Subversion Repositories Kolibri OS

Rev

Go to most recent revision | Blame | Last modification | View Log | Download | RSS feed

  1. /*
  2.  * Mesa 3-D graphics library
  3.  * Version:  6.3
  4.  *
  5.  * Copyright (C) 1999-2005  Brian Paul   All Rights Reserved.
  6.  *
  7.  * Permission is hereby granted, free of charge, to any person obtaining a
  8.  * copy of this software and associated documentation files (the "Software"),
  9.  * to deal in the Software without restriction, including without limitation
  10.  * the rights to use, copy, modify, merge, publish, distribute, sublicense,
  11.  * and/or sell copies of the Software, and to permit persons to whom the
  12.  * Software is furnished to do so, subject to the following conditions:
  13.  *
  14.  * The above copyright notice and this permission notice shall be included
  15.  * in all copies or substantial portions of the Software.
  16.  *
  17.  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
  18.  * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  19.  * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
  20.  * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
  21.  * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
  22.  * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
  23.  */
  24.  
  25.  
  26. /**
  27.  * \file m_matrix.c
  28.  * Matrix operations.
  29.  *
  30.  * \note
  31.  * -# 4x4 transformation matrices are stored in memory in column major order.
  32.  * -# Points/vertices are to be thought of as column vectors.
  33.  * -# Transformation of a point p by a matrix M is: p' = M * p
  34.  */
  35.  
  36.  
  37. #include "main/glheader.h"
  38. #include "main/imports.h"
  39. #include "main/macros.h"
  40.  
  41. #include "m_matrix.h"
  42.  
  43.  
  44. /**
  45.  * \defgroup MatFlags MAT_FLAG_XXX-flags
  46.  *
  47.  * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags
  48.  * It would be nice to make all these flags private to m_matrix.c
  49.  */
  50. /*@{*/
  51. #define MAT_FLAG_IDENTITY       0     /**< is an identity matrix flag.
  52.                                        *   (Not actually used - the identity
  53.                                        *   matrix is identified by the absense
  54.                                        *   of all other flags.)
  55.                                        */
  56. #define MAT_FLAG_GENERAL        0x1   /**< is a general matrix flag */
  57. #define MAT_FLAG_ROTATION       0x2   /**< is a rotation matrix flag */
  58. #define MAT_FLAG_TRANSLATION    0x4   /**< is a translation matrix flag */
  59. #define MAT_FLAG_UNIFORM_SCALE  0x8   /**< is an uniform scaling matrix flag */
  60. #define MAT_FLAG_GENERAL_SCALE  0x10  /**< is a general scaling matrix flag */
  61. #define MAT_FLAG_GENERAL_3D     0x20  /**< general 3D matrix flag */
  62. #define MAT_FLAG_PERSPECTIVE    0x40  /**< is a perspective proj matrix flag */
  63. #define MAT_FLAG_SINGULAR       0x80  /**< is a singular matrix flag */
  64. #define MAT_DIRTY_TYPE          0x100  /**< matrix type is dirty */
  65. #define MAT_DIRTY_FLAGS         0x200  /**< matrix flags are dirty */
  66. #define MAT_DIRTY_INVERSE       0x400  /**< matrix inverse is dirty */
  67.  
  68. /** angle preserving matrix flags mask */
  69. #define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \
  70.                                     MAT_FLAG_TRANSLATION | \
  71.                                     MAT_FLAG_UNIFORM_SCALE)
  72.  
  73. /** geometry related matrix flags mask */
  74. #define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \
  75.                             MAT_FLAG_ROTATION | \
  76.                             MAT_FLAG_TRANSLATION | \
  77.                             MAT_FLAG_UNIFORM_SCALE | \
  78.                             MAT_FLAG_GENERAL_SCALE | \
  79.                             MAT_FLAG_GENERAL_3D | \
  80.                             MAT_FLAG_PERSPECTIVE | \
  81.                             MAT_FLAG_SINGULAR)
  82.  
  83. /** length preserving matrix flags mask */
  84. #define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \
  85.                                      MAT_FLAG_TRANSLATION)
  86.  
  87.  
  88. /** 3D (non-perspective) matrix flags mask */
  89. #define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \
  90.                       MAT_FLAG_TRANSLATION | \
  91.                       MAT_FLAG_UNIFORM_SCALE | \
  92.                       MAT_FLAG_GENERAL_SCALE | \
  93.                       MAT_FLAG_GENERAL_3D)
  94.  
  95. /** dirty matrix flags mask */
  96. #define MAT_DIRTY          (MAT_DIRTY_TYPE | \
  97.                             MAT_DIRTY_FLAGS | \
  98.                             MAT_DIRTY_INVERSE)
  99.  
  100. /*@}*/
  101.  
  102.  
  103. /**
  104.  * Test geometry related matrix flags.
  105.  *
  106.  * \param mat a pointer to a GLmatrix structure.
  107.  * \param a flags mask.
  108.  *
  109.  * \returns non-zero if all geometry related matrix flags are contained within
  110.  * the mask, or zero otherwise.
  111.  */
  112. #define TEST_MAT_FLAGS(mat, a)  \
  113.     ((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0)
  114.  
  115.  
  116.  
  117. /**
  118.  * Names of the corresponding GLmatrixtype values.
  119.  */
  120. static const char *types[] = {
  121.    "MATRIX_GENERAL",
  122.    "MATRIX_IDENTITY",
  123.    "MATRIX_3D_NO_ROT",
  124.    "MATRIX_PERSPECTIVE",
  125.    "MATRIX_2D",
  126.    "MATRIX_2D_NO_ROT",
  127.    "MATRIX_3D"
  128. };
  129.  
  130.  
  131. /**
  132.  * Identity matrix.
  133.  */
  134. static GLfloat Identity[16] = {
  135.    1.0, 0.0, 0.0, 0.0,
  136.    0.0, 1.0, 0.0, 0.0,
  137.    0.0, 0.0, 1.0, 0.0,
  138.    0.0, 0.0, 0.0, 1.0
  139. };
  140.  
  141.  
  142.  
  143. /**********************************************************************/
  144. /** \name Matrix multiplication */
  145. /*@{*/
  146.  
  147. #define A(row,col)  a[(col<<2)+row]
  148. #define B(row,col)  b[(col<<2)+row]
  149. #define P(row,col)  product[(col<<2)+row]
  150.  
  151. /**
  152.  * Perform a full 4x4 matrix multiplication.
  153.  *
  154.  * \param a matrix.
  155.  * \param b matrix.
  156.  * \param product will receive the product of \p a and \p b.
  157.  *
  158.  * \warning Is assumed that \p product != \p b. \p product == \p a is allowed.
  159.  *
  160.  * \note KW: 4*16 = 64 multiplications
  161.  *
  162.  * \author This \c matmul was contributed by Thomas Malik
  163.  */
  164. static void matmul4( GLfloat *product, const GLfloat *a, const GLfloat *b )
  165. {
  166.    GLint i;
  167.    for (i = 0; i < 4; i++) {
  168.       const GLfloat ai0=A(i,0),  ai1=A(i,1),  ai2=A(i,2),  ai3=A(i,3);
  169.       P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0);
  170.       P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1);
  171.       P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2);
  172.       P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3);
  173.    }
  174. }
  175.  
  176. /**
  177.  * Multiply two matrices known to occupy only the top three rows, such
  178.  * as typical model matrices, and orthogonal matrices.
  179.  *
  180.  * \param a matrix.
  181.  * \param b matrix.
  182.  * \param product will receive the product of \p a and \p b.
  183.  */
  184. static void matmul34( GLfloat *product, const GLfloat *a, const GLfloat *b )
  185. {
  186.    GLint i;
  187.    for (i = 0; i < 3; i++) {
  188.       const GLfloat ai0=A(i,0),  ai1=A(i,1),  ai2=A(i,2),  ai3=A(i,3);
  189.       P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0);
  190.       P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1);
  191.       P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2);
  192.       P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3;
  193.    }
  194.    P(3,0) = 0;
  195.    P(3,1) = 0;
  196.    P(3,2) = 0;
  197.    P(3,3) = 1;
  198. }
  199.  
  200. #undef A
  201. #undef B
  202. #undef P
  203.  
  204. /**
  205.  * Multiply a matrix by an array of floats with known properties.
  206.  *
  207.  * \param mat pointer to a GLmatrix structure containing the left multiplication
  208.  * matrix, and that will receive the product result.
  209.  * \param m right multiplication matrix array.
  210.  * \param flags flags of the matrix \p m.
  211.  *
  212.  * Joins both flags and marks the type and inverse as dirty.  Calls matmul34()
  213.  * if both matrices are 3D, or matmul4() otherwise.
  214.  */
  215. static void matrix_multf( GLmatrix *mat, const GLfloat *m, GLuint flags )
  216. {
  217.    mat->flags |= (flags | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE);
  218.  
  219.    if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D))
  220.       matmul34( mat->m, mat->m, m );
  221.    else
  222.       matmul4( mat->m, mat->m, m );
  223. }
  224.  
  225. /**
  226.  * Matrix multiplication.
  227.  *
  228.  * \param dest destination matrix.
  229.  * \param a left matrix.
  230.  * \param b right matrix.
  231.  *
  232.  * Joins both flags and marks the type and inverse as dirty.  Calls matmul34()
  233.  * if both matrices are 3D, or matmul4() otherwise.
  234.  */
  235. void
  236. _math_matrix_mul_matrix( GLmatrix *dest, const GLmatrix *a, const GLmatrix *b )
  237. {
  238.    dest->flags = (a->flags |
  239.                   b->flags |
  240.                   MAT_DIRTY_TYPE |
  241.                   MAT_DIRTY_INVERSE);
  242.  
  243.    if (TEST_MAT_FLAGS(dest, MAT_FLAGS_3D))
  244.       matmul34( dest->m, a->m, b->m );
  245.    else
  246.       matmul4( dest->m, a->m, b->m );
  247. }
  248.  
  249. /**
  250.  * Matrix multiplication.
  251.  *
  252.  * \param dest left and destination matrix.
  253.  * \param m right matrix array.
  254.  *
  255.  * Marks the matrix flags with general flag, and type and inverse dirty flags.
  256.  * Calls matmul4() for the multiplication.
  257.  */
  258. void
  259. _math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m )
  260. {
  261.    dest->flags |= (MAT_FLAG_GENERAL |
  262.                    MAT_DIRTY_TYPE |
  263.                    MAT_DIRTY_INVERSE |
  264.                    MAT_DIRTY_FLAGS);
  265.  
  266.    matmul4( dest->m, dest->m, m );
  267. }
  268.  
  269. /*@}*/
  270.  
  271.  
  272. /**********************************************************************/
  273. /** \name Matrix output */
  274. /*@{*/
  275.  
  276. /**
  277.  * Print a matrix array.
  278.  *
  279.  * \param m matrix array.
  280.  *
  281.  * Called by _math_matrix_print() to print a matrix or its inverse.
  282.  */
  283. static void print_matrix_floats( const GLfloat m[16] )
  284. {
  285.    int i;
  286.    for (i=0;i<4;i++) {
  287.       _mesa_debug(NULL,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] );
  288.    }
  289. }
  290.  
  291. /**
  292.  * Dumps the contents of a GLmatrix structure.
  293.  *
  294.  * \param m pointer to the GLmatrix structure.
  295.  */
  296. void
  297. _math_matrix_print( const GLmatrix *m )
  298. {
  299.    _mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags);
  300.    print_matrix_floats(m->m);
  301.    _mesa_debug(NULL, "Inverse: \n");
  302.    if (m->inv) {
  303.       GLfloat prod[16];
  304.       print_matrix_floats(m->inv);
  305.       matmul4(prod, m->m, m->inv);
  306.       _mesa_debug(NULL, "Mat * Inverse:\n");
  307.       print_matrix_floats(prod);
  308.    }
  309.    else {
  310.       _mesa_debug(NULL, "  - not available\n");
  311.    }
  312. }
  313.  
  314. /*@}*/
  315.  
  316.  
  317. /**
  318.  * References an element of 4x4 matrix.
  319.  *
  320.  * \param m matrix array.
  321.  * \param c column of the desired element.
  322.  * \param r row of the desired element.
  323.  *
  324.  * \return value of the desired element.
  325.  *
  326.  * Calculate the linear storage index of the element and references it.
  327.  */
  328. #define MAT(m,r,c) (m)[(c)*4+(r)]
  329.  
  330.  
  331. /**********************************************************************/
  332. /** \name Matrix inversion */
  333. /*@{*/
  334.  
  335. /**
  336.  * Swaps the values of two floating pointer variables.
  337.  *
  338.  * Used by invert_matrix_general() to swap the row pointers.
  339.  */
  340. #define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; }
  341.  
  342. /**
  343.  * Compute inverse of 4x4 transformation matrix.
  344.  *
  345.  * \param mat pointer to a GLmatrix structure. The matrix inverse will be
  346.  * stored in the GLmatrix::inv attribute.
  347.  *
  348.  * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
  349.  *
  350.  * \author
  351.  * Code contributed by Jacques Leroy jle@star.be
  352.  *
  353.  * Calculates the inverse matrix by performing the gaussian matrix reduction
  354.  * with partial pivoting followed by back/substitution with the loops manually
  355.  * unrolled.
  356.  */
  357. static GLboolean invert_matrix_general( GLmatrix *mat )
  358. {
  359.    const GLfloat *m = mat->m;
  360.    GLfloat *out = mat->inv;
  361.    GLfloat wtmp[4][8];
  362.    GLfloat m0, m1, m2, m3, s;
  363.    GLfloat *r0, *r1, *r2, *r3;
  364.  
  365.    r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
  366.  
  367.    r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1),
  368.    r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3),
  369.    r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
  370.  
  371.    r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1),
  372.    r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3),
  373.    r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
  374.  
  375.    r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1),
  376.    r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3),
  377.    r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
  378.  
  379.    r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1),
  380.    r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3),
  381.    r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
  382.  
  383.    /* choose pivot - or die */
  384.    if (FABSF(r3[0])>FABSF(r2[0])) SWAP_ROWS(r3, r2);
  385.    if (FABSF(r2[0])>FABSF(r1[0])) SWAP_ROWS(r2, r1);
  386.    if (FABSF(r1[0])>FABSF(r0[0])) SWAP_ROWS(r1, r0);
  387.    if (0.0 == r0[0])  return GL_FALSE;
  388.  
  389.    /* eliminate first variable     */
  390.    m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0];
  391.    s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s;
  392.    s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s;
  393.    s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s;
  394.    s = r0[4];
  395.    if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; }
  396.    s = r0[5];
  397.    if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; }
  398.    s = r0[6];
  399.    if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; }
  400.    s = r0[7];
  401.    if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; }
  402.  
  403.    /* choose pivot - or die */
  404.    if (FABSF(r3[1])>FABSF(r2[1])) SWAP_ROWS(r3, r2);
  405.    if (FABSF(r2[1])>FABSF(r1[1])) SWAP_ROWS(r2, r1);
  406.    if (0.0 == r1[1])  return GL_FALSE;
  407.  
  408.    /* eliminate second variable */
  409.    m2 = r2[1]/r1[1]; m3 = r3[1]/r1[1];
  410.    r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2];
  411.    r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3];
  412.    s = r1[4]; if (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; }
  413.    s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; }
  414.    s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; }
  415.    s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; }
  416.  
  417.    /* choose pivot - or die */
  418.    if (FABSF(r3[2])>FABSF(r2[2])) SWAP_ROWS(r3, r2);
  419.    if (0.0 == r2[2])  return GL_FALSE;
  420.  
  421.    /* eliminate third variable */
  422.    m3 = r3[2]/r2[2];
  423.    r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
  424.    r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6],
  425.    r3[7] -= m3 * r2[7];
  426.  
  427.    /* last check */
  428.    if (0.0 == r3[3]) return GL_FALSE;
  429.  
  430.    s = 1.0F/r3[3];             /* now back substitute row 3 */
  431.    r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s;
  432.  
  433.    m2 = r2[3];                 /* now back substitute row 2 */
  434.    s  = 1.0F/r2[2];
  435.    r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
  436.    r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
  437.    m1 = r1[3];
  438.    r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
  439.    r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
  440.    m0 = r0[3];
  441.    r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
  442.    r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
  443.  
  444.    m1 = r1[2];                 /* now back substitute row 1 */
  445.    s  = 1.0F/r1[1];
  446.    r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
  447.    r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
  448.    m0 = r0[2];
  449.    r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
  450.    r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
  451.  
  452.    m0 = r0[1];                 /* now back substitute row 0 */
  453.    s  = 1.0F/r0[0];
  454.    r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
  455.    r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
  456.  
  457.    MAT(out,0,0) = r0[4]; MAT(out,0,1) = r0[5],
  458.    MAT(out,0,2) = r0[6]; MAT(out,0,3) = r0[7],
  459.    MAT(out,1,0) = r1[4]; MAT(out,1,1) = r1[5],
  460.    MAT(out,1,2) = r1[6]; MAT(out,1,3) = r1[7],
  461.    MAT(out,2,0) = r2[4]; MAT(out,2,1) = r2[5],
  462.    MAT(out,2,2) = r2[6]; MAT(out,2,3) = r2[7],
  463.    MAT(out,3,0) = r3[4]; MAT(out,3,1) = r3[5],
  464.    MAT(out,3,2) = r3[6]; MAT(out,3,3) = r3[7];
  465.  
  466.    return GL_TRUE;
  467. }
  468. #undef SWAP_ROWS
  469.  
  470. /**
  471.  * Compute inverse of a general 3d transformation matrix.
  472.  *
  473.  * \param mat pointer to a GLmatrix structure. The matrix inverse will be
  474.  * stored in the GLmatrix::inv attribute.
  475.  *
  476.  * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
  477.  *
  478.  * \author Adapted from graphics gems II.
  479.  *
  480.  * Calculates the inverse of the upper left by first calculating its
  481.  * determinant and multiplying it to the symmetric adjust matrix of each
  482.  * element. Finally deals with the translation part by transforming the
  483.  * original translation vector using by the calculated submatrix inverse.
  484.  */
  485. static GLboolean invert_matrix_3d_general( GLmatrix *mat )
  486. {
  487.    const GLfloat *in = mat->m;
  488.    GLfloat *out = mat->inv;
  489.    GLfloat pos, neg, t;
  490.    GLfloat det;
  491.  
  492.    /* Calculate the determinant of upper left 3x3 submatrix and
  493.     * determine if the matrix is singular.
  494.     */
  495.    pos = neg = 0.0;
  496.    t =  MAT(in,0,0) * MAT(in,1,1) * MAT(in,2,2);
  497.    if (t >= 0.0) pos += t; else neg += t;
  498.  
  499.    t =  MAT(in,1,0) * MAT(in,2,1) * MAT(in,0,2);
  500.    if (t >= 0.0) pos += t; else neg += t;
  501.  
  502.    t =  MAT(in,2,0) * MAT(in,0,1) * MAT(in,1,2);
  503.    if (t >= 0.0) pos += t; else neg += t;
  504.  
  505.    t = -MAT(in,2,0) * MAT(in,1,1) * MAT(in,0,2);
  506.    if (t >= 0.0) pos += t; else neg += t;
  507.  
  508.    t = -MAT(in,1,0) * MAT(in,0,1) * MAT(in,2,2);
  509.    if (t >= 0.0) pos += t; else neg += t;
  510.  
  511.    t = -MAT(in,0,0) * MAT(in,2,1) * MAT(in,1,2);
  512.    if (t >= 0.0) pos += t; else neg += t;
  513.  
  514.    det = pos + neg;
  515.  
  516.    if (det*det < 1e-25)
  517.       return GL_FALSE;
  518.  
  519.    det = 1.0F / det;
  520.    MAT(out,0,0) = (  (MAT(in,1,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,1,2) )*det);
  521.    MAT(out,0,1) = (- (MAT(in,0,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,0,2) )*det);
  522.    MAT(out,0,2) = (  (MAT(in,0,1)*MAT(in,1,2) - MAT(in,1,1)*MAT(in,0,2) )*det);
  523.    MAT(out,1,0) = (- (MAT(in,1,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,1,2) )*det);
  524.    MAT(out,1,1) = (  (MAT(in,0,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,0,2) )*det);
  525.    MAT(out,1,2) = (- (MAT(in,0,0)*MAT(in,1,2) - MAT(in,1,0)*MAT(in,0,2) )*det);
  526.    MAT(out,2,0) = (  (MAT(in,1,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,1,1) )*det);
  527.    MAT(out,2,1) = (- (MAT(in,0,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,0,1) )*det);
  528.    MAT(out,2,2) = (  (MAT(in,0,0)*MAT(in,1,1) - MAT(in,1,0)*MAT(in,0,1) )*det);
  529.  
  530.    /* Do the translation part */
  531.    MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
  532.                      MAT(in,1,3) * MAT(out,0,1) +
  533.                      MAT(in,2,3) * MAT(out,0,2) );
  534.    MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
  535.                      MAT(in,1,3) * MAT(out,1,1) +
  536.                      MAT(in,2,3) * MAT(out,1,2) );
  537.    MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
  538.                      MAT(in,1,3) * MAT(out,2,1) +
  539.                      MAT(in,2,3) * MAT(out,2,2) );
  540.  
  541.    return GL_TRUE;
  542. }
  543.  
  544. /**
  545.  * Compute inverse of a 3d transformation matrix.
  546.  *
  547.  * \param mat pointer to a GLmatrix structure. The matrix inverse will be
  548.  * stored in the GLmatrix::inv attribute.
  549.  *
  550.  * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
  551.  *
  552.  * If the matrix is not an angle preserving matrix then calls
  553.  * invert_matrix_3d_general for the actual calculation. Otherwise calculates
  554.  * the inverse matrix analyzing and inverting each of the scaling, rotation and
  555.  * translation parts.
  556.  */
  557. static GLboolean invert_matrix_3d( GLmatrix *mat )
  558. {
  559.    const GLfloat *in = mat->m;
  560.    GLfloat *out = mat->inv;
  561.  
  562.    if (!TEST_MAT_FLAGS(mat, MAT_FLAGS_ANGLE_PRESERVING)) {
  563.       return invert_matrix_3d_general( mat );
  564.    }
  565.  
  566.    if (mat->flags & MAT_FLAG_UNIFORM_SCALE) {
  567.       GLfloat scale = (MAT(in,0,0) * MAT(in,0,0) +
  568.                        MAT(in,0,1) * MAT(in,0,1) +
  569.                        MAT(in,0,2) * MAT(in,0,2));
  570.  
  571.       if (scale == 0.0)
  572.          return GL_FALSE;
  573.  
  574.       scale = 1.0F / scale;
  575.  
  576.       /* Transpose and scale the 3 by 3 upper-left submatrix. */
  577.       MAT(out,0,0) = scale * MAT(in,0,0);
  578.       MAT(out,1,0) = scale * MAT(in,0,1);
  579.       MAT(out,2,0) = scale * MAT(in,0,2);
  580.       MAT(out,0,1) = scale * MAT(in,1,0);
  581.       MAT(out,1,1) = scale * MAT(in,1,1);
  582.       MAT(out,2,1) = scale * MAT(in,1,2);
  583.       MAT(out,0,2) = scale * MAT(in,2,0);
  584.       MAT(out,1,2) = scale * MAT(in,2,1);
  585.       MAT(out,2,2) = scale * MAT(in,2,2);
  586.    }
  587.    else if (mat->flags & MAT_FLAG_ROTATION) {
  588.       /* Transpose the 3 by 3 upper-left submatrix. */
  589.       MAT(out,0,0) = MAT(in,0,0);
  590.       MAT(out,1,0) = MAT(in,0,1);
  591.       MAT(out,2,0) = MAT(in,0,2);
  592.       MAT(out,0,1) = MAT(in,1,0);
  593.       MAT(out,1,1) = MAT(in,1,1);
  594.       MAT(out,2,1) = MAT(in,1,2);
  595.       MAT(out,0,2) = MAT(in,2,0);
  596.       MAT(out,1,2) = MAT(in,2,1);
  597.       MAT(out,2,2) = MAT(in,2,2);
  598.    }
  599.    else {
  600.       /* pure translation */
  601.       memcpy( out, Identity, sizeof(Identity) );
  602.       MAT(out,0,3) = - MAT(in,0,3);
  603.       MAT(out,1,3) = - MAT(in,1,3);
  604.       MAT(out,2,3) = - MAT(in,2,3);
  605.       return GL_TRUE;
  606.    }
  607.  
  608.    if (mat->flags & MAT_FLAG_TRANSLATION) {
  609.       /* Do the translation part */
  610.       MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
  611.                         MAT(in,1,3) * MAT(out,0,1) +
  612.                         MAT(in,2,3) * MAT(out,0,2) );
  613.       MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
  614.                         MAT(in,1,3) * MAT(out,1,1) +
  615.                         MAT(in,2,3) * MAT(out,1,2) );
  616.       MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
  617.                         MAT(in,1,3) * MAT(out,2,1) +
  618.                         MAT(in,2,3) * MAT(out,2,2) );
  619.    }
  620.    else {
  621.       MAT(out,0,3) = MAT(out,1,3) = MAT(out,2,3) = 0.0;
  622.    }
  623.  
  624.    return GL_TRUE;
  625. }
  626.  
  627. /**
  628.  * Compute inverse of an identity transformation matrix.
  629.  *
  630.  * \param mat pointer to a GLmatrix structure. The matrix inverse will be
  631.  * stored in the GLmatrix::inv attribute.
  632.  *
  633.  * \return always GL_TRUE.
  634.  *
  635.  * Simply copies Identity into GLmatrix::inv.
  636.  */
  637. static GLboolean invert_matrix_identity( GLmatrix *mat )
  638. {
  639.    memcpy( mat->inv, Identity, sizeof(Identity) );
  640.    return GL_TRUE;
  641. }
  642.  
  643. /**
  644.  * Compute inverse of a no-rotation 3d transformation matrix.
  645.  *
  646.  * \param mat pointer to a GLmatrix structure. The matrix inverse will be
  647.  * stored in the GLmatrix::inv attribute.
  648.  *
  649.  * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
  650.  *
  651.  * Calculates the
  652.  */
  653. static GLboolean invert_matrix_3d_no_rot( GLmatrix *mat )
  654. {
  655.    const GLfloat *in = mat->m;
  656.    GLfloat *out = mat->inv;
  657.  
  658.    if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0 || MAT(in,2,2) == 0 )
  659.       return GL_FALSE;
  660.  
  661.    memcpy( out, Identity, 16 * sizeof(GLfloat) );
  662.    MAT(out,0,0) = 1.0F / MAT(in,0,0);
  663.    MAT(out,1,1) = 1.0F / MAT(in,1,1);
  664.    MAT(out,2,2) = 1.0F / MAT(in,2,2);
  665.  
  666.    if (mat->flags & MAT_FLAG_TRANSLATION) {
  667.       MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0));
  668.       MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1));
  669.       MAT(out,2,3) = - (MAT(in,2,3) * MAT(out,2,2));
  670.    }
  671.  
  672.    return GL_TRUE;
  673. }
  674.  
  675. /**
  676.  * Compute inverse of a no-rotation 2d transformation matrix.
  677.  *
  678.  * \param mat pointer to a GLmatrix structure. The matrix inverse will be
  679.  * stored in the GLmatrix::inv attribute.
  680.  *
  681.  * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
  682.  *
  683.  * Calculates the inverse matrix by applying the inverse scaling and
  684.  * translation to the identity matrix.
  685.  */
  686. static GLboolean invert_matrix_2d_no_rot( GLmatrix *mat )
  687. {
  688.    const GLfloat *in = mat->m;
  689.    GLfloat *out = mat->inv;
  690.  
  691.    if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0)
  692.       return GL_FALSE;
  693.  
  694.    memcpy( out, Identity, 16 * sizeof(GLfloat) );
  695.    MAT(out,0,0) = 1.0F / MAT(in,0,0);
  696.    MAT(out,1,1) = 1.0F / MAT(in,1,1);
  697.  
  698.    if (mat->flags & MAT_FLAG_TRANSLATION) {
  699.       MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0));
  700.       MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1));
  701.    }
  702.  
  703.    return GL_TRUE;
  704. }
  705.  
  706. #if 0
  707. /* broken */
  708. static GLboolean invert_matrix_perspective( GLmatrix *mat )
  709. {
  710.    const GLfloat *in = mat->m;
  711.    GLfloat *out = mat->inv;
  712.  
  713.    if (MAT(in,2,3) == 0)
  714.       return GL_FALSE;
  715.  
  716.    memcpy( out, Identity, 16 * sizeof(GLfloat) );
  717.  
  718.    MAT(out,0,0) = 1.0F / MAT(in,0,0);
  719.    MAT(out,1,1) = 1.0F / MAT(in,1,1);
  720.  
  721.    MAT(out,0,3) = MAT(in,0,2);
  722.    MAT(out,1,3) = MAT(in,1,2);
  723.  
  724.    MAT(out,2,2) = 0;
  725.    MAT(out,2,3) = -1;
  726.  
  727.    MAT(out,3,2) = 1.0F / MAT(in,2,3);
  728.    MAT(out,3,3) = MAT(in,2,2) * MAT(out,3,2);
  729.  
  730.    return GL_TRUE;
  731. }
  732. #endif
  733.  
  734. /**
  735.  * Matrix inversion function pointer type.
  736.  */
  737. typedef GLboolean (*inv_mat_func)( GLmatrix *mat );
  738.  
  739. /**
  740.  * Table of the matrix inversion functions according to the matrix type.
  741.  */
  742. static inv_mat_func inv_mat_tab[7] = {
  743.    invert_matrix_general,
  744.    invert_matrix_identity,
  745.    invert_matrix_3d_no_rot,
  746. #if 0
  747.    /* Don't use this function for now - it fails when the projection matrix
  748.     * is premultiplied by a translation (ala Chromium's tilesort SPU).
  749.     */
  750.    invert_matrix_perspective,
  751. #else
  752.    invert_matrix_general,
  753. #endif
  754.    invert_matrix_3d,            /* lazy! */
  755.    invert_matrix_2d_no_rot,
  756.    invert_matrix_3d
  757. };
  758.  
  759. /**
  760.  * Compute inverse of a transformation matrix.
  761.  *
  762.  * \param mat pointer to a GLmatrix structure. The matrix inverse will be
  763.  * stored in the GLmatrix::inv attribute.
  764.  *
  765.  * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
  766.  *
  767.  * Calls the matrix inversion function in inv_mat_tab corresponding to the
  768.  * given matrix type.  In case of failure, updates the MAT_FLAG_SINGULAR flag,
  769.  * and copies the identity matrix into GLmatrix::inv.
  770.  */
  771. static GLboolean matrix_invert( GLmatrix *mat )
  772. {
  773.    if (inv_mat_tab[mat->type](mat)) {
  774.       mat->flags &= ~MAT_FLAG_SINGULAR;
  775.       return GL_TRUE;
  776.    } else {
  777.       mat->flags |= MAT_FLAG_SINGULAR;
  778.       memcpy( mat->inv, Identity, sizeof(Identity) );
  779.       return GL_FALSE;
  780.    }
  781. }
  782.  
  783. /*@}*/
  784.  
  785.  
  786. /**********************************************************************/
  787. /** \name Matrix generation */
  788. /*@{*/
  789.  
  790. /**
  791.  * Generate a 4x4 transformation matrix from glRotate parameters, and
  792.  * post-multiply the input matrix by it.
  793.  *
  794.  * \author
  795.  * This function was contributed by Erich Boleyn (erich@uruk.org).
  796.  * Optimizations contributed by Rudolf Opalla (rudi@khm.de).
  797.  */
  798. void
  799. _math_matrix_rotate( GLmatrix *mat,
  800.                      GLfloat angle, GLfloat x, GLfloat y, GLfloat z )
  801. {
  802.    GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c;
  803.    GLfloat m[16];
  804.    GLboolean optimized;
  805.  
  806.    s = (GLfloat) sin( angle * DEG2RAD );
  807.    c = (GLfloat) cos( angle * DEG2RAD );
  808.  
  809.    memcpy(m, Identity, sizeof(GLfloat)*16);
  810.    optimized = GL_FALSE;
  811.  
  812. #define M(row,col)  m[col*4+row]
  813.  
  814.    if (x == 0.0F) {
  815.       if (y == 0.0F) {
  816.          if (z != 0.0F) {
  817.             optimized = GL_TRUE;
  818.             /* rotate only around z-axis */
  819.             M(0,0) = c;
  820.             M(1,1) = c;
  821.             if (z < 0.0F) {
  822.                M(0,1) = s;
  823.                M(1,0) = -s;
  824.             }
  825.             else {
  826.                M(0,1) = -s;
  827.                M(1,0) = s;
  828.             }
  829.          }
  830.       }
  831.       else if (z == 0.0F) {
  832.          optimized = GL_TRUE;
  833.          /* rotate only around y-axis */
  834.          M(0,0) = c;
  835.          M(2,2) = c;
  836.          if (y < 0.0F) {
  837.             M(0,2) = -s;
  838.             M(2,0) = s;
  839.          }
  840.          else {
  841.             M(0,2) = s;
  842.             M(2,0) = -s;
  843.          }
  844.       }
  845.    }
  846.    else if (y == 0.0F) {
  847.       if (z == 0.0F) {
  848.          optimized = GL_TRUE;
  849.          /* rotate only around x-axis */
  850.          M(1,1) = c;
  851.          M(2,2) = c;
  852.          if (x < 0.0F) {
  853.             M(1,2) = s;
  854.             M(2,1) = -s;
  855.          }
  856.          else {
  857.             M(1,2) = -s;
  858.             M(2,1) = s;
  859.          }
  860.       }
  861.    }
  862.  
  863.    if (!optimized) {
  864.       const GLfloat mag = SQRTF(x * x + y * y + z * z);
  865.  
  866.       if (mag <= 1.0e-4) {
  867.          /* no rotation, leave mat as-is */
  868.          return;
  869.       }
  870.  
  871.       x /= mag;
  872.       y /= mag;
  873.       z /= mag;
  874.  
  875.  
  876.       /*
  877.        *     Arbitrary axis rotation matrix.
  878.        *
  879.        *  This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied
  880.        *  like so:  Rz * Ry * T * Ry' * Rz'.  T is the final rotation
  881.        *  (which is about the X-axis), and the two composite transforms
  882.        *  Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary
  883.        *  from the arbitrary axis to the X-axis then back.  They are
  884.        *  all elementary rotations.
  885.        *
  886.        *  Rz' is a rotation about the Z-axis, to bring the axis vector
  887.        *  into the x-z plane.  Then Ry' is applied, rotating about the
  888.        *  Y-axis to bring the axis vector parallel with the X-axis.  The
  889.        *  rotation about the X-axis is then performed.  Ry and Rz are
  890.        *  simply the respective inverse transforms to bring the arbitrary
  891.        *  axis back to its original orientation.  The first transforms
  892.        *  Rz' and Ry' are considered inverses, since the data from the
  893.        *  arbitrary axis gives you info on how to get to it, not how
  894.        *  to get away from it, and an inverse must be applied.
  895.        *
  896.        *  The basic calculation used is to recognize that the arbitrary
  897.        *  axis vector (x, y, z), since it is of unit length, actually
  898.        *  represents the sines and cosines of the angles to rotate the
  899.        *  X-axis to the same orientation, with theta being the angle about
  900.        *  Z and phi the angle about Y (in the order described above)
  901.        *  as follows:
  902.        *
  903.        *  cos ( theta ) = x / sqrt ( 1 - z^2 )
  904.        *  sin ( theta ) = y / sqrt ( 1 - z^2 )
  905.        *
  906.        *  cos ( phi ) = sqrt ( 1 - z^2 )
  907.        *  sin ( phi ) = z
  908.        *
  909.        *  Note that cos ( phi ) can further be inserted to the above
  910.        *  formulas:
  911.        *
  912.        *  cos ( theta ) = x / cos ( phi )
  913.        *  sin ( theta ) = y / sin ( phi )
  914.        *
  915.        *  ...etc.  Because of those relations and the standard trigonometric
  916.        *  relations, it is pssible to reduce the transforms down to what
  917.        *  is used below.  It may be that any primary axis chosen will give the
  918.        *  same results (modulo a sign convention) using thie method.
  919.        *
  920.        *  Particularly nice is to notice that all divisions that might
  921.        *  have caused trouble when parallel to certain planes or
  922.        *  axis go away with care paid to reducing the expressions.
  923.        *  After checking, it does perform correctly under all cases, since
  924.        *  in all the cases of division where the denominator would have
  925.        *  been zero, the numerator would have been zero as well, giving
  926.        *  the expected result.
  927.        */
  928.  
  929.       xx = x * x;
  930.       yy = y * y;
  931.       zz = z * z;
  932.       xy = x * y;
  933.       yz = y * z;
  934.       zx = z * x;
  935.       xs = x * s;
  936.       ys = y * s;
  937.       zs = z * s;
  938.       one_c = 1.0F - c;
  939.  
  940.       /* We already hold the identity-matrix so we can skip some statements */
  941.       M(0,0) = (one_c * xx) + c;
  942.       M(0,1) = (one_c * xy) - zs;
  943.       M(0,2) = (one_c * zx) + ys;
  944. /*    M(0,3) = 0.0F; */
  945.  
  946.       M(1,0) = (one_c * xy) + zs;
  947.       M(1,1) = (one_c * yy) + c;
  948.       M(1,2) = (one_c * yz) - xs;
  949. /*    M(1,3) = 0.0F; */
  950.  
  951.       M(2,0) = (one_c * zx) - ys;
  952.       M(2,1) = (one_c * yz) + xs;
  953.       M(2,2) = (one_c * zz) + c;
  954. /*    M(2,3) = 0.0F; */
  955.  
  956. /*
  957.       M(3,0) = 0.0F;
  958.       M(3,1) = 0.0F;
  959.       M(3,2) = 0.0F;
  960.       M(3,3) = 1.0F;
  961. */
  962.    }
  963. #undef M
  964.  
  965.    matrix_multf( mat, m, MAT_FLAG_ROTATION );
  966. }
  967.  
  968. /**
  969.  * Apply a perspective projection matrix.
  970.  *
  971.  * \param mat matrix to apply the projection.
  972.  * \param left left clipping plane coordinate.
  973.  * \param right right clipping plane coordinate.
  974.  * \param bottom bottom clipping plane coordinate.
  975.  * \param top top clipping plane coordinate.
  976.  * \param nearval distance to the near clipping plane.
  977.  * \param farval distance to the far clipping plane.
  978.  *
  979.  * Creates the projection matrix and multiplies it with \p mat, marking the
  980.  * MAT_FLAG_PERSPECTIVE flag.
  981.  */
  982. void
  983. _math_matrix_frustum( GLmatrix *mat,
  984.                       GLfloat left, GLfloat right,
  985.                       GLfloat bottom, GLfloat top,
  986.                       GLfloat nearval, GLfloat farval )
  987. {
  988.    GLfloat x, y, a, b, c, d;
  989.    GLfloat m[16];
  990.  
  991.    x = (2.0F*nearval) / (right-left);
  992.    y = (2.0F*nearval) / (top-bottom);
  993.    a = (right+left) / (right-left);
  994.    b = (top+bottom) / (top-bottom);
  995.    c = -(farval+nearval) / ( farval-nearval);
  996.    d = -(2.0F*farval*nearval) / (farval-nearval);  /* error? */
  997.  
  998. #define M(row,col)  m[col*4+row]
  999.    M(0,0) = x;     M(0,1) = 0.0F;  M(0,2) = a;      M(0,3) = 0.0F;
  1000.    M(1,0) = 0.0F;  M(1,1) = y;     M(1,2) = b;      M(1,3) = 0.0F;
  1001.    M(2,0) = 0.0F;  M(2,1) = 0.0F;  M(2,2) = c;      M(2,3) = d;
  1002.    M(3,0) = 0.0F;  M(3,1) = 0.0F;  M(3,2) = -1.0F;  M(3,3) = 0.0F;
  1003. #undef M
  1004.  
  1005.    matrix_multf( mat, m, MAT_FLAG_PERSPECTIVE );
  1006. }
  1007.  
  1008. /**
  1009.  * Apply an orthographic projection matrix.
  1010.  *
  1011.  * \param mat matrix to apply the projection.
  1012.  * \param left left clipping plane coordinate.
  1013.  * \param right right clipping plane coordinate.
  1014.  * \param bottom bottom clipping plane coordinate.
  1015.  * \param top top clipping plane coordinate.
  1016.  * \param nearval distance to the near clipping plane.
  1017.  * \param farval distance to the far clipping plane.
  1018.  *
  1019.  * Creates the projection matrix and multiplies it with \p mat, marking the
  1020.  * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags.
  1021.  */
  1022. void
  1023. _math_matrix_ortho( GLmatrix *mat,
  1024.                     GLfloat left, GLfloat right,
  1025.                     GLfloat bottom, GLfloat top,
  1026.                     GLfloat nearval, GLfloat farval )
  1027. {
  1028.    GLfloat m[16];
  1029.  
  1030. #define M(row,col)  m[col*4+row]
  1031.    M(0,0) = 2.0F / (right-left);
  1032.    M(0,1) = 0.0F;
  1033.    M(0,2) = 0.0F;
  1034.    M(0,3) = -(right+left) / (right-left);
  1035.  
  1036.    M(1,0) = 0.0F;
  1037.    M(1,1) = 2.0F / (top-bottom);
  1038.    M(1,2) = 0.0F;
  1039.    M(1,3) = -(top+bottom) / (top-bottom);
  1040.  
  1041.    M(2,0) = 0.0F;
  1042.    M(2,1) = 0.0F;
  1043.    M(2,2) = -2.0F / (farval-nearval);
  1044.    M(2,3) = -(farval+nearval) / (farval-nearval);
  1045.  
  1046.    M(3,0) = 0.0F;
  1047.    M(3,1) = 0.0F;
  1048.    M(3,2) = 0.0F;
  1049.    M(3,3) = 1.0F;
  1050. #undef M
  1051.  
  1052.    matrix_multf( mat, m, (MAT_FLAG_GENERAL_SCALE|MAT_FLAG_TRANSLATION));
  1053. }
  1054.  
  1055. /**
  1056.  * Multiply a matrix with a general scaling matrix.
  1057.  *
  1058.  * \param mat matrix.
  1059.  * \param x x axis scale factor.
  1060.  * \param y y axis scale factor.
  1061.  * \param z z axis scale factor.
  1062.  *
  1063.  * Multiplies in-place the elements of \p mat by the scale factors. Checks if
  1064.  * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE
  1065.  * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and
  1066.  * MAT_DIRTY_INVERSE dirty flags.
  1067.  */
  1068. void
  1069. _math_matrix_scale( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
  1070. {
  1071.    GLfloat *m = mat->m;
  1072.    m[0] *= x;   m[4] *= y;   m[8]  *= z;
  1073.    m[1] *= x;   m[5] *= y;   m[9]  *= z;
  1074.    m[2] *= x;   m[6] *= y;   m[10] *= z;
  1075.    m[3] *= x;   m[7] *= y;   m[11] *= z;
  1076.  
  1077.    if (FABSF(x - y) < 1e-8 && FABSF(x - z) < 1e-8)
  1078.       mat->flags |= MAT_FLAG_UNIFORM_SCALE;
  1079.    else
  1080.       mat->flags |= MAT_FLAG_GENERAL_SCALE;
  1081.  
  1082.    mat->flags |= (MAT_DIRTY_TYPE |
  1083.                   MAT_DIRTY_INVERSE);
  1084. }
  1085.  
  1086. /**
  1087.  * Multiply a matrix with a translation matrix.
  1088.  *
  1089.  * \param mat matrix.
  1090.  * \param x translation vector x coordinate.
  1091.  * \param y translation vector y coordinate.
  1092.  * \param z translation vector z coordinate.
  1093.  *
  1094.  * Adds the translation coordinates to the elements of \p mat in-place.  Marks
  1095.  * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE
  1096.  * dirty flags.
  1097.  */
  1098. void
  1099. _math_matrix_translate( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
  1100. {
  1101.    GLfloat *m = mat->m;
  1102.    m[12] = m[0] * x + m[4] * y + m[8]  * z + m[12];
  1103.    m[13] = m[1] * x + m[5] * y + m[9]  * z + m[13];
  1104.    m[14] = m[2] * x + m[6] * y + m[10] * z + m[14];
  1105.    m[15] = m[3] * x + m[7] * y + m[11] * z + m[15];
  1106.  
  1107.    mat->flags |= (MAT_FLAG_TRANSLATION |
  1108.                   MAT_DIRTY_TYPE |
  1109.                   MAT_DIRTY_INVERSE);
  1110. }
  1111.  
  1112.  
  1113. /**
  1114.  * Set matrix to do viewport and depthrange mapping.
  1115.  * Transforms Normalized Device Coords to window/Z values.
  1116.  */
  1117. void
  1118. _math_matrix_viewport(GLmatrix *m, GLint x, GLint y, GLint width, GLint height,
  1119.                       GLfloat zNear, GLfloat zFar, GLfloat depthMax)
  1120. {
  1121.    m->m[MAT_SX] = (GLfloat) width / 2.0F;
  1122.    m->m[MAT_TX] = m->m[MAT_SX] + x;
  1123.    m->m[MAT_SY] = (GLfloat) height / 2.0F;
  1124.    m->m[MAT_TY] = m->m[MAT_SY] + y;
  1125.    m->m[MAT_SZ] = depthMax * ((zFar - zNear) / 2.0F);
  1126.    m->m[MAT_TZ] = depthMax * ((zFar - zNear) / 2.0F + zNear);
  1127.    m->flags = MAT_FLAG_GENERAL_SCALE | MAT_FLAG_TRANSLATION;
  1128.    m->type = MATRIX_3D_NO_ROT;
  1129. }
  1130.  
  1131.  
  1132. /**
  1133.  * Set a matrix to the identity matrix.
  1134.  *
  1135.  * \param mat matrix.
  1136.  *
  1137.  * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL.
  1138.  * Sets the matrix type to identity, and clear the dirty flags.
  1139.  */
  1140. void
  1141. _math_matrix_set_identity( GLmatrix *mat )
  1142. {
  1143.    memcpy( mat->m, Identity, 16*sizeof(GLfloat) );
  1144.  
  1145.    if (mat->inv)
  1146.       memcpy( mat->inv, Identity, 16*sizeof(GLfloat) );
  1147.  
  1148.    mat->type = MATRIX_IDENTITY;
  1149.    mat->flags &= ~(MAT_DIRTY_FLAGS|
  1150.                    MAT_DIRTY_TYPE|
  1151.                    MAT_DIRTY_INVERSE);
  1152. }
  1153.  
  1154. /*@}*/
  1155.  
  1156.  
  1157. /**********************************************************************/
  1158. /** \name Matrix analysis */
  1159. /*@{*/
  1160.  
  1161. #define ZERO(x) (1<<x)
  1162. #define ONE(x)  (1<<(x+16))
  1163.  
  1164. #define MASK_NO_TRX      (ZERO(12) | ZERO(13) | ZERO(14))
  1165. #define MASK_NO_2D_SCALE ( ONE(0)  | ONE(5))
  1166.  
  1167. #define MASK_IDENTITY    ( ONE(0)  | ZERO(4)  | ZERO(8)  | ZERO(12) |\
  1168.                           ZERO(1)  |  ONE(5)  | ZERO(9)  | ZERO(13) |\
  1169.                           ZERO(2)  | ZERO(6)  |  ONE(10) | ZERO(14) |\
  1170.                           ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )
  1171.  
  1172. #define MASK_2D_NO_ROT   (           ZERO(4)  | ZERO(8)  |           \
  1173.                           ZERO(1)  |            ZERO(9)  |           \
  1174.                           ZERO(2)  | ZERO(6)  |  ONE(10) | ZERO(14) |\
  1175.                           ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )
  1176.  
  1177. #define MASK_2D          (                      ZERO(8)  |           \
  1178.                                                 ZERO(9)  |           \
  1179.                           ZERO(2)  | ZERO(6)  |  ONE(10) | ZERO(14) |\
  1180.                           ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )
  1181.  
  1182.  
  1183. #define MASK_3D_NO_ROT   (           ZERO(4)  | ZERO(8)  |           \
  1184.                           ZERO(1)  |            ZERO(9)  |           \
  1185.                           ZERO(2)  | ZERO(6)  |                      \
  1186.                           ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )
  1187.  
  1188. #define MASK_3D          (                                           \
  1189.                                                                      \
  1190.                                                                      \
  1191.                           ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )
  1192.  
  1193.  
  1194. #define MASK_PERSPECTIVE (           ZERO(4)  |            ZERO(12) |\
  1195.                           ZERO(1)  |                       ZERO(13) |\
  1196.                           ZERO(2)  | ZERO(6)  |                      \
  1197.                           ZERO(3)  | ZERO(7)  |            ZERO(15) )
  1198.  
  1199. #define SQ(x) ((x)*(x))
  1200.  
  1201. /**
  1202.  * Determine type and flags from scratch.  
  1203.  *
  1204.  * \param mat matrix.
  1205.  *
  1206.  * This is expensive enough to only want to do it once.
  1207.  */
  1208. static void analyse_from_scratch( GLmatrix *mat )
  1209. {
  1210.    const GLfloat *m = mat->m;
  1211.    GLuint mask = 0;
  1212.    GLuint i;
  1213.  
  1214.    for (i = 0 ; i < 16 ; i++) {
  1215.       if (m[i] == 0.0) mask |= (1<<i);
  1216.    }
  1217.  
  1218.    if (m[0] == 1.0F) mask |= (1<<16);
  1219.    if (m[5] == 1.0F) mask |= (1<<21);
  1220.    if (m[10] == 1.0F) mask |= (1<<26);
  1221.    if (m[15] == 1.0F) mask |= (1<<31);
  1222.  
  1223.    mat->flags &= ~MAT_FLAGS_GEOMETRY;
  1224.  
  1225.    /* Check for translation - no-one really cares
  1226.     */
  1227.    if ((mask & MASK_NO_TRX) != MASK_NO_TRX)
  1228.       mat->flags |= MAT_FLAG_TRANSLATION;
  1229.  
  1230.    /* Do the real work
  1231.     */
  1232.    if (mask == (GLuint) MASK_IDENTITY) {
  1233.       mat->type = MATRIX_IDENTITY;
  1234.    }
  1235.    else if ((mask & MASK_2D_NO_ROT) == (GLuint) MASK_2D_NO_ROT) {
  1236.       mat->type = MATRIX_2D_NO_ROT;
  1237.  
  1238.       if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE)
  1239.          mat->flags |= MAT_FLAG_GENERAL_SCALE;
  1240.    }
  1241.    else if ((mask & MASK_2D) == (GLuint) MASK_2D) {
  1242.       GLfloat mm = DOT2(m, m);
  1243.       GLfloat m4m4 = DOT2(m+4,m+4);
  1244.       GLfloat mm4 = DOT2(m,m+4);
  1245.  
  1246.       mat->type = MATRIX_2D;
  1247.  
  1248.       /* Check for scale */
  1249.       if (SQ(mm-1) > SQ(1e-6) ||
  1250.           SQ(m4m4-1) > SQ(1e-6))
  1251.          mat->flags |= MAT_FLAG_GENERAL_SCALE;
  1252.  
  1253.       /* Check for rotation */
  1254.       if (SQ(mm4) > SQ(1e-6))
  1255.          mat->flags |= MAT_FLAG_GENERAL_3D;
  1256.       else
  1257.          mat->flags |= MAT_FLAG_ROTATION;
  1258.  
  1259.    }
  1260.    else if ((mask & MASK_3D_NO_ROT) == (GLuint) MASK_3D_NO_ROT) {
  1261.       mat->type = MATRIX_3D_NO_ROT;
  1262.  
  1263.       /* Check for scale */
  1264.       if (SQ(m[0]-m[5]) < SQ(1e-6) &&
  1265.           SQ(m[0]-m[10]) < SQ(1e-6)) {
  1266.          if (SQ(m[0]-1.0) > SQ(1e-6)) {
  1267.             mat->flags |= MAT_FLAG_UNIFORM_SCALE;
  1268.          }
  1269.       }
  1270.       else {
  1271.          mat->flags |= MAT_FLAG_GENERAL_SCALE;
  1272.       }
  1273.    }
  1274.    else if ((mask & MASK_3D) == (GLuint) MASK_3D) {
  1275.       GLfloat c1 = DOT3(m,m);
  1276.       GLfloat c2 = DOT3(m+4,m+4);
  1277.       GLfloat c3 = DOT3(m+8,m+8);
  1278.       GLfloat d1 = DOT3(m, m+4);
  1279.       GLfloat cp[3];
  1280.  
  1281.       mat->type = MATRIX_3D;
  1282.  
  1283.       /* Check for scale */
  1284.       if (SQ(c1-c2) < SQ(1e-6) && SQ(c1-c3) < SQ(1e-6)) {
  1285.          if (SQ(c1-1.0) > SQ(1e-6))
  1286.             mat->flags |= MAT_FLAG_UNIFORM_SCALE;
  1287.          /* else no scale at all */
  1288.       }
  1289.       else {
  1290.          mat->flags |= MAT_FLAG_GENERAL_SCALE;
  1291.       }
  1292.  
  1293.       /* Check for rotation */
  1294.       if (SQ(d1) < SQ(1e-6)) {
  1295.          CROSS3( cp, m, m+4 );
  1296.          SUB_3V( cp, cp, (m+8) );
  1297.          if (LEN_SQUARED_3FV(cp) < SQ(1e-6))
  1298.             mat->flags |= MAT_FLAG_ROTATION;
  1299.          else
  1300.             mat->flags |= MAT_FLAG_GENERAL_3D;
  1301.       }
  1302.       else {
  1303.          mat->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */
  1304.       }
  1305.    }
  1306.    else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0F) {
  1307.       mat->type = MATRIX_PERSPECTIVE;
  1308.       mat->flags |= MAT_FLAG_GENERAL;
  1309.    }
  1310.    else {
  1311.       mat->type = MATRIX_GENERAL;
  1312.       mat->flags |= MAT_FLAG_GENERAL;
  1313.    }
  1314. }
  1315.  
  1316. /**
  1317.  * Analyze a matrix given that its flags are accurate.
  1318.  *
  1319.  * This is the more common operation, hopefully.
  1320.  */
  1321. static void analyse_from_flags( GLmatrix *mat )
  1322. {
  1323.    const GLfloat *m = mat->m;
  1324.  
  1325.    if (TEST_MAT_FLAGS(mat, 0)) {
  1326.       mat->type = MATRIX_IDENTITY;
  1327.    }
  1328.    else if (TEST_MAT_FLAGS(mat, (MAT_FLAG_TRANSLATION |
  1329.                                  MAT_FLAG_UNIFORM_SCALE |
  1330.                                  MAT_FLAG_GENERAL_SCALE))) {
  1331.       if ( m[10]==1.0F && m[14]==0.0F ) {
  1332.          mat->type = MATRIX_2D_NO_ROT;
  1333.       }
  1334.       else {
  1335.          mat->type = MATRIX_3D_NO_ROT;
  1336.       }
  1337.    }
  1338.    else if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) {
  1339.       if (                                 m[ 8]==0.0F
  1340.             &&                             m[ 9]==0.0F
  1341.             && m[2]==0.0F && m[6]==0.0F && m[10]==1.0F && m[14]==0.0F) {
  1342.          mat->type = MATRIX_2D;
  1343.       }
  1344.       else {
  1345.          mat->type = MATRIX_3D;
  1346.       }
  1347.    }
  1348.    else if (                 m[4]==0.0F                 && m[12]==0.0F
  1349.             && m[1]==0.0F                               && m[13]==0.0F
  1350.             && m[2]==0.0F && m[6]==0.0F
  1351.             && m[3]==0.0F && m[7]==0.0F && m[11]==-1.0F && m[15]==0.0F) {
  1352.       mat->type = MATRIX_PERSPECTIVE;
  1353.    }
  1354.    else {
  1355.       mat->type = MATRIX_GENERAL;
  1356.    }
  1357. }
  1358.  
  1359. /**
  1360.  * Analyze and update a matrix.
  1361.  *
  1362.  * \param mat matrix.
  1363.  *
  1364.  * If the matrix type is dirty then calls either analyse_from_scratch() or
  1365.  * analyse_from_flags() to determine its type, according to whether the flags
  1366.  * are dirty or not, respectively. If the matrix has an inverse and it's dirty
  1367.  * then calls matrix_invert(). Finally clears the dirty flags.
  1368.  */
  1369. void
  1370. _math_matrix_analyse( GLmatrix *mat )
  1371. {
  1372.    if (mat->flags & MAT_DIRTY_TYPE) {
  1373.       if (mat->flags & MAT_DIRTY_FLAGS)
  1374.          analyse_from_scratch( mat );
  1375.       else
  1376.          analyse_from_flags( mat );
  1377.    }
  1378.  
  1379.    if (mat->inv && (mat->flags & MAT_DIRTY_INVERSE)) {
  1380.       matrix_invert( mat );
  1381.       mat->flags &= ~MAT_DIRTY_INVERSE;
  1382.    }
  1383.  
  1384.    mat->flags &= ~(MAT_DIRTY_FLAGS | MAT_DIRTY_TYPE);
  1385. }
  1386.  
  1387. /*@}*/
  1388.  
  1389.  
  1390. /**
  1391.  * Test if the given matrix preserves vector lengths.
  1392.  */
  1393. GLboolean
  1394. _math_matrix_is_length_preserving( const GLmatrix *m )
  1395. {
  1396.    return TEST_MAT_FLAGS( m, MAT_FLAGS_LENGTH_PRESERVING);
  1397. }
  1398.  
  1399.  
  1400. /**
  1401.  * Test if the given matrix does any rotation.
  1402.  * (or perhaps if the upper-left 3x3 is non-identity)
  1403.  */
  1404. GLboolean
  1405. _math_matrix_has_rotation( const GLmatrix *m )
  1406. {
  1407.    if (m->flags & (MAT_FLAG_GENERAL |
  1408.                    MAT_FLAG_ROTATION |
  1409.                    MAT_FLAG_GENERAL_3D |
  1410.                    MAT_FLAG_PERSPECTIVE))
  1411.       return GL_TRUE;
  1412.    else
  1413.       return GL_FALSE;
  1414. }
  1415.  
  1416.  
  1417. GLboolean
  1418. _math_matrix_is_general_scale( const GLmatrix *m )
  1419. {
  1420.    return (m->flags & MAT_FLAG_GENERAL_SCALE) ? GL_TRUE : GL_FALSE;
  1421. }
  1422.  
  1423.  
  1424. GLboolean
  1425. _math_matrix_is_dirty( const GLmatrix *m )
  1426. {
  1427.    return (m->flags & MAT_DIRTY) ? GL_TRUE : GL_FALSE;
  1428. }
  1429.  
  1430.  
  1431. /**********************************************************************/
  1432. /** \name Matrix setup */
  1433. /*@{*/
  1434.  
  1435. /**
  1436.  * Copy a matrix.
  1437.  *
  1438.  * \param to destination matrix.
  1439.  * \param from source matrix.
  1440.  *
  1441.  * Copies all fields in GLmatrix, creating an inverse array if necessary.
  1442.  */
  1443. void
  1444. _math_matrix_copy( GLmatrix *to, const GLmatrix *from )
  1445. {
  1446.    memcpy( to->m, from->m, sizeof(Identity) );
  1447.    to->flags = from->flags;
  1448.    to->type = from->type;
  1449.  
  1450.    if (to->inv != 0) {
  1451.       if (from->inv == 0) {
  1452.          matrix_invert( to );
  1453.       }
  1454.       else {
  1455.          memcpy(to->inv, from->inv, sizeof(GLfloat)*16);
  1456.       }
  1457.    }
  1458. }
  1459.  
  1460. /**
  1461.  * Loads a matrix array into GLmatrix.
  1462.  *
  1463.  * \param m matrix array.
  1464.  * \param mat matrix.
  1465.  *
  1466.  * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY
  1467.  * flags.
  1468.  */
  1469. void
  1470. _math_matrix_loadf( GLmatrix *mat, const GLfloat *m )
  1471. {
  1472.    memcpy( mat->m, m, 16*sizeof(GLfloat) );
  1473.    mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY);
  1474. }
  1475.  
  1476. /**
  1477.  * Matrix constructor.
  1478.  *
  1479.  * \param m matrix.
  1480.  *
  1481.  * Initialize the GLmatrix fields.
  1482.  */
  1483. void
  1484. _math_matrix_ctr( GLmatrix *m )
  1485. {
  1486.    m->m = (GLfloat *) _mesa_align_malloc( 16 * sizeof(GLfloat), 16 );
  1487.    if (m->m)
  1488.       memcpy( m->m, Identity, sizeof(Identity) );
  1489.    m->inv = NULL;
  1490.    m->type = MATRIX_IDENTITY;
  1491.    m->flags = 0;
  1492. }
  1493.  
  1494. /**
  1495.  * Matrix destructor.
  1496.  *
  1497.  * \param m matrix.
  1498.  *
  1499.  * Frees the data in a GLmatrix.
  1500.  */
  1501. void
  1502. _math_matrix_dtr( GLmatrix *m )
  1503. {
  1504.    if (m->m) {
  1505.       _mesa_align_free( m->m );
  1506.       m->m = NULL;
  1507.    }
  1508.    if (m->inv) {
  1509.       _mesa_align_free( m->inv );
  1510.       m->inv = NULL;
  1511.    }
  1512. }
  1513.  
  1514. /**
  1515.  * Allocate a matrix inverse.
  1516.  *
  1517.  * \param m matrix.
  1518.  *
  1519.  * Allocates the matrix inverse, GLmatrix::inv, and sets it to Identity.
  1520.  */
  1521. void
  1522. _math_matrix_alloc_inv( GLmatrix *m )
  1523. {
  1524.    if (!m->inv) {
  1525.       m->inv = (GLfloat *) _mesa_align_malloc( 16 * sizeof(GLfloat), 16 );
  1526.       if (m->inv)
  1527.          memcpy( m->inv, Identity, 16 * sizeof(GLfloat) );
  1528.    }
  1529. }
  1530.  
  1531. /*@}*/
  1532.  
  1533.  
  1534. /**********************************************************************/
  1535. /** \name Matrix transpose */
  1536. /*@{*/
  1537.  
  1538. /**
  1539.  * Transpose a GLfloat matrix.
  1540.  *
  1541.  * \param to destination array.
  1542.  * \param from source array.
  1543.  */
  1544. void
  1545. _math_transposef( GLfloat to[16], const GLfloat from[16] )
  1546. {
  1547.    to[0] = from[0];
  1548.    to[1] = from[4];
  1549.    to[2] = from[8];
  1550.    to[3] = from[12];
  1551.    to[4] = from[1];
  1552.    to[5] = from[5];
  1553.    to[6] = from[9];
  1554.    to[7] = from[13];
  1555.    to[8] = from[2];
  1556.    to[9] = from[6];
  1557.    to[10] = from[10];
  1558.    to[11] = from[14];
  1559.    to[12] = from[3];
  1560.    to[13] = from[7];
  1561.    to[14] = from[11];
  1562.    to[15] = from[15];
  1563. }
  1564.  
  1565. /**
  1566.  * Transpose a GLdouble matrix.
  1567.  *
  1568.  * \param to destination array.
  1569.  * \param from source array.
  1570.  */
  1571. void
  1572. _math_transposed( GLdouble to[16], const GLdouble from[16] )
  1573. {
  1574.    to[0] = from[0];
  1575.    to[1] = from[4];
  1576.    to[2] = from[8];
  1577.    to[3] = from[12];
  1578.    to[4] = from[1];
  1579.    to[5] = from[5];
  1580.    to[6] = from[9];
  1581.    to[7] = from[13];
  1582.    to[8] = from[2];
  1583.    to[9] = from[6];
  1584.    to[10] = from[10];
  1585.    to[11] = from[14];
  1586.    to[12] = from[3];
  1587.    to[13] = from[7];
  1588.    to[14] = from[11];
  1589.    to[15] = from[15];
  1590. }
  1591.  
  1592. /**
  1593.  * Transpose a GLdouble matrix and convert to GLfloat.
  1594.  *
  1595.  * \param to destination array.
  1596.  * \param from source array.
  1597.  */
  1598. void
  1599. _math_transposefd( GLfloat to[16], const GLdouble from[16] )
  1600. {
  1601.    to[0] = (GLfloat) from[0];
  1602.    to[1] = (GLfloat) from[4];
  1603.    to[2] = (GLfloat) from[8];
  1604.    to[3] = (GLfloat) from[12];
  1605.    to[4] = (GLfloat) from[1];
  1606.    to[5] = (GLfloat) from[5];
  1607.    to[6] = (GLfloat) from[9];
  1608.    to[7] = (GLfloat) from[13];
  1609.    to[8] = (GLfloat) from[2];
  1610.    to[9] = (GLfloat) from[6];
  1611.    to[10] = (GLfloat) from[10];
  1612.    to[11] = (GLfloat) from[14];
  1613.    to[12] = (GLfloat) from[3];
  1614.    to[13] = (GLfloat) from[7];
  1615.    to[14] = (GLfloat) from[11];
  1616.    to[15] = (GLfloat) from[15];
  1617. }
  1618.  
  1619. /*@}*/
  1620.  
  1621.  
  1622. /**
  1623.  * Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix.  This
  1624.  * function is used for transforming clipping plane equations and spotlight
  1625.  * directions.
  1626.  * Mathematically,  u = v * m.
  1627.  * Input:  v - input vector
  1628.  *         m - transformation matrix
  1629.  * Output:  u - transformed vector
  1630.  */
  1631. void
  1632. _mesa_transform_vector( GLfloat u[4], const GLfloat v[4], const GLfloat m[16] )
  1633. {
  1634.    const GLfloat v0 = v[0], v1 = v[1], v2 = v[2], v3 = v[3];
  1635. #define M(row,col)  m[row + col*4]
  1636.    u[0] = v0 * M(0,0) + v1 * M(1,0) + v2 * M(2,0) + v3 * M(3,0);
  1637.    u[1] = v0 * M(0,1) + v1 * M(1,1) + v2 * M(2,1) + v3 * M(3,1);
  1638.    u[2] = v0 * M(0,2) + v1 * M(1,2) + v2 * M(2,2) + v3 * M(3,2);
  1639.    u[3] = v0 * M(0,3) + v1 * M(1,3) + v2 * M(2,3) + v3 * M(3,3);
  1640. #undef M
  1641. }
  1642.