/* * 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 * THE AUTHORS 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 */ /*@{*/ #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 ) { GLfloat prod[16]; _mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags); print_matrix_floats(m->m); _mesa_debug(NULL, "Inverse: \n"); print_matrix_floats(m->inv); matmul4(prod, m->m, m->inv); _mesa_debug(NULL, "Mat * Inverse:\n"); print_matrix_floats(prod); } /*@}*/ /** * 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 point 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 (FABSF(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) ); 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<m; GLuint mask = 0; GLuint i; for (i = 0 ; i < 16 ; i++) { if (m[i] == 0.0) mask |= (1<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) ); memcpy(to->inv, from->inv, 16 * sizeof(GLfloat)); to->flags = from->flags; to->type = from->type; } /** * 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 = _mesa_align_malloc( 16 * sizeof(GLfloat), 16 ); if (m->m) memcpy( m->m, Identity, sizeof(Identity) ); m->inv = _mesa_align_malloc( 16 * sizeof(GLfloat), 16 ); if (m->inv) memcpy( m->inv, Identity, sizeof(Identity) ); 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; } } /*@}*/ /**********************************************************************/ /** \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 }