OpenHarmony/third_party_mesa3d
2
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity
Files
dee627a16ee46ffd9d049217cbb394d4ad5c6043
third_party_mesa3d/src/mesa/math/m_matrix.c
Ian Romanick 5318bd351e mesa: Mark Identity as const 
I was going to send this as review for dce1e1a8, but I missed that
window.  This saves 64 bytes of unshared data and prelaces it with 96
bytes shared text.  My guess is that some of the calls to memcpy get
optimized to something else.

   text	   data	    bss	    dec	    hex	filename
7847613	 220208	  27432	8095253	 7b8615	i965_dri.so before
7847709	 220144	  27432	8095285	 7b8635	i965_dri.so after

Signed-off-by: Ian Romanick <ian.d.romanick@intel.com>
Reviewed-by: Ilia Mirkin <imirkin@alum.mit.edu>
Cc: Brian Paul <brianp@vmware.com>
2016-01-11 14:34:38 -08:00

1610 lines
45 KiB
C
Raw Blame History

/*
* Mesa 3-D graphics library
*
* 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
* 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.
*/
/**
* \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 "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",
"MATRIX_3D_NO_ROT",
"MATRIX_PERSPECTIVE",
"MATRIX_2D",
"MATRIX_2D_NO_ROT",
"MATRIX_3D"
};
/**
* Identity matrix.
*/
static const 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 )
{
GLfloat prod[16];
_mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags);
print_matrix_floats(m->m);
_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; }
/**
* 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 (0.0F == 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 != 0.0F) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; }
s = r0[5];
if (s != 0.0F) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; }
s = r0[6];
if (s != 0.0F) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; }
s = r0[7];
if (s != 0.0F) { 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 (0.0F == 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 (0.0F != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; }
s = r1[5]; if (0.0F != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; }
s = r1[6]; if (0.0F != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; }
s = r1[7]; if (0.0F != 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 (0.0F == 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 (0.0F == 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 >= 0.0F) pos += t; else neg += t;
t = MAT(in,1,0) * MAT(in,2,1) * MAT(in,0,2);
if (t >= 0.0F) pos += t; else neg += t;
t = MAT(in,2,0) * MAT(in,0,1) * MAT(in,1,2);
if (t >= 0.0F) pos += t; else neg += t;
t = -MAT(in,2,0) * MAT(in,1,1) * MAT(in,0,2);
if (t >= 0.0F) pos += t; else neg += t;
t = -MAT(in,1,0) * MAT(in,0,1) * MAT(in,2,2);
if (t >= 0.0F) pos += t; else neg += t;
t = -MAT(in,0,0) * MAT(in,2,1) * MAT(in,1,2);
if (t >= 0.0F) pos += t; else neg += t;
det = pos + neg;
if (fabsf(det) < 1e-25F)
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 == 0.0F)
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, sizeof(Identity) );
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, sizeof(Identity) );
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, sizeof(Identity) );
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 = sinf( angle * M_PI / 180.0 );
c = cosf( angle * M_PI / 180.0 );
memcpy(m, Identity, sizeof(Identity));
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-4F) {
/* 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-8F && fabsf(x - z) < 1e-8F)
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 float scale[3],
const float 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, sizeof(Identity) );
memcpy( mat->inv, Identity, sizeof(Identity) );
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] == 0.0F) 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-6F) ||
SQ(m4m4-1) > SQ(1e-6F))
mat->flags |= MAT_FLAG_GENERAL_SCALE;
/* Check for rotation */
if (SQ(mm4) > SQ(1e-6F))
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-6F) &&
SQ(m[0]-m[10]) < SQ(1e-6F)) {
if (SQ(m[0]-1.0F) > SQ(1e-6F)) {
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-6F) && SQ(c1-c3) < SQ(1e-6F)) {
if (SQ(c1-1.0F) > SQ(1e-6F))
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-6F)) {
CROSS3( cp, m, m+4 );
SUB_3V( cp, cp, (m+8) );
if (LEN_SQUARED_3FV(cp) < SQ(1e-6F))
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, 16 * sizeof(GLfloat));
memcpy(to->inv, from->inv, 16 * sizeof(GLfloat));
to->flags = from->flags;
to->type = from->type;
}
/**
* 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 = _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;
}
/**
* Matrix destructor.
*
* \param m matrix.
*
* Frees the data in a GLmatrix.
*/
void
_math_matrix_dtr( GLmatrix *m )
{
_mesa_align_free( m->m );
m->m = NULL;
_mesa_align_free( m->inv );
m->inv = NULL;
}
/*@}*/
/**********************************************************************/
/** \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
}
Reference in New Issue View Git Blame Copy Permalink