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Diffstat (limited to 'src/mesa/math/m_matrix.c')
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diff --git a/src/mesa/math/m_matrix.c b/src/mesa/math/m_matrix.c new file mode 100644 index 00000000000..ae55c946d9c --- /dev/null +++ b/src/mesa/math/m_matrix.c @@ -0,0 +1,1113 @@ +/* $Id: m_matrix.c,v 1.1 2000/11/16 21:05:41 keithw 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 [email protected] + * 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 ([email protected]) */ + 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<<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. This is expensive enough to + * only want to do it once. + */ +static void analyze_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 == 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]; +} |