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mutter/cogl/cogl-matrix.c
Robert Bragg 680f63a48c Remove all internal includes of cogl.h 
The cogl.h header is meant to be the public header for including the 1.x
api used by Clutter so we should stop using that as a convenient way to
include all likely prototypes and typedefs. Actually we already do a
good job of listing the specific headers we depend on in each of the .c
files we have so mostly this patch just strip out the redundant
includes for cogl.h with a few fixups where that broke the build.

Reviewed-by: Neil Roberts <neil@linux.intel.com>
2012-02-20 23:12:45 +00:00

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/*
* Cogl
*
* An object oriented GL/GLES Abstraction/Utility Layer
*
* Copyright (C) 2009,2010,2011 Intel Corporation.
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library. If not, see <http://www.gnu.org/licenses/>.
*
* Authors:
* Robert Bragg <robert@linux.intel.com>
*/
/*
* 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.
*/
/*
* Note: a lot of this code is based on code that was taken from Mesa.
*
* Changes compared to the original code from Mesa:
*
* - instead of allocating matrix->m and matrix->inv using malloc, our
* public CoglMatrix typedef is large enough to directly contain the
* matrix, its inverse, a type and a set of flags.
* - instead of having a _cogl_matrix_analyse which updates the type,
* flags and inverse, we have _cogl_matrix_update_inverse which
* essentially does the same thing (internally making use of
* _cogl_matrix_update_type_and_flags()) but with additional guards in
* place to bail out when the inverse matrix is still valid.
* - when initializing a matrix with the identity matrix we don't
* immediately initialize the inverse matrix; rather we just set the
* dirty flag for the inverse (since it's likely the user won't request
* the inverse of the identity matrix)
*/
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include <cogl-util.h>
#include <cogl-debug.h>
#include <cogl-quaternion.h>
#include <cogl-quaternion-private.h>
#include <cogl-matrix.h>
#include <cogl-matrix-private.h>
#include <cogl-quaternion-private.h>
#include <glib.h>
#include <math.h>
#include <string.h>
#ifdef _COGL_SUPPORTS_GTYPE_INTEGRATION
#include <cogl-gtype-private.h>
COGL_GTYPE_DEFINE_BOXED ("Matrix", matrix,
cogl_matrix_copy,
cogl_matrix_free);
#endif
/*
* Symbolic names to some of the entries in the matrix
*
* These are handy for the viewport mapping, which is expressed as a matrix.
*/
#define MAT_SX 0
#define MAT_SY 5
#define MAT_SZ 10
#define MAT_TX 12
#define MAT_TY 13
#define MAT_TZ 14
/*
* These identify different kinds of 4x4 transformation matrices and we use
* this information to find fast-paths when available.
*/
enum CoglMatrixType {
COGL_MATRIX_TYPE_GENERAL, /**< general 4x4 matrix */
COGL_MATRIX_TYPE_IDENTITY, /**< identity matrix */
COGL_MATRIX_TYPE_3D_NO_ROT, /**< orthogonal projection and others... */
COGL_MATRIX_TYPE_PERSPECTIVE, /**< perspective projection matrix */
COGL_MATRIX_TYPE_2D, /**< 2-D transformation */
COGL_MATRIX_TYPE_2D_NO_ROT, /**< 2-D scale & translate only */
COGL_MATRIX_TYPE_3D, /**< 3-D transformation */
COGL_MATRIX_N_TYPES
} ;
#define DEG2RAD (G_PI/180.0)
/* Dot product of two 2-element vectors */
#define DOT2(A,B) ( (A)[0]*(B)[0] + (A)[1]*(B)[1] )
/* Dot product of two 3-element vectors */
#define DOT3(A,B) ( (A)[0]*(B)[0] + (A)[1]*(B)[1] + (A)[2]*(B)[2] )
#define CROSS3(N, U, V) \
do { \
(N)[0] = (U)[1]*(V)[2] - (U)[2]*(V)[1]; \
(N)[1] = (U)[2]*(V)[0] - (U)[0]*(V)[2]; \
(N)[2] = (U)[0]*(V)[1] - (U)[1]*(V)[0]; \
} while (0)
#define SUB_3V(DST, SRCA, SRCB) \
do { \
(DST)[0] = (SRCA)[0] - (SRCB)[0]; \
(DST)[1] = (SRCA)[1] - (SRCB)[1]; \
(DST)[2] = (SRCA)[2] - (SRCB)[2]; \
} while (0)
#define LEN_SQUARED_3FV( V ) ((V)[0]*(V)[0]+(V)[1]*(V)[1]+(V)[2]*(V)[2])
/*
* \defgroup MatFlags MAT_FLAG_XXX-flags
*
* Bitmasks to indicate different kinds of 4x4 matrices in CoglMatrix::flags
*/
#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_ALL (MAT_DIRTY_TYPE | \
MAT_DIRTY_FLAGS | \
MAT_DIRTY_INVERSE)
/*
* Test geometry related matrix flags.
*
* @mat a pointer to a CoglMatrix structure.
* @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 CoglMatrixType values.
*/
static const char *types[] = {
"COGL_MATRIX_TYPE_GENERAL",
"COGL_MATRIX_TYPE_IDENTITY",
"COGL_MATRIX_TYPE_3D_NO_ROT",
"COGL_MATRIX_TYPE_PERSPECTIVE",
"COGL_MATRIX_TYPE_2D",
"COGL_MATRIX_TYPE_2D_NO_ROT",
"COGL_MATRIX_TYPE_3D"
};
/*
* Identity matrix.
*/
static float 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
};
#define A(row,col) a[(col<<2)+row]
#define B(row,col) b[(col<<2)+row]
#define R(row,col) result[(col<<2)+row]
/*
* Perform a full 4x4 matrix multiplication.
*
* <note>It's assumed that @result != @b. @product == @a is allowed.</note>
*
* <note>KW: 4*16 = 64 multiplications</note>
*/
static void
matrix_multiply4x4 (float *result, const float *a, const float *b)
{
int i;
for (i = 0; i < 4; i++)
{
const float ai0 = A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3);
R(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0);
R(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1);
R(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2);
R(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.
*
* @a matrix.
* @b matrix.
* @product will receive the product of \p a and \p b.
*/
static void
matrix_multiply3x4 (float *result, const float *a, const float *b)
{
int i;
for (i = 0; i < 3; i++)
{
const float ai0 = A(i,0), ai1 = A(i,1), ai2 = A(i,2), ai3 = A(i,3);
R(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0);
R(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1);
R(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2);
R(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3;
}
R(3,0) = 0;
R(3,1) = 0;
R(3,2) = 0;
R(3,3) = 1;
}
#undef A
#undef B
#undef R
/*
* Multiply a matrix by an array of floats with known properties.
*
* @mat pointer to a CoglMatrix structure containing the left multiplication
* matrix, and that will receive the product result.
* @m right multiplication matrix array.
* @flags flags of the matrix \p m.
*
* Joins both flags and marks the type and inverse as dirty. Calls
* matrix_multiply3x4() if both matrices are 3D, or matrix_multiply4x4()
* otherwise.
*/
static void
matrix_multiply_array_with_flags (CoglMatrix *result,
const float *array,
unsigned int flags)
{
result->flags |= (flags | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE);
if (TEST_MAT_FLAGS (result, MAT_FLAGS_3D))
matrix_multiply3x4 ((float *)result, (float *)result, array);
else
matrix_multiply4x4 ((float *)result, (float *)result, array);
}
/* Joins both flags and marks the type and inverse as dirty. Calls
* matrix_multiply3x4() if both matrices are 3D, or matrix_multiply4x4()
* otherwise.
*/
static void
_cogl_matrix_multiply (CoglMatrix *result,
const CoglMatrix *a,
const CoglMatrix *b)
{
result->flags = (a->flags |
b->flags |
MAT_DIRTY_TYPE |
MAT_DIRTY_INVERSE);
if (TEST_MAT_FLAGS(result, MAT_FLAGS_3D))
matrix_multiply3x4 ((float *)result, (float *)a, (float *)b);
else
matrix_multiply4x4 ((float *)result, (float *)a, (float *)b);
}
void
cogl_matrix_multiply (CoglMatrix *result,
const CoglMatrix *a,
const CoglMatrix *b)
{
_cogl_matrix_multiply (result, a, b);
_COGL_MATRIX_DEBUG_PRINT (result);
}
#if 0
/* Marks the matrix flags with general flag, and type and inverse dirty flags.
* Calls matrix_multiply4x4() for the multiplication.
*/
static void
_cogl_matrix_multiply_array (CoglMatrix *result, const float *array)
{
result->flags |= (MAT_FLAG_GENERAL |
MAT_DIRTY_TYPE |
MAT_DIRTY_INVERSE |
MAT_DIRTY_FLAGS);
matrix_multiply4x4 ((float *)result, (float *)result, (float *)array);
}
#endif
/*
* Print a matrix array.
*
* Called by _cogl_matrix_print() to print a matrix or its inverse.
*/
static void
print_matrix_floats (const float m[16])
{
int i;
for (i = 0;i < 4; i++)
g_print ("\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] );
}
/*
* Dumps the contents of a CoglMatrix structure.
*/
void
_cogl_matrix_print (const CoglMatrix *matrix)
{
if (!(matrix->flags & MAT_DIRTY_TYPE))
{
_COGL_RETURN_IF_FAIL (matrix->type < COGL_MATRIX_N_TYPES);
g_print ("Matrix type: %s, flags: %x\n",
types[matrix->type], (int)matrix->flags);
}
else
g_print ("Matrix type: DIRTY, flags: %x\n", (int)matrix->flags);
print_matrix_floats ((float *)matrix);
g_print ("Inverse: \n");
if (!(matrix->flags & MAT_DIRTY_INVERSE))
{
float prod[16];
print_matrix_floats (matrix->inv);
matrix_multiply4x4 (prod, (float *)matrix, matrix->inv);
g_print ("Mat * Inverse:\n");
print_matrix_floats (prod);
}
else
g_print (" - not available\n");
}
/*
* References an element of 4x4 matrix.
*
* @m matrix array.
* @c column of the desired element.
* @r row of the desired element.
*
* Returns: 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)]
/*
* Swaps the values of two floating pointer variables.
*
* Used by invert_matrix_general() to swap the row pointers.
*/
#define SWAP_ROWS(a, b) { float *_tmp = a; (a)=(b); (b)=_tmp; }
/*
* Compute inverse of 4x4 transformation matrix.
*
* @mat pointer to a CoglMatrix structure. The matrix inverse will be
* stored in the CoglMatrix::inv attribute.
*
* Returns: %TRUE for success, %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 gboolean
invert_matrix_general (CoglMatrix *matrix)
{
const float *m = (float *)matrix;
float *out = matrix->inv;
float wtmp[4][8];
float m0, m1, m2, m3, s;
float *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 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 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 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 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 TRUE;
}
#undef SWAP_ROWS
/*
* Compute inverse of a general 3d transformation matrix.
*
* @mat pointer to a CoglMatrix structure. The matrix inverse will be
* stored in the CoglMatrix::inv attribute.
*
* Returns: %TRUE for success, %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 gboolean
invert_matrix_3d_general (CoglMatrix *matrix)
{
const float *in = (float *)matrix;
float *out = matrix->inv;
float pos, neg, t;
float 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 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 TRUE;
}
/*
* Compute inverse of a 3d transformation matrix.
*
* @mat pointer to a CoglMatrix structure. The matrix inverse will be
* stored in the CoglMatrix::inv attribute.
*
* Returns: %TRUE for success, %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 gboolean
invert_matrix_3d (CoglMatrix *matrix)
{
const float *in = (float *)matrix;
float *out = matrix->inv;
if (!TEST_MAT_FLAGS(matrix, MAT_FLAGS_ANGLE_PRESERVING))
return invert_matrix_3d_general (matrix);
if (matrix->flags & MAT_FLAG_UNIFORM_SCALE)
{
float 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 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 (matrix->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, 16 * sizeof (float));
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 TRUE;
}
if (matrix->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 TRUE;
}
/*
* Compute inverse of an identity transformation matrix.
*
* @mat pointer to a CoglMatrix structure. The matrix inverse will be
* stored in the CoglMatrix::inv attribute.
*
* Returns: always %TRUE.
*
* Simply copies identity into CoglMatrix::inv.
*/
static gboolean
invert_matrix_identity (CoglMatrix *matrix)
{
memcpy (matrix->inv, identity, 16 * sizeof (float));
return TRUE;
}
/*
* Compute inverse of a no-rotation 3d transformation matrix.
*
* @mat pointer to a CoglMatrix structure. The matrix inverse will be
* stored in the CoglMatrix::inv attribute.
*
* Returns: %TRUE for success, %FALSE for failure (\p singular matrix).
*
* Calculates the
*/
static gboolean
invert_matrix_3d_no_rotation (CoglMatrix *matrix)
{
const float *in = (float *)matrix;
float *out = matrix->inv;
if (MAT (in,0,0) == 0 || MAT (in,1,1) == 0 || MAT (in,2,2) == 0)
return FALSE;
memcpy (out, identity, 16 * sizeof (float));
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 (matrix->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 TRUE;
}
/*
* Compute inverse of a no-rotation 2d transformation matrix.
*
* @mat pointer to a CoglMatrix structure. The matrix inverse will be
* stored in the CoglMatrix::inv attribute.
*
* Returns: %TRUE for success, %FALSE for failure (\p singular matrix).
*
* Calculates the inverse matrix by applying the inverse scaling and
* translation to the identity matrix.
*/
static gboolean
invert_matrix_2d_no_rotation (CoglMatrix *matrix)
{
const float *in = (float *)matrix;
float *out = matrix->inv;
if (MAT (in, 0, 0) == 0 || MAT (in, 1, 1) == 0)
return FALSE;
memcpy (out, identity, 16 * sizeof (float));
MAT (out, 0, 0) = 1.0f / MAT (in, 0, 0);
MAT (out, 1, 1) = 1.0f / MAT (in, 1, 1);
if (matrix->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 TRUE;
}
#if 0
/* broken */
static gboolean
invert_matrix_perspective (CoglMatrix *matrix)
{
const float *in = matrix;
float *out = matrix->inv;
if (MAT (in,2,3) == 0)
return FALSE;
memcpy( out, identity, 16 * sizeof(float) );
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 TRUE;
}
#endif
/*
* Matrix inversion function pointer type.
*/
typedef gboolean (*inv_mat_func)(CoglMatrix *matrix);
/*
* 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_rotation,
#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_rotation,
invert_matrix_3d
};
#define ZERO(x) (1<<x)
#define ONE(x) (1<<(x+16))
#define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14))
#define MASK_NO_2D_SCALE ( ONE(0) | ONE(5))
#define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\
ZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\
ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
#define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \
ZERO(1) | ZERO(9) | \
ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
#define MASK_2D ( ZERO(8) | \
ZERO(9) | \
ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
#define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \
ZERO(1) | ZERO(9) | \
ZERO(2) | ZERO(6) | \
ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
#define MASK_3D ( \
\
\
ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
#define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\
ZERO(1) | ZERO(13) |\
ZERO(2) | ZERO(6) | \
ZERO(3) | ZERO(7) | ZERO(15) )
#define SQ(x) ((x)*(x))
/*
* Determine type and flags from scratch.
*
* This is expensive enough to only want to do it once.
*/
static void
analyse_from_scratch (CoglMatrix *matrix)
{
const float *m = (float *)matrix;
unsigned int mask = 0;
unsigned int 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);
matrix->flags &= ~MAT_FLAGS_GEOMETRY;
/* Check for translation - no-one really cares
*/
if ((mask & MASK_NO_TRX) != MASK_NO_TRX)
matrix->flags |= MAT_FLAG_TRANSLATION;
/* Do the real work
*/
if (mask == (unsigned int) MASK_IDENTITY)
matrix->type = COGL_MATRIX_TYPE_IDENTITY;
else if ((mask & MASK_2D_NO_ROT) == (unsigned int) MASK_2D_NO_ROT)
{
matrix->type = COGL_MATRIX_TYPE_2D_NO_ROT;
if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE)
matrix->flags |= MAT_FLAG_GENERAL_SCALE;
}
else if ((mask & MASK_2D) == (unsigned int) MASK_2D)
{
float mm = DOT2 (m, m);
float m4m4 = DOT2 (m+4,m+4);
float mm4 = DOT2 (m,m+4);
matrix->type = COGL_MATRIX_TYPE_2D;
/* Check for scale */
if (SQ (mm-1) > SQ (1e-6) ||
SQ (m4m4-1) > SQ (1e-6))
matrix->flags |= MAT_FLAG_GENERAL_SCALE;
/* Check for rotation */
if (SQ (mm4) > SQ (1e-6))
matrix->flags |= MAT_FLAG_GENERAL_3D;
else
matrix->flags |= MAT_FLAG_ROTATION;
}
else if ((mask & MASK_3D_NO_ROT) == (unsigned int) MASK_3D_NO_ROT)
{
matrix->type = COGL_MATRIX_TYPE_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))
matrix->flags |= MAT_FLAG_UNIFORM_SCALE;
}
else
matrix->flags |= MAT_FLAG_GENERAL_SCALE;
}
else if ((mask & MASK_3D) == (unsigned int) MASK_3D)
{
float c1 = DOT3 (m,m);
float c2 = DOT3 (m+4,m+4);
float c3 = DOT3 (m+8,m+8);
float d1 = DOT3 (m, m+4);
float cp[3];
matrix->type = COGL_MATRIX_TYPE_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))
matrix->flags |= MAT_FLAG_UNIFORM_SCALE;
/* else no scale at all */
}
else
matrix->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))
matrix->flags |= MAT_FLAG_ROTATION;
else
matrix->flags |= MAT_FLAG_GENERAL_3D;
}
else
matrix->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */
}
else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0f)
{
matrix->type = COGL_MATRIX_TYPE_PERSPECTIVE;
matrix->flags |= MAT_FLAG_GENERAL;
}
else
{
matrix->type = COGL_MATRIX_TYPE_GENERAL;
matrix->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 (CoglMatrix *matrix)
{
const float *m = (float *)matrix;
if (TEST_MAT_FLAGS(matrix, 0))
matrix->type = COGL_MATRIX_TYPE_IDENTITY;
else if (TEST_MAT_FLAGS(matrix, (MAT_FLAG_TRANSLATION |
MAT_FLAG_UNIFORM_SCALE |
MAT_FLAG_GENERAL_SCALE)))
{
if ( m[10] == 1.0f && m[14] == 0.0f )
matrix->type = COGL_MATRIX_TYPE_2D_NO_ROT;
else
matrix->type = COGL_MATRIX_TYPE_3D_NO_ROT;
}
else if (TEST_MAT_FLAGS (matrix, 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)
{
matrix->type = COGL_MATRIX_TYPE_2D;
}
else
matrix->type = COGL_MATRIX_TYPE_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)
{
matrix->type = COGL_MATRIX_TYPE_PERSPECTIVE;
}
else
matrix->type = COGL_MATRIX_TYPE_GENERAL;
}
/*
* Analyze and update the type and flags of a 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.
*/
static void
_cogl_matrix_update_type_and_flags (CoglMatrix *matrix)
{
if (matrix->flags & MAT_DIRTY_TYPE)
{
if (matrix->flags & MAT_DIRTY_FLAGS)
analyse_from_scratch (matrix);
else
analyse_from_flags (matrix);
}
matrix->flags &= ~(MAT_DIRTY_FLAGS | MAT_DIRTY_TYPE);
}
/*
* Compute inverse of a transformation matrix.
*
* @mat pointer to a CoglMatrix structure. The matrix inverse will be
* stored in the CoglMatrix::inv attribute.
*
* Returns: %TRUE for success, %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 CoglMatrix::inv.
*/
static gboolean
_cogl_matrix_update_inverse (CoglMatrix *matrix)
{
if (matrix->flags & MAT_DIRTY_FLAGS ||
matrix->flags & MAT_DIRTY_INVERSE)
{
_cogl_matrix_update_type_and_flags (matrix);
if (inv_mat_tab[matrix->type](matrix))
matrix->flags &= ~MAT_FLAG_SINGULAR;
else
{
matrix->flags |= MAT_FLAG_SINGULAR;
memcpy (matrix->inv, identity, 16 * sizeof (float));
}
matrix->flags &= ~MAT_DIRTY_INVERSE;
}
if (matrix->flags & MAT_FLAG_SINGULAR)
return FALSE;
else
return TRUE;
}
gboolean
cogl_matrix_get_inverse (const CoglMatrix *matrix, CoglMatrix *inverse)
{
if (_cogl_matrix_update_inverse ((CoglMatrix *)matrix))
{
cogl_matrix_init_from_array (inverse, matrix->inv);
return TRUE;
}
else
{
cogl_matrix_init_identity (inverse);
return FALSE;
}
}
/*
* 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).
*/
static void
_cogl_matrix_rotate (CoglMatrix *matrix,
float angle,
float x,
float y,
float z)
{
float xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c;
float m[16];
gboolean optimized;
s = sinf (angle * DEG2RAD);
c = cosf (angle * DEG2RAD);
memcpy (m, identity, 16 * sizeof (float));
optimized = FALSE;
#define M(row,col) m[col*4+row]
if (x == 0.0f)
{
if (y == 0.0f)
{
if (z != 0.0f)
{
optimized = 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 = 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 = 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 float 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 it's original orientation. The first transforms
* Rz' and Ry' are considered inverses, since the data from the
* arbitrary axis gives you info on how to get to it, not how
* to get away from it, and an inverse must be applied.
*
* The basic calculation used is to recognize that the arbitrary
* axis vector (x, y, z), since it is of unit length, actually
* represents the sines and cosines of the angles to rotate the
* X-axis to the same orientation, with theta being the angle about
* Z and phi the angle about Y (in the order described above)
* as follows:
*
* cos ( theta ) = x / sqrt ( 1 - z^2 )
* sin ( theta ) = y / sqrt ( 1 - z^2 )
*
* cos ( phi ) = sqrt ( 1 - z^2 )
* sin ( phi ) = z
*
* Note that cos ( phi ) can further be inserted to the above
* formulas:
*
* cos ( theta ) = x / cos ( phi )
* sin ( theta ) = y / sin ( phi )
*
* ...etc. Because of those relations and the standard trigonometric
* relations, it is pssible to reduce the transforms down to what
* is used below. It may be that any primary axis chosen will give the
* same results (modulo a sign convention) using thie method.
*
* Particularly nice is to notice that all divisions that might
* have caused trouble when parallel to certain planes or
* axis go away with care paid to reducing the expressions.
* After checking, it does perform correctly under all cases, since
* in all the cases of division where the denominator would have
* been zero, the numerator would have been zero as well, giving
* the expected result.
*/
xx = x * x;
yy = y * y;
zz = z * z;
xy = x * y;
yz = y * z;
zx = z * x;
xs = x * s;
ys = y * s;
zs = z * s;
one_c = 1.0f - c;
/* 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_multiply_array_with_flags (matrix, m, MAT_FLAG_ROTATION);
}
void
cogl_matrix_rotate (CoglMatrix *matrix,
float angle,
float x,
float y,
float z)
{
_cogl_matrix_rotate (matrix, angle, x, y, z);
_COGL_MATRIX_DEBUG_PRINT (matrix);
}
/*
* Apply a perspective projection matrix.
*
* Creates the projection matrix and multiplies it with matrix, marking the
* MAT_FLAG_PERSPECTIVE flag.
*/
static void
_cogl_matrix_frustum (CoglMatrix *matrix,
float left,
float right,
float bottom,
float top,
float nearval,
float farval)
{
float x, y, a, b, c, d;
float 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_multiply_array_with_flags (matrix, m, MAT_FLAG_PERSPECTIVE);
}
void
cogl_matrix_frustum (CoglMatrix *matrix,
float left,
float right,
float bottom,
float top,
float z_near,
float z_far)
{
_cogl_matrix_frustum (matrix, left, right, bottom, top, z_near, z_far);
_COGL_MATRIX_DEBUG_PRINT (matrix);
}
void
cogl_matrix_perspective (CoglMatrix *matrix,
float fov_y,
float aspect,
float z_near,
float z_far)
{
float ymax = z_near * tan (fov_y * G_PI / 360.0);
cogl_matrix_frustum (matrix,
-ymax * aspect, /* left */
ymax * aspect, /* right */
-ymax, /* bottom */
ymax, /* top */
z_near,
z_far);
_COGL_MATRIX_DEBUG_PRINT (matrix);
}
/*
* Apply an orthographic projection matrix.
*
* Creates the projection matrix and multiplies it with matrix, marking the
* MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags.
*/
static void
_cogl_matrix_orthographic (CoglMatrix *matrix,
float x_1,
float y_1,
float x_2,
float y_2,
float nearval,
float farval)
{
float m[16];
#define M(row, col) m[col * 4 + row]
M (0,0) = 2.0f / (x_2 - x_1);
M (0,1) = 0.0f;
M (0,2) = 0.0f;
M (0,3) = -(x_2 + x_1) / (x_2 - x_1);
M (1,0) = 0.0f;
M (1,1) = 2.0f / (y_1 - y_2);
M (1,2) = 0.0f;
M (1,3) = -(y_1 + y_2) / (y_1 - y_2);
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_multiply_array_with_flags (matrix, m,
(MAT_FLAG_GENERAL_SCALE |
MAT_FLAG_TRANSLATION));
}
void
cogl_matrix_ortho (CoglMatrix *matrix,
float left,
float right,
float bottom,
float top,
float near,
float far)
{
_cogl_matrix_orthographic (matrix, left, top, right, bottom, near, far);
_COGL_MATRIX_DEBUG_PRINT (matrix);
}
void
cogl_matrix_orthographic (CoglMatrix *matrix,
float x_1,
float y_1,
float x_2,
float y_2,
float near,
float far)
{
_cogl_matrix_orthographic (matrix, x_1, y_1, x_2, y_2, near, far);
_COGL_MATRIX_DEBUG_PRINT (matrix);
}
/*
* Multiply a matrix with a general scaling matrix.
*
* Multiplies in-place the elements of matrix 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.
*/
static void
_cogl_matrix_scale (CoglMatrix *matrix, float x, float y, float z)
{
float *m = (float *)matrix;
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)
matrix->flags |= MAT_FLAG_UNIFORM_SCALE;
else
matrix->flags |= MAT_FLAG_GENERAL_SCALE;
matrix->flags |= (MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE);
}
void
cogl_matrix_scale (CoglMatrix *matrix,
float sx,
float sy,
float sz)
{
_cogl_matrix_scale (matrix, sx, sy, sz);
_COGL_MATRIX_DEBUG_PRINT (matrix);
}
/*
* Multiply a matrix with a translation matrix.
*
* Adds the translation coordinates to the elements of matrix in-place. Marks
* the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE
* dirty flags.
*/
static void
_cogl_matrix_translate (CoglMatrix *matrix, float x, float y, float z)
{
float *m = (float *)matrix;
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];
matrix->flags |= (MAT_FLAG_TRANSLATION |
MAT_DIRTY_TYPE |
MAT_DIRTY_INVERSE);
}
void
cogl_matrix_translate (CoglMatrix *matrix,
float x,
float y,
float z)
{
_cogl_matrix_translate (matrix, x, y, z);
_COGL_MATRIX_DEBUG_PRINT (matrix);
}
#if 0
/*
* Set matrix to do viewport and depthrange mapping.
* Transforms Normalized Device Coords to window/Z values.
*/
static void
_cogl_matrix_viewport (CoglMatrix *matrix,
float x, float y,
float width, float height,
float zNear, float zFar, float depthMax)
{
float *m = (float *)matrix;
m[MAT_SX] = width / 2.0f;
m[MAT_TX] = m[MAT_SX] + x;
m[MAT_SY] = height / 2.0f;
m[MAT_TY] = m[MAT_SY] + y;
m[MAT_SZ] = depthMax * ((zFar - zNear) / 2.0f);
m[MAT_TZ] = depthMax * ((zFar - zNear) / 2.0f + zNear);
matrix->flags = MAT_FLAG_GENERAL_SCALE | MAT_FLAG_TRANSLATION;
matrix->type = COGL_MATRIX_TYPE_3D_NO_ROT;
}
#endif
/*
* Set a matrix to the identity matrix.
*
* @mat matrix.
*
* Copies ::identity into \p CoglMatrix::m, and into CoglMatrix::inv if
* not NULL. Sets the matrix type to identity, resets the flags. It
* doesn't initialize the inverse matrix, it just marks it dirty.
*/
static void
_cogl_matrix_init_identity (CoglMatrix *matrix)
{
memcpy (matrix, identity, 16 * sizeof (float));
matrix->type = COGL_MATRIX_TYPE_IDENTITY;
matrix->flags = MAT_DIRTY_INVERSE;
}
void
cogl_matrix_init_identity (CoglMatrix *matrix)
{
_cogl_matrix_init_identity (matrix);
_COGL_MATRIX_DEBUG_PRINT (matrix);
}
#if 0
/*
* Test if the given matrix preserves vector lengths.
*/
static gboolean
_cogl_matrix_is_length_preserving (const CoglMatrix *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)
*/
static gboolean
_cogl_matrix_has_rotation (const CoglMatrix *matrix)
{
if (matrix->flags & (MAT_FLAG_GENERAL |
MAT_FLAG_ROTATION |
MAT_FLAG_GENERAL_3D |
MAT_FLAG_PERSPECTIVE))
return TRUE;
else
return FALSE;
}
static gboolean
_cogl_matrix_is_general_scale (const CoglMatrix *matrix)
{
return (matrix->flags & MAT_FLAG_GENERAL_SCALE) ? TRUE : FALSE;
}
static gboolean
_cogl_matrix_is_dirty (const CoglMatrix *matrix)
{
return (matrix->flags & MAT_DIRTY_ALL) ? TRUE : FALSE;
}
#endif
/*
* Loads a matrix array into CoglMatrix.
*
* @m matrix array.
* @mat matrix.
*
* Copies \p m into CoglMatrix::m and marks the MAT_FLAG_GENERAL and
* MAT_DIRTY_ALL
* flags.
*/
static void
_cogl_matrix_init_from_array (CoglMatrix *matrix, const float *array)
{
memcpy (matrix, array, 16 * sizeof (float));
matrix->flags = (MAT_FLAG_GENERAL | MAT_DIRTY_ALL);
}
void
cogl_matrix_init_from_array (CoglMatrix *matrix, const float *array)
{
_cogl_matrix_init_from_array (matrix, array);
_COGL_MATRIX_DEBUG_PRINT (matrix);
}
static void
_cogl_matrix_init_from_quaternion (CoglMatrix *matrix,
CoglQuaternion *quaternion)
{
float qnorm = _COGL_QUATERNION_NORM (quaternion);
float s = (qnorm > 0.0f) ? (2.0f / qnorm) : 0.0f;
float xs = quaternion->x * s;
float ys = quaternion->y * s;
float zs = quaternion->z * s;
float wx = quaternion->w * xs;
float wy = quaternion->w * ys;
float wz = quaternion->w * zs;
float xx = quaternion->x * xs;
float xy = quaternion->x * ys;
float xz = quaternion->x * zs;
float yy = quaternion->y * ys;
float yz = quaternion->y * zs;
float zz = quaternion->z * zs;
matrix->xx = 1.0f - (yy + zz);
matrix->yx = xy + wz;
matrix->zx = xz - wy;
matrix->xy = xy - wz;
matrix->yy = 1.0f - (xx + zz);
matrix->zy = yz + wx;
matrix->xz = xz + wy;
matrix->yz = yz - wx;
matrix->zz = 1.0f - (xx + yy);
matrix->xw = matrix->yw = matrix->zw = 0.0f;
matrix->wx = matrix->wy = matrix->wz = 0.0f;
matrix->ww = 1.0f;
matrix->flags = (MAT_FLAG_GENERAL | MAT_DIRTY_ALL);
}
void
cogl_matrix_init_from_quaternion (CoglMatrix *matrix,
CoglQuaternion *quaternion)
{
_cogl_matrix_init_from_quaternion (matrix, quaternion);
}
/*
* Transpose a float matrix.
*/
static void
_cogl_matrix_util_transposef (float to[16], const float from[16])
{
to[0] = from[0];
to[1] = from[4];
to[2] = from[8];
to[3] = from[12];
to[4] = from[1];
to[5] = from[5];
to[6] = from[9];
to[7] = from[13];
to[8] = from[2];
to[9] = from[6];
to[10] = from[10];
to[11] = from[14];
to[12] = from[3];
to[13] = from[7];
to[14] = from[11];
to[15] = from[15];
}
void
cogl_matrix_view_2d_in_frustum (CoglMatrix *matrix,
float left,
float right,
float bottom,
float top,
float z_near,
float z_2d,
float width_2d,
float height_2d)
{
float left_2d_plane = left / z_near * z_2d;
float right_2d_plane = right / z_near * z_2d;
float bottom_2d_plane = bottom / z_near * z_2d;
float top_2d_plane = top / z_near * z_2d;
float width_2d_start = right_2d_plane - left_2d_plane;
float height_2d_start = top_2d_plane - bottom_2d_plane;
/* Factors to scale from framebuffer geometry to frustum
* cross-section geometry. */
float width_scale = width_2d_start / width_2d;
float height_scale = height_2d_start / height_2d;
cogl_matrix_translate (matrix,
left_2d_plane, top_2d_plane, -z_2d);
cogl_matrix_scale (matrix, width_scale, -height_scale, width_scale);
}
/* Assuming a symmetric perspective matrix is being used for your
* projective transform this convenience function lets you compose a
* view transform such that geometry on the z=0 plane will map to
* screen coordinates with a top left origin of (0,0) and with the
* given width and height.
*/
void
cogl_matrix_view_2d_in_perspective (CoglMatrix *matrix,
float fov_y,
float aspect,
float z_near,
float z_2d,
float width_2d,
float height_2d)
{
float top = z_near * tan (fov_y * G_PI / 360.0);
cogl_matrix_view_2d_in_frustum (matrix,
-top * aspect,
top * aspect,
-top,
top,
z_near,
z_2d,
width_2d,
height_2d);
}
gboolean
cogl_matrix_equal (gconstpointer v1, gconstpointer v2)
{
const CoglMatrix *a = v1;
const CoglMatrix *b = v2;
_COGL_RETURN_VAL_IF_FAIL (v1 != NULL, FALSE);
_COGL_RETURN_VAL_IF_FAIL (v2 != NULL, FALSE);
/* We want to avoid having a fuzzy _equal() function (e.g. that uses
* an arbitrary epsilon value) since this function noteably conforms
* to the prototype suitable for use with g_hash_table_new() and a
* fuzzy hash function isn't really appropriate for comparing hash
* table keys since it's possible that you could end up fetching
* different values if you end up with multiple similar keys in use
* at the same time. If you consider that fuzzyness allows cases
* such as A == B == C but A != C then you could also end up loosing
* values in a hash table.
*
* We do at least use the == operator to compare values though so
* that -0 is considered equal to 0.
*/
/* XXX: We don't compare the flags, inverse matrix or padding */
if (a->xx == b->xx &&
a->xy == b->xy &&
a->xz == b->xz &&
a->xw == b->xw &&
a->yx == b->yx &&
a->yy == b->yy &&
a->yz == b->yz &&
a->yw == b->yw &&
a->zx == b->zx &&
a->zy == b->zy &&
a->zz == b->zz &&
a->zw == b->zw &&
a->wx == b->wx &&
a->wy == b->wy &&
a->wz == b->wz &&
a->ww == b->ww)
return TRUE;
else
return FALSE;
}
CoglMatrix *
cogl_matrix_copy (const CoglMatrix *matrix)
{
if (G_LIKELY (matrix))
return g_slice_dup (CoglMatrix, matrix);
return NULL;
}
void
cogl_matrix_free (CoglMatrix *matrix)
{
g_slice_free (CoglMatrix, matrix);
}
const float *
cogl_matrix_get_array (const CoglMatrix *matrix)
{
return (float *)matrix;
}
void
cogl_matrix_transform_point (const CoglMatrix *matrix,
float *x,
float *y,
float *z,
float *w)
{
float _x = *x, _y = *y, _z = *z, _w = *w;
*x = matrix->xx * _x + matrix->xy * _y + matrix->xz * _z + matrix->xw * _w;
*y = matrix->yx * _x + matrix->yy * _y + matrix->yz * _z + matrix->yw * _w;
*z = matrix->zx * _x + matrix->zy * _y + matrix->zz * _z + matrix->zw * _w;
*w = matrix->wx * _x + matrix->wy * _y + matrix->wz * _z + matrix->ww * _w;
}
typedef struct _Point2f
{
float x;
float y;
} Point2f;
typedef struct _Point3f
{
float x;
float y;
float z;
} Point3f;
typedef struct _Point4f
{
float x;
float y;
float z;
float w;
} Point4f;
static void
_cogl_matrix_transform_points_f2 (const CoglMatrix *matrix,
size_t stride_in,
const void *points_in,
size_t stride_out,
void *points_out,
int n_points)
{
int i;
for (i = 0; i < n_points; i++)
{
Point2f p = *(Point2f *)((guint8 *)points_in + i * stride_in);
Point3f *o = (Point3f *)((guint8 *)points_out + i * stride_out);
o->x = matrix->xx * p.x + matrix->xy * p.y + matrix->xw;
o->y = matrix->yx * p.x + matrix->yy * p.y + matrix->yw;
o->z = matrix->zx * p.x + matrix->zy * p.y + matrix->zw;
}
}
static void
_cogl_matrix_project_points_f2 (const CoglMatrix *matrix,
size_t stride_in,
const void *points_in,
size_t stride_out,
void *points_out,
int n_points)
{
int i;
for (i = 0; i < n_points; i++)
{
Point2f p = *(Point2f *)((guint8 *)points_in + i * stride_in);
Point4f *o = (Point4f *)((guint8 *)points_out + i * stride_out);
o->x = matrix->xx * p.x + matrix->xy * p.y + matrix->xw;
o->y = matrix->yx * p.x + matrix->yy * p.y + matrix->yw;
o->z = matrix->zx * p.x + matrix->zy * p.y + matrix->zw;
o->w = matrix->wx * p.x + matrix->wy * p.y + matrix->ww;
}
}
static void
_cogl_matrix_transform_points_f3 (const CoglMatrix *matrix,
size_t stride_in,
const void *points_in,
size_t stride_out,
void *points_out,
int n_points)
{
int i;
for (i = 0; i < n_points; i++)
{
Point3f p = *(Point3f *)((guint8 *)points_in + i * stride_in);
Point3f *o = (Point3f *)((guint8 *)points_out + i * stride_out);
o->x = matrix->xx * p.x + matrix->xy * p.y +
matrix->xz * p.z + matrix->xw;
o->y = matrix->yx * p.x + matrix->yy * p.y +
matrix->yz * p.z + matrix->yw;
o->z = matrix->zx * p.x + matrix->zy * p.y +
matrix->zz * p.z + matrix->zw;
}
}
static void
_cogl_matrix_project_points_f3 (const CoglMatrix *matrix,
size_t stride_in,
const void *points_in,
size_t stride_out,
void *points_out,
int n_points)
{
int i;
for (i = 0; i < n_points; i++)
{
Point3f p = *(Point3f *)((guint8 *)points_in + i * stride_in);
Point4f *o = (Point4f *)((guint8 *)points_out + i * stride_out);
o->x = matrix->xx * p.x + matrix->xy * p.y +
matrix->xz * p.z + matrix->xw;
o->y = matrix->yx * p.x + matrix->yy * p.y +
matrix->yz * p.z + matrix->yw;
o->z = matrix->zx * p.x + matrix->zy * p.y +
matrix->zz * p.z + matrix->zw;
o->w = matrix->wx * p.x + matrix->wy * p.y +
matrix->wz * p.z + matrix->ww;
}
}
static void
_cogl_matrix_project_points_f4 (const CoglMatrix *matrix,
size_t stride_in,
const void *points_in,
size_t stride_out,
void *points_out,
int n_points)
{
int i;
for (i = 0; i < n_points; i++)
{
Point4f p = *(Point4f *)((guint8 *)points_in + i * stride_in);
Point4f *o = (Point4f *)((guint8 *)points_out + i * stride_out);
o->x = matrix->xx * p.x + matrix->xy * p.y +
matrix->xz * p.z + matrix->xw * p.w;
o->y = matrix->yx * p.x + matrix->yy * p.y +
matrix->yz * p.z + matrix->yw * p.w;
o->z = matrix->zx * p.x + matrix->zy * p.y +
matrix->zz * p.z + matrix->zw * p.w;
o->w = matrix->wx * p.x + matrix->wy * p.y +
matrix->wz * p.z + matrix->ww * p.w;
}
}
void
cogl_matrix_transform_points (const CoglMatrix *matrix,
int n_components,
size_t stride_in,
const void *points_in,
size_t stride_out,
void *points_out,
int n_points)
{
/* The results of transforming always have three components... */
_COGL_RETURN_IF_FAIL (stride_out >= sizeof (Point3f));
if (n_components == 2)
_cogl_matrix_transform_points_f2 (matrix,
stride_in, points_in,
stride_out, points_out,
n_points);
else
{
_COGL_RETURN_IF_FAIL (n_components == 3);
_cogl_matrix_transform_points_f3 (matrix,
stride_in, points_in,
stride_out, points_out,
n_points);
}
}
void
cogl_matrix_project_points (const CoglMatrix *matrix,
int n_components,
size_t stride_in,
const void *points_in,
size_t stride_out,
void *points_out,
int n_points)
{
if (n_components == 2)
_cogl_matrix_project_points_f2 (matrix,
stride_in, points_in,
stride_out, points_out,
n_points);
else if (n_components == 3)
_cogl_matrix_project_points_f3 (matrix,
stride_in, points_in,
stride_out, points_out,
n_points);
else
{
_COGL_RETURN_IF_FAIL (n_components == 4);
_cogl_matrix_project_points_f4 (matrix,
stride_in, points_in,
stride_out, points_out,
n_points);
}
}
gboolean
cogl_matrix_is_identity (const CoglMatrix *matrix)
{
if (!(matrix->flags & MAT_DIRTY_TYPE) &&
matrix->type == COGL_MATRIX_TYPE_IDENTITY)
return TRUE;
else
return memcmp (matrix, identity, sizeof (float) * 16) == 0;
}
void
cogl_matrix_look_at (CoglMatrix *matrix,
float eye_position_x,
float eye_position_y,
float eye_position_z,
float object_x,
float object_y,
float object_z,
float world_up_x,
float world_up_y,
float world_up_z)
{
CoglMatrix tmp;
float forward[3];
float side[3];
float up[3];
/* Get a unit viewing direction vector */
cogl_vector3_init (forward,
object_x - eye_position_x,
object_y - eye_position_y,
object_z - eye_position_z);
cogl_vector3_normalize (forward);
cogl_vector3_init (up, world_up_x, world_up_y, world_up_z);
/* Take the sideways direction as being perpendicular to the viewing
* direction and the word up vector. */
cogl_vector3_cross_product (side, forward, up);
cogl_vector3_normalize (side);
/* Now we have unit sideways and forward-direction vectors calculate
* a new mutually perpendicular up vector. */
cogl_vector3_cross_product (up, side, forward);
tmp.xx = side[0];
tmp.yx = side[1];
tmp.zx = side[2];
tmp.wx = 0;
tmp.xy = up[0];
tmp.yy = up[1];
tmp.zy = up[2];
tmp.wy = 0;
tmp.xz = -forward[0];
tmp.yz = -forward[1];
tmp.zz = -forward[2];
tmp.wz = 0;
tmp.xw = 0;
tmp.yw = 0;
tmp.zw = 0;
tmp.ww = 1;
tmp.flags = (MAT_FLAG_GENERAL_3D | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE);
cogl_matrix_translate (&tmp, -eye_position_x, -eye_position_y, -eye_position_z);
cogl_matrix_multiply (matrix, matrix, &tmp);
}
void
cogl_matrix_transpose (CoglMatrix *matrix)
{
float new_values[16];
/* We don't need to do anything if the matrix is the identity matrix */
if (!(matrix->flags & MAT_DIRTY_TYPE) &&
matrix->type == COGL_MATRIX_TYPE_IDENTITY)
return;
_cogl_matrix_util_transposef (new_values, cogl_matrix_get_array (matrix));
cogl_matrix_init_from_array (matrix, new_values);
}
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