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mutter/cogl/cogl-matrix.c
Robert Bragg f37d9bbb4d matrix: Add cogl_matrix_look_at 
Similar to the widely used gluLookAt API, this adds a CoglMatrix utility
for setting up a view transform in terms of positioning a camera/eye
position that points to a given object position aligned to a given
world-up vector.

Reviewed-by: Neil Roberts <neil@linux.intel.com>
2011-08-12 15:28:44 +01:00

2116 lines
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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.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 */
} ;
#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)
{
g_print ("Matrix type: %s, flags: %x\n",
types[matrix->type], (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_ortho (CoglMatrix *matrix,
float left,
float right,
float bottom,
float top,
float nearval,
float farval)
{
float 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_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_val,
float far_val)
{
_cogl_matrix_ortho (matrix, left, right, bottom, top, near_val, far_val);
_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);
}
#if 0
/*
* 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];
}
#endif
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;
g_return_val_if_fail (v1 != NULL, FALSE);
g_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... */
g_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
{
g_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
{
g_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;
CoglVector3 forward;
CoglVector3 side;
CoglVector3 up;
/* 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.x;
tmp.yx = side.y;
tmp.zx = side.z;
tmp.wx = 0;
tmp.xy = up.x;
tmp.yy = up.y;
tmp.zy = up.z;
tmp.wy = 0;
tmp.xz = -forward.x;
tmp.yz = -forward.y;
tmp.zz = -forward.z;
tmp.wz = 0;
tmp.xw = 0;
tmp.yw = 0;
tmp.zw = 0;
tmp.ww = 1;
cogl_matrix_translate (&tmp, -eye_position_x, -eye_position_y, -eye_position_z);
tmp.flags = (MAT_FLAG_GENERAL_3D | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE);
cogl_matrix_multiply (matrix, matrix, &tmp);
}
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