-/* $Id: m_matrix.c,v 1.5 2001/01/05 05:31:42 keithw Exp $ */
-
/*
* Mesa 3-D graphics library
- * Version: 3.5
- *
- * Copyright (C) 1999-2000 Brian Paul All Rights Reserved.
- *
+ *
+ * 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.
+ * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+ * OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+ * OTHER DEALINGS IN THE SOFTWARE.
*/
-/*
- * Matrix operations
+/**
+ * \file m_matrix.c
+ * Matrix operations.
*
- * NOTES:
- * 1. 4x4 transformation matrices are stored in memory in column major order.
- * 2. Points/vertices are to be thought of as column vectors.
- * 3. Transformation of a point p by a matrix M is: p' = M * p
+ * \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 <math.h>
-#include "glheader.h"
-#include "macros.h"
-#include "mem.h"
-#include "mmath.h"
+#include "c99_math.h"
+#include "main/glheader.h"
+#include "main/imports.h"
+#include "main/macros.h"
#include "m_matrix.h"
+/**
+ * \defgroup MatFlags MAT_FLAG_XXX-flags
+ *
+ * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags
+ */
+/*@{*/
+#define MAT_FLAG_IDENTITY 0 /**< is an identity matrix flag.
+ * (Not actually used - the identity
+ * matrix is identified by the absence
+ * 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",
};
+/**
+ * Identity matrix.
+ */
static GLfloat Identity[16] = {
1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
+/**********************************************************************/
+/** \name Matrix multiplication */
+/*@{*/
-/*
- * This matmul was contributed by Thomas Malik
- *
- * Perform a 4x4 matrix multiplication (product = a x b).
- * Input: a, b - matrices to multiply
- * Output: product - product of a and b
- * WARNING: (product != b) assumed
- * NOTE: (product == a) allowed
- *
- * KW: 4*16 = 64 muls
- */
#define A(row,col) a[(col<<2)+row]
#define B(row,col) b[(col<<2)+row]
#define P(row,col) product[(col<<2)+row]
+/**
+ * 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;
}
}
-
-/* Multiply two matrices known to occupy only the top three rows, such
- * as typical model matrices, and ortho matrices.
+/**
+ * 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 )
{
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 )
{
if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D))
matmul34( mat->m, mat->m, m );
- else
- matmul4( 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++) {
- fprintf(stderr,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] );
+ _mesa_debug(NULL,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] );
}
}
-void
+/**
+ * Dumps the contents of a GLmatrix structure.
+ *
+ * \param m pointer to the GLmatrix structure.
+ */
+void
_math_matrix_print( const GLmatrix *m )
{
- fprintf(stderr, "Matrix type: %s, flags: %x\n", types[m->type], m->flags);
+ GLfloat prod[16];
+
+ _mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags);
print_matrix_floats(m->m);
- fprintf(stderr, "Inverse: \n");
- if (m->inv) {
- GLfloat prod[16];
- print_matrix_floats(m->inv);
- matmul4(prod, m->m, m->inv);
- fprintf(stderr, "Mat * Inverse:\n");
- print_matrix_floats(prod);
- }
- else {
- fprintf(stderr, " - not available\n");
- }
+ _mesa_debug(NULL, "Inverse: \n");
+ print_matrix_floats(m->inv);
+ matmul4(prod, m->m, m->inv);
+ _mesa_debug(NULL, "Mat * Inverse:\n");
+ print_matrix_floats(prod);
}
+/*@}*/
+/**
+ * References an element of 4x4 matrix.
+ *
+ * \param m matrix array.
+ * \param c column of the desired element.
+ * \param r row of the desired element.
+ *
+ * \return value of the desired element.
+ *
+ * Calculate the linear storage index of the element and references it.
+ */
+#define MAT(m,r,c) (m)[(c)*4+(r)]
+
+
+/**********************************************************************/
+/** \name Matrix inversion */
+/*@{*/
+/**
+ * Swaps the values of two floating point variables.
+ *
+ * Used by invert_matrix_general() to swap the row pointers.
+ */
#define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; }
-#define MAT(m,r,c) (m)[(c)*4+(r)]
-/*
+/**
* 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
- * Return GL_TRUE for success, GL_FALSE for failure (singular matrix)
+ *
+ * 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 )
{
GLfloat wtmp[4][8];
GLfloat m0, m1, m2, m3, s;
GLfloat *r0, *r1, *r2, *r3;
-
+
r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
-
+
r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1),
r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3),
r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
-
+
r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1),
r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3),
r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
-
+
r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1),
r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3),
r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
-
+
r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1),
r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3),
r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
-
+
/* choose pivot - or die */
- if (fabs(r3[0])>fabs(r2[0])) SWAP_ROWS(r3, r2);
- if (fabs(r2[0])>fabs(r1[0])) SWAP_ROWS(r2, r1);
- if (fabs(r1[0])>fabs(r0[0])) SWAP_ROWS(r1, r0);
+ if (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;
if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; }
s = r0[7];
if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; }
-
+
/* choose pivot - or die */
- if (fabs(r3[1])>fabs(r2[1])) SWAP_ROWS(r3, r2);
- if (fabs(r2[1])>fabs(r1[1])) SWAP_ROWS(r2, r1);
+ if (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];
s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; }
s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; }
s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; }
-
+
/* choose pivot - or die */
- if (fabs(r3[2])>fabs(r2[2])) SWAP_ROWS(r3, r2);
+ if (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 = 1.0/r3[3]; /* now back substitute row 3 */
+
+ 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 = 1.0/r2[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];
m0 = r0[3];
r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
-
+
m1 = r1[2]; /* now back substitute row 1 */
- s = 1.0/r1[1];
+ 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 = 1.0/r0[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,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];
-
+ MAT(out,3,2) = r3[6]; MAT(out,3,3) = r3[7];
+
return GL_TRUE;
}
#undef SWAP_ROWS
-
-/* Adapted from graphics gems II.
- */
+/**
+ * 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 det;
/* Calculate the determinant of upper left 3x3 submatrix and
- * determine if the matrix is singular.
+ * determine if the matrix is singular.
*/
pos = neg = 0.0;
t = MAT(in,0,0) * MAT(in,1,1) * MAT(in,2,2);
det = pos + neg;
- if (det*det < 1e-25)
+ if (fabsf(det) < 1e-25)
return GL_FALSE;
-
- det = 1.0 / det;
+
+ 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,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;
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)
+ if (scale == 0.0)
return GL_FALSE;
- scale = 1.0 / scale;
+ scale = 1.0F / scale;
/* Transpose and scale the 3 by 3 upper-left submatrix. */
MAT(out,0,0) = scale * MAT(in,0,0);
}
else {
/* pure translation */
- MEMCPY( out, Identity, sizeof(Identity) );
+ 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) +
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) );
+ 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 )
+ if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0 || MAT(in,2,2) == 0 )
return GL_FALSE;
-
- MEMCPY( out, Identity, 16 * sizeof(GLfloat) );
- MAT(out,0,0) = 1.0 / MAT(in,0,0);
- MAT(out,1,1) = 1.0 / MAT(in,1,1);
- MAT(out,2,2) = 1.0 / MAT(in,2,2);
+
+ 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));
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)
+ if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0)
return GL_FALSE;
-
- MEMCPY( out, Identity, 16 * sizeof(GLfloat) );
- MAT(out,0,0) = 1.0 / MAT(in,0,0);
- MAT(out,1,1) = 1.0 / MAT(in,1,1);
+
+ 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));
return GL_TRUE;
}
-
+#if 0
+/* broken */
static GLboolean invert_matrix_perspective( GLmatrix *mat )
{
const GLfloat *in = mat->m;
if (MAT(in,2,3) == 0)
return GL_FALSE;
- MEMCPY( out, Identity, 16 * sizeof(GLfloat) );
+ memcpy( out, Identity, 16 * sizeof(GLfloat) );
- MAT(out,0,0) = 1.0 / MAT(in,0,0);
- MAT(out,1,1) = 1.0 / MAT(in,1,1);
+ MAT(out,0,0) = 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) = 1.0 / MAT(in,2,3);
+ 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)) {
return GL_TRUE;
} else {
mat->flags |= MAT_FLAG_SINGULAR;
- MEMCPY( mat->inv, Identity, sizeof(Identity) );
+ memcpy( mat->inv, Identity, sizeof(Identity) );
return GL_FALSE;
- }
+ }
}
+/*@}*/
+/**********************************************************************/
+/** \name Matrix generation */
+/*@{*/
-
-
-/*
+/**
* Generate a 4x4 transformation matrix from glRotate parameters, and
- * postmultiply the input matrix by it.
+ * 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,
+void
+_math_matrix_rotate( GLmatrix *mat,
GLfloat angle, GLfloat x, GLfloat y, GLfloat z )
{
- /* This function contributed by Erich Boleyn (erich@uruk.org) */
- GLfloat mag, s, c;
- GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c;
+ GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c;
GLfloat m[16];
-
- s = sin( angle * DEG2RAD );
- c = cos( angle * DEG2RAD );
+ GLboolean optimized;
- mag = GL_SQRT( x*x + y*y + z*z );
+ s = (GLfloat) sin( angle * M_PI / 180.0 );
+ c = (GLfloat) cos( angle * M_PI / 180.0 );
- if (mag <= 1.0e-4) {
- /* generate an identity matrix and return */
- MEMCPY(m, Identity, sizeof(GLfloat)*16);
- return;
- }
-
- x /= mag;
- y /= mag;
- z /= mag;
+ memcpy(m, Identity, sizeof(GLfloat)*16);
+ optimized = GL_FALSE;
#define M(row,col) m[col*4+row]
- /*
- * Arbitrary axis rotation matrix.
- *
- * This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied
- * like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation
- * (which is about the X-axis), and the two composite transforms
- * Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary
- * from the arbitrary axis to the X-axis then back. They are
- * all elementary rotations.
- *
- * Rz' is a rotation about the Z-axis, to bring the axis vector
- * into the x-z plane. Then Ry' is applied, rotating about the
- * Y-axis to bring the axis vector parallel with the X-axis. The
- * rotation about the X-axis is then performed. Ry and Rz are
- * simply the respective inverse transforms to bring the arbitrary
- * axis back to it's original orientation. The first transforms
- * Rz' and Ry' are considered inverses, since the data from the
- * arbitrary axis gives you info on how to get to it, not how
- * to get away from it, and an inverse must be applied.
- *
- * The basic calculation used is to recognize that the arbitrary
- * axis vector (x, y, z), since it is of unit length, actually
- * represents the sines and cosines of the angles to rotate the
- * X-axis to the same orientation, with theta being the angle about
- * Z and phi the angle about Y (in the order described above)
- * as follows:
- *
- * cos ( theta ) = x / sqrt ( 1 - z^2 )
- * sin ( theta ) = y / sqrt ( 1 - z^2 )
- *
- * cos ( phi ) = sqrt ( 1 - z^2 )
- * sin ( phi ) = z
- *
- * Note that cos ( phi ) can further be inserted to the above
- * formulas:
- *
- * cos ( theta ) = x / cos ( phi )
- * sin ( theta ) = y / sin ( phi )
- *
- * ...etc. Because of those relations and the standard trigonometric
- * relations, it is pssible to reduce the transforms down to what
- * is used below. It may be that any primary axis chosen will give the
- * same results (modulo a sign convention) using thie method.
- *
- * Particularly nice is to notice that all divisions that might
- * have caused trouble when parallel to certain planes or
- * axis go away with care paid to reducing the expressions.
- * After checking, it does perform correctly under all cases, since
- * in all the cases of division where the denominator would have
- * been zero, the numerator would have been zero as well, giving
- * the expected result.
- */
+ 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;
+ }
+ }
+ }
- xx = x * x;
- yy = y * y;
- zz = z * z;
- xy = x * y;
- yz = y * z;
- zx = z * x;
- xs = x * s;
- ys = y * s;
- zs = z * s;
- one_c = 1.0F - c;
-
- M(0,0) = (one_c * xx) + c;
- M(0,1) = (one_c * xy) - zs;
- M(0,2) = (one_c * zx) + ys;
- M(0,3) = 0.0F;
-
- M(1,0) = (one_c * xy) + zs;
- M(1,1) = (one_c * yy) + c;
- M(1,2) = (one_c * yz) - xs;
- M(1,3) = 0.0F;
-
- M(2,0) = (one_c * zx) - ys;
- M(2,1) = (one_c * yz) + xs;
- M(2,2) = (one_c * zz) + c;
- M(2,3) = 0.0F;
+ if (!optimized) {
+ const GLfloat mag = sqrtf(x * x + y * y + z * z);
- M(3,0) = 0.0F;
- M(3,1) = 0.0F;
- M(3,2) = 0.0F;
- M(3,3) = 1.0F;
+ 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_frustrum( GLmatrix *mat,
- GLfloat left, GLfloat right,
- GLfloat bottom, GLfloat top,
- GLfloat nearval, GLfloat farval )
+_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 = (2.0*nearval) / (right-left);
- y = (2.0*nearval) / (top-bottom);
+ 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 = -(2.0*farval*nearval) / (farval-nearval); /* error? */
+ 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;
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,
+_math_matrix_ortho( GLmatrix *mat,
GLfloat left, GLfloat right,
- GLfloat bottom, GLfloat top,
+ GLfloat bottom, GLfloat top,
GLfloat nearval, GLfloat farval )
{
- GLfloat x, y, z;
- GLfloat tx, ty, tz;
GLfloat m[16];
- x = 2.0 / (right-left);
- y = 2.0 / (top-bottom);
- z = -2.0 / (farval-nearval);
- tx = -(right+left) / (right-left);
- ty = -(top+bottom) / (top-bottom);
- tz = -(farval+nearval) / (farval-nearval);
-
#define M(row,col) m[col*4+row]
- M(0,0) = x; M(0,1) = 0.0F; M(0,2) = 0.0F; M(0,3) = tx;
- M(1,0) = 0.0F; M(1,1) = y; M(1,2) = 0.0F; M(1,3) = ty;
- M(2,0) = 0.0F; M(2,1) = 0.0F; M(2,2) = z; M(2,3) = tz;
- M(3,0) = 0.0F; M(3,1) = 0.0F; M(3,2) = 0.0F; M(3,3) = 1.0F;
+ 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, const double scale[3],
+ const double translate[3], double depthMax)
+{
+ m->m[MAT_SX] = scale[0];
+ m->m[MAT_TX] = translate[0];
+ m->m[MAT_SY] = scale[1];
+ m->m[MAT_TY] = translate[1];
+ m->m[MAT_SZ] = depthMax*scale[2];
+ m->m[MAT_TZ] = depthMax*translate[2];
+ m->flags = MAT_FLAG_GENERAL_SCALE | MAT_FLAG_TRANSLATION;
+ m->type = MATRIX_3D_NO_ROT;
+}
+
+
+/**
+ * Set a matrix to the identity matrix.
+ *
+ * \param mat matrix.
+ *
+ * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL.
+ * Sets the matrix type to identity, and clear the dirty flags.
+ */
+void
+_math_matrix_set_identity( GLmatrix *mat )
+{
+ memcpy( mat->m, Identity, 16*sizeof(GLfloat) );
+ memcpy( mat->inv, Identity, 16*sizeof(GLfloat) );
+
+ mat->type = MATRIX_IDENTITY;
+ mat->flags &= ~(MAT_DIRTY_FLAGS|
+ MAT_DIRTY_TYPE|
+ MAT_DIRTY_INVERSE);
+}
+
+/*@}*/
+
+
+/**********************************************************************/
+/** \name Matrix analysis */
+/*@{*/
#define ZERO(x) (1<<x)
#define ONE(x) (1<<(x+16))
ZERO(3) | ZERO(7) | ZERO(15) )
#define SQ(x) ((x)*(x))
-
-/* Determine type and flags from scratch. This is expensive enough to
- * only want to do it once.
+
+/**
+ * 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 )
{
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);
mat->flags &= ~MAT_FLAGS_GEOMETRY;
- /* Check for translation - no-one really cares
+ /* Check for translation - no-one really cares
*/
- if ((mask & MASK_NO_TRX) != MASK_NO_TRX)
- mat->flags |= MAT_FLAG_TRANSLATION;
+ if ((mask & MASK_NO_TRX) != MASK_NO_TRX)
+ mat->flags |= MAT_FLAG_TRANSLATION;
/* Do the real work
*/
- if (mask == MASK_IDENTITY) {
+ if (mask == (GLuint) MASK_IDENTITY) {
mat->type = MATRIX_IDENTITY;
}
- else if ((mask & MASK_2D_NO_ROT) == MASK_2D_NO_ROT) {
+ 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;
+ mat->flags |= MAT_FLAG_GENERAL_SCALE;
}
- else if ((mask & MASK_2D) == MASK_2D) {
+ 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);
/* Check for scale */
if (SQ(mm-1) > SQ(1e-6) ||
- SQ(m4m4-1) > SQ(1e-6))
+ SQ(m4m4-1) > SQ(1e-6))
mat->flags |= MAT_FLAG_GENERAL_SCALE;
/* Check for rotation */
mat->flags |= MAT_FLAG_ROTATION;
}
- else if ((mask & MASK_3D_NO_ROT) == MASK_3D_NO_ROT) {
+ 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) &&
+ 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;
mat->flags |= MAT_FLAG_GENERAL_SCALE;
}
}
- else if ((mask & MASK_3D) == MASK_3D) {
+ 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);
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))
+ if (LEN_SQUARED_3FV(cp) < SQ(1e-6))
mat->flags |= MAT_FLAG_ROTATION;
else
mat->flags |= MAT_FLAG_GENERAL_3D;
}
}
-
-/* Analyse a matrix given that its flags are accurate - this is the
- * more common operation, hopefully.
+/**
+ * Analyze a matrix given that its flags are accurate.
+ *
+ * This is the more common operation, hopefully.
*/
static void analyse_from_flags( GLmatrix *mat )
{
}
}
else if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) {
- if ( m[ 8]==0.0F
+ 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;
}
}
-
-void
-_math_matrix_analyse( GLmatrix *mat )
+/**
+ * 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)
+ 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|
- MAT_DIRTY_INVERSE);
+ mat->flags &= ~(MAT_DIRTY_FLAGS | MAT_DIRTY_TYPE);
}
+/*@}*/
-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);
- }
- }
+/**
+ * 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);
}
-void
-_math_matrix_scale( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
+/**
+ * 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 )
{
- GLfloat *m = mat->m;
- m[0] *= x; m[4] *= y; m[8] *= z;
- m[1] *= x; m[5] *= y; m[9] *= z;
- m[2] *= x; m[6] *= y; m[10] *= z;
- m[3] *= x; m[7] *= y; m[11] *= z;
-
- if (fabs(x - y) < 1e-8 && fabs(x - z) < 1e-8)
- mat->flags |= MAT_FLAG_UNIFORM_SCALE;
+ if (m->flags & (MAT_FLAG_GENERAL |
+ MAT_FLAG_ROTATION |
+ MAT_FLAG_GENERAL_3D |
+ MAT_FLAG_PERSPECTIVE))
+ return GL_TRUE;
else
- mat->flags |= MAT_FLAG_GENERAL_SCALE;
-
- mat->flags |= (MAT_DIRTY_TYPE |
- MAT_DIRTY_INVERSE);
+ return GL_FALSE;
}
-void
-_math_matrix_translate( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
+GLboolean
+_math_matrix_is_general_scale( const GLmatrix *m )
{
- 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);
+ return (m->flags & MAT_FLAG_GENERAL_SCALE) ? GL_TRUE : GL_FALSE;
}
-void
-_math_matrix_loadf( GLmatrix *mat, const GLfloat *m )
+GLboolean
+_math_matrix_is_dirty( const GLmatrix *m )
{
- MEMCPY( mat->m, m, 16*sizeof(GLfloat) );
- mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY);
+ return (m->flags & MAT_DIRTY) ? GL_TRUE : GL_FALSE;
}
-void
-_math_matrix_ctr( GLmatrix *m )
-{
- if ( m->m == 0 ) {
- m->m = (GLfloat *) ALIGN_MALLOC( 16 * sizeof(GLfloat), 16 );
- }
- MEMCPY( m->m, Identity, sizeof(Identity) );
- m->inv = 0;
- m->type = MATRIX_IDENTITY;
- m->flags = 0;
-}
-void
-_math_matrix_dtr( GLmatrix *m )
-{
- if ( m->m != 0 ) {
- ALIGN_FREE( m->m );
- m->m = 0;
- }
- if ( m->inv != 0 ) {
- ALIGN_FREE( m->inv );
- m->inv = 0;
- }
-}
+/**********************************************************************/
+/** \name Matrix setup */
+/*@{*/
-
-void
-_math_matrix_alloc_inv( GLmatrix *m )
+/**
+ * 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 )
{
- if ( m->inv == 0 ) {
- m->inv = (GLfloat *) ALIGN_MALLOC( 16 * sizeof(GLfloat), 16 );
- MEMCPY( m->inv, Identity, 16 * sizeof(GLfloat) );
- }
+ memcpy( to->m, from->m, sizeof(Identity) );
+ memcpy(to->inv, from->inv, 16 * sizeof(GLfloat));
+ to->flags = from->flags;
+ to->type = from->type;
}
-
-void
-_math_matrix_mul_matrix( GLmatrix *dest, const GLmatrix *a, const GLmatrix *b )
+/**
+ * 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 )
{
- 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 );
+ memcpy( mat->m, m, 16*sizeof(GLfloat) );
+ mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY);
}
-
-void
-_math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m )
+/**
+ * Matrix constructor.
+ *
+ * \param m matrix.
+ *
+ * Initialize the GLmatrix fields.
+ */
+void
+_math_matrix_ctr( GLmatrix *m )
{
- dest->flags |= (MAT_FLAG_GENERAL |
- MAT_DIRTY_TYPE |
- MAT_DIRTY_INVERSE);
-
- matmul4( dest->m, dest->m, m );
+ m->m = _mesa_align_malloc( 16 * sizeof(GLfloat), 16 );
+ if (m->m)
+ memcpy( m->m, Identity, sizeof(Identity) );
+ m->inv = _mesa_align_malloc( 16 * sizeof(GLfloat), 16 );
+ if (m->inv)
+ memcpy( m->inv, Identity, sizeof(Identity) );
+ m->type = MATRIX_IDENTITY;
+ m->flags = 0;
}
-void
-_math_matrix_set_identity( GLmatrix *mat )
+/**
+ * Matrix destructor.
+ *
+ * \param m matrix.
+ *
+ * Frees the data in a GLmatrix.
+ */
+void
+_math_matrix_dtr( GLmatrix *m )
{
- MEMCPY( mat->m, Identity, 16*sizeof(GLfloat) );
-
- if (mat->inv)
- MEMCPY( mat->inv, Identity, 16*sizeof(GLfloat) );
+ _mesa_align_free( m->m );
+ m->m = NULL;
- mat->type = MATRIX_IDENTITY;
- mat->flags &= ~(MAT_DIRTY_FLAGS|
- MAT_DIRTY_TYPE|
- MAT_DIRTY_INVERSE);
+ _mesa_align_free( m->inv );
+ m->inv = NULL;
}
+/*@}*/
+
+/**********************************************************************/
+/** \name Matrix transpose */
+/*@{*/
-void
+/**
+ * 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[15] = from[15];
}
-
-void
+/**
+ * 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[15] = from[15];
}
-void
+/**
+ * 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] = 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];
+ 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
}
projects / mesa.git / blobdiff