/* $Id: m_matrix.c,v 1.3 2000/11/20 15:16:33 brianp Exp $ */ /* * Mesa 3-D graphics library * Version: 3.5 * * Copyright (C) 1999-2000 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. */ /* * Matrix operations * * NOTES: * 1. 4x4 transformation matrices are stored in memory in column major order. * 2. Points/vertices are to be thought of as column vectors. * 3. Transformation of a point p by a matrix M is: p' = M * p */ #include "glheader.h" #include "macros.h" #include "mem.h" #include "mmath.h" #include "m_matrix.h" static const char *types[] = { "MATRIX_GENERAL", "MATRIX_IDENTITY", "MATRIX_3D_NO_ROT", "MATRIX_PERSPECTIVE", "MATRIX_2D", "MATRIX_2D_NO_ROT", "MATRIX_3D" }; 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 }; /* * This matmul was contributed by Thomas Malik * * Perform a 4x4 matrix multiplication (product = a x b). * Input: a, b - matrices to multiply * Output: product - product of a and b * WARNING: (product != b) assumed * NOTE: (product == a) allowed * * KW: 4*16 = 64 muls */ #define A(row,col) a[(col<<2)+row] #define B(row,col) b[(col<<2)+row] #define P(row,col) product[(col<<2)+row] 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 ortho matrices. */ 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. */ 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 ); } static void print_matrix_floats( const GLfloat m[16] ) { int i; for (i=0;i<4;i++) { fprintf(stderr,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] ); } } void _math_matrix_print( const GLmatrix *m ) { fprintf(stderr, "Matrix type: %s, flags: %x\n", types[m->type], m->flags); print_matrix_floats(m->m); fprintf(stderr, "Inverse: \n"); if (m->inv) { GLfloat prod[16]; print_matrix_floats(m->inv); matmul4(prod, m->m, m->inv); fprintf(stderr, "Mat * Inverse:\n"); print_matrix_floats(prod); } else { fprintf(stderr, " - not available\n"); } } #define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; } #define MAT(m,r,c) (m)[(c)*4+(r)] /* * Compute inverse of 4x4 transformation matrix. * Code contributed by Jacques Leroy jle@star.be * Return GL_TRUE for success, GL_FALSE for failure (singular matrix) */ 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 (fabs(r3[0])>fabs(r2[0])) SWAP_ROWS(r3, r2); if (fabs(r2[0])>fabs(r1[0])) SWAP_ROWS(r2, r1); if (fabs(r1[0])>fabs(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 (fabs(r3[1])>fabs(r2[1])) SWAP_ROWS(r3, r2); if (fabs(r2[1])>fabs(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 (fabs(r3[2])>fabs(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 = 1.0/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 = 1.0/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 = 1.0/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 = 1.0/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 /* Adapted from graphics gems II. */ 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 = 1.0 / 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; } 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 = 1.0 / 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; } static GLboolean invert_matrix_identity( GLmatrix *mat ) { MEMCPY( mat->inv, Identity, sizeof(Identity) ); return GL_TRUE; } 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) = 1.0 / MAT(in,0,0); MAT(out,1,1) = 1.0 / MAT(in,1,1); MAT(out,2,2) = 1.0 / 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; } 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) = 1.0 / MAT(in,0,0); MAT(out,1,1) = 1.0 / 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; } 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) = 1.0 / MAT(in,0,0); MAT(out,1,1) = 1.0 / 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) = 1.0 / MAT(in,2,3); MAT(out,3,3) = MAT(in,2,2) * MAT(out,3,2); return GL_TRUE; } typedef GLboolean (*inv_mat_func)( GLmatrix *mat ); static inv_mat_func inv_mat_tab[7] = { invert_matrix_general, invert_matrix_identity, invert_matrix_3d_no_rot, invert_matrix_perspective, invert_matrix_3d, /* lazy! */ invert_matrix_2d_no_rot, invert_matrix_3d }; 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; } } /* * Generate a 4x4 transformation matrix from glRotate parameters, and * postmultiply the input matrix by it. */ void _math_matrix_rotate( GLmatrix *mat, GLfloat angle, GLfloat x, GLfloat y, GLfloat z ) { /* This function contributed by Erich Boleyn (erich@uruk.org) */ GLfloat mag, s, c; GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c; GLfloat m[16]; s = sin( angle * DEG2RAD ); c = cos( angle * DEG2RAD ); mag = GL_SQRT( x*x + y*y + z*z ); if (mag <= 1.0e-4) { /* generate an identity matrix and return */ MEMCPY(m, Identity, sizeof(GLfloat)*16); return; } x /= mag; y /= mag; z /= mag; #define M(row,col) m[col*4+row] /* * 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 it's 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; 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 ); } void _math_matrix_frustrum( 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 = (2.0*nearval) / (right-left); y = (2.0*nearval) / (top-bottom); a = (right+left) / (right-left); b = (top+bottom) / (top-bottom); c = -(farval+nearval) / ( farval-nearval); d = -(2.0*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 ); } void _math_matrix_ortho( GLmatrix *mat, GLfloat left, GLfloat right, GLfloat bottom, GLfloat top, GLfloat nearval, GLfloat farval ) { GLfloat x, y, z; GLfloat tx, ty, tz; GLfloat m[16]; x = 2.0 / (right-left); y = 2.0 / (top-bottom); z = -2.0 / (farval-nearval); tx = -(right+left) / (right-left); ty = -(top+bottom) / (top-bottom); tz = -(farval+nearval) / (farval-nearval); #define M(row,col) m[col*4+row] M(0,0) = x; M(0,1) = 0.0F; M(0,2) = 0.0F; M(0,3) = tx; M(1,0) = 0.0F; M(1,1) = y; M(1,2) = 0.0F; M(1,3) = ty; M(2,0) = 0.0F; M(2,1) = 0.0F; M(2,2) = z; M(2,3) = tz; 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)); } #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 == MASK_IDENTITY) { mat->type = MATRIX_IDENTITY; } else if ((mask & MASK_2D_NO_ROT) == 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) == 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) == 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) == 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; } } /* Analyse a matrix given that its flags are accurate - this is the * more common operation, hopefully. */ static void analyze_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; } } void _math_matrix_analyze( GLmatrix *mat ) { if (mat->flags & MAT_DIRTY_TYPE) { if (mat->flags & MAT_DIRTY_FLAGS) analyze_from_scratch( mat ); else analyze_from_flags( mat ); } if (mat->inv && (mat->flags & MAT_DIRTY_INVERSE)) { matrix_invert( mat ); } mat->flags &= ~(MAT_DIRTY_FLAGS| MAT_DIRTY_TYPE| MAT_DIRTY_INVERSE); } 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); } } } 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 (fabs(x - y) < 1e-8 && fabs(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); } 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); } void _math_matrix_loadf( GLmatrix *mat, const GLfloat *m ) { MEMCPY( mat->m, m, 16*sizeof(GLfloat) ); mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY); } void _math_matrix_ctr( GLmatrix *m ) { if ( m->m == 0 ) { m->m = (GLfloat *) ALIGN_MALLOC( 16 * sizeof(GLfloat), 16 ); } MEMCPY( m->m, Identity, sizeof(Identity) ); m->inv = 0; m->type = MATRIX_IDENTITY; m->flags = 0; } void _math_matrix_dtr( GLmatrix *m ) { if ( m->m != 0 ) { ALIGN_FREE( m->m ); m->m = 0; } if ( m->inv != 0 ) { ALIGN_FREE( m->inv ); m->inv = 0; } } void _math_matrix_alloc_inv( GLmatrix *m ) { if ( m->inv == 0 ) { m->inv = (GLfloat *) ALIGN_MALLOC( 16 * sizeof(GLfloat), 16 ); MEMCPY( m->inv, Identity, 16 * sizeof(GLfloat) ); } } 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 ); } void _math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m ) { dest->flags |= (MAT_FLAG_GENERAL | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE); matmul4( dest->m, dest->m, m ); } 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); } 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]; } 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]; } void _math_transposefd( GLfloat 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]; }