GLfloat) ); - - MAT(out,0,0) = 1.0F / MAT(in,0,0); - MAT(out,1,1) = 1.0F / MAT(in,1,1); - - MAT(out,0,3) = MAT(in,0,2); - MAT(out,1,3) = MAT(in,1,2); - - MAT(out,2,2) = 0; - MAT(out,2,3) = -1; - - MAT(out,3,2) = 1.0F / MAT(in,2,3); - MAT(out,3,3) = MAT(in,2,2) * MAT(out,3,2); - - return GL_TRUE; -} -#endif - -/** - * Matrix inversion function pointer type. - */ -typedef GLboolean (*inv_mat_func)( GLmatrix *mat ); - -/** - * Table of the matrix inversion functions according to the matrix type. - */ -static inv_mat_func inv_mat_tab[7] = { - invert_matrix_general, - invert_matrix_identity, - invert_matrix_3d_no_rot, -#if 0 - /* Don't use this function for now - it fails when the projection matrix - * is premultiplied by a translation (ala Chromium's tilesort SPU). - */ - invert_matrix_perspective, -#else - invert_matrix_general, -#endif - invert_matrix_3d, /* lazy! */ - invert_matrix_2d_no_rot, - invert_matrix_3d -}; - -/** - * Compute inverse of a transformation matrix. - * - * \param mat pointer to a GLmatrix structure. The matrix inverse will be - * stored in the GLmatrix::inv attribute. - * - * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). - * - * Calls the matrix inversion function in inv_mat_tab corresponding to the - * given matrix type. In case of failure, updates the MAT_FLAG_SINGULAR flag, - * and copies the identity matrix into GLmatrix::inv. - */ -static GLboolean matrix_invert( GLmatrix *mat ) -{ - if (inv_mat_tab[mat->type](mat)) { - mat->flags &= ~MAT_FLAG_SINGULAR; - return GL_TRUE; - } else { - mat->flags |= MAT_FLAG_SINGULAR; - memcpy( mat->inv, Identity, sizeof(Identity) ); - return GL_FALSE; - } -} - -/*@}*/ - - -/**********************************************************************/ -/** \name Matrix generation */ -/*@{*/ - -/** - * Generate a 4x4 transformation matrix from glRotate parameters, and - * post-multiply the input matrix by it. - * - * \author - * This function was contributed by Erich Boleyn (erich@uruk.org). - * Optimizations contributed by Rudolf Opalla (rudi@khm.de). - */ -void -_math_matrix_rotate( GLmatrix *mat, - GLfloat angle, GLfloat x, GLfloat y, GLfloat z ) -{ - GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c; - GLfloat m[16]; - GLboolean optimized; - - s = (GLfloat) sin( angle * DEG2RAD ); - c = (GLfloat) cos( angle * DEG2RAD ); - - memcpy(m, Identity, sizeof(GLfloat)*16); - optimized = GL_FALSE; - -#define M(row,col) m[col*4+row] - - if (x == 0.0F) { - if (y == 0.0F) { - if (z != 0.0F) { - optimized = GL_TRUE; - /* rotate only around z-axis */ - M(0,0) = c; - M(1,1) = c; - if (z < 0.0F) { - M(0,1) = s; - M(1,0) = -s; - } - else { - M(0,1) = -s; - M(1,0) = s; - } - } - } - else if (z == 0.0F) { - optimized = GL_TRUE; - /* rotate only around y-axis */ - M(0,0) = c; - M(2,2) = c; - if (y < 0.0F) { - M(0,2) = -s; - M(2,0) = s; - } - else { - M(0,2) = s; - M(2,0) = -s; - } - } - } - else if (y == 0.0F) { - if (z == 0.0F) { - optimized = GL_TRUE; - /* rotate only around x-axis */ - M(1,1) = c; - M(2,2) = c; - if (x < 0.0F) { - M(1,2) = s; - M(2,1) = -s; - } - else { - M(1,2) = -s; - M(2,1) = s; - } - } - } - - if (!optimized) { - const GLfloat mag = SQRTF(x * x + y * y + z * z); - - if (mag <= 1.0e-4) { - /* no rotation, leave mat as-is */ - return; - } - - x /= mag; - y /= mag; - z /= mag; - - - /* - * Arbitrary axis rotation matrix. - * - * This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied - * like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation - * (which is about the X-axis), and the two composite transforms - * Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary - * from the arbitrary axis to the X-axis then back. They are - * all elementary rotations. - * - * Rz' is a rotation about the Z-axis, to bring the axis vector - * into the x-z plane. Then Ry' is applied, rotating about the - * Y-axis to bring the axis vector parallel with the X-axis. The - * rotation about the X-axis is then performed. Ry and Rz are - * simply the respective inverse transforms to bring the arbitrary - * axis back to its original orientation. The first transforms - * Rz' and Ry' are considered inverses, since the data from the - * arbitrary axis gives you info on how to get to it, not how - * to get away from it, and an inverse must be applied. - * - * The basic calculation used is to recognize that the arbitrary - * axis vector (x, y, z), since it is of unit length, actually - * represents the sines and cosines of the angles to rotate the - * X-axis to the same orientation, with theta being the angle about - * Z and phi the angle about Y (in the order described above) - * as follows: - * - * cos ( theta ) = x / sqrt ( 1 - z^2 ) - * sin ( theta ) = y / sqrt ( 1 - z^2 ) - * - * cos ( phi ) = sqrt ( 1 - z^2 ) - * sin ( phi ) = z - * - * Note that cos ( phi ) can further be inserted to the above - * formulas: - * - * cos ( theta ) = x / cos ( phi ) - * sin ( theta ) = y / sin ( phi ) - * - * ...etc. Because of those relations and the standard trigonometric - * relations, it is pssible to reduce the transforms down to what - * is used below. It may be that any primary axis chosen will give the - * same results (modulo a sign convention) using thie method. - * - * Particularly nice is to notice that all divisions that might - * have caused trouble when parallel to certain planes or - * axis go away with care paid to reducing the expressions. - * After checking, it does perform correctly under all cases, since - * in all the cases of division where the denominator would have - * been zero, the numerator would have been zero as well, giving - * the expected result. - */ - - xx = x * x; - yy = y * y; - zz = z * z; - xy = x * y; - yz = y * z; - zx = z * x; - xs = x * s; - ys = y * s; - zs = z * s; - one_c = 1.0F - c; - - /* We already hold the identity-matrix so we can skip some statements */ - M(0,0) = (one_c * xx) + c; - M(0,1) = (one_c * xy) - zs; - M(0,2) = (one_c * zx) + ys; -/* M(0,3) = 0.0F; */ - - M(1,0) = (one_c * xy) + zs; - M(1,1) = (one_c * yy) + c; - M(1,2) = (one_c * yz) - xs; -/* M(1,3) = 0.0F; */ - - M(2,0) = (one_c * zx) - ys; - M(2,1) = (one_c * yz) + xs; - M(2,2) = (one_c * zz) + c; -/* M(2,3) = 0.0F; */ - -/* - M(3,0) = 0.0F; - M(3,1) = 0.0F; - M(3,2) = 0.0F; - M(3,3) = 1.0F; -*/ - } -#undef M - - matrix_multf( mat, m, MAT_FLAG_ROTATION ); -} - -/** - * Apply a perspective projection matrix. - * - * \param mat matrix to apply the projection. - * \param left left clipping plane coordinate. - * \param right right clipping plane coordinate. - * \param bottom bottom clipping plane coordinate. - * \param top top clipping plane coordinate. - * \param nearval distance to the near clipping plane. - * \param farval distance to the far clipping plane. - * - * Creates the projection matrix and multiplies it with \p mat, marking the - * MAT_FLAG_PERSPECTIVE flag. - */ -void -_math_matrix_frustum( GLmatrix *mat, - GLfloat left, GLfloat right, - GLfloat bottom, GLfloat top, - GLfloat nearval, GLfloat farval ) -{ - GLfloat x, y, a, b, c, d; - GLfloat m[16]; - - x = (2.0F*nearval) / (right-left); - y = (2.0F*nearval) / (top-bottom); - a = (right+left) / (right-left); - b = (top+bottom) / (top-bottom); - c = -(farval+nearval) / ( farval-nearval); - d = -(2.0F*farval*nearval) / (farval-nearval); /* error? */ - -#define M(row,col) m[col*4+row] - M(0,0) = x; M(0,1) = 0.0F; M(0,2) = a; M(0,3) = 0.0F; - M(1,0) = 0.0F; M(1,1) = y; M(1,2) = b; M(1,3) = 0.0F; - M(2,0) = 0.0F; M(2,1) = 0.0F; M(2,2) = c; M(2,3) = d; - M(3,0) = 0.0F; M(3,1) = 0.0F; M(3,2) = -1.0F; M(3,3) = 0.0F; -#undef M - - matrix_multf( mat, m, MAT_FLAG_PERSPECTIVE ); -} - -/** - * Apply an orthographic projection matrix. - * - * \param mat matrix to apply the projection. - * \param left left clipping plane coordinate. - * \param right right clipping plane coordinate. - * \param bottom bottom clipping plane coordinate. - * \param top top clipping plane coordinate. - * \param nearval distance to the near clipping plane. - * \param farval distance to the far clipping plane. - * - * Creates the projection matrix and multiplies it with \p mat, marking the - * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags. - */ -void -_math_matrix_ortho( GLmatrix *mat, - GLfloat left, GLfloat right, - GLfloat bottom, GLfloat top, - GLfloat nearval, GLfloat farval ) -{ - GLfloat m[16]; - -#define M(row,col) m[col*4+row] - M(0,0) = 2.0F / (right-left); - M(0,1) = 0.0F; - M(0,2) = 0.0F; - M(0,3) = -(right+left) / (right-left); - - M(1,0) = 0.0F; - M(1,1) = 2.0F / (top-bottom); - M(1,2) = 0.0F; - M(1,3) = -(top+bottom) / (top-bottom); - - M(2,0) = 0.0F; - M(2,1) = 0.0F; - M(2,2) = -2.0F / (farval-nearval); - M(2,3) = -(farval+nearval) / (farval-nearval); - - M(3,0) = 0.0F; - M(3,1) = 0.0F; - M(3,2) = 0.0F; - M(3,3) = 1.0F; -#undef M - - matrix_multf( mat, m, (MAT_FLAG_GENERAL_SCALE|MAT_FLAG_TRANSLATION)); -} - -/** - * Multiply a matrix with a general scaling matrix. - * - * \param mat matrix. - * \param x x axis scale factor. - * \param y y axis scale factor. - * \param z z axis scale factor. - * - * Multiplies in-place the elements of \p mat by the scale factors. Checks if - * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE - * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and - * MAT_DIRTY_INVERSE dirty flags. - */ -void -_math_matrix_scale( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z ) -{ - GLfloat *m = mat->m; - m[0] *= x; m[4] *= y; m[8] *= z; - m[1] *= x; m[5] *= y; m[9] *= z; - m[2] *= x; m[6] *= y; m[10] *= z; - m[3] *= x; m[7] *= y; m[11] *= z; - - if (FABSF(x - y) < 1e-8 && FABSF(x - z) < 1e-8) - mat->flags |= MAT_FLAG_UNIFORM_SCALE; - else - mat->flags |= MAT_FLAG_GENERAL_SCALE; - - mat->flags |= (MAT_DIRTY_TYPE | - MAT_DIRTY_INVERSE); -} - -/** - * Multiply a matrix with a translation matrix. - * - * \param mat matrix. - * \param x translation vector x coordinate. - * \param y translation vector y coordinate. - * \param z translation vector z coordinate. - * - * Adds the translation coordinates to the elements of \p mat in-place. Marks - * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE - * dirty flags. - */ -void -_math_matrix_translate( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z ) -{ - GLfloat *m = mat->m; - m[12] = m[0] * x + m[4] * y + m[8] * z + m[12]; - m[13] = m[1] * x + m[5] * y + m[9] * z + m[13]; - m[14] = m[2] * x + m[6] * y + m[10] * z + m[14]; - m[15] = m[3] * x + m[7] * y + m[11] * z + m[15]; - - mat->flags |= (MAT_FLAG_TRANSLATION | - MAT_DIRTY_TYPE | - MAT_DIRTY_INVERSE); -} - - -/** - * Set matrix to do viewport and depthrange mapping. - * Transforms Normalized Device Coords to window/Z values. - */ -void -_math_matrix_viewport(GLmatrix *m, GLint x, GLint y, GLint width, GLint height, - GLfloat zNear, GLfloat zFar, GLfloat depthMax) -{ - m->m[MAT_SX] = (GLfloat) width / 2.0F; - m->m[MAT_TX] = m->m[MAT_SX] + x; - m->m[MAT_SY] = (GLfloat) height / 2.0F; - m->m[MAT_TY] = m->m[MAT_SY] + y; - m->m[MAT_SZ] = depthMax * ((zFar - zNear) / 2.0F); - m->m[MAT_TZ] = depthMax * ((zFar - zNear) / 2.0F + zNear); - m->flags = MAT_FLAG_GENERAL_SCALE | MAT_FLAG_TRANSLATION; - m->type = MATRIX_3D_NO_ROT; -} - - -/** - * Set a matrix to the identity matrix. - * - * \param mat matrix. - * - * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL. - * Sets the matrix type to identity, and clear the dirty flags. - */ -void -_math_matrix_set_identity( GLmatrix *mat ) -{ - memcpy( mat->m, Identity, 16*sizeof(GLfloat) ); - - if (mat->inv) - memcpy( mat->inv, Identity, 16*sizeof(GLfloat) ); - - mat->type = MATRIX_IDENTITY; - mat->flags &= ~(MAT_DIRTY_FLAGS| - MAT_DIRTY_TYPE| - MAT_DIRTY_INVERSE); -} - -/*@}*/ - - -/**********************************************************************/ -/** \name Matrix analysis */ -/*@{*/ - -#define ZERO(x) (1<<x) -#define ONE(x) (1<<(x+16)) - -#define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14)) -#define MASK_NO_2D_SCALE ( ONE(0) | ONE(5)) - -#define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\ - ZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\ - ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ - ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) - -#define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \ - ZERO(1) | ZERO(9) | \ - ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ - ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) - -#define MASK_2D ( ZERO(8) | \ - ZERO(9) | \ - ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ - ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) - - -#define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \ - ZERO(1) | ZERO(9) | \ - ZERO(2) | ZERO(6) | \ - ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) - -#define MASK_3D ( \ - \ - \ - ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) - - -#define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\ - ZERO(1) | ZERO(13) |\ - ZERO(2) | ZERO(6) | \ - ZERO(3) | ZERO(7) | ZERO(15) ) - -#define SQ(x) ((x)*(x)) - -/** - * Determine type and flags from scratch. - * - * \param mat matrix. - * - * This is expensive enough to only want to do it once. - */ -static void analyse_from_scratch( GLmatrix *mat ) -{ - const GLfloat *m = mat->m; - GLuint mask = 0; - GLuint i; - - for (i = 0 ; i < 16 ; i++) { - if (m[i] == 0.0) mask |= (1<<i); - } - - if (m[0] == 1.0F) mask |= (1<<16); - if (m[5] == 1.0F) mask |= (1<<21); - if (m[10] == 1.0F) mask |= (1<<26); - if (m[15] == 1.0F) mask |= (1<<31); - - mat->flags &= ~MAT_FLAGS_GEOMETRY; - - /* Check for translation - no-one really cares - */ - if ((mask & MASK_NO_TRX) != MASK_NO_TRX) - mat->flags |= MAT_FLAG_TRANSLATION; - - /* Do the real work - */ - if (mask == (GLuint) MASK_IDENTITY) { - mat->type = MATRIX_IDENTITY; - } - else if ((mask & MASK_2D_NO_ROT) == (GLuint) MASK_2D_NO_ROT) { - mat->type = MATRIX_2D_NO_ROT; - - if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE) - mat->flags |= MAT_FLAG_GENERAL_SCALE; - } - else if ((mask & MASK_2D) == (GLuint) MASK_2D) { - GLfloat mm = DOT2(m, m); - GLfloat m4m4 = DOT2(m+4,m+4); - GLfloat mm4 = DOT2(m,m+4); - - mat->type = MATRIX_2D; - - /* Check for scale */ - if (SQ(mm-1) > SQ(1e-6) || - SQ(m4m4-1) > SQ(1e-6)) - mat->flags |= MAT_FLAG_GENERAL_SCALE; - - /* Check for rotation */ - if (SQ(mm4) > SQ(1e-6)) - mat->flags |= MAT_FLAG_GENERAL_3D; - else - mat->flags |= MAT_FLAG_ROTATION; - - } - else if ((mask & MASK_3D_NO_ROT) == (GLuint) MASK_3D_NO_ROT) { - mat->type = MATRIX_3D_NO_ROT; - - /* Check for scale */ - if (SQ(m[0]-m[5]) < SQ(1e-6) && - SQ(m[0]-m[10]) < SQ(1e-6)) { - if (SQ(m[0]-1.0) > SQ(1e-6)) { - mat->flags |= MAT_FLAG_UNIFORM_SCALE; - } - } - else { - mat->flags |= MAT_FLAG_GENERAL_SCALE; - } - } - else if ((mask & MASK_3D) == (GLuint) MASK_3D) { - GLfloat c1 = DOT3(m,m); - GLfloat c2 = DOT3(m+4,m+4); - GLfloat c3 = DOT3(m+8,m+8); - GLfloat d1 = DOT3(m, m+4); - GLfloat cp[3]; - - mat->type = MATRIX_3D; - - /* Check for scale */ - if (SQ(c1-c2) < SQ(1e-6) && SQ(c1-c3) < SQ(1e-6)) { - if (SQ(c1-1.0) > SQ(1e-6)) - mat->flags |= MAT_FLAG_UNIFORM_SCALE; - /* else no scale at all */ - } - else { - mat->flags |= MAT_FLAG_GENERAL_SCALE; - } - - /* Check for rotation */ - if (SQ(d1) < SQ(1e-6)) { - CROSS3( cp, m, m+4 ); - SUB_3V( cp, cp, (m+8) ); - if (LEN_SQUARED_3FV(cp) < SQ(1e-6)) - mat->flags |= MAT_FLAG_ROTATION; - else - mat->flags |= MAT_FLAG_GENERAL_3D; - } - else { - mat->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */ - } - } - else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0F) { - mat->type = MATRIX_PERSPECTIVE; - mat->flags |= MAT_FLAG_GENERAL; - } - else { - mat->type = MATRIX_GENERAL; - mat->flags |= MAT_FLAG_GENERAL; - } -} - -/** - * Analyze a matrix given that its flags are accurate. - * - * This is the more common operation, hopefully. - */ -static void analyse_from_flags( GLmatrix *mat ) -{ - const GLfloat *m = mat->m; - - if (TEST_MAT_FLAGS(mat, 0)) { - mat->type = MATRIX_IDENTITY; - } - else if (TEST_MAT_FLAGS(mat, (MAT_FLAG_TRANSLATION | - MAT_FLAG_UNIFORM_SCALE | - MAT_FLAG_GENERAL_SCALE))) { - if ( m[10]==1.0F && m[14]==0.0F ) { - mat->type = MATRIX_2D_NO_ROT; - } - else { - mat->type = MATRIX_3D_NO_ROT; - } - } - else if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) { - if ( m[ 8]==0.0F - && m[ 9]==0.0F - && m[2]==0.0F && m[6]==0.0F && m[10]==1.0F && m[14]==0.0F) { - mat->type = MATRIX_2D; - } - else { - mat->type = MATRIX_3D; - } - } - else if ( m[4]==0.0F && m[12]==0.0F - && m[1]==0.0F && m[13]==0.0F - && m[2]==0.0F && m[6]==0.0F - && m[3]==0.0F && m[7]==0.0F && m[11]==-1.0F && m[15]==0.0F) { - mat->type = MATRIX_PERSPECTIVE; - } - else { - mat->type = MATRIX_GENERAL; - } -} - -/** - * Analyze and update a matrix. - * - * \param mat matrix. - * - * If the matrix type is dirty then calls either analyse_from_scratch() or - * analyse_from_flags() to determine its type, according to whether the flags - * are dirty or not, respectively. If the matrix has an inverse and it's dirty - * then calls matrix_invert(). Finally clears the dirty flags. - */ -void -_math_matrix_analyse( GLmatrix *mat ) -{ - if (mat->flags & MAT_DIRTY_TYPE) { - if (mat->flags & MAT_DIRTY_FLAGS) - analyse_from_scratch( mat ); - else - analyse_from_flags( mat ); - } - - if (mat->inv && (mat->flags & MAT_DIRTY_INVERSE)) { - matrix_invert( mat ); - mat->flags &= ~MAT_DIRTY_INVERSE; - } - - mat->flags &= ~(MAT_DIRTY_FLAGS | MAT_DIRTY_TYPE); -} - -/*@}*/ - - -/** - * Test if the given matrix preserves vector lengths. - */ -GLboolean -_math_matrix_is_length_preserving( const GLmatrix *m ) -{ - return TEST_MAT_FLAGS( m, MAT_FLAGS_LENGTH_PRESERVING); -} - - -/** - * Test if the given matrix does any rotation. - * (or perhaps if the upper-left 3x3 is non-identity) - */ -GLboolean -_math_matrix_has_rotation( const GLmatrix *m ) -{ - if (m->flags & (MAT_FLAG_GENERAL | - MAT_FLAG_ROTATION | - MAT_FLAG_GENERAL_3D | - MAT_FLAG_PERSPECTIVE)) - return GL_TRUE; - else - return GL_FALSE; -} - - -GLboolean -_math_matrix_is_general_scale( const GLmatrix *m ) -{ - return (m->flags & MAT_FLAG_GENERAL_SCALE) ? GL_TRUE : GL_FALSE; -} - - -GLboolean -_math_matrix_is_dirty( const GLmatrix *m ) -{ - return (m->flags & MAT_DIRTY) ? GL_TRUE : GL_FALSE; -} - - -/**********************************************************************/ -/** \name Matrix setup */ -/*@{*/ - -/** - * Copy a matrix. - * - * \param to destination matrix. - * \param from source matrix. - * - * Copies all fields in GLmatrix, creating an inverse array if necessary. - */ -void -_math_matrix_copy( GLmatrix *to, const GLmatrix *from ) -{ - memcpy( to->m, from->m, sizeof(Identity) ); - to->flags = from->flags; - to->type = from->type; - - if (to->inv != 0) { - if (from->inv == 0) { - matrix_invert( to ); - } - else { - memcpy(to->inv, from->inv, sizeof(GLfloat)*16); - } - } -} - -/** - * Loads a matrix array into GLmatrix. - * - * \param m matrix array. - * \param mat matrix. - * - * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY - * flags. - */ -void -_math_matrix_loadf( GLmatrix *mat, const GLfloat *m ) -{ - memcpy( mat->m, m, 16*sizeof(GLfloat) ); - mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY); -} - -/** - * Matrix constructor. - * - * \param m matrix. - * - * Initialize the GLmatrix fields. - */ -void -_math_matrix_ctr( GLmatrix *m ) -{ - m->m = (GLfloat *) _mesa_align_malloc( 16 * sizeof(GLfloat), 16 ); - if (m->m) - memcpy( m->m, Identity, sizeof(Identity) ); - m->inv = NULL; - m->type = MATRIX_IDENTITY; - m->flags = 0; -} - -/** - * Matrix destructor. - * - * \param m matrix. - * - * Frees the data in a GLmatrix. - */ -void -_math_matrix_dtr( GLmatrix *m ) -{ - if (m->m) { - _mesa_align_free( m->m ); - m->m = NULL; - } - if (m->inv) { - _mesa_align_free( m->inv ); - m->inv = NULL; - } -} - -/** - * Allocate a matrix inverse. - * - * \param m matrix. - * - * Allocates the matrix inverse, GLmatrix::inv, and sets it to Identity. - */ -void -_math_matrix_alloc_inv( GLmatrix *m ) -{ - if (!m->inv) { - m->inv = (GLfloat *) _mesa_align_malloc( 16 * sizeof(GLfloat), 16 ); - if (m->inv) - memcpy( m->inv, Identity, 16 * sizeof(GLfloat) ); - } -} - -/*@}*/ - - -/**********************************************************************/ -/** \name Matrix transpose */ -/*@{*/ - -/** - * Transpose a GLfloat matrix. - * - * \param to destination array. - * \param from source array. - */ -void -_math_transposef( GLfloat to[16], const GLfloat from[16] ) -{ - to[0] = from[0]; - to[1] = from[4]; - to[2] = from[8]; - to[3] = from[12]; - to[4] = from[1]; - to[5] = from[5]; - to[6] = from[9]; - to[7] = from[13]; - to[8] = from[2]; - to[9] = from[6]; - to[10] = from[10]; - to[11] = from[14]; - to[12] = from[3]; - to[13] = from[7]; - to[14] = from[11]; - to[15] = from[15]; -} - -/** - * Transpose a GLdouble matrix. - * - * \param to destination array. - * \param from source array. - */ -void -_math_transposed( GLdouble to[16], const GLdouble from[16] ) -{ - to[0] = from[0]; - to[1] = from[4]; - to[2] = from[8]; - to[3] = from[12]; - to[4] = from[1]; - to[5] = from[5]; - to[6] = from[9]; - to[7] = from[13]; - to[8] = from[2]; - to[9] = from[6]; - to[10] = from[10]; - to[11] = from[14]; - to[12] = from[3]; - to[13] = from[7]; - to[14] = from[11]; - to[15] = from[15]; -} - -/** - * Transpose a GLdouble matrix and convert to GLfloat. - * - * \param to destination array. - * \param from source array. - */ -void -_math_transposefd( GLfloat to[16], const GLdouble from[16] ) -{ - to[0] = (GLfloat) from[0]; - to[1] = (GLfloat) from[4]; - to[2] = (GLfloat) from[8]; - to[3] = (GLfloat) from[12]; - to[4] = (GLfloat) from[1]; - to[5] = (GLfloat) from[5]; - to[6] = (GLfloat) from[9]; - to[7] = (GLfloat) from[13]; - to[8] = (GLfloat) from[2]; - to[9] = (GLfloat) from[6]; - to[10] = (GLfloat) from[10]; - to[11] = (GLfloat) from[14]; - to[12] = (GLfloat) from[3]; - to[13] = (GLfloat) from[7]; - to[14] = (GLfloat) from[11]; - to[15] = (GLfloat) from[15]; -} - -/*@}*/ - - -/** - * Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix. This - * function is used for transforming clipping plane equations and spotlight - * directions. - * Mathematically, u = v * m. - * Input: v - input vector - * m - transformation matrix - * Output: u - transformed vector - */ -void -_mesa_transform_vector( GLfloat u[4], const GLfloat v[4], const GLfloat m[16] ) -{ - const GLfloat v0 = v[0], v1 = v[1], v2 = v[2], v3 = v[3]; -#define M(row,col) m[row + col*4] - u[0] = v0 * M(0,0) + v1 * M(1,0) + v2 * M(2,0) + v3 * M(3,0); - u[1] = v0 * M(0,1) + v1 * M(1,1) + v2 * M(2,1) + v3 * M(3,1); - u[2] = v0 * M(0,2) + v1 * M(1,2) + v2 * M(2,2) + v3 * M(3,2); - u[3] = v0 * M(0,3) + v1 * M(1,3) + v2 * M(2,3) + v3 * M(3,3); -#undef M -} +/*
+ * Mesa 3-D graphics library
+ * Version: 6.3
+ *
+ * Copyright (C) 1999-2005 Brian Paul All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included
+ * in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
+ * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+ */
+
+
+/**
+ * \file m_matrix.c
+ * Matrix operations.
+ *
+ * \note
+ * -# 4x4 transformation matrices are stored in memory in column major order.
+ * -# Points/vertices are to be thought of as column vectors.
+ * -# Transformation of a point p by a matrix M is: p' = M * p
+ */
+
+
+#include "main/glheader.h"
+#include "main/imports.h"
+#include "main/macros.h"
+
+#include "m_matrix.h"
+
+
+/**
+ * \defgroup MatFlags MAT_FLAG_XXX-flags
+ *
+ * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags
+ * It would be nice to make all these flags private to m_matrix.c
+ */
+/*@{*/
+#define MAT_FLAG_IDENTITY 0 /**< is an identity matrix flag.
+ * (Not actually used - the identity
+ * matrix is identified by the absense
+ * of all other flags.)
+ */
+#define MAT_FLAG_GENERAL 0x1 /**< is a general matrix flag */
+#define MAT_FLAG_ROTATION 0x2 /**< is a rotation matrix flag */
+#define MAT_FLAG_TRANSLATION 0x4 /**< is a translation matrix flag */
+#define MAT_FLAG_UNIFORM_SCALE 0x8 /**< is an uniform scaling matrix flag */
+#define MAT_FLAG_GENERAL_SCALE 0x10 /**< is a general scaling matrix flag */
+#define MAT_FLAG_GENERAL_3D 0x20 /**< general 3D matrix flag */
+#define MAT_FLAG_PERSPECTIVE 0x40 /**< is a perspective proj matrix flag */
+#define MAT_FLAG_SINGULAR 0x80 /**< is a singular matrix flag */
+#define MAT_DIRTY_TYPE 0x100 /**< matrix type is dirty */
+#define MAT_DIRTY_FLAGS 0x200 /**< matrix flags are dirty */
+#define MAT_DIRTY_INVERSE 0x400 /**< matrix inverse is dirty */
+
+/** angle preserving matrix flags mask */
+#define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \
+ MAT_FLAG_TRANSLATION | \
+ MAT_FLAG_UNIFORM_SCALE)
+
+/** geometry related matrix flags mask */
+#define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \
+ MAT_FLAG_ROTATION | \
+ MAT_FLAG_TRANSLATION | \
+ MAT_FLAG_UNIFORM_SCALE | \
+ MAT_FLAG_GENERAL_SCALE | \
+ MAT_FLAG_GENERAL_3D | \
+ MAT_FLAG_PERSPECTIVE | \
+ MAT_FLAG_SINGULAR)
+
+/** length preserving matrix flags mask */
+#define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \
+ MAT_FLAG_TRANSLATION)
+
+
+/** 3D (non-perspective) matrix flags mask */
+#define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \
+ MAT_FLAG_TRANSLATION | \
+ MAT_FLAG_UNIFORM_SCALE | \
+ MAT_FLAG_GENERAL_SCALE | \
+ MAT_FLAG_GENERAL_3D)
+
+/** dirty matrix flags mask */
+#define MAT_DIRTY (MAT_DIRTY_TYPE | \
+ MAT_DIRTY_FLAGS | \
+ MAT_DIRTY_INVERSE)
+
+/*@}*/
+
+
+/**
+ * Test geometry related matrix flags.
+ *
+ * \param mat a pointer to a GLmatrix structure.
+ * \param a flags mask.
+ *
+ * \returns non-zero if all geometry related matrix flags are contained within
+ * the mask, or zero otherwise.
+ */
+#define TEST_MAT_FLAGS(mat, a) \
+ ((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0)
+
+
+
+/**
+ * Names of the corresponding GLmatrixtype values.
+ */
+static const char *types[] = {
+ "MATRIX_GENERAL",
+ "MATRIX_IDENTITY",
+ "MATRIX_3D_NO_ROT",
+ "MATRIX_PERSPECTIVE",
+ "MATRIX_2D",
+ "MATRIX_2D_NO_ROT",
+ "MATRIX_3D"
+};
+
+
+/**
+ * Identity matrix.
+ */
+static GLfloat Identity[16] = {
+ 1.0, 0.0, 0.0, 0.0,
+ 0.0, 1.0, 0.0, 0.0,
+ 0.0, 0.0, 1.0, 0.0,
+ 0.0, 0.0, 0.0, 1.0
+};
+
+
+
+/**********************************************************************/
+/** \name Matrix multiplication */
+/*@{*/
+
+#define A(row,col) a[(col<<2)+row]
+#define B(row,col) b[(col<<2)+row]
+#define P(row,col) product[(col<<2)+row]
+
+/**
+ * Perform a full 4x4 matrix multiplication.
+ *
+ * \param a matrix.
+ * \param b matrix.
+ * \param product will receive the product of \p a and \p b.
+ *
+ * \warning Is assumed that \p product != \p b. \p product == \p a is allowed.
+ *
+ * \note KW: 4*16 = 64 multiplications
+ *
+ * \author This \c matmul was contributed by Thomas Malik
+ */
+static void matmul4( GLfloat *product, const GLfloat *a, const GLfloat *b )
+{
+ GLint i;
+ for (i = 0; i < 4; i++) {
+ const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3);
+ P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0);
+ P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1);
+ P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2);
+ P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3);
+ }
+}
+
+/**
+ * Multiply two matrices known to occupy only the top three rows, such
+ * as typical model matrices, and orthogonal matrices.
+ *
+ * \param a matrix.
+ * \param b matrix.
+ * \param product will receive the product of \p a and \p b.
+ */
+static void matmul34( GLfloat *product, const GLfloat *a, const GLfloat *b )
+{
+ GLint i;
+ for (i = 0; i < 3; i++) {
+ const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3);
+ P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0);
+ P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1);
+ P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2);
+ P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3;
+ }
+ P(3,0) = 0;
+ P(3,1) = 0;
+ P(3,2) = 0;
+ P(3,3) = 1;
+}
+
+#undef A
+#undef B
+#undef P
+
+/**
+ * Multiply a matrix by an array of floats with known properties.
+ *
+ * \param mat pointer to a GLmatrix structure containing the left multiplication
+ * matrix, and that will receive the product result.
+ * \param m right multiplication matrix array.
+ * \param flags flags of the matrix \p m.
+ *
+ * Joins both flags and marks the type and inverse as dirty. Calls matmul34()
+ * if both matrices are 3D, or matmul4() otherwise.
+ */
+static void matrix_multf( GLmatrix *mat, const GLfloat *m, GLuint flags )
+{
+ mat->flags |= (flags | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE);
+
+ if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D))
+ matmul34( mat->m, mat->m, m );
+ else
+ matmul4( mat->m, mat->m, m );
+}
+
+/**
+ * Matrix multiplication.
+ *
+ * \param dest destination matrix.
+ * \param a left matrix.
+ * \param b right matrix.
+ *
+ * Joins both flags and marks the type and inverse as dirty. Calls matmul34()
+ * if both matrices are 3D, or matmul4() otherwise.
+ */
+void
+_math_matrix_mul_matrix( GLmatrix *dest, const GLmatrix *a, const GLmatrix *b )
+{
+ dest->flags = (a->flags |
+ b->flags |
+ MAT_DIRTY_TYPE |
+ MAT_DIRTY_INVERSE);
+
+ if (TEST_MAT_FLAGS(dest, MAT_FLAGS_3D))
+ matmul34( dest->m, a->m, b->m );
+ else
+ matmul4( dest->m, a->m, b->m );
+}
+
+/**
+ * Matrix multiplication.
+ *
+ * \param dest left and destination matrix.
+ * \param m right matrix array.
+ *
+ * Marks the matrix flags with general flag, and type and inverse dirty flags.
+ * Calls matmul4() for the multiplication.
+ */
+void
+_math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m )
+{
+ dest->flags |= (MAT_FLAG_GENERAL |
+ MAT_DIRTY_TYPE |
+ MAT_DIRTY_INVERSE |
+ MAT_DIRTY_FLAGS);
+
+ matmul4( dest->m, dest->m, m );
+}
+
+/*@}*/
+
+
+/**********************************************************************/
+/** \name Matrix output */
+/*@{*/
+
+/**
+ * Print a matrix array.
+ *
+ * \param m matrix array.
+ *
+ * Called by _math_matrix_print() to print a matrix or its inverse.
+ */
+static void print_matrix_floats( const GLfloat m[16] )
+{
+ int i;
+ for (i=0;i<4;i++) {
+ _mesa_debug(NULL,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] );
+ }
+}
+
+/**
+ * Dumps the contents of a GLmatrix structure.
+ *
+ * \param m pointer to the GLmatrix structure.
+ */
+void
+_math_matrix_print( const GLmatrix *m )
+{
+ _mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags);
+ print_matrix_floats(m->m);
+ _mesa_debug(NULL, "Inverse: \n");
+ if (m->inv) {
+ GLfloat prod[16];
+ print_matrix_floats(m->inv);
+ matmul4(prod, m->m, m->inv);
+ _mesa_debug(NULL, "Mat * Inverse:\n");
+ print_matrix_floats(prod);
+ }
+ else {
+ _mesa_debug(NULL, " - not available\n");
+ }
+}
+
+/*@}*/
+
+
+/**
+ * References an element of 4x4 matrix.
+ *
+ * \param m matrix array.
+ * \param c column of the desired element.
+ * \param r row of the desired element.
+ *
+ * \return value of the desired element.
+ *
+ * Calculate the linear storage index of the element and references it.
+ */
+#define MAT(m,r,c) (m)[(c)*4+(r)]
+
+
+/**********************************************************************/
+/** \name Matrix inversion */
+/*@{*/
+
+/**
+ * Swaps the values of two floating pointer variables.
+ *
+ * Used by invert_matrix_general() to swap the row pointers.
+ */
+#define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; }
+
+/**
+ * Compute inverse of 4x4 transformation matrix.
+ *
+ * \param mat pointer to a GLmatrix structure. The matrix inverse will be
+ * stored in the GLmatrix::inv attribute.
+ *
+ * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
+ *
+ * \author
+ * Code contributed by Jacques Leroy jle@star.be
+ *
+ * Calculates the inverse matrix by performing the gaussian matrix reduction
+ * with partial pivoting followed by back/substitution with the loops manually
+ * unrolled.
+ */
+static GLboolean invert_matrix_general( GLmatrix *mat )
+{
+ const GLfloat *m = mat->m;
+ GLfloat *out = mat->inv;
+ GLfloat wtmp[4][8];
+ GLfloat m0, m1, m2, m3, s;
+ GLfloat *r0, *r1, *r2, *r3;
+
+ r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
+
+ r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1),
+ r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3),
+ r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
+
+ r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1),
+ r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3),
+ r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
+
+ r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1),
+ r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3),
+ r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
+
+ r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1),
+ r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3),
+ r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
+
+ /* choose pivot - or die */
+ if (FABSF(r3[0])>FABSF(r2[0])) SWAP_ROWS(r3, r2);
+ if (FABSF(r2[0])>FABSF(r1[0])) SWAP_ROWS(r2, r1);
+ if (FABSF(r1[0])>FABSF(r0[0])) SWAP_ROWS(r1, r0);
+ if (0.0 == r0[0]) return GL_FALSE;
+
+ /* eliminate first variable */
+ m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0];
+ s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s;
+ s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s;
+ s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s;
+ s = r0[4];
+ if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; }
+ s = r0[5];
+ if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; }
+ s = r0[6];
+ if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; }
+ s = r0[7];
+ if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; }
+
+ /* choose pivot - or die */
+ if (FABSF(r3[1])>FABSF(r2[1])) SWAP_ROWS(r3, r2);
+ if (FABSF(r2[1])>FABSF(r1[1])) SWAP_ROWS(r2, r1);
+ if (0.0 == r1[1]) return GL_FALSE;
+
+ /* eliminate second variable */
+ m2 = r2[1]/r1[1]; m3 = r3[1]/r1[1];
+ r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2];
+ r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3];
+ s = r1[4]; if (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; }
+ s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; }
+ s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; }
+ s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; }
+
+ /* choose pivot - or die */
+ if (FABSF(r3[2])>FABSF(r2[2])) SWAP_ROWS(r3, r2);
+ if (0.0 == r2[2]) return GL_FALSE;
+
+ /* eliminate third variable */
+ m3 = r3[2]/r2[2];
+ r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
+ r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6],
+ r3[7] -= m3 * r2[7];
+
+ /* last check */
+ if (0.0 == r3[3]) return GL_FALSE;
+
+ s = 1.0F/r3[3]; /* now back substitute row 3 */
+ r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s;
+
+ m2 = r2[3]; /* now back substitute row 2 */
+ s = 1.0F/r2[2];
+ r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
+ r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
+ m1 = r1[3];
+ r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
+ r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
+ m0 = r0[3];
+ r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
+ r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
+
+ m1 = r1[2]; /* now back substitute row 1 */
+ s = 1.0F/r1[1];
+ r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
+ r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
+ m0 = r0[2];
+ r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
+ r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
+
+ m0 = r0[1]; /* now back substitute row 0 */
+ s = 1.0F/r0[0];
+ r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
+ r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
+
+ MAT(out,0,0) = r0[4]; MAT(out,0,1) = r0[5],
+ MAT(out,0,2) = r0[6]; MAT(out,0,3) = r0[7],
+ MAT(out,1,0) = r1[4]; MAT(out,1,1) = r1[5],
+ MAT(out,1,2) = r1[6]; MAT(out,1,3) = r1[7],
+ MAT(out,2,0) = r2[4]; MAT(out,2,1) = r2[5],
+ MAT(out,2,2) = r2[6]; MAT(out,2,3) = r2[7],
+ MAT(out,3,0) = r3[4]; MAT(out,3,1) = r3[5],
+ MAT(out,3,2) = r3[6]; MAT(out,3,3) = r3[7];
+
+ return GL_TRUE;
+}
+#undef SWAP_ROWS
+
+/**
+ * Compute inverse of a general 3d transformation matrix.
+ *
+ * \param mat pointer to a GLmatrix structure. The matrix inverse will be
+ * stored in the GLmatrix::inv attribute.
+ *
+ * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
+ *
+ * \author Adapted from graphics gems II.
+ *
+ * Calculates the inverse of the upper left by first calculating its
+ * determinant and multiplying it to the symmetric adjust matrix of each
+ * element. Finally deals with the translation part by transforming the
+ * original translation vector using by the calculated submatrix inverse.
+ */
+static GLboolean invert_matrix_3d_general( GLmatrix *mat )
+{
+ const GLfloat *in = mat->m;
+ GLfloat *out = mat->inv;
+ GLfloat pos, neg, t;
+ GLfloat det;
+
+ /* Calculate the determinant of upper left 3x3 submatrix and
+ * determine if the matrix is singular.
+ */
+ pos = neg = 0.0;
+ t = MAT(in,0,0) * MAT(in,1,1) * MAT(in,2,2);
+ if (t >= 0.0) pos += t; else neg += t;
+
+ t = MAT(in,1,0) * MAT(in,2,1) * MAT(in,0,2);
+ if (t >= 0.0) pos += t; else neg += t;
+
+ t = MAT(in,2,0) * MAT(in,0,1) * MAT(in,1,2);
+ if (t >= 0.0) pos += t; else neg += t;
+
+ t = -MAT(in,2,0) * MAT(in,1,1) * MAT(in,0,2);
+ if (t >= 0.0) pos += t; else neg += t;
+
+ t = -MAT(in,1,0) * MAT(in,0,1) * MAT(in,2,2);
+ if (t >= 0.0) pos += t; else neg += t;
+
+ t = -MAT(in,0,0) * MAT(in,2,1) * MAT(in,1,2);
+ if (t >= 0.0) pos += t; else neg += t;
+
+ det = pos + neg;
+
+ if (det*det < 1e-25)
+ return GL_FALSE;
+
+ det = 1.0F / det;
+ MAT(out,0,0) = ( (MAT(in,1,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,1,2) )*det);
+ MAT(out,0,1) = (- (MAT(in,0,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,0,2) )*det);
+ MAT(out,0,2) = ( (MAT(in,0,1)*MAT(in,1,2) - MAT(in,1,1)*MAT(in,0,2) )*det);
+ MAT(out,1,0) = (- (MAT(in,1,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,1,2) )*det);
+ MAT(out,1,1) = ( (MAT(in,0,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,0,2) )*det);
+ MAT(out,1,2) = (- (MAT(in,0,0)*MAT(in,1,2) - MAT(in,1,0)*MAT(in,0,2) )*det);
+ MAT(out,2,0) = ( (MAT(in,1,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,1,1) )*det);
+ MAT(out,2,1) = (- (MAT(in,0,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,0,1) )*det);
+ MAT(out,2,2) = ( (MAT(in,0,0)*MAT(in,1,1) - MAT(in,1,0)*MAT(in,0,1) )*det);
+
+ /* Do the translation part */
+ MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
+ MAT(in,1,3) * MAT(out,0,1) +
+ MAT(in,2,3) * MAT(out,0,2) );
+ MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
+ MAT(in,1,3) * MAT(out,1,1) +
+ MAT(in,2,3) * MAT(out,1,2) );
+ MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
+ MAT(in,1,3) * MAT(out,2,1) +
+ MAT(in,2,3) * MAT(out,2,2) );
+
+ return GL_TRUE;
+}
+
+/**
+ * Compute inverse of a 3d transformation matrix.
+ *
+ * \param mat pointer to a GLmatrix structure. The matrix inverse will be
+ * stored in the GLmatrix::inv attribute.
+ *
+ * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
+ *
+ * If the matrix is not an angle preserving matrix then calls
+ * invert_matrix_3d_general for the actual calculation. Otherwise calculates
+ * the inverse matrix analyzing and inverting each of the scaling, rotation and
+ * translation parts.
+ */
+static GLboolean invert_matrix_3d( GLmatrix *mat )
+{
+ const GLfloat *in = mat->m;
+ GLfloat *out = mat->inv;
+
+ if (!TEST_MAT_FLAGS(mat, MAT_FLAGS_ANGLE_PRESERVING)) {
+ return invert_matrix_3d_general( mat );
+ }
+
+ if (mat->flags & MAT_FLAG_UNIFORM_SCALE) {
+ GLfloat scale = (MAT(in,0,0) * MAT(in,0,0) +
+ MAT(in,0,1) * MAT(in,0,1) +
+ MAT(in,0,2) * MAT(in,0,2));
+
+ if (scale == 0.0)
+ return GL_FALSE;
+
+ scale = 1.0F / scale;
+
+ /* Transpose and scale the 3 by 3 upper-left submatrix. */
+ MAT(out,0,0) = scale * MAT(in,0,0);
+ MAT(out,1,0) = scale * MAT(in,0,1);
+ MAT(out,2,0) = scale * MAT(in,0,2);
+ MAT(out,0,1) = scale * MAT(in,1,0);
+ MAT(out,1,1) = scale * MAT(in,1,1);
+ MAT(out,2,1) = scale * MAT(in,1,2);
+ MAT(out,0,2) = scale * MAT(in,2,0);
+ MAT(out,1,2) = scale * MAT(in,2,1);
+ MAT(out,2,2) = scale * MAT(in,2,2);
+ }
+ else if (mat->flags & MAT_FLAG_ROTATION) {
+ /* Transpose the 3 by 3 upper-left submatrix. */
+ MAT(out,0,0) = MAT(in,0,0);
+ MAT(out,1,0) = MAT(in,0,1);
+ MAT(out,2,0) = MAT(in,0,2);
+ MAT(out,0,1) = MAT(in,1,0);
+ MAT(out,1,1) = MAT(in,1,1);
+ MAT(out,2,1) = MAT(in,1,2);
+ MAT(out,0,2) = MAT(in,2,0);
+ MAT(out,1,2) = MAT(in,2,1);
+ MAT(out,2,2) = MAT(in,2,2);
+ }
+ else {
+ /* pure translation */
+ memcpy( out, Identity, sizeof(Identity) );
+ MAT(out,0,3) = - MAT(in,0,3);
+ MAT(out,1,3) = - MAT(in,1,3);
+ MAT(out,2,3) = - MAT(in,2,3);
+ return GL_TRUE;
+ }
+
+ if (mat->flags & MAT_FLAG_TRANSLATION) {
+ /* Do the translation part */
+ MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
+ MAT(in,1,3) * MAT(out,0,1) +
+ MAT(in,2,3) * MAT(out,0,2) );
+ MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
+ MAT(in,1,3) * MAT(out,1,1) +
+ MAT(in,2,3) * MAT(out,1,2) );
+ MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
+ MAT(in,1,3) * MAT(out,2,1) +
+ MAT(in,2,3) * MAT(out,2,2) );
+ }
+ else {
+ MAT(out,0,3) = MAT(out,1,3) = MAT(out,2,3) = 0.0;
+ }
+
+ return GL_TRUE;
+}
+
+/**
+ * Compute inverse of an identity transformation matrix.
+ *
+ * \param mat pointer to a GLmatrix structure. The matrix inverse will be
+ * stored in the GLmatrix::inv attribute.
+ *
+ * \return always GL_TRUE.
+ *
+ * Simply copies Identity into GLmatrix::inv.
+ */
+static GLboolean invert_matrix_identity( GLmatrix *mat )
+{
+ memcpy( mat->inv, Identity, sizeof(Identity) );
+ return GL_TRUE;
+}
+
+/**
+ * Compute inverse of a no-rotation 3d transformation matrix.
+ *
+ * \param mat pointer to a GLmatrix structure. The matrix inverse will be
+ * stored in the GLmatrix::inv attribute.
+ *
+ * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
+ *
+ * Calculates the
+ */
+static GLboolean invert_matrix_3d_no_rot( GLmatrix *mat )
+{
+ const GLfloat *in = mat->m;
+ GLfloat *out = mat->inv;
+
+ if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0 || MAT(in,2,2) == 0 )
+ return GL_FALSE;
+
+ memcpy( out, Identity, 16 * sizeof(GLfloat) );
+ MAT(out,0,0) = 1.0F / MAT(in,0,0);
+ MAT(out,1,1) = 1.0F / MAT(in,1,1);
+ MAT(out,2,2) = 1.0F / MAT(in,2,2);
+
+ if (mat->flags & MAT_FLAG_TRANSLATION) {
+ MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0));
+ MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1));
+ MAT(out,2,3) = - (MAT(in,2,3) * MAT(out,2,2));
+ }
+
+ return GL_TRUE;
+}
+
+/**
+ * Compute inverse of a no-rotation 2d transformation matrix.
+ *
+ * \param mat pointer to a GLmatrix structure. The matrix inverse will be
+ * stored in the GLmatrix::inv attribute.
+ *
+ * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
+ *
+ * Calculates the inverse matrix by applying the inverse scaling and
+ * translation to the identity matrix.
+ */
+static GLboolean invert_matrix_2d_no_rot( GLmatrix *mat )
+{
+ const GLfloat *in = mat->m;
+ GLfloat *out = mat->inv;
+
+ if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0)
+ return GL_FALSE;
+
+ memcpy( out, Identity, 16 * sizeof(GLfloat) );
+ MAT(out,0,0) = 1.0F / MAT(in,0,0);
+ MAT(out,1,1) = 1.0F / MAT(in,1,1);
+
+ if (mat->flags & MAT_FLAG_TRANSLATION) {
+ MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0));
+ MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1));
+ }
+
+ return GL_TRUE;
+}
+
+#if 0
+/* broken */
+static GLboolean invert_matrix_perspective( GLmatrix *mat )
+{
+ const GLfloat *in = mat->m;
+ GLfloat *out = mat->inv;
+
+ if (MAT(in,2,3) == 0)
+ return GL_FALSE;
+
+ memcpy( out, Identity, 16 * sizeof(GLfloat) );
+
+ MAT(out,0,0) = 1.0F / MAT(in,0,0);
+ MAT(out,1,1) = 1.0F / MAT(in,1,1);
+
+ MAT(out,0,3) = MAT(in,0,2);
+ MAT(out,1,3) = MAT(in,1,2);
+
+ MAT(out,2,2) = 0;
+ MAT(out,2,3) = -1;
+
+ MAT(out,3,2) = 1.0F / MAT(in,2,3);
+ MAT(out,3,3) = MAT(in,2,2) * MAT(out,3,2);
+
+ return GL_TRUE;
+}
+#endif
+
+/**
+ * Matrix inversion function pointer type.
+ */
+typedef GLboolean (*inv_mat_func)( GLmatrix *mat );
+
+/**
+ * Table of the matrix inversion functions according to the matrix type.
+ */
+static inv_mat_func inv_mat_tab[7] = {
+ invert_matrix_general,
+ invert_matrix_identity,
+ invert_matrix_3d_no_rot,
+#if 0
+ /* Don't use this function for now - it fails when the projection matrix
+ * is premultiplied by a translation (ala Chromium's tilesort SPU).
+ */
+ invert_matrix_perspective,
+#else
+ invert_matrix_general,
+#endif
+ invert_matrix_3d, /* lazy! */
+ invert_matrix_2d_no_rot,
+ invert_matrix_3d
+};
+
+/**
+ * Compute inverse of a transformation matrix.
+ *
+ * \param mat pointer to a GLmatrix structure. The matrix inverse will be
+ * stored in the GLmatrix::inv attribute.
+ *
+ * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
+ *
+ * Calls the matrix inversion function in inv_mat_tab corresponding to the
+ * given matrix type. In case of failure, updates the MAT_FLAG_SINGULAR flag,
+ * and copies the identity matrix into GLmatrix::inv.
+ */
+static GLboolean matrix_invert( GLmatrix *mat )
+{
+ if (inv_mat_tab[mat->type](mat)) {
+ mat->flags &= ~MAT_FLAG_SINGULAR;
+ return GL_TRUE;
+ } else {
+ mat->flags |= MAT_FLAG_SINGULAR;
+ memcpy( mat->inv, Identity, sizeof(Identity) );
+ return GL_FALSE;
+ }
+}
+
+/*@}*/
+
+
+/**********************************************************************/
+/** \name Matrix generation */
+/*@{*/
+
+/**
+ * Generate a 4x4 transformation matrix from glRotate parameters, and
+ * post-multiply the input matrix by it.
+ *
+ * \author
+ * This function was contributed by Erich Boleyn (erich@uruk.org).
+ * Optimizations contributed by Rudolf Opalla (rudi@khm.de).
+ */
+void
+_math_matrix_rotate( GLmatrix *mat,
+ GLfloat angle, GLfloat x, GLfloat y, GLfloat z )
+{
+ GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c;
+ GLfloat m[16];
+ GLboolean optimized;
+
+ s = (GLfloat) sin( angle * DEG2RAD );
+ c = (GLfloat) cos( angle * DEG2RAD );
+
+ memcpy(m, Identity, sizeof(GLfloat)*16);
+ optimized = GL_FALSE;
+
+#define M(row,col) m[col*4+row]
+
+ if (x == 0.0F) {
+ if (y == 0.0F) {
+ if (z != 0.0F) {
+ optimized = GL_TRUE;
+ /* rotate only around z-axis */
+ M(0,0) = c;
+ M(1,1) = c;
+ if (z < 0.0F) {
+ M(0,1) = s;
+ M(1,0) = -s;
+ }
+ else {
+ M(0,1) = -s;
+ M(1,0) = s;
+ }
+ }
+ }
+ else if (z == 0.0F) {
+ optimized = GL_TRUE;
+ /* rotate only around y-axis */
+ M(0,0) = c;
+ M(2,2) = c;
+ if (y < 0.0F) {
+ M(0,2) = -s;
+ M(2,0) = s;
+ }
+ else {
+ M(0,2) = s;
+ M(2,0) = -s;
+ }
+ }
+ }
+ else if (y == 0.0F) {
+ if (z == 0.0F) {
+ optimized = GL_TRUE;
+ /* rotate only around x-axis */
+ M(1,1) = c;
+ M(2,2) = c;
+ if (x < 0.0F) {
+ M(1,2) = s;
+ M(2,1) = -s;
+ }
+ else {
+ M(1,2) = -s;
+ M(2,1) = s;
+ }
+ }
+ }
+
+ if (!optimized) {
+ const GLfloat mag = SQRTF(x * x + y * y + z * z);
+
+ if (mag <= 1.0e-4) {
+ /* no rotation, leave mat as-is */
+ return;
+ }
+
+ x /= mag;
+ y /= mag;
+ z /= mag;
+
+
+ /*
+ * Arbitrary axis rotation matrix.
+ *
+ * This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied
+ * like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation
+ * (which is about the X-axis), and the two composite transforms
+ * Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary
+ * from the arbitrary axis to the X-axis then back. They are
+ * all elementary rotations.
+ *
+ * Rz' is a rotation about the Z-axis, to bring the axis vector
+ * into the x-z plane. Then Ry' is applied, rotating about the
+ * Y-axis to bring the axis vector parallel with the X-axis. The
+ * rotation about the X-axis is then performed. Ry and Rz are
+ * simply the respective inverse transforms to bring the arbitrary
+ * axis back to its original orientation. The first transforms
+ * Rz' and Ry' are considered inverses, since the data from the
+ * arbitrary axis gives you info on how to get to it, not how
+ * to get away from it, and an inverse must be applied.
+ *
+ * The basic calculation used is to recognize that the arbitrary
+ * axis vector (x, y, z), since it is of unit length, actually
+ * represents the sines and cosines of the angles to rotate the
+ * X-axis to the same orientation, with theta being the angle about
+ * Z and phi the angle about Y (in the order described above)
+ * as follows:
+ *
+ * cos ( theta ) = x / sqrt ( 1 - z^2 )
+ * sin ( theta ) = y / sqrt ( 1 - z^2 )
+ *
+ * cos ( phi ) = sqrt ( 1 - z^2 )
+ * sin ( phi ) = z
+ *
+ * Note that cos ( phi ) can further be inserted to the above
+ * formulas:
+ *
+ * cos ( theta ) = x / cos ( phi )
+ * sin ( theta ) = y / sin ( phi )
+ *
+ * ...etc. Because of those relations and the standard trigonometric
+ * relations, it is pssible to reduce the transforms down to what
+ * is used below. It may be that any primary axis chosen will give the
+ * same results (modulo a sign convention) using thie method.
+ *
+ * Particularly nice is to notice that all divisions that might
+ * have caused trouble when parallel to certain planes or
+ * axis go away with care paid to reducing the expressions.
+ * After checking, it does perform correctly under all cases, since
+ * in all the cases of division where the denominator would have
+ * been zero, the numerator would have been zero as well, giving
+ * the expected result.
+ */
+
+ xx = x * x;
+ yy = y * y;
+ zz = z * z;
+ xy = x * y;
+ yz = y * z;
+ zx = z * x;
+ xs = x * s;
+ ys = y * s;
+ zs = z * s;
+ one_c = 1.0F - c;
+
+ /* We already hold the identity-matrix so we can skip some statements */
+ M(0,0) = (one_c * xx) + c;
+ M(0,1) = (one_c * xy) - zs;
+ M(0,2) = (one_c * zx) + ys;
+/* M(0,3) = 0.0F; */
+
+ M(1,0) = (one_c * xy) + zs;
+ M(1,1) = (one_c * yy) + c;
+ M(1,2) = (one_c * yz) - xs;
+/* M(1,3) = 0.0F; */
+
+ M(2,0) = (one_c * zx) - ys;
+ M(2,1) = (one_c * yz) + xs;
+ M(2,2) = (one_c * zz) + c;
+/* M(2,3) = 0.0F; */
+
+/*
+ M(3,0) = 0.0F;
+ M(3,1) = 0.0F;
+ M(3,2) = 0.0F;
+ M(3,3) = 1.0F;
+*/
+ }
+#undef M
+
+ matrix_multf( mat, m, MAT_FLAG_ROTATION );
+}
+
+/**
+ * Apply a perspective projection matrix.
+ *
+ * \param mat matrix to apply the projection.
+ * \param left left clipping plane coordinate.
+ * \param right right clipping plane coordinate.
+ * \param bottom bottom clipping plane coordinate.
+ * \param top top clipping plane coordinate.
+ * \param nearval distance to the near clipping plane.
+ * \param farval distance to the far clipping plane.
+ *
+ * Creates the projection matrix and multiplies it with \p mat, marking the
+ * MAT_FLAG_PERSPECTIVE flag.
+ */
+void
+_math_matrix_frustum( GLmatrix *mat,
+ GLfloat left, GLfloat right,
+ GLfloat bottom, GLfloat top,
+ GLfloat nearval, GLfloat farval )
+{
+ GLfloat x, y, a, b, c, d;
+ GLfloat m[16];
+
+ x = (2.0F*nearval) / (right-left);
+ y = (2.0F*nearval) / (top-bottom);
+ a = (right+left) / (right-left);
+ b = (top+bottom) / (top-bottom);
+ c = -(farval+nearval) / ( farval-nearval);
+ d = -(2.0F*farval*nearval) / (farval-nearval); /* error? */
+
+#define M(row,col) m[col*4+row]
+ M(0,0) = x; M(0,1) = 0.0F; M(0,2) = a; M(0,3) = 0.0F;
+ M(1,0) = 0.0F; M(1,1) = y; M(1,2) = b; M(1,3) = 0.0F;
+ M(2,0) = 0.0F; M(2,1) = 0.0F; M(2,2) = c; M(2,3) = d;
+ M(3,0) = 0.0F; M(3,1) = 0.0F; M(3,2) = -1.0F; M(3,3) = 0.0F;
+#undef M
+
+ matrix_multf( mat, m, MAT_FLAG_PERSPECTIVE );
+}
+
+/**
+ * Apply an orthographic projection matrix.
+ *
+ * \param mat matrix to apply the projection.
+ * \param left left clipping plane coordinate.
+ * \param right right clipping plane coordinate.
+ * \param bottom bottom clipping plane coordinate.
+ * \param top top clipping plane coordinate.
+ * \param nearval distance to the near clipping plane.
+ * \param farval distance to the far clipping plane.
+ *
+ * Creates the projection matrix and multiplies it with \p mat, marking the
+ * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags.
+ */
+void
+_math_matrix_ortho( GLmatrix *mat,
+ GLfloat left, GLfloat right,
+ GLfloat bottom, GLfloat top,
+ GLfloat nearval, GLfloat farval )
+{
+ GLfloat m[16];
+
+#define M(row,col) m[col*4+row]
+ M(0,0) = 2.0F / (right-left);
+ M(0,1) = 0.0F;
+ M(0,2) = 0.0F;
+ M(0,3) = -(right+left) / (right-left);
+
+ M(1,0) = 0.0F;
+ M(1,1) = 2.0F / (top-bottom);
+ M(1,2) = 0.0F;
+ M(1,3) = -(top+bottom) / (top-bottom);
+
+ M(2,0) = 0.0F;
+ M(2,1) = 0.0F;
+ M(2,2) = -2.0F / (farval-nearval);
+ M(2,3) = -(farval+nearval) / (farval-nearval);
+
+ M(3,0) = 0.0F;
+ M(3,1) = 0.0F;
+ M(3,2) = 0.0F;
+ M(3,3) = 1.0F;
+#undef M
+
+ matrix_multf( mat, m, (MAT_FLAG_GENERAL_SCALE|MAT_FLAG_TRANSLATION));
+}
+
+/**
+ * Multiply a matrix with a general scaling matrix.
+ *
+ * \param mat matrix.
+ * \param x x axis scale factor.
+ * \param y y axis scale factor.
+ * \param z z axis scale factor.
+ *
+ * Multiplies in-place the elements of \p mat by the scale factors. Checks if
+ * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE
+ * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and
+ * MAT_DIRTY_INVERSE dirty flags.
+ */
+void
+_math_matrix_scale( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
+{
+ GLfloat *m = mat->m;
+ m[0] *= x; m[4] *= y; m[8] *= z;
+ m[1] *= x; m[5] *= y; m[9] *= z;
+ m[2] *= x; m[6] *= y; m[10] *= z;
+ m[3] *= x; m[7] *= y; m[11] *= z;
+
+ if (FABSF(x - y) < 1e-8 && FABSF(x - z) < 1e-8)
+ mat->flags |= MAT_FLAG_UNIFORM_SCALE;
+ else
+ mat->flags |= MAT_FLAG_GENERAL_SCALE;
+
+ mat->flags |= (MAT_DIRTY_TYPE |
+ MAT_DIRTY_INVERSE);
+}
+
+/**
+ * Multiply a matrix with a translation matrix.
+ *
+ * \param mat matrix.
+ * \param x translation vector x coordinate.
+ * \param y translation vector y coordinate.
+ * \param z translation vector z coordinate.
+ *
+ * Adds the translation coordinates to the elements of \p mat in-place. Marks
+ * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE
+ * dirty flags.
+ */
+void
+_math_matrix_translate( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
+{
+ GLfloat *m = mat->m;
+ m[12] = m[0] * x + m[4] * y + m[8] * z + m[12];
+ m[13] = m[1] * x + m[5] * y + m[9] * z + m[13];
+ m[14] = m[2] * x + m[6] * y + m[10] * z + m[14];
+ m[15] = m[3] * x + m[7] * y + m[11] * z + m[15];
+
+ mat->flags |= (MAT_FLAG_TRANSLATION |
+ MAT_DIRTY_TYPE |
+ MAT_DIRTY_INVERSE);
+}
+
+
+/**
+ * Set matrix to do viewport and depthrange mapping.
+ * Transforms Normalized Device Coords to window/Z values.
+ */
+void
+_math_matrix_viewport(GLmatrix *m, GLint x, GLint y, GLint width, GLint height,
+ GLfloat zNear, GLfloat zFar, GLfloat depthMax)
+{
+ m->m[MAT_SX] = (GLfloat) width / 2.0F;
+ m->m[MAT_TX] = m->m[MAT_SX] + x;
+ m->m[MAT_SY] = (GLfloat) height / 2.0F;
+ m->m[MAT_TY] = m->m[MAT_SY] + y;
+ m->m[MAT_SZ] = depthMax * ((zFar - zNear) / 2.0F);
+ m->m[MAT_TZ] = depthMax * ((zFar - zNear) / 2.0F + zNear);
+ m->flags = MAT_FLAG_GENERAL_SCALE | MAT_FLAG_TRANSLATION;
+ m->type = MATRIX_3D_NO_ROT;
+}
+
+
+/**
+ * Set a matrix to the identity matrix.
+ *
+ * \param mat matrix.
+ *
+ * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL.
+ * Sets the matrix type to identity, and clear the dirty flags.
+ */
+void
+_math_matrix_set_identity( GLmatrix *mat )
+{
+ memcpy( mat->m, Identity, 16*sizeof(GLfloat) );
+
+ if (mat->inv)
+ memcpy( mat->inv, Identity, 16*sizeof(GLfloat) );
+
+ mat->type = MATRIX_IDENTITY;
+ mat->flags &= ~(MAT_DIRTY_FLAGS|
+ MAT_DIRTY_TYPE|
+ MAT_DIRTY_INVERSE);
+}
+
+/*@}*/
+
+
+/**********************************************************************/
+/** \name Matrix analysis */
+/*@{*/
+
+#define ZERO(x) (1<<x)
+#define ONE(x) (1<<(x+16))
+
+#define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14))
+#define MASK_NO_2D_SCALE ( ONE(0) | ONE(5))
+
+#define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\
+ ZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\
+ ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
+ ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
+
+#define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \
+ ZERO(1) | ZERO(9) | \
+ ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
+ ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
+
+#define MASK_2D ( ZERO(8) | \
+ ZERO(9) | \
+ ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
+ ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
+
+
+#define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \
+ ZERO(1) | ZERO(9) | \
+ ZERO(2) | ZERO(6) | \
+ ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
+
+#define MASK_3D ( \
+ \
+ \
+ ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
+
+
+#define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\
+ ZERO(1) | ZERO(13) |\
+ ZERO(2) | ZERO(6) | \
+ ZERO(3) | ZERO(7) | ZERO(15) )
+
+#define SQ(x) ((x)*(x))
+
+/**
+ * Determine type and flags from scratch.
+ *
+ * \param mat matrix.
+ *
+ * This is expensive enough to only want to do it once.
+ */
+static void analyse_from_scratch( GLmatrix *mat )
+{
+ const GLfloat *m = mat->m;
+ GLuint mask = 0;
+ GLuint i;
+
+ for (i = 0 ; i < 16 ; i++) {
+ if (m[i] == 0.0) mask |= (1<<i);
+ }
+
+ if (m[0] == 1.0F) mask |= (1<<16);
+ if (m[5] == 1.0F) mask |= (1<<21);
+ if (m[10] == 1.0F) mask |= (1<<26);
+ if (m[15] == 1.0F) mask |= (1<<31);
+
+ mat->flags &= ~MAT_FLAGS_GEOMETRY;
+
+ /* Check for translation - no-one really cares
+ */
+ if ((mask & MASK_NO_TRX) != MASK_NO_TRX)
+ mat->flags |= MAT_FLAG_TRANSLATION;
+
+ /* Do the real work
+ */
+ if (mask == (GLuint) MASK_IDENTITY) {
+ mat->type = MATRIX_IDENTITY;
+ }
+ else if ((mask & MASK_2D_NO_ROT) == (GLuint) MASK_2D_NO_ROT) {
+ mat->type = MATRIX_2D_NO_ROT;
+
+ if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE)
+ mat->flags |= MAT_FLAG_GENERAL_SCALE;
+ }
+ else if ((mask & MASK_2D) == (GLuint) MASK_2D) {
+ GLfloat mm = DOT2(m, m);
+ GLfloat m4m4 = DOT2(m+4,m+4);
+ GLfloat mm4 = DOT2(m,m+4);
+
+ mat->type = MATRIX_2D;
+
+ /* Check for scale */
+ if (SQ(mm-1) > SQ(1e-6) ||
+ SQ(m4m4-1) > SQ(1e-6))
+ mat->flags |= MAT_FLAG_GENERAL_SCALE;
+
+ /* Check for rotation */
+ if (SQ(mm4) > SQ(1e-6))
+ mat->flags |= MAT_FLAG_GENERAL_3D;
+ else
+ mat->flags |= MAT_FLAG_ROTATION;
+
+ }
+ else if ((mask & MASK_3D_NO_ROT) == (GLuint) MASK_3D_NO_ROT) {
+ mat->type = MATRIX_3D_NO_ROT;
+
+ /* Check for scale */
+ if (SQ(m[0]-m[5]) < SQ(1e-6) &&
+ SQ(m[0]-m[10]) < SQ(1e-6)) {
+ if (SQ(m[0]-1.0) > SQ(1e-6)) {
+ mat->flags |= MAT_FLAG_UNIFORM_SCALE;
+ }
+ }
+ else {
+ mat->flags |= MAT_FLAG_GENERAL_SCALE;
+ }
+ }
+ else if ((mask & MASK_3D) == (GLuint) MASK_3D) {
+ GLfloat c1 = DOT3(m,m);
+ GLfloat c2 = DOT3(m+4,m+4);
+ GLfloat c3 = DOT3(m+8,m+8);
+ GLfloat d1 = DOT3(m, m+4);
+ GLfloat cp[3];
+
+ mat->type = MATRIX_3D;
+
+ /* Check for scale */
+ if (SQ(c1-c2) < SQ(1e-6) && SQ(c1-c3) < SQ(1e-6)) {
+ if (SQ(c1-1.0) > SQ(1e-6))
+ mat->flags |= MAT_FLAG_UNIFORM_SCALE;
+ /* else no scale at all */
+ }
+ else {
+ mat->flags |= MAT_FLAG_GENERAL_SCALE;
+ }
+
+ /* Check for rotation */
+ if (SQ(d1) < SQ(1e-6)) {
+ CROSS3( cp, m, m+4 );
+ SUB_3V( cp, cp, (m+8) );
+ if (LEN_SQUARED_3FV(cp) < SQ(1e-6))
+ mat->flags |= MAT_FLAG_ROTATION;
+ else
+ mat->flags |= MAT_FLAG_GENERAL_3D;
+ }
+ else {
+ mat->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */
+ }
+ }
+ else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0F) {
+ mat->type = MATRIX_PERSPECTIVE;
+ mat->flags |= MAT_FLAG_GENERAL;
+ }
+ else {
+ mat->type = MATRIX_GENERAL;
+ mat->flags |= MAT_FLAG_GENERAL;
+ }
+}
+
+/**
+ * Analyze a matrix given that its flags are accurate.
+ *
+ * This is the more common operation, hopefully.
+ */
+static void analyse_from_flags( GLmatrix *mat )
+{
+ const GLfloat *m = mat->m;
+
+ if (TEST_MAT_FLAGS(mat, 0)) {
+ mat->type = MATRIX_IDENTITY;
+ }
+ else if (TEST_MAT_FLAGS(mat, (MAT_FLAG_TRANSLATION |
+ MAT_FLAG_UNIFORM_SCALE |
+ MAT_FLAG_GENERAL_SCALE))) {
+ if ( m[10]==1.0F && m[14]==0.0F ) {
+ mat->type = MATRIX_2D_NO_ROT;
+ }
+ else {
+ mat->type = MATRIX_3D_NO_ROT;
+ }
+ }
+ else if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) {
+ if ( m[ 8]==0.0F
+ && m[ 9]==0.0F
+ && m[2]==0.0F && m[6]==0.0F && m[10]==1.0F && m[14]==0.0F) {
+ mat->type = MATRIX_2D;
+ }
+ else {
+ mat->type = MATRIX_3D;
+ }
+ }
+ else if ( m[4]==0.0F && m[12]==0.0F
+ && m[1]==0.0F && m[13]==0.0F
+ && m[2]==0.0F && m[6]==0.0F
+ && m[3]==0.0F && m[7]==0.0F && m[11]==-1.0F && m[15]==0.0F) {
+ mat->type = MATRIX_PERSPECTIVE;
+ }
+ else {
+ mat->type = MATRIX_GENERAL;
+ }
+}
+
+/**
+ * Analyze and update a matrix.
+ *
+ * \param mat matrix.
+ *
+ * If the matrix type is dirty then calls either analyse_from_scratch() or
+ * analyse_from_flags() to determine its type, according to whether the flags
+ * are dirty or not, respectively. If the matrix has an inverse and it's dirty
+ * then calls matrix_invert(). Finally clears the dirty flags.
+ */
+void
+_math_matrix_analyse( GLmatrix *mat )
+{
+ if (mat->flags & MAT_DIRTY_TYPE) {
+ if (mat->flags & MAT_DIRTY_FLAGS)
+ analyse_from_scratch( mat );
+ else
+ analyse_from_flags( mat );
+ }
+
+ if (mat->inv && (mat->flags & MAT_DIRTY_INVERSE)) {
+ matrix_invert( mat );
+ mat->flags &= ~MAT_DIRTY_INVERSE;
+ }
+
+ mat->flags &= ~(MAT_DIRTY_FLAGS | MAT_DIRTY_TYPE);
+}
+
+/*@}*/
+
+
+/**
+ * Test if the given matrix preserves vector lengths.
+ */
+GLboolean
+_math_matrix_is_length_preserving( const GLmatrix *m )
+{
+ return TEST_MAT_FLAGS( m, MAT_FLAGS_LENGTH_PRESERVING);
+}
+
+
+/**
+ * Test if the given matrix does any rotation.
+ * (or perhaps if the upper-left 3x3 is non-identity)
+ */
+GLboolean
+_math_matrix_has_rotation( const GLmatrix *m )
+{
+ if (m->flags & (MAT_FLAG_GENERAL |
+ MAT_FLAG_ROTATION |
+ MAT_FLAG_GENERAL_3D |
+ MAT_FLAG_PERSPECTIVE))
+ return GL_TRUE;
+ else
+ return GL_FALSE;
+}
+
+
+GLboolean
+_math_matrix_is_general_scale( const GLmatrix *m )
+{
+ return (m->flags & MAT_FLAG_GENERAL_SCALE) ? GL_TRUE : GL_FALSE;
+}
+
+
+GLboolean
+_math_matrix_is_dirty( const GLmatrix *m )
+{
+ return (m->flags & MAT_DIRTY) ? GL_TRUE : GL_FALSE;
+}
+
+
+/**********************************************************************/
+/** \name Matrix setup */
+/*@{*/
+
+/**
+ * Copy a matrix.
+ *
+ * \param to destination matrix.
+ * \param from source matrix.
+ *
+ * Copies all fields in GLmatrix, creating an inverse array if necessary.
+ */
+void
+_math_matrix_copy( GLmatrix *to, const GLmatrix *from )
+{
+ memcpy( to->m, from->m, sizeof(Identity) );
+ to->flags = from->flags;
+ to->type = from->type;
+
+ if (to->inv != 0) {
+ if (from->inv == 0) {
+ matrix_invert( to );
+ }
+ else {
+ memcpy(to->inv, from->inv, sizeof(GLfloat)*16);
+ }
+ }
+}
+
+/**
+ * Loads a matrix array into GLmatrix.
+ *
+ * \param m matrix array.
+ * \param mat matrix.
+ *
+ * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY
+ * flags.
+ */
+void
+_math_matrix_loadf( GLmatrix *mat, const GLfloat *m )
+{
+ memcpy( mat->m, m, 16*sizeof(GLfloat) );
+ mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY);
+}
+
+/**
+ * Matrix constructor.
+ *
+ * \param m matrix.
+ *
+ * Initialize the GLmatrix fields.
+ */
+void
+_math_matrix_ctr( GLmatrix *m )
+{
+ m->m = (GLfloat *) _mesa_align_malloc( 16 * sizeof(GLfloat), 16 );
+ if (m->m)
+ memcpy( m->m, Identity, sizeof(Identity) );
+ m->inv = NULL;
+ m->type = MATRIX_IDENTITY;
+ m->flags = 0;
+}
+
+/**
+ * Matrix destructor.
+ *
+ * \param m matrix.
+ *
+ * Frees the data in a GLmatrix.
+ */
+void
+_math_matrix_dtr( GLmatrix *m )
+{
+ if (m->m) {
+ _mesa_align_free( m->m );
+ m->m = NULL;
+ }
+ if (m->inv) {
+ _mesa_align_free( m->inv );
+ m->inv = NULL;
+ }
+}
+
+/**
+ * Allocate a matrix inverse.
+ *
+ * \param m matrix.
+ *
+ * Allocates the matrix inverse, GLmatrix::inv, and sets it to Identity.
+ */
+void
+_math_matrix_alloc_inv( GLmatrix *m )
+{
+ if (!m->inv) {
+ m->inv = (GLfloat *) _mesa_align_malloc( 16 * sizeof(GLfloat), 16 );
+ if (m->inv)
+ memcpy( m->inv, Identity, 16 * sizeof(GLfloat) );
+ }
+}
+
+/*@}*/
+
+
+/**********************************************************************/
+/** \name Matrix transpose */
+/*@{*/
+
+/**
+ * Transpose a GLfloat matrix.
+ *
+ * \param to destination array.
+ * \param from source array.
+ */
+void
+_math_transposef( GLfloat to[16], const GLfloat from[16] )
+{
+ to[0] = from[0];
+ to[1] = from[4];
+ to[2] = from[8];
+ to[3] = from[12];
+ to[4] = from[1];
+ to[5] = from[5];
+ to[6] = from[9];
+ to[7] = from[13];
+ to[8] = from[2];
+ to[9] = from[6];
+ to[10] = from[10];
+ to[11] = from[14];
+ to[12] = from[3];
+ to[13] = from[7];
+ to[14] = from[11];
+ to[15] = from[15];
+}
+
+/**
+ * Transpose a GLdouble matrix.
+ *
+ * \param to destination array.
+ * \param from source array.
+ */
+void
+_math_transposed( GLdouble to[16], const GLdouble from[16] )
+{
+ to[0] = from[0];
+ to[1] = from[4];
+ to[2] = from[8];
+ to[3] = from[12];
+ to[4] = from[1];
+ to[5] = from[5];
+ to[6] = from[9];
+ to[7] = from[13];
+ to[8] = from[2];
+ to[9] = from[6];
+ to[10] = from[10];
+ to[11] = from[14];
+ to[12] = from[3];
+ to[13] = from[7];
+ to[14] = from[11];
+ to[15] = from[15];
+}
+
+/**
+ * Transpose a GLdouble matrix and convert to GLfloat.
+ *
+ * \param to destination array.
+ * \param from source array.
+ */
+void
+_math_transposefd( GLfloat to[16], const GLdouble from[16] )
+{
+ to[0] = (GLfloat) from[0];
+ to[1] = (GLfloat) from[4];
+ to[2] = (GLfloat) from[8];
+ to[3] = (GLfloat) from[12];
+ to[4] = (GLfloat) from[1];
+ to[5] = (GLfloat) from[5];
+ to[6] = (GLfloat) from[9];
+ to[7] = (GLfloat) from[13];
+ to[8] = (GLfloat) from[2];
+ to[9] = (GLfloat) from[6];
+ to[10] = (GLfloat) from[10];
+ to[11] = (GLfloat) from[14];
+ to[12] = (GLfloat) from[3];
+ to[13] = (GLfloat) from[7];
+ to[14] = (GLfloat) from[11];
+ to[15] = (GLfloat) from[15];
+}
+
+/*@}*/
+
+
+/**
+ * Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix. This
+ * function is used for transforming clipping plane equations and spotlight
+ * directions.
+ * Mathematically, u = v * m.
+ * Input: v - input vector
+ * m - transformation matrix
+ * Output: u - transformed vector
+ */
+void
+_mesa_transform_vector( GLfloat u[4], const GLfloat v[4], const GLfloat m[16] )
+{
+ const GLfloat v0 = v[0], v1 = v[1], v2 = v[2], v3 = v[3];
+#define M(row,col) m[row + col*4]
+ u[0] = v0 * M(0,0) + v1 * M(1,0) + v2 * M(2,0) + v3 * M(3,0);
+ u[1] = v0 * M(0,1) + v1 * M(1,1) + v2 * M(2,1) + v3 * M(3,1);
+ u[2] = v0 * M(0,2) + v1 * M(1,2) + v2 * M(2,2) + v3 * M(3,2);
+ u[3] = v0 * M(0,3) + v1 * M(1,3) + v2 * M(2,3) + v3 * M(3,3);
+#undef M
+}
|