diff options
Diffstat (limited to 'mesalib/src/mesa/math/m_matrix.c')
| -rw-r--r-- | mesalib/src/mesa/math/m_matrix.c | 3282 |
1 files changed, 1641 insertions, 1641 deletions
diff --git a/mesalib/src/mesa/math/m_matrix.c b/mesalib/src/mesa/math/m_matrix.c index 83eb787c7..02aedbad8 100644 --- a/mesalib/src/mesa/math/m_matrix.c +++ b/mesalib/src/mesa/math/m_matrix.c @@ -1,1641 +1,1641 @@ -/*
- * Mesa 3-D graphics library
- * Version: 6.3
- *
- * Copyright (C) 1999-2005 Brian Paul All Rights Reserved.
- *
- * Permission is hereby granted, free of charge, to any person obtaining a
- * copy of this software and associated documentation files (the "Software"),
- * to deal in the Software without restriction, including without limitation
- * the rights to use, copy, modify, merge, publish, distribute, sublicense,
- * and/or sell copies of the Software, and to permit persons to whom the
- * Software is furnished to do so, subject to the following conditions:
- *
- * The above copyright notice and this permission notice shall be included
- * in all copies or substantial portions of the Software.
- *
- * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
- * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
- * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
- * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
- * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
- * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
- */
-
-
-/**
- * \file m_matrix.c
- * Matrix operations.
- *
- * \note
- * -# 4x4 transformation matrices are stored in memory in column major order.
- * -# Points/vertices are to be thought of as column vectors.
- * -# Transformation of a point p by a matrix M is: p' = M * p
- */
-
-
-#include "main/glheader.h"
-#include "main/imports.h"
-#include "main/macros.h"
-
-#include "m_matrix.h"
-
-
-/**
- * \defgroup MatFlags MAT_FLAG_XXX-flags
- *
- * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags
- * It would be nice to make all these flags private to m_matrix.c
- */
-/*@{*/
-#define MAT_FLAG_IDENTITY 0 /**< is an identity matrix flag.
- * (Not actually used - the identity
- * matrix is identified by the absense
- * of all other flags.)
- */
-#define MAT_FLAG_GENERAL 0x1 /**< is a general matrix flag */
-#define MAT_FLAG_ROTATION 0x2 /**< is a rotation matrix flag */
-#define MAT_FLAG_TRANSLATION 0x4 /**< is a translation matrix flag */
-#define MAT_FLAG_UNIFORM_SCALE 0x8 /**< is an uniform scaling matrix flag */
-#define MAT_FLAG_GENERAL_SCALE 0x10 /**< is a general scaling matrix flag */
-#define MAT_FLAG_GENERAL_3D 0x20 /**< general 3D matrix flag */
-#define MAT_FLAG_PERSPECTIVE 0x40 /**< is a perspective proj matrix flag */
-#define MAT_FLAG_SINGULAR 0x80 /**< is a singular matrix flag */
-#define MAT_DIRTY_TYPE 0x100 /**< matrix type is dirty */
-#define MAT_DIRTY_FLAGS 0x200 /**< matrix flags are dirty */
-#define MAT_DIRTY_INVERSE 0x400 /**< matrix inverse is dirty */
-
-/** angle preserving matrix flags mask */
-#define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \
- MAT_FLAG_TRANSLATION | \
- MAT_FLAG_UNIFORM_SCALE)
-
-/** geometry related matrix flags mask */
-#define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \
- MAT_FLAG_ROTATION | \
- MAT_FLAG_TRANSLATION | \
- MAT_FLAG_UNIFORM_SCALE | \
- MAT_FLAG_GENERAL_SCALE | \
- MAT_FLAG_GENERAL_3D | \
- MAT_FLAG_PERSPECTIVE | \
- MAT_FLAG_SINGULAR)
-
-/** length preserving matrix flags mask */
-#define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \
- MAT_FLAG_TRANSLATION)
-
-
-/** 3D (non-perspective) matrix flags mask */
-#define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \
- MAT_FLAG_TRANSLATION | \
- MAT_FLAG_UNIFORM_SCALE | \
- MAT_FLAG_GENERAL_SCALE | \
- MAT_FLAG_GENERAL_3D)
-
-/** dirty matrix flags mask */
-#define MAT_DIRTY (MAT_DIRTY_TYPE | \
- MAT_DIRTY_FLAGS | \
- MAT_DIRTY_INVERSE)
-
-/*@}*/
-
-
-/**
- * Test geometry related matrix flags.
- *
- * \param mat a pointer to a GLmatrix structure.
- * \param a flags mask.
- *
- * \returns non-zero if all geometry related matrix flags are contained within
- * the mask, or zero otherwise.
- */
-#define TEST_MAT_FLAGS(mat, a) \
- ((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0)
-
-
-
-/**
- * Names of the corresponding GLmatrixtype values.
- */
-static const char *types[] = {
- "MATRIX_GENERAL",
- "MATRIX_IDENTITY",
- "MATRIX_3D_NO_ROT",
- "MATRIX_PERSPECTIVE",
- "MATRIX_2D",
- "MATRIX_2D_NO_ROT",
- "MATRIX_3D"
-};
-
-
-/**
- * Identity matrix.
- */
-static GLfloat Identity[16] = {
- 1.0, 0.0, 0.0, 0.0,
- 0.0, 1.0, 0.0, 0.0,
- 0.0, 0.0, 1.0, 0.0,
- 0.0, 0.0, 0.0, 1.0
-};
-
-
-
-/**********************************************************************/
-/** \name Matrix multiplication */
-/*@{*/
-
-#define A(row,col) a[(col<<2)+row]
-#define B(row,col) b[(col<<2)+row]
-#define P(row,col) product[(col<<2)+row]
-
-/**
- * Perform a full 4x4 matrix multiplication.
- *
- * \param a matrix.
- * \param b matrix.
- * \param product will receive the product of \p a and \p b.
- *
- * \warning Is assumed that \p product != \p b. \p product == \p a is allowed.
- *
- * \note KW: 4*16 = 64 multiplications
- *
- * \author This \c matmul was contributed by Thomas Malik
- */
-static void matmul4( GLfloat *product, const GLfloat *a, const GLfloat *b )
-{
- GLint i;
- for (i = 0; i < 4; i++) {
- const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3);
- P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0);
- P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1);
- P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2);
- P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3);
- }
-}
-
-/**
- * Multiply two matrices known to occupy only the top three rows, such
- * as typical model matrices, and orthogonal matrices.
- *
- * \param a matrix.
- * \param b matrix.
- * \param product will receive the product of \p a and \p b.
- */
-static void matmul34( GLfloat *product, const GLfloat *a, const GLfloat *b )
-{
- GLint i;
- for (i = 0; i < 3; i++) {
- const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3);
- P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0);
- P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1);
- P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2);
- P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3;
- }
- P(3,0) = 0;
- P(3,1) = 0;
- P(3,2) = 0;
- P(3,3) = 1;
-}
-
-#undef A
-#undef B
-#undef P
-
-/**
- * Multiply a matrix by an array of floats with known properties.
- *
- * \param mat pointer to a GLmatrix structure containing the left multiplication
- * matrix, and that will receive the product result.
- * \param m right multiplication matrix array.
- * \param flags flags of the matrix \p m.
- *
- * Joins both flags and marks the type and inverse as dirty. Calls matmul34()
- * if both matrices are 3D, or matmul4() otherwise.
- */
-static void matrix_multf( GLmatrix *mat, const GLfloat *m, GLuint flags )
-{
- mat->flags |= (flags | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE);
-
- if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D))
- matmul34( mat->m, mat->m, m );
- else
- matmul4( mat->m, mat->m, m );
-}
-
-/**
- * Matrix multiplication.
- *
- * \param dest destination matrix.
- * \param a left matrix.
- * \param b right matrix.
- *
- * Joins both flags and marks the type and inverse as dirty. Calls matmul34()
- * if both matrices are 3D, or matmul4() otherwise.
- */
-void
-_math_matrix_mul_matrix( GLmatrix *dest, const GLmatrix *a, const GLmatrix *b )
-{
- dest->flags = (a->flags |
- b->flags |
- MAT_DIRTY_TYPE |
- MAT_DIRTY_INVERSE);
-
- if (TEST_MAT_FLAGS(dest, MAT_FLAGS_3D))
- matmul34( dest->m, a->m, b->m );
- else
- matmul4( dest->m, a->m, b->m );
-}
-
-/**
- * Matrix multiplication.
- *
- * \param dest left and destination matrix.
- * \param m right matrix array.
- *
- * Marks the matrix flags with general flag, and type and inverse dirty flags.
- * Calls matmul4() for the multiplication.
- */
-void
-_math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m )
-{
- dest->flags |= (MAT_FLAG_GENERAL |
- MAT_DIRTY_TYPE |
- MAT_DIRTY_INVERSE |
- MAT_DIRTY_FLAGS);
-
- matmul4( dest->m, dest->m, m );
-}
-
-/*@}*/
-
-
-/**********************************************************************/
-/** \name Matrix output */
-/*@{*/
-
-/**
- * Print a matrix array.
- *
- * \param m matrix array.
- *
- * Called by _math_matrix_print() to print a matrix or its inverse.
- */
-static void print_matrix_floats( const GLfloat m[16] )
-{
- int i;
- for (i=0;i<4;i++) {
- _mesa_debug(NULL,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] );
- }
-}
-
-/**
- * Dumps the contents of a GLmatrix structure.
- *
- * \param m pointer to the GLmatrix structure.
- */
-void
-_math_matrix_print( const GLmatrix *m )
-{
- _mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags);
- print_matrix_floats(m->m);
- _mesa_debug(NULL, "Inverse: \n");
- if (m->inv) {
- GLfloat prod[16];
- print_matrix_floats(m->inv);
- matmul4(prod, m->m, m->inv);
- _mesa_debug(NULL, "Mat * Inverse:\n");
- print_matrix_floats(prod);
- }
- else {
- _mesa_debug(NULL, " - not available\n");
- }
-}
-
-/*@}*/
-
-
-/**
- * References an element of 4x4 matrix.
- *
- * \param m matrix array.
- * \param c column of the desired element.
- * \param r row of the desired element.
- *
- * \return value of the desired element.
- *
- * Calculate the linear storage index of the element and references it.
- */
-#define MAT(m,r,c) (m)[(c)*4+(r)]
-
-
-/**********************************************************************/
-/** \name Matrix inversion */
-/*@{*/
-
-/**
- * Swaps the values of two floating pointer variables.
- *
- * Used by invert_matrix_general() to swap the row pointers.
- */
-#define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; }
-
-/**
- * Compute inverse of 4x4 transformation matrix.
- *
- * \param mat pointer to a GLmatrix structure. The matrix inverse will be
- * stored in the GLmatrix::inv attribute.
- *
- * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
- *
- * \author
- * Code contributed by Jacques Leroy jle@star.be
- *
- * Calculates the inverse matrix by performing the gaussian matrix reduction
- * with partial pivoting followed by back/substitution with the loops manually
- * unrolled.
- */
-static GLboolean invert_matrix_general( GLmatrix *mat )
-{
- const GLfloat *m = mat->m;
- GLfloat *out = mat->inv;
- GLfloat wtmp[4][8];
- GLfloat m0, m1, m2, m3, s;
- GLfloat *r0, *r1, *r2, *r3;
-
- r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
-
- r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1),
- r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3),
- r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
-
- r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1),
- r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3),
- r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
-
- r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1),
- r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3),
- r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
-
- r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1),
- r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3),
- r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
-
- /* choose pivot - or die */
- if (FABSF(r3[0])>FABSF(r2[0])) SWAP_ROWS(r3, r2);
- if (FABSF(r2[0])>FABSF(r1[0])) SWAP_ROWS(r2, r1);
- if (FABSF(r1[0])>FABSF(r0[0])) SWAP_ROWS(r1, r0);
- if (0.0 == r0[0]) return GL_FALSE;
-
- /* eliminate first variable */
- m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0];
- s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s;
- s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s;
- s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s;
- s = r0[4];
- if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; }
- s = r0[5];
- if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; }
- s = r0[6];
- if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; }
- s = r0[7];
- if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; }
-
- /* choose pivot - or die */
- if (FABSF(r3[1])>FABSF(r2[1])) SWAP_ROWS(r3, r2);
- if (FABSF(r2[1])>FABSF(r1[1])) SWAP_ROWS(r2, r1);
- if (0.0 == r1[1]) return GL_FALSE;
-
- /* eliminate second variable */
- m2 = r2[1]/r1[1]; m3 = r3[1]/r1[1];
- r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2];
- r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3];
- s = r1[4]; if (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; }
- s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; }
- s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; }
- s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; }
-
- /* choose pivot - or die */
- if (FABSF(r3[2])>FABSF(r2[2])) SWAP_ROWS(r3, r2);
- if (0.0 == r2[2]) return GL_FALSE;
-
- /* eliminate third variable */
- m3 = r3[2]/r2[2];
- r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
- r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6],
- r3[7] -= m3 * r2[7];
-
- /* last check */
- if (0.0 == r3[3]) return GL_FALSE;
-
- s = 1.0F/r3[3]; /* now back substitute row 3 */
- r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s;
-
- m2 = r2[3]; /* now back substitute row 2 */
- s = 1.0F/r2[2];
- r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
- r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
- m1 = r1[3];
- r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
- r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
- m0 = r0[3];
- r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
- r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
-
- m1 = r1[2]; /* now back substitute row 1 */
- s = 1.0F/r1[1];
- r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
- r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
- m0 = r0[2];
- r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
- r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
-
- m0 = r0[1]; /* now back substitute row 0 */
- s = 1.0F/r0[0];
- r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
- r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
-
- MAT(out,0,0) = r0[4]; MAT(out,0,1) = r0[5],
- MAT(out,0,2) = r0[6]; MAT(out,0,3) = r0[7],
- MAT(out,1,0) = r1[4]; MAT(out,1,1) = r1[5],
- MAT(out,1,2) = r1[6]; MAT(out,1,3) = r1[7],
- MAT(out,2,0) = r2[4]; MAT(out,2,1) = r2[5],
- MAT(out,2,2) = r2[6]; MAT(out,2,3) = r2[7],
- MAT(out,3,0) = r3[4]; MAT(out,3,1) = r3[5],
- MAT(out,3,2) = r3[6]; MAT(out,3,3) = r3[7];
-
- return GL_TRUE;
-}
-#undef SWAP_ROWS
-
-/**
- * Compute inverse of a general 3d transformation matrix.
- *
- * \param mat pointer to a GLmatrix structure. The matrix inverse will be
- * stored in the GLmatrix::inv attribute.
- *
- * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
- *
- * \author Adapted from graphics gems II.
- *
- * Calculates the inverse of the upper left by first calculating its
- * determinant and multiplying it to the symmetric adjust matrix of each
- * element. Finally deals with the translation part by transforming the
- * original translation vector using by the calculated submatrix inverse.
- */
-static GLboolean invert_matrix_3d_general( GLmatrix *mat )
-{
- const GLfloat *in = mat->m;
- GLfloat *out = mat->inv;
- GLfloat pos, neg, t;
- GLfloat det;
-
- /* Calculate the determinant of upper left 3x3 submatrix and
- * determine if the matrix is singular.
- */
- pos = neg = 0.0;
- t = MAT(in,0,0) * MAT(in,1,1) * MAT(in,2,2);
- if (t >= 0.0) pos += t; else neg += t;
-
- t = MAT(in,1,0) * MAT(in,2,1) * MAT(in,0,2);
- if (t >= 0.0) pos += t; else neg += t;
-
- t = MAT(in,2,0) * MAT(in,0,1) * MAT(in,1,2);
- if (t >= 0.0) pos += t; else neg += t;
-
- t = -MAT(in,2,0) * MAT(in,1,1) * MAT(in,0,2);
- if (t >= 0.0) pos += t; else neg += t;
-
- t = -MAT(in,1,0) * MAT(in,0,1) * MAT(in,2,2);
- if (t >= 0.0) pos += t; else neg += t;
-
- t = -MAT(in,0,0) * MAT(in,2,1) * MAT(in,1,2);
- if (t >= 0.0) pos += t; else neg += t;
-
- det = pos + neg;
-
- if (det*det < 1e-25)
- return GL_FALSE;
-
- det = 1.0F / det;
- MAT(out,0,0) = ( (MAT(in,1,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,1,2) )*det);
- MAT(out,0,1) = (- (MAT(in,0,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,0,2) )*det);
- MAT(out,0,2) = ( (MAT(in,0,1)*MAT(in,1,2) - MAT(in,1,1)*MAT(in,0,2) )*det);
- MAT(out,1,0) = (- (MAT(in,1,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,1,2) )*det);
- MAT(out,1,1) = ( (MAT(in,0,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,0,2) )*det);
- MAT(out,1,2) = (- (MAT(in,0,0)*MAT(in,1,2) - MAT(in,1,0)*MAT(in,0,2) )*det);
- MAT(out,2,0) = ( (MAT(in,1,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,1,1) )*det);
- MAT(out,2,1) = (- (MAT(in,0,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,0,1) )*det);
- MAT(out,2,2) = ( (MAT(in,0,0)*MAT(in,1,1) - MAT(in,1,0)*MAT(in,0,1) )*det);
-
- /* Do the translation part */
- MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
- MAT(in,1,3) * MAT(out,0,1) +
- MAT(in,2,3) * MAT(out,0,2) );
- MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
- MAT(in,1,3) * MAT(out,1,1) +
- MAT(in,2,3) * MAT(out,1,2) );
- MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
- MAT(in,1,3) * MAT(out,2,1) +
- MAT(in,2,3) * MAT(out,2,2) );
-
- return GL_TRUE;
-}
-
-/**
- * Compute inverse of a 3d transformation matrix.
- *
- * \param mat pointer to a GLmatrix structure. The matrix inverse will be
- * stored in the GLmatrix::inv attribute.
- *
- * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
- *
- * If the matrix is not an angle preserving matrix then calls
- * invert_matrix_3d_general for the actual calculation. Otherwise calculates
- * the inverse matrix analyzing and inverting each of the scaling, rotation and
- * translation parts.
- */
-static GLboolean invert_matrix_3d( GLmatrix *mat )
-{
- const GLfloat *in = mat->m;
- GLfloat *out = mat->inv;
-
- if (!TEST_MAT_FLAGS(mat, MAT_FLAGS_ANGLE_PRESERVING)) {
- return invert_matrix_3d_general( mat );
- }
-
- if (mat->flags & MAT_FLAG_UNIFORM_SCALE) {
- GLfloat scale = (MAT(in,0,0) * MAT(in,0,0) +
- MAT(in,0,1) * MAT(in,0,1) +
- MAT(in,0,2) * MAT(in,0,2));
-
- if (scale == 0.0)
- return GL_FALSE;
-
- scale = 1.0F / scale;
-
- /* Transpose and scale the 3 by 3 upper-left submatrix. */
- MAT(out,0,0) = scale * MAT(in,0,0);
- MAT(out,1,0) = scale * MAT(in,0,1);
- MAT(out,2,0) = scale * MAT(in,0,2);
- MAT(out,0,1) = scale * MAT(in,1,0);
- MAT(out,1,1) = scale * MAT(in,1,1);
- MAT(out,2,1) = scale * MAT(in,1,2);
- MAT(out,0,2) = scale * MAT(in,2,0);
- MAT(out,1,2) = scale * MAT(in,2,1);
- MAT(out,2,2) = scale * MAT(in,2,2);
- }
- else if (mat->flags & MAT_FLAG_ROTATION) {
- /* Transpose the 3 by 3 upper-left submatrix. */
- MAT(out,0,0) = MAT(in,0,0);
- MAT(out,1,0) = MAT(in,0,1);
- MAT(out,2,0) = MAT(in,0,2);
- MAT(out,0,1) = MAT(in,1,0);
- MAT(out,1,1) = MAT(in,1,1);
- MAT(out,2,1) = MAT(in,1,2);
- MAT(out,0,2) = MAT(in,2,0);
- MAT(out,1,2) = MAT(in,2,1);
- MAT(out,2,2) = MAT(in,2,2);
- }
- else {
- /* pure translation */
- memcpy( out, Identity, sizeof(Identity) );
- MAT(out,0,3) = - MAT(in,0,3);
- MAT(out,1,3) = - MAT(in,1,3);
- MAT(out,2,3) = - MAT(in,2,3);
- return GL_TRUE;
- }
-
- if (mat->flags & MAT_FLAG_TRANSLATION) {
- /* Do the translation part */
- MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
- MAT(in,1,3) * MAT(out,0,1) +
- MAT(in,2,3) * MAT(out,0,2) );
- MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
- MAT(in,1,3) * MAT(out,1,1) +
- MAT(in,2,3) * MAT(out,1,2) );
- MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
- MAT(in,1,3) * MAT(out,2,1) +
- MAT(in,2,3) * MAT(out,2,2) );
- }
- else {
- MAT(out,0,3) = MAT(out,1,3) = MAT(out,2,3) = 0.0;
- }
-
- return GL_TRUE;
-}
-
-/**
- * Compute inverse of an identity transformation matrix.
- *
- * \param mat pointer to a GLmatrix structure. The matrix inverse will be
- * stored in the GLmatrix::inv attribute.
- *
- * \return always GL_TRUE.
- *
- * Simply copies Identity into GLmatrix::inv.
- */
-static GLboolean invert_matrix_identity( GLmatrix *mat )
-{
- memcpy( mat->inv, Identity, sizeof(Identity) );
- return GL_TRUE;
-}
-
-/**
- * Compute inverse of a no-rotation 3d transformation matrix.
- *
- * \param mat pointer to a GLmatrix structure. The matrix inverse will be
- * stored in the GLmatrix::inv attribute.
- *
- * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
- *
- * Calculates the
- */
-static GLboolean invert_matrix_3d_no_rot( GLmatrix *mat )
-{
- const GLfloat *in = mat->m;
- GLfloat *out = mat->inv;
-
- if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0 || MAT(in,2,2) == 0 )
- return GL_FALSE;
-
- memcpy( out, Identity, 16 * sizeof(GLfloat) );
- MAT(out,0,0) = 1.0F / MAT(in,0,0);
- MAT(out,1,1) = 1.0F / MAT(in,1,1);
- MAT(out,2,2) = 1.0F / MAT(in,2,2);
-
- if (mat->flags & MAT_FLAG_TRANSLATION) {
- MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0));
- MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1));
- MAT(out,2,3) = - (MAT(in,2,3) * MAT(out,2,2));
- }
-
- return GL_TRUE;
-}
-
-/**
- * Compute inverse of a no-rotation 2d transformation matrix.
- *
- * \param mat pointer to a GLmatrix structure. The matrix inverse will be
- * stored in the GLmatrix::inv attribute.
- *
- * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
- *
- * Calculates the inverse matrix by applying the inverse scaling and
- * translation to the identity matrix.
- */
-static GLboolean invert_matrix_2d_no_rot( GLmatrix *mat )
-{
- const GLfloat *in = mat->m;
- GLfloat *out = mat->inv;
-
- if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0)
- return GL_FALSE;
-
- memcpy( out, Identity, 16 * sizeof(GLfloat) );
- MAT(out,0,0) = 1.0F / MAT(in,0,0);
- MAT(out,1,1) = 1.0F / MAT(in,1,1);
-
- if (mat->flags & MAT_FLAG_TRANSLATION) {
- MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0));
- MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1));
- }
-
- return GL_TRUE;
-}
-
-#if 0
-/* broken */
-static GLboolean invert_matrix_perspective( GLmatrix *mat )
-{
- const GLfloat *in = mat->m;
- GLfloat *out = mat->inv;
-
- if (MAT(in,2,3) == 0)
- return GL_FALSE;
-
- memcpy( out, Identity, 16 * sizeof(GLfloat) );
-
- MAT(out,0,0) = 1.0F / MAT(in,0,0);
- MAT(out,1,1) = 1.0F / MAT(in,1,1);
-
- MAT(out,0,3) = MAT(in,0,2);
- MAT(out,1,3) = MAT(in,1,2);
-
- MAT(out,2,2) = 0;
- MAT(out,2,3) = -1;
-
- MAT(out,3,2) = 1.0F / MAT(in,2,3);
- MAT(out,3,3) = MAT(in,2,2) * MAT(out,3,2);
-
- return GL_TRUE;
-}
-#endif
-
-/**
- * Matrix inversion function pointer type.
- */
-typedef GLboolean (*inv_mat_func)( GLmatrix *mat );
-
-/**
- * Table of the matrix inversion functions according to the matrix type.
- */
-static inv_mat_func inv_mat_tab[7] = {
- invert_matrix_general,
- invert_matrix_identity,
- invert_matrix_3d_no_rot,
-#if 0
- /* Don't use this function for now - it fails when the projection matrix
- * is premultiplied by a translation (ala Chromium's tilesort SPU).
- */
- invert_matrix_perspective,
-#else
- invert_matrix_general,
-#endif
- invert_matrix_3d, /* lazy! */
- invert_matrix_2d_no_rot,
- invert_matrix_3d
-};
-
-/**
- * Compute inverse of a transformation matrix.
- *
- * \param mat pointer to a GLmatrix structure. The matrix inverse will be
- * stored in the GLmatrix::inv attribute.
- *
- * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
- *
- * Calls the matrix inversion function in inv_mat_tab corresponding to the
- * given matrix type. In case of failure, updates the MAT_FLAG_SINGULAR flag,
- * and copies the identity matrix into GLmatrix::inv.
- */
-static GLboolean matrix_invert( GLmatrix *mat )
-{
- if (inv_mat_tab[mat->type](mat)) {
- mat->flags &= ~MAT_FLAG_SINGULAR;
- return GL_TRUE;
- } else {
- mat->flags |= MAT_FLAG_SINGULAR;
- memcpy( mat->inv, Identity, sizeof(Identity) );
- return GL_FALSE;
- }
-}
-
-/*@}*/
-
-
-/**********************************************************************/
-/** \name Matrix generation */
-/*@{*/
-
-/**
- * Generate a 4x4 transformation matrix from glRotate parameters, and
- * post-multiply the input matrix by it.
- *
- * \author
- * This function was contributed by Erich Boleyn (erich@uruk.org).
- * Optimizations contributed by Rudolf Opalla (rudi@khm.de).
- */
-void
-_math_matrix_rotate( GLmatrix *mat,
- GLfloat angle, GLfloat x, GLfloat y, GLfloat z )
-{
- GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c;
- GLfloat m[16];
- GLboolean optimized;
-
- s = (GLfloat) sin( angle * DEG2RAD );
- c = (GLfloat) cos( angle * DEG2RAD );
-
- memcpy(m, Identity, sizeof(GLfloat)*16);
- optimized = GL_FALSE;
-
-#define M(row,col) m[col*4+row]
-
- if (x == 0.0F) {
- if (y == 0.0F) {
- if (z != 0.0F) {
- optimized = GL_TRUE;
- /* rotate only around z-axis */
- M(0,0) = c;
- M(1,1) = c;
- if (z < 0.0F) {
- M(0,1) = s;
- M(1,0) = -s;
- }
- else {
- M(0,1) = -s;
- M(1,0) = s;
- }
- }
- }
- else if (z == 0.0F) {
- optimized = GL_TRUE;
- /* rotate only around y-axis */
- M(0,0) = c;
- M(2,2) = c;
- if (y < 0.0F) {
- M(0,2) = -s;
- M(2,0) = s;
- }
- else {
- M(0,2) = s;
- M(2,0) = -s;
- }
- }
- }
- else if (y == 0.0F) {
- if (z == 0.0F) {
- optimized = GL_TRUE;
- /* rotate only around x-axis */
- M(1,1) = c;
- M(2,2) = c;
- if (x < 0.0F) {
- M(1,2) = s;
- M(2,1) = -s;
- }
- else {
- M(1,2) = -s;
- M(2,1) = s;
- }
- }
- }
-
- if (!optimized) {
- const GLfloat mag = SQRTF(x * x + y * y + z * z);
-
- if (mag <= 1.0e-4) {
- /* no rotation, leave mat as-is */
- return;
- }
-
- x /= mag;
- y /= mag;
- z /= mag;
-
-
- /*
- * Arbitrary axis rotation matrix.
- *
- * This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied
- * like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation
- * (which is about the X-axis), and the two composite transforms
- * Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary
- * from the arbitrary axis to the X-axis then back. They are
- * all elementary rotations.
- *
- * Rz' is a rotation about the Z-axis, to bring the axis vector
- * into the x-z plane. Then Ry' is applied, rotating about the
- * Y-axis to bring the axis vector parallel with the X-axis. The
- * rotation about the X-axis is then performed. Ry and Rz are
- * simply the respective inverse transforms to bring the arbitrary
- * axis back to its original orientation. The first transforms
- * Rz' and Ry' are considered inverses, since the data from the
- * arbitrary axis gives you info on how to get to it, not how
- * to get away from it, and an inverse must be applied.
- *
- * The basic calculation used is to recognize that the arbitrary
- * axis vector (x, y, z), since it is of unit length, actually
- * represents the sines and cosines of the angles to rotate the
- * X-axis to the same orientation, with theta being the angle about
- * Z and phi the angle about Y (in the order described above)
- * as follows:
- *
- * cos ( theta ) = x / sqrt ( 1 - z^2 )
- * sin ( theta ) = y / sqrt ( 1 - z^2 )
- *
- * cos ( phi ) = sqrt ( 1 - z^2 )
- * sin ( phi ) = z
- *
- * Note that cos ( phi ) can further be inserted to the above
- * formulas:
- *
- * cos ( theta ) = x / cos ( phi )
- * sin ( theta ) = y / sin ( phi )
- *
- * ...etc. Because of those relations and the standard trigonometric
- * relations, it is pssible to reduce the transforms down to what
- * is used below. It may be that any primary axis chosen will give the
- * same results (modulo a sign convention) using thie method.
- *
- * Particularly nice is to notice that all divisions that might
- * have caused trouble when parallel to certain planes or
- * axis go away with care paid to reducing the expressions.
- * After checking, it does perform correctly under all cases, since
- * in all the cases of division where the denominator would have
- * been zero, the numerator would have been zero as well, giving
- * the expected result.
- */
-
- xx = x * x;
- yy = y * y;
- zz = z * z;
- xy = x * y;
- yz = y * z;
- zx = z * x;
- xs = x * s;
- ys = y * s;
- zs = z * s;
- one_c = 1.0F - c;
-
- /* We already hold the identity-matrix so we can skip some statements */
- M(0,0) = (one_c * xx) + c;
- M(0,1) = (one_c * xy) - zs;
- M(0,2) = (one_c * zx) + ys;
-/* M(0,3) = 0.0F; */
-
- M(1,0) = (one_c * xy) + zs;
- M(1,1) = (one_c * yy) + c;
- M(1,2) = (one_c * yz) - xs;
-/* M(1,3) = 0.0F; */
-
- M(2,0) = (one_c * zx) - ys;
- M(2,1) = (one_c * yz) + xs;
- M(2,2) = (one_c * zz) + c;
-/* M(2,3) = 0.0F; */
-
-/*
- M(3,0) = 0.0F;
- M(3,1) = 0.0F;
- M(3,2) = 0.0F;
- M(3,3) = 1.0F;
-*/
- }
-#undef M
-
- matrix_multf( mat, m, MAT_FLAG_ROTATION );
-}
-
-/**
- * Apply a perspective projection matrix.
- *
- * \param mat matrix to apply the projection.
- * \param left left clipping plane coordinate.
- * \param right right clipping plane coordinate.
- * \param bottom bottom clipping plane coordinate.
- * \param top top clipping plane coordinate.
- * \param nearval distance to the near clipping plane.
- * \param farval distance to the far clipping plane.
- *
- * Creates the projection matrix and multiplies it with \p mat, marking the
- * MAT_FLAG_PERSPECTIVE flag.
- */
-void
-_math_matrix_frustum( GLmatrix *mat,
- GLfloat left, GLfloat right,
- GLfloat bottom, GLfloat top,
- GLfloat nearval, GLfloat farval )
-{
- GLfloat x, y, a, b, c, d;
- GLfloat m[16];
-
- x = (2.0F*nearval) / (right-left);
- y = (2.0F*nearval) / (top-bottom);
- a = (right+left) / (right-left);
- b = (top+bottom) / (top-bottom);
- c = -(farval+nearval) / ( farval-nearval);
- d = -(2.0F*farval*nearval) / (farval-nearval); /* error? */
-
-#define M(row,col) m[col*4+row]
- M(0,0) = x; M(0,1) = 0.0F; M(0,2) = a; M(0,3) = 0.0F;
- M(1,0) = 0.0F; M(1,1) = y; M(1,2) = b; M(1,3) = 0.0F;
- M(2,0) = 0.0F; M(2,1) = 0.0F; M(2,2) = c; M(2,3) = d;
- M(3,0) = 0.0F; M(3,1) = 0.0F; M(3,2) = -1.0F; M(3,3) = 0.0F;
-#undef M
-
- matrix_multf( mat, m, MAT_FLAG_PERSPECTIVE );
-}
-
-/**
- * Apply an orthographic projection matrix.
- *
- * \param mat matrix to apply the projection.
- * \param left left clipping plane coordinate.
- * \param right right clipping plane coordinate.
- * \param bottom bottom clipping plane coordinate.
- * \param top top clipping plane coordinate.
- * \param nearval distance to the near clipping plane.
- * \param farval distance to the far clipping plane.
- *
- * Creates the projection matrix and multiplies it with \p mat, marking the
- * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags.
- */
-void
-_math_matrix_ortho( GLmatrix *mat,
- GLfloat left, GLfloat right,
- GLfloat bottom, GLfloat top,
- GLfloat nearval, GLfloat farval )
-{
- GLfloat m[16];
-
-#define M(row,col) m[col*4+row]
- M(0,0) = 2.0F / (right-left);
- M(0,1) = 0.0F;
- M(0,2) = 0.0F;
- M(0,3) = -(right+left) / (right-left);
-
- M(1,0) = 0.0F;
- M(1,1) = 2.0F / (top-bottom);
- M(1,2) = 0.0F;
- M(1,3) = -(top+bottom) / (top-bottom);
-
- M(2,0) = 0.0F;
- M(2,1) = 0.0F;
- M(2,2) = -2.0F / (farval-nearval);
- M(2,3) = -(farval+nearval) / (farval-nearval);
-
- M(3,0) = 0.0F;
- M(3,1) = 0.0F;
- M(3,2) = 0.0F;
- M(3,3) = 1.0F;
-#undef M
-
- matrix_multf( mat, m, (MAT_FLAG_GENERAL_SCALE|MAT_FLAG_TRANSLATION));
-}
-
-/**
- * Multiply a matrix with a general scaling matrix.
- *
- * \param mat matrix.
- * \param x x axis scale factor.
- * \param y y axis scale factor.
- * \param z z axis scale factor.
- *
- * Multiplies in-place the elements of \p mat by the scale factors. Checks if
- * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE
- * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and
- * MAT_DIRTY_INVERSE dirty flags.
- */
-void
-_math_matrix_scale( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
-{
- GLfloat *m = mat->m;
- m[0] *= x; m[4] *= y; m[8] *= z;
- m[1] *= x; m[5] *= y; m[9] *= z;
- m[2] *= x; m[6] *= y; m[10] *= z;
- m[3] *= x; m[7] *= y; m[11] *= z;
-
- if (FABSF(x - y) < 1e-8 && FABSF(x - z) < 1e-8)
- mat->flags |= MAT_FLAG_UNIFORM_SCALE;
- else
- mat->flags |= MAT_FLAG_GENERAL_SCALE;
-
- mat->flags |= (MAT_DIRTY_TYPE |
- MAT_DIRTY_INVERSE);
-}
-
-/**
- * Multiply a matrix with a translation matrix.
- *
- * \param mat matrix.
- * \param x translation vector x coordinate.
- * \param y translation vector y coordinate.
- * \param z translation vector z coordinate.
- *
- * Adds the translation coordinates to the elements of \p mat in-place. Marks
- * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE
- * dirty flags.
- */
-void
-_math_matrix_translate( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
-{
- GLfloat *m = mat->m;
- m[12] = m[0] * x + m[4] * y + m[8] * z + m[12];
- m[13] = m[1] * x + m[5] * y + m[9] * z + m[13];
- m[14] = m[2] * x + m[6] * y + m[10] * z + m[14];
- m[15] = m[3] * x + m[7] * y + m[11] * z + m[15];
-
- mat->flags |= (MAT_FLAG_TRANSLATION |
- MAT_DIRTY_TYPE |
- MAT_DIRTY_INVERSE);
-}
-
-
-/**
- * Set matrix to do viewport and depthrange mapping.
- * Transforms Normalized Device Coords to window/Z values.
- */
-void
-_math_matrix_viewport(GLmatrix *m, GLint x, GLint y, GLint width, GLint height,
- GLfloat zNear, GLfloat zFar, GLfloat depthMax)
-{
- m->m[MAT_SX] = (GLfloat) width / 2.0F;
- m->m[MAT_TX] = m->m[MAT_SX] + x;
- m->m[MAT_SY] = (GLfloat) height / 2.0F;
- m->m[MAT_TY] = m->m[MAT_SY] + y;
- m->m[MAT_SZ] = depthMax * ((zFar - zNear) / 2.0F);
- m->m[MAT_TZ] = depthMax * ((zFar - zNear) / 2.0F + zNear);
- m->flags = MAT_FLAG_GENERAL_SCALE | MAT_FLAG_TRANSLATION;
- m->type = MATRIX_3D_NO_ROT;
-}
-
-
-/**
- * Set a matrix to the identity matrix.
- *
- * \param mat matrix.
- *
- * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL.
- * Sets the matrix type to identity, and clear the dirty flags.
- */
-void
-_math_matrix_set_identity( GLmatrix *mat )
-{
- memcpy( mat->m, Identity, 16*sizeof(GLfloat) );
-
- if (mat->inv)
- memcpy( mat->inv, Identity, 16*sizeof(GLfloat) );
-
- mat->type = MATRIX_IDENTITY;
- mat->flags &= ~(MAT_DIRTY_FLAGS|
- MAT_DIRTY_TYPE|
- MAT_DIRTY_INVERSE);
-}
-
-/*@}*/
-
-
-/**********************************************************************/
-/** \name Matrix analysis */
-/*@{*/
-
-#define ZERO(x) (1<<x)
-#define ONE(x) (1<<(x+16))
-
-#define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14))
-#define MASK_NO_2D_SCALE ( ONE(0) | ONE(5))
-
-#define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\
- ZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\
- ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
- ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
-
-#define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \
- ZERO(1) | ZERO(9) | \
- ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
- ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
-
-#define MASK_2D ( ZERO(8) | \
- ZERO(9) | \
- ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
- ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
-
-
-#define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \
- ZERO(1) | ZERO(9) | \
- ZERO(2) | ZERO(6) | \
- ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
-
-#define MASK_3D ( \
- \
- \
- ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
-
-
-#define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\
- ZERO(1) | ZERO(13) |\
- ZERO(2) | ZERO(6) | \
- ZERO(3) | ZERO(7) | ZERO(15) )
-
-#define SQ(x) ((x)*(x))
-
-/**
- * Determine type and flags from scratch.
- *
- * \param mat matrix.
- *
- * This is expensive enough to only want to do it once.
- */
-static void analyse_from_scratch( GLmatrix *mat )
-{
- const GLfloat *m = mat->m;
- GLuint mask = 0;
- GLuint i;
-
- for (i = 0 ; i < 16 ; i++) {
- if (m[i] == 0.0) mask |= (1<<i);
- }
-
- if (m[0] == 1.0F) mask |= (1<<16);
- if (m[5] == 1.0F) mask |= (1<<21);
- if (m[10] == 1.0F) mask |= (1<<26);
- if (m[15] == 1.0F) mask |= (1<<31);
-
- mat->flags &= ~MAT_FLAGS_GEOMETRY;
-
- /* Check for translation - no-one really cares
- */
- if ((mask & MASK_NO_TRX) != MASK_NO_TRX)
- mat->flags |= MAT_FLAG_TRANSLATION;
-
- /* Do the real work
- */
- if (mask == (GLuint) MASK_IDENTITY) {
- mat->type = MATRIX_IDENTITY;
- }
- else if ((mask & MASK_2D_NO_ROT) == (GLuint) MASK_2D_NO_ROT) {
- mat->type = MATRIX_2D_NO_ROT;
-
- if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE)
- mat->flags |= MAT_FLAG_GENERAL_SCALE;
- }
- else if ((mask & MASK_2D) == (GLuint) MASK_2D) {
- GLfloat mm = DOT2(m, m);
- GLfloat m4m4 = DOT2(m+4,m+4);
- GLfloat mm4 = DOT2(m,m+4);
-
- mat->type = MATRIX_2D;
-
- /* Check for scale */
- if (SQ(mm-1) > SQ(1e-6) ||
- SQ(m4m4-1) > SQ(1e-6))
- mat->flags |= MAT_FLAG_GENERAL_SCALE;
-
- /* Check for rotation */
- if (SQ(mm4) > SQ(1e-6))
- mat->flags |= MAT_FLAG_GENERAL_3D;
- else
- mat->flags |= MAT_FLAG_ROTATION;
-
- }
- else if ((mask & MASK_3D_NO_ROT) == (GLuint) MASK_3D_NO_ROT) {
- mat->type = MATRIX_3D_NO_ROT;
-
- /* Check for scale */
- if (SQ(m[0]-m[5]) < SQ(1e-6) &&
- SQ(m[0]-m[10]) < SQ(1e-6)) {
- if (SQ(m[0]-1.0) > SQ(1e-6)) {
- mat->flags |= MAT_FLAG_UNIFORM_SCALE;
- }
- }
- else {
- mat->flags |= MAT_FLAG_GENERAL_SCALE;
- }
- }
- else if ((mask & MASK_3D) == (GLuint) MASK_3D) {
- GLfloat c1 = DOT3(m,m);
- GLfloat c2 = DOT3(m+4,m+4);
- GLfloat c3 = DOT3(m+8,m+8);
- GLfloat d1 = DOT3(m, m+4);
- GLfloat cp[3];
-
- mat->type = MATRIX_3D;
-
- /* Check for scale */
- if (SQ(c1-c2) < SQ(1e-6) && SQ(c1-c3) < SQ(1e-6)) {
- if (SQ(c1-1.0) > SQ(1e-6))
- mat->flags |= MAT_FLAG_UNIFORM_SCALE;
- /* else no scale at all */
- }
- else {
- mat->flags |= MAT_FLAG_GENERAL_SCALE;
- }
-
- /* Check for rotation */
- if (SQ(d1) < SQ(1e-6)) {
- CROSS3( cp, m, m+4 );
- SUB_3V( cp, cp, (m+8) );
- if (LEN_SQUARED_3FV(cp) < SQ(1e-6))
- mat->flags |= MAT_FLAG_ROTATION;
- else
- mat->flags |= MAT_FLAG_GENERAL_3D;
- }
- else {
- mat->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */
- }
- }
- else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0F) {
- mat->type = MATRIX_PERSPECTIVE;
- mat->flags |= MAT_FLAG_GENERAL;
- }
- else {
- mat->type = MATRIX_GENERAL;
- mat->flags |= MAT_FLAG_GENERAL;
- }
-}
-
-/**
- * Analyze a matrix given that its flags are accurate.
- *
- * This is the more common operation, hopefully.
- */
-static void analyse_from_flags( GLmatrix *mat )
-{
- const GLfloat *m = mat->m;
-
- if (TEST_MAT_FLAGS(mat, 0)) {
- mat->type = MATRIX_IDENTITY;
- }
- else if (TEST_MAT_FLAGS(mat, (MAT_FLAG_TRANSLATION |
- MAT_FLAG_UNIFORM_SCALE |
- MAT_FLAG_GENERAL_SCALE))) {
- if ( m[10]==1.0F && m[14]==0.0F ) {
- mat->type = MATRIX_2D_NO_ROT;
- }
- else {
- mat->type = MATRIX_3D_NO_ROT;
- }
- }
- else if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) {
- if ( m[ 8]==0.0F
- && m[ 9]==0.0F
- && m[2]==0.0F && m[6]==0.0F && m[10]==1.0F && m[14]==0.0F) {
- mat->type = MATRIX_2D;
- }
- else {
- mat->type = MATRIX_3D;
- }
- }
- else if ( m[4]==0.0F && m[12]==0.0F
- && m[1]==0.0F && m[13]==0.0F
- && m[2]==0.0F && m[6]==0.0F
- && m[3]==0.0F && m[7]==0.0F && m[11]==-1.0F && m[15]==0.0F) {
- mat->type = MATRIX_PERSPECTIVE;
- }
- else {
- mat->type = MATRIX_GENERAL;
- }
-}
-
-/**
- * Analyze and update a matrix.
- *
- * \param mat matrix.
- *
- * If the matrix type is dirty then calls either analyse_from_scratch() or
- * analyse_from_flags() to determine its type, according to whether the flags
- * are dirty or not, respectively. If the matrix has an inverse and it's dirty
- * then calls matrix_invert(). Finally clears the dirty flags.
- */
-void
-_math_matrix_analyse( GLmatrix *mat )
-{
- if (mat->flags & MAT_DIRTY_TYPE) {
- if (mat->flags & MAT_DIRTY_FLAGS)
- analyse_from_scratch( mat );
- else
- analyse_from_flags( mat );
- }
-
- if (mat->inv && (mat->flags & MAT_DIRTY_INVERSE)) {
- matrix_invert( mat );
- mat->flags &= ~MAT_DIRTY_INVERSE;
- }
-
- mat->flags &= ~(MAT_DIRTY_FLAGS | MAT_DIRTY_TYPE);
-}
-
-/*@}*/
-
-
-/**
- * Test if the given matrix preserves vector lengths.
- */
-GLboolean
-_math_matrix_is_length_preserving( const GLmatrix *m )
-{
- return TEST_MAT_FLAGS( m, MAT_FLAGS_LENGTH_PRESERVING);
-}
-
-
-/**
- * Test if the given matrix does any rotation.
- * (or perhaps if the upper-left 3x3 is non-identity)
- */
-GLboolean
-_math_matrix_has_rotation( const GLmatrix *m )
-{
- if (m->flags & (MAT_FLAG_GENERAL |
- MAT_FLAG_ROTATION |
- MAT_FLAG_GENERAL_3D |
- MAT_FLAG_PERSPECTIVE))
- return GL_TRUE;
- else
- return GL_FALSE;
-}
-
-
-GLboolean
-_math_matrix_is_general_scale( const GLmatrix *m )
-{
- return (m->flags & MAT_FLAG_GENERAL_SCALE) ? GL_TRUE : GL_FALSE;
-}
-
-
-GLboolean
-_math_matrix_is_dirty( const GLmatrix *m )
-{
- return (m->flags & MAT_DIRTY) ? GL_TRUE : GL_FALSE;
-}
-
-
-/**********************************************************************/
-/** \name Matrix setup */
-/*@{*/
-
-/**
- * Copy a matrix.
- *
- * \param to destination matrix.
- * \param from source matrix.
- *
- * Copies all fields in GLmatrix, creating an inverse array if necessary.
- */
-void
-_math_matrix_copy( GLmatrix *to, const GLmatrix *from )
-{
- memcpy( to->m, from->m, sizeof(Identity) );
- to->flags = from->flags;
- to->type = from->type;
-
- if (to->inv != 0) {
- if (from->inv == 0) {
- matrix_invert( to );
- }
- else {
- memcpy(to->inv, from->inv, sizeof(GLfloat)*16);
- }
- }
-}
-
-/**
- * Loads a matrix array into GLmatrix.
- *
- * \param m matrix array.
- * \param mat matrix.
- *
- * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY
- * flags.
- */
-void
-_math_matrix_loadf( GLmatrix *mat, const GLfloat *m )
-{
- memcpy( mat->m, m, 16*sizeof(GLfloat) );
- mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY);
-}
-
-/**
- * Matrix constructor.
- *
- * \param m matrix.
- *
- * Initialize the GLmatrix fields.
- */
-void
-_math_matrix_ctr( GLmatrix *m )
-{
- m->m = (GLfloat *) _mesa_align_malloc( 16 * sizeof(GLfloat), 16 );
- if (m->m)
- memcpy( m->m, Identity, sizeof(Identity) );
- m->inv = NULL;
- m->type = MATRIX_IDENTITY;
- m->flags = 0;
-}
-
-/**
- * Matrix destructor.
- *
- * \param m matrix.
- *
- * Frees the data in a GLmatrix.
- */
-void
-_math_matrix_dtr( GLmatrix *m )
-{
- if (m->m) {
- _mesa_align_free( m->m );
- m->m = NULL;
- }
- if (m->inv) {
- _mesa_align_free( m->inv );
- m->inv = NULL;
- }
-}
-
-/**
- * Allocate a matrix inverse.
- *
- * \param m matrix.
- *
- * Allocates the matrix inverse, GLmatrix::inv, and sets it to Identity.
- */
-void
-_math_matrix_alloc_inv( GLmatrix *m )
-{
- if (!m->inv) {
- m->inv = (GLfloat *) _mesa_align_malloc( 16 * sizeof(GLfloat), 16 );
- if (m->inv)
- memcpy( m->inv, Identity, 16 * sizeof(GLfloat) );
- }
-}
-
-/*@}*/
-
-
-/**********************************************************************/
-/** \name Matrix transpose */
-/*@{*/
-
-/**
- * Transpose a GLfloat matrix.
- *
- * \param to destination array.
- * \param from source array.
- */
-void
-_math_transposef( GLfloat to[16], const GLfloat from[16] )
-{
- to[0] = from[0];
- to[1] = from[4];
- to[2] = from[8];
- to[3] = from[12];
- to[4] = from[1];
- to[5] = from[5];
- to[6] = from[9];
- to[7] = from[13];
- to[8] = from[2];
- to[9] = from[6];
- to[10] = from[10];
- to[11] = from[14];
- to[12] = from[3];
- to[13] = from[7];
- to[14] = from[11];
- to[15] = from[15];
-}
-
-/**
- * Transpose a GLdouble matrix.
- *
- * \param to destination array.
- * \param from source array.
- */
-void
-_math_transposed( GLdouble to[16], const GLdouble from[16] )
-{
- to[0] = from[0];
- to[1] = from[4];
- to[2] = from[8];
- to[3] = from[12];
- to[4] = from[1];
- to[5] = from[5];
- to[6] = from[9];
- to[7] = from[13];
- to[8] = from[2];
- to[9] = from[6];
- to[10] = from[10];
- to[11] = from[14];
- to[12] = from[3];
- to[13] = from[7];
- to[14] = from[11];
- to[15] = from[15];
-}
-
-/**
- * Transpose a GLdouble matrix and convert to GLfloat.
- *
- * \param to destination array.
- * \param from source array.
- */
-void
-_math_transposefd( GLfloat to[16], const GLdouble from[16] )
-{
- to[0] = (GLfloat) from[0];
- to[1] = (GLfloat) from[4];
- to[2] = (GLfloat) from[8];
- to[3] = (GLfloat) from[12];
- to[4] = (GLfloat) from[1];
- to[5] = (GLfloat) from[5];
- to[6] = (GLfloat) from[9];
- to[7] = (GLfloat) from[13];
- to[8] = (GLfloat) from[2];
- to[9] = (GLfloat) from[6];
- to[10] = (GLfloat) from[10];
- to[11] = (GLfloat) from[14];
- to[12] = (GLfloat) from[3];
- to[13] = (GLfloat) from[7];
- to[14] = (GLfloat) from[11];
- to[15] = (GLfloat) from[15];
-}
-
-/*@}*/
-
-
-/**
- * Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix. This
- * function is used for transforming clipping plane equations and spotlight
- * directions.
- * Mathematically, u = v * m.
- * Input: v - input vector
- * m - transformation matrix
- * Output: u - transformed vector
- */
-void
-_mesa_transform_vector( GLfloat u[4], const GLfloat v[4], const GLfloat m[16] )
-{
- const GLfloat v0 = v[0], v1 = v[1], v2 = v[2], v3 = v[3];
-#define M(row,col) m[row + col*4]
- u[0] = v0 * M(0,0) + v1 * M(1,0) + v2 * M(2,0) + v3 * M(3,0);
- u[1] = v0 * M(0,1) + v1 * M(1,1) + v2 * M(2,1) + v3 * M(3,1);
- u[2] = v0 * M(0,2) + v1 * M(1,2) + v2 * M(2,2) + v3 * M(3,2);
- u[3] = v0 * M(0,3) + v1 * M(1,3) + v2 * M(2,3) + v3 * M(3,3);
-#undef M
-}
+/* + * Mesa 3-D graphics library + * Version: 6.3 + * + * Copyright (C) 1999-2005 Brian Paul All Rights Reserved. + * + * Permission is hereby granted, free of charge, to any person obtaining a + * copy of this software and associated documentation files (the "Software"), + * to deal in the Software without restriction, including without limitation + * the rights to use, copy, modify, merge, publish, distribute, sublicense, + * and/or sell copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included + * in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS + * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN + * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN + * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + */ + + +/** + * \file m_matrix.c + * Matrix operations. + * + * \note + * -# 4x4 transformation matrices are stored in memory in column major order. + * -# Points/vertices are to be thought of as column vectors. + * -# Transformation of a point p by a matrix M is: p' = M * p + */ + + +#include "main/glheader.h" +#include "main/imports.h" +#include "main/macros.h" + +#include "m_matrix.h" + + +/** + * \defgroup MatFlags MAT_FLAG_XXX-flags + * + * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags + * It would be nice to make all these flags private to m_matrix.c + */ +/*@{*/ +#define MAT_FLAG_IDENTITY 0 /**< is an identity matrix flag. + * (Not actually used - the identity + * matrix is identified by the absense + * of all other flags.) + */ +#define MAT_FLAG_GENERAL 0x1 /**< is a general matrix flag */ +#define MAT_FLAG_ROTATION 0x2 /**< is a rotation matrix flag */ +#define MAT_FLAG_TRANSLATION 0x4 /**< is a translation matrix flag */ +#define MAT_FLAG_UNIFORM_SCALE 0x8 /**< is an uniform scaling matrix flag */ +#define MAT_FLAG_GENERAL_SCALE 0x10 /**< is a general scaling matrix flag */ +#define MAT_FLAG_GENERAL_3D 0x20 /**< general 3D matrix flag */ +#define MAT_FLAG_PERSPECTIVE 0x40 /**< is a perspective proj matrix flag */ +#define MAT_FLAG_SINGULAR 0x80 /**< is a singular matrix flag */ +#define MAT_DIRTY_TYPE 0x100 /**< matrix type is dirty */ +#define MAT_DIRTY_FLAGS 0x200 /**< matrix flags are dirty */ +#define MAT_DIRTY_INVERSE 0x400 /**< matrix inverse is dirty */ + +/** angle preserving matrix flags mask */ +#define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \ + MAT_FLAG_TRANSLATION | \ + MAT_FLAG_UNIFORM_SCALE) + +/** geometry related matrix flags mask */ +#define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \ + MAT_FLAG_ROTATION | \ + MAT_FLAG_TRANSLATION | \ + MAT_FLAG_UNIFORM_SCALE | \ + MAT_FLAG_GENERAL_SCALE | \ + MAT_FLAG_GENERAL_3D | \ + MAT_FLAG_PERSPECTIVE | \ + MAT_FLAG_SINGULAR) + +/** length preserving matrix flags mask */ +#define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \ + MAT_FLAG_TRANSLATION) + + +/** 3D (non-perspective) matrix flags mask */ +#define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \ + MAT_FLAG_TRANSLATION | \ + MAT_FLAG_UNIFORM_SCALE | \ + MAT_FLAG_GENERAL_SCALE | \ + MAT_FLAG_GENERAL_3D) + +/** dirty matrix flags mask */ +#define MAT_DIRTY (MAT_DIRTY_TYPE | \ + MAT_DIRTY_FLAGS | \ + MAT_DIRTY_INVERSE) + +/*@}*/ + + +/** + * Test geometry related matrix flags. + * + * \param mat a pointer to a GLmatrix structure. + * \param a flags mask. + * + * \returns non-zero if all geometry related matrix flags are contained within + * the mask, or zero otherwise. + */ +#define TEST_MAT_FLAGS(mat, a) \ + ((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0) + + + +/** + * Names of the corresponding GLmatrixtype values. + */ +static const char *types[] = { + "MATRIX_GENERAL", + "MATRIX_IDENTITY", + "MATRIX_3D_NO_ROT", + "MATRIX_PERSPECTIVE", + "MATRIX_2D", + "MATRIX_2D_NO_ROT", + "MATRIX_3D" +}; + + +/** + * Identity matrix. + */ +static GLfloat Identity[16] = { + 1.0, 0.0, 0.0, 0.0, + 0.0, 1.0, 0.0, 0.0, + 0.0, 0.0, 1.0, 0.0, + 0.0, 0.0, 0.0, 1.0 +}; + + + +/**********************************************************************/ +/** \name Matrix multiplication */ +/*@{*/ + +#define A(row,col) a[(col<<2)+row] +#define B(row,col) b[(col<<2)+row] +#define P(row,col) product[(col<<2)+row] + +/** + * Perform a full 4x4 matrix multiplication. + * + * \param a matrix. + * \param b matrix. + * \param product will receive the product of \p a and \p b. + * + * \warning Is assumed that \p product != \p b. \p product == \p a is allowed. + * + * \note KW: 4*16 = 64 multiplications + * + * \author This \c matmul was contributed by Thomas Malik + */ +static void matmul4( GLfloat *product, const GLfloat *a, const GLfloat *b ) +{ + GLint i; + for (i = 0; i < 4; i++) { + const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3); + P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0); + P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1); + P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2); + P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3); + } +} + +/** + * Multiply two matrices known to occupy only the top three rows, such + * as typical model matrices, and orthogonal matrices. + * + * \param a matrix. + * \param b matrix. + * \param product will receive the product of \p a and \p b. + */ +static void matmul34( GLfloat *product, const GLfloat *a, const GLfloat *b ) +{ + GLint i; + for (i = 0; i < 3; i++) { + const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3); + P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0); + P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1); + P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2); + P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3; + } + P(3,0) = 0; + P(3,1) = 0; + P(3,2) = 0; + P(3,3) = 1; +} + +#undef A +#undef B +#undef P + +/** + * Multiply a matrix by an array of floats with known properties. + * + * \param mat pointer to a GLmatrix structure containing the left multiplication + * matrix, and that will receive the product result. + * \param m right multiplication matrix array. + * \param flags flags of the matrix \p m. + * + * Joins both flags and marks the type and inverse as dirty. Calls matmul34() + * if both matrices are 3D, or matmul4() otherwise. + */ +static void matrix_multf( GLmatrix *mat, const GLfloat *m, GLuint flags ) +{ + mat->flags |= (flags | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE); + + if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) + matmul34( mat->m, mat->m, m ); + else + matmul4( mat->m, mat->m, m ); +} + +/** + * Matrix multiplication. + * + * \param dest destination matrix. + * \param a left matrix. + * \param b right matrix. + * + * Joins both flags and marks the type and inverse as dirty. Calls matmul34() + * if both matrices are 3D, or matmul4() otherwise. + */ +void +_math_matrix_mul_matrix( GLmatrix *dest, const GLmatrix *a, const GLmatrix *b ) +{ + dest->flags = (a->flags | + b->flags | + MAT_DIRTY_TYPE | + MAT_DIRTY_INVERSE); + + if (TEST_MAT_FLAGS(dest, MAT_FLAGS_3D)) + matmul34( dest->m, a->m, b->m ); + else + matmul4( dest->m, a->m, b->m ); +} + +/** + * Matrix multiplication. + * + * \param dest left and destination matrix. + * \param m right matrix array. + * + * Marks the matrix flags with general flag, and type and inverse dirty flags. + * Calls matmul4() for the multiplication. + */ +void +_math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m ) +{ + dest->flags |= (MAT_FLAG_GENERAL | + MAT_DIRTY_TYPE | + MAT_DIRTY_INVERSE | + MAT_DIRTY_FLAGS); + + matmul4( dest->m, dest->m, m ); +} + +/*@}*/ + + +/**********************************************************************/ +/** \name Matrix output */ +/*@{*/ + +/** + * Print a matrix array. + * + * \param m matrix array. + * + * Called by _math_matrix_print() to print a matrix or its inverse. + */ +static void print_matrix_floats( const GLfloat m[16] ) +{ + int i; + for (i=0;i<4;i++) { + _mesa_debug(NULL,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] ); + } +} + +/** + * Dumps the contents of a GLmatrix structure. + * + * \param m pointer to the GLmatrix structure. + */ +void +_math_matrix_print( const GLmatrix *m ) +{ + _mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags); + print_matrix_floats(m->m); + _mesa_debug(NULL, "Inverse: \n"); + if (m->inv) { + GLfloat prod[16]; + print_matrix_floats(m->inv); + matmul4(prod, m->m, m->inv); + _mesa_debug(NULL, "Mat * Inverse:\n"); + print_matrix_floats(prod); + } + else { + _mesa_debug(NULL, " - not available\n"); + } +} + +/*@}*/ + + +/** + * References an element of 4x4 matrix. + * + * \param m matrix array. + * \param c column of the desired element. + * \param r row of the desired element. + * + * \return value of the desired element. + * + * Calculate the linear storage index of the element and references it. + */ +#define MAT(m,r,c) (m)[(c)*4+(r)] + + +/**********************************************************************/ +/** \name Matrix inversion */ +/*@{*/ + +/** + * Swaps the values of two floating pointer variables. + * + * Used by invert_matrix_general() to swap the row pointers. + */ +#define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; } + +/** + * Compute inverse of 4x4 transformation matrix. + * + * \param mat pointer to a GLmatrix structure. The matrix inverse will be + * stored in the GLmatrix::inv attribute. + * + * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). + * + * \author + * Code contributed by Jacques Leroy jle@star.be + * + * Calculates the inverse matrix by performing the gaussian matrix reduction + * with partial pivoting followed by back/substitution with the loops manually + * unrolled. + */ +static GLboolean invert_matrix_general( GLmatrix *mat ) +{ + const GLfloat *m = mat->m; + GLfloat *out = mat->inv; + GLfloat wtmp[4][8]; + GLfloat m0, m1, m2, m3, s; + GLfloat *r0, *r1, *r2, *r3; + + r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3]; + + r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1), + r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3), + r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0, + + r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1), + r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3), + r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0, + + r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1), + r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3), + r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0, + + r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1), + r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3), + r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0; + + /* choose pivot - or die */ + if (FABSF(r3[0])>FABSF(r2[0])) SWAP_ROWS(r3, r2); + if (FABSF(r2[0])>FABSF(r1[0])) SWAP_ROWS(r2, r1); + if (FABSF(r1[0])>FABSF(r0[0])) SWAP_ROWS(r1, r0); + if (0.0 == r0[0]) return GL_FALSE; + + /* eliminate first variable */ + m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0]; + s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s; + s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s; + s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s; + s = r0[4]; + if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; } + s = r0[5]; + if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; } + s = r0[6]; + if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; } + s = r0[7]; + if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; } + + /* choose pivot - or die */ + if (FABSF(r3[1])>FABSF(r2[1])) SWAP_ROWS(r3, r2); + if (FABSF(r2[1])>FABSF(r1[1])) SWAP_ROWS(r2, r1); + if (0.0 == r1[1]) return GL_FALSE; + + /* eliminate second variable */ + m2 = r2[1]/r1[1]; m3 = r3[1]/r1[1]; + r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2]; + r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3]; + s = r1[4]; if (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; } + s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; } + s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; } + s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; } + + /* choose pivot - or die */ + if (FABSF(r3[2])>FABSF(r2[2])) SWAP_ROWS(r3, r2); + if (0.0 == r2[2]) return GL_FALSE; + + /* eliminate third variable */ + m3 = r3[2]/r2[2]; + r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4], + r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], + r3[7] -= m3 * r2[7]; + + /* last check */ + if (0.0 == r3[3]) return GL_FALSE; + + s = 1.0F/r3[3]; /* now back substitute row 3 */ + r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s; + + m2 = r2[3]; /* now back substitute row 2 */ + s = 1.0F/r2[2]; + r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2), + r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2); + m1 = r1[3]; + r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1, + r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1; + m0 = r0[3]; + r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0, + r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0; + + m1 = r1[2]; /* now back substitute row 1 */ + s = 1.0F/r1[1]; + r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1), + r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1); + m0 = r0[2]; + r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0, + r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0; + + m0 = r0[1]; /* now back substitute row 0 */ + s = 1.0F/r0[0]; + r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0), + r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0); + + MAT(out,0,0) = r0[4]; MAT(out,0,1) = r0[5], + MAT(out,0,2) = r0[6]; MAT(out,0,3) = r0[7], + MAT(out,1,0) = r1[4]; MAT(out,1,1) = r1[5], + MAT(out,1,2) = r1[6]; MAT(out,1,3) = r1[7], + MAT(out,2,0) = r2[4]; MAT(out,2,1) = r2[5], + MAT(out,2,2) = r2[6]; MAT(out,2,3) = r2[7], + MAT(out,3,0) = r3[4]; MAT(out,3,1) = r3[5], + MAT(out,3,2) = r3[6]; MAT(out,3,3) = r3[7]; + + return GL_TRUE; +} +#undef SWAP_ROWS + +/** + * Compute inverse of a general 3d transformation matrix. + * + * \param mat pointer to a GLmatrix structure. The matrix inverse will be + * stored in the GLmatrix::inv attribute. + * + * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). + * + * \author Adapted from graphics gems II. + * + * Calculates the inverse of the upper left by first calculating its + * determinant and multiplying it to the symmetric adjust matrix of each + * element. Finally deals with the translation part by transforming the + * original translation vector using by the calculated submatrix inverse. + */ +static GLboolean invert_matrix_3d_general( GLmatrix *mat ) +{ + const GLfloat *in = mat->m; + GLfloat *out = mat->inv; + GLfloat pos, neg, t; + GLfloat det; + + /* Calculate the determinant of upper left 3x3 submatrix and + * determine if the matrix is singular. + */ + pos = neg = 0.0; + t = MAT(in,0,0) * MAT(in,1,1) * MAT(in,2,2); + if (t >= 0.0) pos += t; else neg += t; + + t = MAT(in,1,0) * MAT(in,2,1) * MAT(in,0,2); + if (t >= 0.0) pos += t; else neg += t; + + t = MAT(in,2,0) * MAT(in,0,1) * MAT(in,1,2); + if (t >= 0.0) pos += t; else neg += t; + + t = -MAT(in,2,0) * MAT(in,1,1) * MAT(in,0,2); + if (t >= 0.0) pos += t; else neg += t; + + t = -MAT(in,1,0) * MAT(in,0,1) * MAT(in,2,2); + if (t >= 0.0) pos += t; else neg += t; + + t = -MAT(in,0,0) * MAT(in,2,1) * MAT(in,1,2); + if (t >= 0.0) pos += t; else neg += t; + + det = pos + neg; + + if (det*det < 1e-25) + return GL_FALSE; + + det = 1.0F / det; + MAT(out,0,0) = ( (MAT(in,1,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,1,2) )*det); + MAT(out,0,1) = (- (MAT(in,0,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,0,2) )*det); + MAT(out,0,2) = ( (MAT(in,0,1)*MAT(in,1,2) - MAT(in,1,1)*MAT(in,0,2) )*det); + MAT(out,1,0) = (- (MAT(in,1,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,1,2) )*det); + MAT(out,1,1) = ( (MAT(in,0,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,0,2) )*det); + MAT(out,1,2) = (- (MAT(in,0,0)*MAT(in,1,2) - MAT(in,1,0)*MAT(in,0,2) )*det); + MAT(out,2,0) = ( (MAT(in,1,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,1,1) )*det); + MAT(out,2,1) = (- (MAT(in,0,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,0,1) )*det); + MAT(out,2,2) = ( (MAT(in,0,0)*MAT(in,1,1) - MAT(in,1,0)*MAT(in,0,1) )*det); + + /* Do the translation part */ + MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) + + MAT(in,1,3) * MAT(out,0,1) + + MAT(in,2,3) * MAT(out,0,2) ); + MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) + + MAT(in,1,3) * MAT(out,1,1) + + MAT(in,2,3) * MAT(out,1,2) ); + MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) + + MAT(in,1,3) * MAT(out,2,1) + + MAT(in,2,3) * MAT(out,2,2) ); + + return GL_TRUE; +} + +/** + * Compute inverse of a 3d transformation matrix. + * + * \param mat pointer to a GLmatrix structure. The matrix inverse will be + * stored in the GLmatrix::inv attribute. + * + * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). + * + * If the matrix is not an angle preserving matrix then calls + * invert_matrix_3d_general for the actual calculation. Otherwise calculates + * the inverse matrix analyzing and inverting each of the scaling, rotation and + * translation parts. + */ +static GLboolean invert_matrix_3d( GLmatrix *mat ) +{ + const GLfloat *in = mat->m; + GLfloat *out = mat->inv; + + if (!TEST_MAT_FLAGS(mat, MAT_FLAGS_ANGLE_PRESERVING)) { + return invert_matrix_3d_general( mat ); + } + + if (mat->flags & MAT_FLAG_UNIFORM_SCALE) { + GLfloat scale = (MAT(in,0,0) * MAT(in,0,0) + + MAT(in,0,1) * MAT(in,0,1) + + MAT(in,0,2) * MAT(in,0,2)); + + if (scale == 0.0) + return GL_FALSE; + + scale = 1.0F / scale; + + /* Transpose and scale the 3 by 3 upper-left submatrix. */ + MAT(out,0,0) = scale * MAT(in,0,0); + MAT(out,1,0) = scale * MAT(in,0,1); + MAT(out,2,0) = scale * MAT(in,0,2); + MAT(out,0,1) = scale * MAT(in,1,0); + MAT(out,1,1) = scale * MAT(in,1,1); + MAT(out,2,1) = scale * MAT(in,1,2); + MAT(out,0,2) = scale * MAT(in,2,0); + MAT(out,1,2) = scale * MAT(in,2,1); + MAT(out,2,2) = scale * MAT(in,2,2); + } + else if (mat->flags & MAT_FLAG_ROTATION) { + /* Transpose the 3 by 3 upper-left submatrix. */ + MAT(out,0,0) = MAT(in,0,0); + MAT(out,1,0) = MAT(in,0,1); + MAT(out,2,0) = MAT(in,0,2); + MAT(out,0,1) = MAT(in,1,0); + MAT(out,1,1) = MAT(in,1,1); + MAT(out,2,1) = MAT(in,1,2); + MAT(out,0,2) = MAT(in,2,0); + MAT(out,1,2) = MAT(in,2,1); + MAT(out,2,2) = MAT(in,2,2); + } + else { + /* pure translation */ + memcpy( out, Identity, sizeof(Identity) ); + MAT(out,0,3) = - MAT(in,0,3); + MAT(out,1,3) = - MAT(in,1,3); + MAT(out,2,3) = - MAT(in,2,3); + return GL_TRUE; + } + + if (mat->flags & MAT_FLAG_TRANSLATION) { + /* Do the translation part */ + MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) + + MAT(in,1,3) * MAT(out,0,1) + + MAT(in,2,3) * MAT(out,0,2) ); + MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) + + MAT(in,1,3) * MAT(out,1,1) + + MAT(in,2,3) * MAT(out,1,2) ); + MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) + + MAT(in,1,3) * MAT(out,2,1) + + MAT(in,2,3) * MAT(out,2,2) ); + } + else { + MAT(out,0,3) = MAT(out,1,3) = MAT(out,2,3) = 0.0; + } + + return GL_TRUE; +} + +/** + * Compute inverse of an identity transformation matrix. + * + * \param mat pointer to a GLmatrix structure. The matrix inverse will be + * stored in the GLmatrix::inv attribute. + * + * \return always GL_TRUE. + * + * Simply copies Identity into GLmatrix::inv. + */ +static GLboolean invert_matrix_identity( GLmatrix *mat ) +{ + memcpy( mat->inv, Identity, sizeof(Identity) ); + return GL_TRUE; +} + +/** + * Compute inverse of a no-rotation 3d transformation matrix. + * + * \param mat pointer to a GLmatrix structure. The matrix inverse will be + * stored in the GLmatrix::inv attribute. + * + * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). + * + * Calculates the + */ +static GLboolean invert_matrix_3d_no_rot( GLmatrix *mat ) +{ + const GLfloat *in = mat->m; + GLfloat *out = mat->inv; + + if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0 || MAT(in,2,2) == 0 ) + return GL_FALSE; + + memcpy( out, Identity, 16 * sizeof(GLfloat) ); + MAT(out,0,0) = 1.0F / MAT(in,0,0); + MAT(out,1,1) = 1.0F / MAT(in,1,1); + MAT(out,2,2) = 1.0F / MAT(in,2,2); + + if (mat->flags & MAT_FLAG_TRANSLATION) { + MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0)); + MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1)); + MAT(out,2,3) = - (MAT(in,2,3) * MAT(out,2,2)); + } + + return GL_TRUE; +} + +/** + * Compute inverse of a no-rotation 2d transformation matrix. + * + * \param mat pointer to a GLmatrix structure. The matrix inverse will be + * stored in the GLmatrix::inv attribute. + * + * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). + * + * Calculates the inverse matrix by applying the inverse scaling and + * translation to the identity matrix. + */ +static GLboolean invert_matrix_2d_no_rot( GLmatrix *mat ) +{ + const GLfloat *in = mat->m; + GLfloat *out = mat->inv; + + if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0) + return GL_FALSE; + + memcpy( out, Identity, 16 * sizeof(GLfloat) ); + MAT(out,0,0) = 1.0F / MAT(in,0,0); + MAT(out,1,1) = 1.0F / MAT(in,1,1); + + if (mat->flags & MAT_FLAG_TRANSLATION) { + MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0)); + MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1)); + } + + return GL_TRUE; +} + +#if 0 +/* broken */ +static GLboolean invert_matrix_perspective( GLmatrix *mat ) +{ + const GLfloat *in = mat->m; + GLfloat *out = mat->inv; + + if (MAT(in,2,3) == 0) + return GL_FALSE; + + memcpy( out, Identity, 16 * sizeof(GLfloat) ); + + MAT(out,0,0) = 1.0F / MAT(in,0,0); + MAT(out,1,1) = 1.0F / MAT(in,1,1); + + MAT(out,0,3) = MAT(in,0,2); + MAT(out,1,3) = MAT(in,1,2); + + MAT(out,2,2) = 0; + MAT(out,2,3) = -1; + + MAT(out,3,2) = 1.0F / MAT(in,2,3); + MAT(out,3,3) = MAT(in,2,2) * MAT(out,3,2); + + return GL_TRUE; +} +#endif + +/** + * Matrix inversion function pointer type. + */ +typedef GLboolean (*inv_mat_func)( GLmatrix *mat ); + +/** + * Table of the matrix inversion functions according to the matrix type. + */ +static inv_mat_func inv_mat_tab[7] = { + invert_matrix_general, + invert_matrix_identity, + invert_matrix_3d_no_rot, +#if 0 + /* Don't use this function for now - it fails when the projection matrix + * is premultiplied by a translation (ala Chromium's tilesort SPU). + */ + invert_matrix_perspective, +#else + invert_matrix_general, +#endif + invert_matrix_3d, /* lazy! */ + invert_matrix_2d_no_rot, + invert_matrix_3d +}; + +/** + * Compute inverse of a transformation matrix. + * + * \param mat pointer to a GLmatrix structure. The matrix inverse will be + * stored in the GLmatrix::inv attribute. + * + * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). + * + * Calls the matrix inversion function in inv_mat_tab corresponding to the + * given matrix type. In case of failure, updates the MAT_FLAG_SINGULAR flag, + * and copies the identity matrix into GLmatrix::inv. + */ +static GLboolean matrix_invert( GLmatrix *mat ) +{ + if (inv_mat_tab[mat->type](mat)) { + mat->flags &= ~MAT_FLAG_SINGULAR; + return GL_TRUE; + } else { + mat->flags |= MAT_FLAG_SINGULAR; + memcpy( mat->inv, Identity, sizeof(Identity) ); + return GL_FALSE; + } +} + +/*@}*/ + + +/**********************************************************************/ +/** \name Matrix generation */ +/*@{*/ + +/** + * Generate a 4x4 transformation matrix from glRotate parameters, and + * post-multiply the input matrix by it. + * + * \author + * This function was contributed by Erich Boleyn (erich@uruk.org). + * Optimizations contributed by Rudolf Opalla (rudi@khm.de). + */ +void +_math_matrix_rotate( GLmatrix *mat, + GLfloat angle, GLfloat x, GLfloat y, GLfloat z ) +{ + GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c; + GLfloat m[16]; + GLboolean optimized; + + s = (GLfloat) sin( angle * DEG2RAD ); + c = (GLfloat) cos( angle * DEG2RAD ); + + memcpy(m, Identity, sizeof(GLfloat)*16); + optimized = GL_FALSE; + +#define M(row,col) m[col*4+row] + + if (x == 0.0F) { + if (y == 0.0F) { + if (z != 0.0F) { + optimized = GL_TRUE; + /* rotate only around z-axis */ + M(0,0) = c; + M(1,1) = c; + if (z < 0.0F) { + M(0,1) = s; + M(1,0) = -s; + } + else { + M(0,1) = -s; + M(1,0) = s; + } + } + } + else if (z == 0.0F) { + optimized = GL_TRUE; + /* rotate only around y-axis */ + M(0,0) = c; + M(2,2) = c; + if (y < 0.0F) { + M(0,2) = -s; + M(2,0) = s; + } + else { + M(0,2) = s; + M(2,0) = -s; + } + } + } + else if (y == 0.0F) { + if (z == 0.0F) { + optimized = GL_TRUE; + /* rotate only around x-axis */ + M(1,1) = c; + M(2,2) = c; + if (x < 0.0F) { + M(1,2) = s; + M(2,1) = -s; + } + else { + M(1,2) = -s; + M(2,1) = s; + } + } + } + + if (!optimized) { + const GLfloat mag = SQRTF(x * x + y * y + z * z); + + if (mag <= 1.0e-4) { + /* no rotation, leave mat as-is */ + return; + } + + x /= mag; + y /= mag; + z /= mag; + + + /* + * Arbitrary axis rotation matrix. + * + * This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied + * like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation + * (which is about the X-axis), and the two composite transforms + * Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary + * from the arbitrary axis to the X-axis then back. They are + * all elementary rotations. + * + * Rz' is a rotation about the Z-axis, to bring the axis vector + * into the x-z plane. Then Ry' is applied, rotating about the + * Y-axis to bring the axis vector parallel with the X-axis. The + * rotation about the X-axis is then performed. Ry and Rz are + * simply the respective inverse transforms to bring the arbitrary + * axis back to its original orientation. The first transforms + * Rz' and Ry' are considered inverses, since the data from the + * arbitrary axis gives you info on how to get to it, not how + * to get away from it, and an inverse must be applied. + * + * The basic calculation used is to recognize that the arbitrary + * axis vector (x, y, z), since it is of unit length, actually + * represents the sines and cosines of the angles to rotate the + * X-axis to the same orientation, with theta being the angle about + * Z and phi the angle about Y (in the order described above) + * as follows: + * + * cos ( theta ) = x / sqrt ( 1 - z^2 ) + * sin ( theta ) = y / sqrt ( 1 - z^2 ) + * + * cos ( phi ) = sqrt ( 1 - z^2 ) + * sin ( phi ) = z + * + * Note that cos ( phi ) can further be inserted to the above + * formulas: + * + * cos ( theta ) = x / cos ( phi ) + * sin ( theta ) = y / sin ( phi ) + * + * ...etc. Because of those relations and the standard trigonometric + * relations, it is pssible to reduce the transforms down to what + * is used below. It may be that any primary axis chosen will give the + * same results (modulo a sign convention) using thie method. + * + * Particularly nice is to notice that all divisions that might + * have caused trouble when parallel to certain planes or + * axis go away with care paid to reducing the expressions. + * After checking, it does perform correctly under all cases, since + * in all the cases of division where the denominator would have + * been zero, the numerator would have been zero as well, giving + * the expected result. + */ + + xx = x * x; + yy = y * y; + zz = z * z; + xy = x * y; + yz = y * z; + zx = z * x; + xs = x * s; + ys = y * s; + zs = z * s; + one_c = 1.0F - c; + + /* We already hold the identity-matrix so we can skip some statements */ + M(0,0) = (one_c * xx) + c; + M(0,1) = (one_c * xy) - zs; + M(0,2) = (one_c * zx) + ys; +/* M(0,3) = 0.0F; */ + + M(1,0) = (one_c * xy) + zs; + M(1,1) = (one_c * yy) + c; + M(1,2) = (one_c * yz) - xs; +/* M(1,3) = 0.0F; */ + + M(2,0) = (one_c * zx) - ys; + M(2,1) = (one_c * yz) + xs; + M(2,2) = (one_c * zz) + c; +/* M(2,3) = 0.0F; */ + +/* + M(3,0) = 0.0F; + M(3,1) = 0.0F; + M(3,2) = 0.0F; + M(3,3) = 1.0F; +*/ + } +#undef M + + matrix_multf( mat, m, MAT_FLAG_ROTATION ); +} + +/** + * Apply a perspective projection matrix. + * + * \param mat matrix to apply the projection. + * \param left left clipping plane coordinate. + * \param right right clipping plane coordinate. + * \param bottom bottom clipping plane coordinate. + * \param top top clipping plane coordinate. + * \param nearval distance to the near clipping plane. + * \param farval distance to the far clipping plane. + * + * Creates the projection matrix and multiplies it with \p mat, marking the + * MAT_FLAG_PERSPECTIVE flag. + */ +void +_math_matrix_frustum( GLmatrix *mat, + GLfloat left, GLfloat right, + GLfloat bottom, GLfloat top, + GLfloat nearval, GLfloat farval ) +{ + GLfloat x, y, a, b, c, d; + GLfloat m[16]; + + x = (2.0F*nearval) / (right-left); + y = (2.0F*nearval) / (top-bottom); + a = (right+left) / (right-left); + b = (top+bottom) / (top-bottom); + c = -(farval+nearval) / ( farval-nearval); + d = -(2.0F*farval*nearval) / (farval-nearval); /* error? */ + +#define M(row,col) m[col*4+row] + M(0,0) = x; M(0,1) = 0.0F; M(0,2) = a; M(0,3) = 0.0F; + M(1,0) = 0.0F; M(1,1) = y; M(1,2) = b; M(1,3) = 0.0F; + M(2,0) = 0.0F; M(2,1) = 0.0F; M(2,2) = c; M(2,3) = d; + M(3,0) = 0.0F; M(3,1) = 0.0F; M(3,2) = -1.0F; M(3,3) = 0.0F; +#undef M + + matrix_multf( mat, m, MAT_FLAG_PERSPECTIVE ); +} + +/** + * Apply an orthographic projection matrix. + * + * \param mat matrix to apply the projection. + * \param left left clipping plane coordinate. + * \param right right clipping plane coordinate. + * \param bottom bottom clipping plane coordinate. + * \param top top clipping plane coordinate. + * \param nearval distance to the near clipping plane. + * \param farval distance to the far clipping plane. + * + * Creates the projection matrix and multiplies it with \p mat, marking the + * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags. + */ +void +_math_matrix_ortho( GLmatrix *mat, + GLfloat left, GLfloat right, + GLfloat bottom, GLfloat top, + GLfloat nearval, GLfloat farval ) +{ + GLfloat m[16]; + +#define M(row,col) m[col*4+row] + M(0,0) = 2.0F / (right-left); + M(0,1) = 0.0F; + M(0,2) = 0.0F; + M(0,3) = -(right+left) / (right-left); + + M(1,0) = 0.0F; + M(1,1) = 2.0F / (top-bottom); + M(1,2) = 0.0F; + M(1,3) = -(top+bottom) / (top-bottom); + + M(2,0) = 0.0F; + M(2,1) = 0.0F; + M(2,2) = -2.0F / (farval-nearval); + M(2,3) = -(farval+nearval) / (farval-nearval); + + M(3,0) = 0.0F; + M(3,1) = 0.0F; + M(3,2) = 0.0F; + M(3,3) = 1.0F; +#undef M + + matrix_multf( mat, m, (MAT_FLAG_GENERAL_SCALE|MAT_FLAG_TRANSLATION)); +} + +/** + * Multiply a matrix with a general scaling matrix. + * + * \param mat matrix. + * \param x x axis scale factor. + * \param y y axis scale factor. + * \param z z axis scale factor. + * + * Multiplies in-place the elements of \p mat by the scale factors. Checks if + * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE + * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and + * MAT_DIRTY_INVERSE dirty flags. + */ +void +_math_matrix_scale( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z ) +{ + GLfloat *m = mat->m; + m[0] *= x; m[4] *= y; m[8] *= z; + m[1] *= x; m[5] *= y; m[9] *= z; + m[2] *= x; m[6] *= y; m[10] *= z; + m[3] *= x; m[7] *= y; m[11] *= z; + + if (FABSF(x - y) < 1e-8 && FABSF(x - z) < 1e-8) + mat->flags |= MAT_FLAG_UNIFORM_SCALE; + else + mat->flags |= MAT_FLAG_GENERAL_SCALE; + + mat->flags |= (MAT_DIRTY_TYPE | + MAT_DIRTY_INVERSE); +} + +/** + * Multiply a matrix with a translation matrix. + * + * \param mat matrix. + * \param x translation vector x coordinate. + * \param y translation vector y coordinate. + * \param z translation vector z coordinate. + * + * Adds the translation coordinates to the elements of \p mat in-place. Marks + * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE + * dirty flags. + */ +void +_math_matrix_translate( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z ) +{ + GLfloat *m = mat->m; + m[12] = m[0] * x + m[4] * y + m[8] * z + m[12]; + m[13] = m[1] * x + m[5] * y + m[9] * z + m[13]; + m[14] = m[2] * x + m[6] * y + m[10] * z + m[14]; + m[15] = m[3] * x + m[7] * y + m[11] * z + m[15]; + + mat->flags |= (MAT_FLAG_TRANSLATION | + MAT_DIRTY_TYPE | + MAT_DIRTY_INVERSE); +} + + +/** + * Set matrix to do viewport and depthrange mapping. + * Transforms Normalized Device Coords to window/Z values. + */ +void +_math_matrix_viewport(GLmatrix *m, GLint x, GLint y, GLint width, GLint height, + GLfloat zNear, GLfloat zFar, GLfloat depthMax) +{ + m->m[MAT_SX] = (GLfloat) width / 2.0F; + m->m[MAT_TX] = m->m[MAT_SX] + x; + m->m[MAT_SY] = (GLfloat) height / 2.0F; + m->m[MAT_TY] = m->m[MAT_SY] + y; + m->m[MAT_SZ] = depthMax * ((zFar - zNear) / 2.0F); + m->m[MAT_TZ] = depthMax * ((zFar - zNear) / 2.0F + zNear); + m->flags = MAT_FLAG_GENERAL_SCALE | MAT_FLAG_TRANSLATION; + m->type = MATRIX_3D_NO_ROT; +} + + +/** + * Set a matrix to the identity matrix. + * + * \param mat matrix. + * + * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL. + * Sets the matrix type to identity, and clear the dirty flags. + */ +void +_math_matrix_set_identity( GLmatrix *mat ) +{ + memcpy( mat->m, Identity, 16*sizeof(GLfloat) ); + + if (mat->inv) + memcpy( mat->inv, Identity, 16*sizeof(GLfloat) ); + + mat->type = MATRIX_IDENTITY; + mat->flags &= ~(MAT_DIRTY_FLAGS| + MAT_DIRTY_TYPE| + MAT_DIRTY_INVERSE); +} + +/*@}*/ + + +/**********************************************************************/ +/** \name Matrix analysis */ +/*@{*/ + +#define ZERO(x) (1<<x) +#define ONE(x) (1<<(x+16)) + +#define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14)) +#define MASK_NO_2D_SCALE ( ONE(0) | ONE(5)) + +#define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\ + ZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\ + ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ + ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) + +#define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \ + ZERO(1) | ZERO(9) | \ + ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ + ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) + +#define MASK_2D ( ZERO(8) | \ + ZERO(9) | \ + ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ + ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) + + +#define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \ + ZERO(1) | ZERO(9) | \ + ZERO(2) | ZERO(6) | \ + ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) + +#define MASK_3D ( \ + \ + \ + ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) + + +#define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\ + ZERO(1) | ZERO(13) |\ + ZERO(2) | ZERO(6) | \ + ZERO(3) | ZERO(7) | ZERO(15) ) + +#define SQ(x) ((x)*(x)) + +/** + * Determine type and flags from scratch. + * + * \param mat matrix. + * + * This is expensive enough to only want to do it once. + */ +static void analyse_from_scratch( GLmatrix *mat ) +{ + const GLfloat *m = mat->m; + GLuint mask = 0; + GLuint i; + + for (i = 0 ; i < 16 ; i++) { + if (m[i] == 0.0) mask |= (1<<i); + } + + if (m[0] == 1.0F) mask |= (1<<16); + if (m[5] == 1.0F) mask |= (1<<21); + if (m[10] == 1.0F) mask |= (1<<26); + if (m[15] == 1.0F) mask |= (1<<31); + + mat->flags &= ~MAT_FLAGS_GEOMETRY; + + /* Check for translation - no-one really cares + */ + if ((mask & MASK_NO_TRX) != MASK_NO_TRX) + mat->flags |= MAT_FLAG_TRANSLATION; + + /* Do the real work + */ + if (mask == (GLuint) MASK_IDENTITY) { + mat->type = MATRIX_IDENTITY; + } + else if ((mask & MASK_2D_NO_ROT) == (GLuint) MASK_2D_NO_ROT) { + mat->type = MATRIX_2D_NO_ROT; + + if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE) + mat->flags |= MAT_FLAG_GENERAL_SCALE; + } + else if ((mask & MASK_2D) == (GLuint) MASK_2D) { + GLfloat mm = DOT2(m, m); + GLfloat m4m4 = DOT2(m+4,m+4); + GLfloat mm4 = DOT2(m,m+4); + + mat->type = MATRIX_2D; + + /* Check for scale */ + if (SQ(mm-1) > SQ(1e-6) || + SQ(m4m4-1) > SQ(1e-6)) + mat->flags |= MAT_FLAG_GENERAL_SCALE; + + /* Check for rotation */ + if (SQ(mm4) > SQ(1e-6)) + mat->flags |= MAT_FLAG_GENERAL_3D; + else + mat->flags |= MAT_FLAG_ROTATION; + + } + else if ((mask & MASK_3D_NO_ROT) == (GLuint) MASK_3D_NO_ROT) { + mat->type = MATRIX_3D_NO_ROT; + + /* Check for scale */ + if (SQ(m[0]-m[5]) < SQ(1e-6) && + SQ(m[0]-m[10]) < SQ(1e-6)) { + if (SQ(m[0]-1.0) > SQ(1e-6)) { + mat->flags |= MAT_FLAG_UNIFORM_SCALE; + } + } + else { + mat->flags |= MAT_FLAG_GENERAL_SCALE; + } + } + else if ((mask & MASK_3D) == (GLuint) MASK_3D) { + GLfloat c1 = DOT3(m,m); + GLfloat c2 = DOT3(m+4,m+4); + GLfloat c3 = DOT3(m+8,m+8); + GLfloat d1 = DOT3(m, m+4); + GLfloat cp[3]; + + mat->type = MATRIX_3D; + + /* Check for scale */ + if (SQ(c1-c2) < SQ(1e-6) && SQ(c1-c3) < SQ(1e-6)) { + if (SQ(c1-1.0) > SQ(1e-6)) + mat->flags |= MAT_FLAG_UNIFORM_SCALE; + /* else no scale at all */ + } + else { + mat->flags |= MAT_FLAG_GENERAL_SCALE; + } + + /* Check for rotation */ + if (SQ(d1) < SQ(1e-6)) { + CROSS3( cp, m, m+4 ); + SUB_3V( cp, cp, (m+8) ); + if (LEN_SQUARED_3FV(cp) < SQ(1e-6)) + mat->flags |= MAT_FLAG_ROTATION; + else + mat->flags |= MAT_FLAG_GENERAL_3D; + } + else { + mat->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */ + } + } + else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0F) { + mat->type = MATRIX_PERSPECTIVE; + mat->flags |= MAT_FLAG_GENERAL; + } + else { + mat->type = MATRIX_GENERAL; + mat->flags |= MAT_FLAG_GENERAL; + } +} + +/** + * Analyze a matrix given that its flags are accurate. + * + * This is the more common operation, hopefully. + */ +static void analyse_from_flags( GLmatrix *mat ) +{ + const GLfloat *m = mat->m; + + if (TEST_MAT_FLAGS(mat, 0)) { + mat->type = MATRIX_IDENTITY; + } + else if (TEST_MAT_FLAGS(mat, (MAT_FLAG_TRANSLATION | + MAT_FLAG_UNIFORM_SCALE | + MAT_FLAG_GENERAL_SCALE))) { + if ( m[10]==1.0F && m[14]==0.0F ) { + mat->type = MATRIX_2D_NO_ROT; + } + else { + mat->type = MATRIX_3D_NO_ROT; + } + } + else if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) { + if ( m[ 8]==0.0F + && m[ 9]==0.0F + && m[2]==0.0F && m[6]==0.0F && m[10]==1.0F && m[14]==0.0F) { + mat->type = MATRIX_2D; + } + else { + mat->type = MATRIX_3D; + } + } + else if ( m[4]==0.0F && m[12]==0.0F + && m[1]==0.0F && m[13]==0.0F + && m[2]==0.0F && m[6]==0.0F + && m[3]==0.0F && m[7]==0.0F && m[11]==-1.0F && m[15]==0.0F) { + mat->type = MATRIX_PERSPECTIVE; + } + else { + mat->type = MATRIX_GENERAL; + } +} + +/** + * Analyze and update a matrix. + * + * \param mat matrix. + * + * If the matrix type is dirty then calls either analyse_from_scratch() or + * analyse_from_flags() to determine its type, according to whether the flags + * are dirty or not, respectively. If the matrix has an inverse and it's dirty + * then calls matrix_invert(). Finally clears the dirty flags. + */ +void +_math_matrix_analyse( GLmatrix *mat ) +{ + if (mat->flags & MAT_DIRTY_TYPE) { + if (mat->flags & MAT_DIRTY_FLAGS) + analyse_from_scratch( mat ); + else + analyse_from_flags( mat ); + } + + if (mat->inv && (mat->flags & MAT_DIRTY_INVERSE)) { + matrix_invert( mat ); + mat->flags &= ~MAT_DIRTY_INVERSE; + } + + mat->flags &= ~(MAT_DIRTY_FLAGS | MAT_DIRTY_TYPE); +} + +/*@}*/ + + +/** + * Test if the given matrix preserves vector lengths. + */ +GLboolean +_math_matrix_is_length_preserving( const GLmatrix *m ) +{ + return TEST_MAT_FLAGS( m, MAT_FLAGS_LENGTH_PRESERVING); +} + + +/** + * Test if the given matrix does any rotation. + * (or perhaps if the upper-left 3x3 is non-identity) + */ +GLboolean +_math_matrix_has_rotation( const GLmatrix *m ) +{ + if (m->flags & (MAT_FLAG_GENERAL | + MAT_FLAG_ROTATION | + MAT_FLAG_GENERAL_3D | + MAT_FLAG_PERSPECTIVE)) + return GL_TRUE; + else + return GL_FALSE; +} + + +GLboolean +_math_matrix_is_general_scale( const GLmatrix *m ) +{ + return (m->flags & MAT_FLAG_GENERAL_SCALE) ? GL_TRUE : GL_FALSE; +} + + +GLboolean +_math_matrix_is_dirty( const GLmatrix *m ) +{ + return (m->flags & MAT_DIRTY) ? GL_TRUE : GL_FALSE; +} + + +/**********************************************************************/ +/** \name Matrix setup */ +/*@{*/ + +/** + * Copy a matrix. + * + * \param to destination matrix. + * \param from source matrix. + * + * Copies all fields in GLmatrix, creating an inverse array if necessary. + */ +void +_math_matrix_copy( GLmatrix *to, const GLmatrix *from ) +{ + memcpy( to->m, from->m, sizeof(Identity) ); + to->flags = from->flags; + to->type = from->type; + + if (to->inv != 0) { + if (from->inv == 0) { + matrix_invert( to ); + } + else { + memcpy(to->inv, from->inv, sizeof(GLfloat)*16); + } + } +} + +/** + * Loads a matrix array into GLmatrix. + * + * \param m matrix array. + * \param mat matrix. + * + * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY + * flags. + */ +void +_math_matrix_loadf( GLmatrix *mat, const GLfloat *m ) +{ + memcpy( mat->m, m, 16*sizeof(GLfloat) ); + mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY); +} + +/** + * Matrix constructor. + * + * \param m matrix. + * + * Initialize the GLmatrix fields. + */ +void +_math_matrix_ctr( GLmatrix *m ) +{ + m->m = (GLfloat *) _mesa_align_malloc( 16 * sizeof(GLfloat), 16 ); + if (m->m) + memcpy( m->m, Identity, sizeof(Identity) ); + m->inv = NULL; + m->type = MATRIX_IDENTITY; + m->flags = 0; +} + +/** + * Matrix destructor. + * + * \param m matrix. + * + * Frees the data in a GLmatrix. + */ +void +_math_matrix_dtr( GLmatrix *m ) +{ + if (m->m) { + _mesa_align_free( m->m ); + m->m = NULL; + } + if (m->inv) { + _mesa_align_free( m->inv ); + m->inv = NULL; + } +} + +/** + * Allocate a matrix inverse. + * + * \param m matrix. + * + * Allocates the matrix inverse, GLmatrix::inv, and sets it to Identity. + */ +void +_math_matrix_alloc_inv( GLmatrix *m ) +{ + if (!m->inv) { + m->inv = (GLfloat *) _mesa_align_malloc( 16 * sizeof(GLfloat), 16 ); + if (m->inv) + memcpy( m->inv, Identity, 16 * sizeof(GLfloat) ); + } +} + +/*@}*/ + + +/**********************************************************************/ +/** \name Matrix transpose */ +/*@{*/ + +/** + * Transpose a GLfloat matrix. + * + * \param to destination array. + * \param from source array. + */ +void +_math_transposef( GLfloat to[16], const GLfloat from[16] ) +{ + to[0] = from[0]; + to[1] = from[4]; + to[2] = from[8]; + to[3] = from[12]; + to[4] = from[1]; + to[5] = from[5]; + to[6] = from[9]; + to[7] = from[13]; + to[8] = from[2]; + to[9] = from[6]; + to[10] = from[10]; + to[11] = from[14]; + to[12] = from[3]; + to[13] = from[7]; + to[14] = from[11]; + to[15] = from[15]; +} + +/** + * Transpose a GLdouble matrix. + * + * \param to destination array. + * \param from source array. + */ +void +_math_transposed( GLdouble to[16], const GLdouble from[16] ) +{ + to[0] = from[0]; + to[1] = from[4]; + to[2] = from[8]; + to[3] = from[12]; + to[4] = from[1]; + to[5] = from[5]; + to[6] = from[9]; + to[7] = from[13]; + to[8] = from[2]; + to[9] = from[6]; + to[10] = from[10]; + to[11] = from[14]; + to[12] = from[3]; + to[13] = from[7]; + to[14] = from[11]; + to[15] = from[15]; +} + +/** + * Transpose a GLdouble matrix and convert to GLfloat. + * + * \param to destination array. + * \param from source array. + */ +void +_math_transposefd( GLfloat to[16], const GLdouble from[16] ) +{ + to[0] = (GLfloat) from[0]; + to[1] = (GLfloat) from[4]; + to[2] = (GLfloat) from[8]; + to[3] = (GLfloat) from[12]; + to[4] = (GLfloat) from[1]; + to[5] = (GLfloat) from[5]; + to[6] = (GLfloat) from[9]; + to[7] = (GLfloat) from[13]; + to[8] = (GLfloat) from[2]; + to[9] = (GLfloat) from[6]; + to[10] = (GLfloat) from[10]; + to[11] = (GLfloat) from[14]; + to[12] = (GLfloat) from[3]; + to[13] = (GLfloat) from[7]; + to[14] = (GLfloat) from[11]; + to[15] = (GLfloat) from[15]; +} + +/*@}*/ + + +/** + * Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix. This + * function is used for transforming clipping plane equations and spotlight + * directions. + * Mathematically, u = v * m. + * Input: v - input vector + * m - transformation matrix + * Output: u - transformed vector + */ +void +_mesa_transform_vector( GLfloat u[4], const GLfloat v[4], const GLfloat m[16] ) +{ + const GLfloat v0 = v[0], v1 = v[1], v2 = v[2], v3 = v[3]; +#define M(row,col) m[row + col*4] + u[0] = v0 * M(0,0) + v1 * M(1,0) + v2 * M(2,0) + v3 * M(3,0); + u[1] = v0 * M(0,1) + v1 * M(1,1) + v2 * M(2,1) + v3 * M(3,1); + u[2] = v0 * M(0,2) + v1 * M(1,2) + v2 * M(2,2) + v3 * M(3,2); + u[3] = v0 * M(0,3) + v1 * M(1,3) + v2 * M(2,3) + v3 * M(3,3); +#undef M +} |