1732 lines
40 KiB
C
1732 lines
40 KiB
C
/*
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* ***** BEGIN GPL LICENSE BLOCK *****
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*
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* This program is free software; you can redistribute it and/or
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* modify it under the terms of the GNU General Public License
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* as published by the Free Software Foundation; either version 2
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* of the License, or (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*
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* The Original Code is Copyright (C) 2001-2002 by NaN Holding BV.
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* All rights reserved.
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*
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* The Original Code is: some of this file.
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*
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* ***** END GPL LICENSE BLOCK *****
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*/
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/** \file blender/blenlib/intern/math_matrix.c
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* \ingroup bli
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*/
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#include <assert.h>
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#include "BLI_math.h"
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/********************************* Init **************************************/
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void zero_m3(float m[3][3])
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{
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memset(m, 0, 3*3*sizeof(float));
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}
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void zero_m4(float m[4][4])
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{
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memset(m, 0, 4*4*sizeof(float));
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}
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void unit_m3(float m[][3])
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{
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m[0][0]= m[1][1]= m[2][2]= 1.0;
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m[0][1]= m[0][2]= 0.0;
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m[1][0]= m[1][2]= 0.0;
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m[2][0]= m[2][1]= 0.0;
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}
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void unit_m4(float m[][4])
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{
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m[0][0]= m[1][1]= m[2][2]= m[3][3]= 1.0;
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m[0][1]= m[0][2]= m[0][3]= 0.0;
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m[1][0]= m[1][2]= m[1][3]= 0.0;
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m[2][0]= m[2][1]= m[2][3]= 0.0;
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m[3][0]= m[3][1]= m[3][2]= 0.0;
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}
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void copy_m3_m3(float m1[][3], float m2[][3])
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{
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/* destination comes first: */
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memcpy(&m1[0], &m2[0], 9*sizeof(float));
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}
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void copy_m4_m4(float m1[][4], float m2[][4])
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{
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memcpy(m1, m2, 4*4*sizeof(float));
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}
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void copy_m3_m4(float m1[][3], float m2[][4])
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{
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m1[0][0]= m2[0][0];
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m1[0][1]= m2[0][1];
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m1[0][2]= m2[0][2];
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m1[1][0]= m2[1][0];
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m1[1][1]= m2[1][1];
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m1[1][2]= m2[1][2];
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m1[2][0]= m2[2][0];
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m1[2][1]= m2[2][1];
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m1[2][2]= m2[2][2];
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}
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void copy_m4_m3(float m1[][4], float m2[][3]) /* no clear */
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{
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m1[0][0]= m2[0][0];
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m1[0][1]= m2[0][1];
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m1[0][2]= m2[0][2];
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m1[1][0]= m2[1][0];
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m1[1][1]= m2[1][1];
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m1[1][2]= m2[1][2];
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m1[2][0]= m2[2][0];
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m1[2][1]= m2[2][1];
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m1[2][2]= m2[2][2];
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/* Reevan's Bugfix */
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m1[0][3]=0.0F;
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m1[1][3]=0.0F;
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m1[2][3]=0.0F;
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m1[3][0]=0.0F;
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m1[3][1]=0.0F;
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m1[3][2]=0.0F;
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m1[3][3]=1.0F;
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}
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void swap_m3m3(float m1[][3], float m2[][3])
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{
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float t;
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int i, j;
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for(i = 0; i < 3; i++) {
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for (j = 0; j < 3; j++) {
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t = m1[i][j];
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m1[i][j] = m2[i][j];
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m2[i][j] = t;
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}
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}
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}
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void swap_m4m4(float m1[][4], float m2[][4])
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{
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float t;
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int i, j;
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for(i = 0; i < 4; i++) {
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for (j = 0; j < 4; j++) {
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t = m1[i][j];
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m1[i][j] = m2[i][j];
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m2[i][j] = t;
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}
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}
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}
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/******************************** Arithmetic *********************************/
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void mul_m4_m4m4(float m1[][4], float m2_[][4], float m3_[][4])
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{
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float m2[4][4], m3[4][4];
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/* copy so it works when m1 is the same pointer as m2 or m3 */
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copy_m4_m4(m2, m2_);
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copy_m4_m4(m3, m3_);
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/* matrix product: m1[j][k] = m2[j][i].m3[i][k] */
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m1[0][0] = m2[0][0]*m3[0][0] + m2[0][1]*m3[1][0] + m2[0][2]*m3[2][0] + m2[0][3]*m3[3][0];
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m1[0][1] = m2[0][0]*m3[0][1] + m2[0][1]*m3[1][1] + m2[0][2]*m3[2][1] + m2[0][3]*m3[3][1];
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m1[0][2] = m2[0][0]*m3[0][2] + m2[0][1]*m3[1][2] + m2[0][2]*m3[2][2] + m2[0][3]*m3[3][2];
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m1[0][3] = m2[0][0]*m3[0][3] + m2[0][1]*m3[1][3] + m2[0][2]*m3[2][3] + m2[0][3]*m3[3][3];
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m1[1][0] = m2[1][0]*m3[0][0] + m2[1][1]*m3[1][0] + m2[1][2]*m3[2][0] + m2[1][3]*m3[3][0];
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m1[1][1] = m2[1][0]*m3[0][1] + m2[1][1]*m3[1][1] + m2[1][2]*m3[2][1] + m2[1][3]*m3[3][1];
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m1[1][2] = m2[1][0]*m3[0][2] + m2[1][1]*m3[1][2] + m2[1][2]*m3[2][2] + m2[1][3]*m3[3][2];
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m1[1][3] = m2[1][0]*m3[0][3] + m2[1][1]*m3[1][3] + m2[1][2]*m3[2][3] + m2[1][3]*m3[3][3];
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m1[2][0] = m2[2][0]*m3[0][0] + m2[2][1]*m3[1][0] + m2[2][2]*m3[2][0] + m2[2][3]*m3[3][0];
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m1[2][1] = m2[2][0]*m3[0][1] + m2[2][1]*m3[1][1] + m2[2][2]*m3[2][1] + m2[2][3]*m3[3][1];
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m1[2][2] = m2[2][0]*m3[0][2] + m2[2][1]*m3[1][2] + m2[2][2]*m3[2][2] + m2[2][3]*m3[3][2];
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m1[2][3] = m2[2][0]*m3[0][3] + m2[2][1]*m3[1][3] + m2[2][2]*m3[2][3] + m2[2][3]*m3[3][3];
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m1[3][0] = m2[3][0]*m3[0][0] + m2[3][1]*m3[1][0] + m2[3][2]*m3[2][0] + m2[3][3]*m3[3][0];
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m1[3][1] = m2[3][0]*m3[0][1] + m2[3][1]*m3[1][1] + m2[3][2]*m3[2][1] + m2[3][3]*m3[3][1];
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m1[3][2] = m2[3][0]*m3[0][2] + m2[3][1]*m3[1][2] + m2[3][2]*m3[2][2] + m2[3][3]*m3[3][2];
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m1[3][3] = m2[3][0]*m3[0][3] + m2[3][1]*m3[1][3] + m2[3][2]*m3[2][3] + m2[3][3]*m3[3][3];
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}
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void mul_m3_m3m3(float m1[][3], float m3_[][3], float m2_[][3])
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{
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float m2[3][3], m3[3][3];
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/* copy so it works when m1 is the same pointer as m2 or m3 */
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copy_m3_m3(m2, m2_);
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copy_m3_m3(m3, m3_);
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/* m1[i][j] = m2[i][k]*m3[k][j], args are flipped! */
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m1[0][0]= m2[0][0]*m3[0][0] + m2[0][1]*m3[1][0] + m2[0][2]*m3[2][0];
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m1[0][1]= m2[0][0]*m3[0][1] + m2[0][1]*m3[1][1] + m2[0][2]*m3[2][1];
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m1[0][2]= m2[0][0]*m3[0][2] + m2[0][1]*m3[1][2] + m2[0][2]*m3[2][2];
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m1[1][0]= m2[1][0]*m3[0][0] + m2[1][1]*m3[1][0] + m2[1][2]*m3[2][0];
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m1[1][1]= m2[1][0]*m3[0][1] + m2[1][1]*m3[1][1] + m2[1][2]*m3[2][1];
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m1[1][2]= m2[1][0]*m3[0][2] + m2[1][1]*m3[1][2] + m2[1][2]*m3[2][2];
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m1[2][0]= m2[2][0]*m3[0][0] + m2[2][1]*m3[1][0] + m2[2][2]*m3[2][0];
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m1[2][1]= m2[2][0]*m3[0][1] + m2[2][1]*m3[1][1] + m2[2][2]*m3[2][1];
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m1[2][2]= m2[2][0]*m3[0][2] + m2[2][1]*m3[1][2] + m2[2][2]*m3[2][2];
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}
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void mul_m4_m4m3(float (*m1)[4], float (*m3)[4], float (*m2)[3])
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{
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m1[0][0]= m2[0][0]*m3[0][0] + m2[0][1]*m3[1][0] + m2[0][2]*m3[2][0];
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m1[0][1]= m2[0][0]*m3[0][1] + m2[0][1]*m3[1][1] + m2[0][2]*m3[2][1];
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m1[0][2]= m2[0][0]*m3[0][2] + m2[0][1]*m3[1][2] + m2[0][2]*m3[2][2];
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m1[1][0]= m2[1][0]*m3[0][0] + m2[1][1]*m3[1][0] + m2[1][2]*m3[2][0];
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m1[1][1]= m2[1][0]*m3[0][1] + m2[1][1]*m3[1][1] + m2[1][2]*m3[2][1];
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m1[1][2]= m2[1][0]*m3[0][2] + m2[1][1]*m3[1][2] + m2[1][2]*m3[2][2];
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m1[2][0]= m2[2][0]*m3[0][0] + m2[2][1]*m3[1][0] + m2[2][2]*m3[2][0];
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m1[2][1]= m2[2][0]*m3[0][1] + m2[2][1]*m3[1][1] + m2[2][2]*m3[2][1];
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m1[2][2]= m2[2][0]*m3[0][2] + m2[2][1]*m3[1][2] + m2[2][2]*m3[2][2];
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}
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/* m1 = m2 * m3, ignore the elements on the 4th row/column of m3*/
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void mul_m3_m3m4(float m1[][3], float m2[][3], float m3[][4])
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{
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/* m1[i][j] = m2[i][k] * m3[k][j] */
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m1[0][0] = m2[0][0] * m3[0][0] + m2[0][1] * m3[1][0] +m2[0][2] * m3[2][0];
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m1[0][1] = m2[0][0] * m3[0][1] + m2[0][1] * m3[1][1] +m2[0][2] * m3[2][1];
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m1[0][2] = m2[0][0] * m3[0][2] + m2[0][1] * m3[1][2] +m2[0][2] * m3[2][2];
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m1[1][0] = m2[1][0] * m3[0][0] + m2[1][1] * m3[1][0] +m2[1][2] * m3[2][0];
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m1[1][1] = m2[1][0] * m3[0][1] + m2[1][1] * m3[1][1] +m2[1][2] * m3[2][1];
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m1[1][2] = m2[1][0] * m3[0][2] + m2[1][1] * m3[1][2] +m2[1][2] * m3[2][2];
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m1[2][0] = m2[2][0] * m3[0][0] + m2[2][1] * m3[1][0] +m2[2][2] * m3[2][0];
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m1[2][1] = m2[2][0] * m3[0][1] + m2[2][1] * m3[1][1] +m2[2][2] * m3[2][1];
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m1[2][2] = m2[2][0] * m3[0][2] + m2[2][1] * m3[1][2] +m2[2][2] * m3[2][2];
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}
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void mul_m4_m3m4(float (*m1)[4], float (*m3)[3], float (*m2)[4])
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{
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m1[0][0]= m2[0][0]*m3[0][0] + m2[0][1]*m3[1][0] + m2[0][2]*m3[2][0];
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m1[0][1]= m2[0][0]*m3[0][1] + m2[0][1]*m3[1][1] + m2[0][2]*m3[2][1];
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m1[0][2]= m2[0][0]*m3[0][2] + m2[0][1]*m3[1][2] + m2[0][2]*m3[2][2];
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m1[1][0]= m2[1][0]*m3[0][0] + m2[1][1]*m3[1][0] + m2[1][2]*m3[2][0];
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m1[1][1]= m2[1][0]*m3[0][1] + m2[1][1]*m3[1][1] + m2[1][2]*m3[2][1];
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m1[1][2]= m2[1][0]*m3[0][2] + m2[1][1]*m3[1][2] + m2[1][2]*m3[2][2];
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m1[2][0]= m2[2][0]*m3[0][0] + m2[2][1]*m3[1][0] + m2[2][2]*m3[2][0];
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m1[2][1]= m2[2][0]*m3[0][1] + m2[2][1]*m3[1][1] + m2[2][2]*m3[2][1];
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m1[2][2]= m2[2][0]*m3[0][2] + m2[2][1]*m3[1][2] + m2[2][2]*m3[2][2];
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}
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void mul_serie_m3(float answ[][3],
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float m1[][3], float m2[][3], float m3[][3],
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float m4[][3], float m5[][3], float m6[][3],
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float m7[][3], float m8[][3])
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{
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float temp[3][3];
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if(m1==NULL || m2==NULL) return;
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mul_m3_m3m3(answ, m2, m1);
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if(m3) {
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mul_m3_m3m3(temp, m3, answ);
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if(m4) {
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mul_m3_m3m3(answ, m4, temp);
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if(m5) {
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mul_m3_m3m3(temp, m5, answ);
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if(m6) {
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mul_m3_m3m3(answ, m6, temp);
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if(m7) {
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mul_m3_m3m3(temp, m7, answ);
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if(m8) {
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mul_m3_m3m3(answ, m8, temp);
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}
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else copy_m3_m3(answ, temp);
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}
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}
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else copy_m3_m3(answ, temp);
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}
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}
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else copy_m3_m3(answ, temp);
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}
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}
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void mul_serie_m4(float answ[][4], float m1[][4],
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float m2[][4], float m3[][4], float m4[][4],
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float m5[][4], float m6[][4], float m7[][4],
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float m8[][4])
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{
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float temp[4][4];
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if(m1==NULL || m2==NULL) return;
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mul_m4_m4m4(answ, m2, m1);
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if(m3) {
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mul_m4_m4m4(temp, m3, answ);
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if(m4) {
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mul_m4_m4m4(answ, m4, temp);
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if(m5) {
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mul_m4_m4m4(temp, m5, answ);
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if(m6) {
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mul_m4_m4m4(answ, m6, temp);
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if(m7) {
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mul_m4_m4m4(temp, m7, answ);
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if(m8) {
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mul_m4_m4m4(answ, m8, temp);
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}
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else copy_m4_m4(answ, temp);
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}
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}
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else copy_m4_m4(answ, temp);
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}
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}
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else copy_m4_m4(answ, temp);
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}
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}
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void mul_m4_v3(float mat[][4], float vec[3])
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{
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float x,y;
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x=vec[0];
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y=vec[1];
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vec[0]=x*mat[0][0] + y*mat[1][0] + mat[2][0]*vec[2] + mat[3][0];
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vec[1]=x*mat[0][1] + y*mat[1][1] + mat[2][1]*vec[2] + mat[3][1];
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vec[2]=x*mat[0][2] + y*mat[1][2] + mat[2][2]*vec[2] + mat[3][2];
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}
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void mul_v3_m4v3(float in[3], float mat[][4], const float vec[3])
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{
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float x,y;
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x=vec[0];
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y=vec[1];
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in[0]= x*mat[0][0] + y*mat[1][0] + mat[2][0]*vec[2] + mat[3][0];
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in[1]= x*mat[0][1] + y*mat[1][1] + mat[2][1]*vec[2] + mat[3][1];
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in[2]= x*mat[0][2] + y*mat[1][2] + mat[2][2]*vec[2] + mat[3][2];
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}
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/* same as mul_m4_v3() but doesnt apply translation component */
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void mul_mat3_m4_v3(float mat[][4], float vec[3])
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{
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float x,y;
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x= vec[0];
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y= vec[1];
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vec[0]= x*mat[0][0] + y*mat[1][0] + mat[2][0]*vec[2];
|
|
vec[1]= x*mat[0][1] + y*mat[1][1] + mat[2][1]*vec[2];
|
|
vec[2]= x*mat[0][2] + y*mat[1][2] + mat[2][2]*vec[2];
|
|
}
|
|
|
|
void mul_project_m4_v3(float mat[][4], float vec[3])
|
|
{
|
|
const float w= vec[0]*mat[0][3] + vec[1]*mat[1][3] + vec[2]*mat[2][3] + mat[3][3];
|
|
mul_m4_v3(mat, vec);
|
|
|
|
vec[0] /= w;
|
|
vec[1] /= w;
|
|
vec[2] /= w;
|
|
}
|
|
|
|
void mul_v4_m4v4(float r[4], float mat[4][4], float v[4])
|
|
{
|
|
float x, y, z;
|
|
|
|
x= v[0];
|
|
y= v[1];
|
|
z= v[2];
|
|
|
|
r[0]= x*mat[0][0] + y*mat[1][0] + z*mat[2][0] + mat[3][0]*v[3];
|
|
r[1]= x*mat[0][1] + y*mat[1][1] + z*mat[2][1] + mat[3][1]*v[3];
|
|
r[2]= x*mat[0][2] + y*mat[1][2] + z*mat[2][2] + mat[3][2]*v[3];
|
|
r[3]= x*mat[0][3] + y*mat[1][3] + z*mat[2][3] + mat[3][3]*v[3];
|
|
}
|
|
|
|
void mul_m4_v4(float mat[4][4], float r[4])
|
|
{
|
|
mul_v4_m4v4(r, mat, r);
|
|
}
|
|
|
|
void mul_v3_m3v3(float r[3], float M[3][3], float a[3])
|
|
{
|
|
r[0]= M[0][0]*a[0] + M[1][0]*a[1] + M[2][0]*a[2];
|
|
r[1]= M[0][1]*a[0] + M[1][1]*a[1] + M[2][1]*a[2];
|
|
r[2]= M[0][2]*a[0] + M[1][2]*a[1] + M[2][2]*a[2];
|
|
}
|
|
|
|
void mul_m3_v3(float M[3][3], float r[3])
|
|
{
|
|
float tmp[3];
|
|
|
|
mul_v3_m3v3(tmp, M, r);
|
|
copy_v3_v3(r, tmp);
|
|
}
|
|
|
|
void mul_transposed_m3_v3(float mat[][3], float vec[3])
|
|
{
|
|
float x,y;
|
|
|
|
x=vec[0];
|
|
y=vec[1];
|
|
vec[0]= x*mat[0][0] + y*mat[0][1] + mat[0][2]*vec[2];
|
|
vec[1]= x*mat[1][0] + y*mat[1][1] + mat[1][2]*vec[2];
|
|
vec[2]= x*mat[2][0] + y*mat[2][1] + mat[2][2]*vec[2];
|
|
}
|
|
|
|
void mul_m3_fl(float m[3][3], float f)
|
|
{
|
|
int i, j;
|
|
|
|
for(i=0;i<3;i++)
|
|
for(j=0;j<3;j++)
|
|
m[i][j] *= f;
|
|
}
|
|
|
|
void mul_m4_fl(float m[4][4], float f)
|
|
{
|
|
int i, j;
|
|
|
|
for(i=0;i<4;i++)
|
|
for(j=0;j<4;j++)
|
|
m[i][j] *= f;
|
|
}
|
|
|
|
void mul_mat3_m4_fl(float m[4][4], float f)
|
|
{
|
|
int i, j;
|
|
|
|
for(i=0; i<3; i++)
|
|
for(j=0; j<3; j++)
|
|
m[i][j] *= f;
|
|
}
|
|
|
|
void mul_m3_v3_double(float mat[][3], double vec[3])
|
|
{
|
|
double x,y;
|
|
|
|
x=vec[0];
|
|
y=vec[1];
|
|
vec[0]= x*mat[0][0] + y*mat[1][0] + mat[2][0]*vec[2];
|
|
vec[1]= x*mat[0][1] + y*mat[1][1] + mat[2][1]*vec[2];
|
|
vec[2]= x*mat[0][2] + y*mat[1][2] + mat[2][2]*vec[2];
|
|
}
|
|
|
|
void add_m3_m3m3(float m1[][3], float m2[][3], float m3[][3])
|
|
{
|
|
int i, j;
|
|
|
|
for(i=0;i<3;i++)
|
|
for(j=0;j<3;j++)
|
|
m1[i][j]= m2[i][j] + m3[i][j];
|
|
}
|
|
|
|
void add_m4_m4m4(float m1[][4], float m2[][4], float m3[][4])
|
|
{
|
|
int i, j;
|
|
|
|
for(i=0;i<4;i++)
|
|
for(j=0;j<4;j++)
|
|
m1[i][j]= m2[i][j] + m3[i][j];
|
|
}
|
|
|
|
void sub_m3_m3m3(float m1[][3], float m2[][3], float m3[][3])
|
|
{
|
|
int i, j;
|
|
|
|
for(i=0;i<3;i++)
|
|
for(j=0;j<3;j++)
|
|
m1[i][j]= m2[i][j] - m3[i][j];
|
|
}
|
|
|
|
void sub_m4_m4m4(float m1[][4], float m2[][4], float m3[][4])
|
|
{
|
|
int i, j;
|
|
|
|
for(i=0;i<4;i++)
|
|
for(j=0;j<4;j++)
|
|
m1[i][j]= m2[i][j] - m3[i][j];
|
|
}
|
|
|
|
int invert_m3(float m[3][3])
|
|
{
|
|
float tmp[3][3];
|
|
int success;
|
|
|
|
success= invert_m3_m3(tmp, m);
|
|
copy_m3_m3(m, tmp);
|
|
|
|
return success;
|
|
}
|
|
|
|
int invert_m3_m3(float m1[3][3], float m2[3][3])
|
|
{
|
|
float det;
|
|
int a, b, success;
|
|
|
|
/* calc adjoint */
|
|
adjoint_m3_m3(m1,m2);
|
|
|
|
/* then determinant old matrix! */
|
|
det= m2[0][0]* (m2[1][1]*m2[2][2] - m2[1][2]*m2[2][1])
|
|
-m2[1][0]* (m2[0][1]*m2[2][2] - m2[0][2]*m2[2][1])
|
|
+m2[2][0]* (m2[0][1]*m2[1][2] - m2[0][2]*m2[1][1]);
|
|
|
|
success= (det != 0);
|
|
|
|
if(det==0) det=1;
|
|
det= 1/det;
|
|
for(a=0;a<3;a++) {
|
|
for(b=0;b<3;b++) {
|
|
m1[a][b]*=det;
|
|
}
|
|
}
|
|
|
|
return success;
|
|
}
|
|
|
|
int invert_m4(float m[4][4])
|
|
{
|
|
float tmp[4][4];
|
|
int success;
|
|
|
|
success= invert_m4_m4(tmp, m);
|
|
copy_m4_m4(m, tmp);
|
|
|
|
return success;
|
|
}
|
|
|
|
/*
|
|
* invertmat -
|
|
* computes the inverse of mat and puts it in inverse. Returns
|
|
* TRUE on success (i.e. can always find a pivot) and FALSE on failure.
|
|
* Uses Gaussian Elimination with partial (maximal column) pivoting.
|
|
*
|
|
* Mark Segal - 1992
|
|
*/
|
|
|
|
int invert_m4_m4(float inverse[4][4], float mat[4][4])
|
|
{
|
|
int i, j, k;
|
|
double temp;
|
|
float tempmat[4][4];
|
|
float max;
|
|
int maxj;
|
|
|
|
/* Set inverse to identity */
|
|
for (i=0; i<4; i++)
|
|
for (j=0; j<4; j++)
|
|
inverse[i][j] = 0;
|
|
for (i=0; i<4; i++)
|
|
inverse[i][i] = 1;
|
|
|
|
/* Copy original matrix so we don't mess it up */
|
|
for(i = 0; i < 4; i++)
|
|
for(j = 0; j <4; j++)
|
|
tempmat[i][j] = mat[i][j];
|
|
|
|
for(i = 0; i < 4; i++) {
|
|
/* Look for row with max pivot */
|
|
max = fabs(tempmat[i][i]);
|
|
maxj = i;
|
|
for(j = i + 1; j < 4; j++) {
|
|
if(fabsf(tempmat[j][i]) > max) {
|
|
max = fabs(tempmat[j][i]);
|
|
maxj = j;
|
|
}
|
|
}
|
|
/* Swap rows if necessary */
|
|
if (maxj != i) {
|
|
for(k = 0; k < 4; k++) {
|
|
SWAP(float, tempmat[i][k], tempmat[maxj][k]);
|
|
SWAP(float, inverse[i][k], inverse[maxj][k]);
|
|
}
|
|
}
|
|
|
|
temp = tempmat[i][i];
|
|
if (temp == 0)
|
|
return 0; /* No non-zero pivot */
|
|
for(k = 0; k < 4; k++) {
|
|
tempmat[i][k] = (float)(tempmat[i][k]/temp);
|
|
inverse[i][k] = (float)(inverse[i][k]/temp);
|
|
}
|
|
for(j = 0; j < 4; j++) {
|
|
if(j != i) {
|
|
temp = tempmat[j][i];
|
|
for(k = 0; k < 4; k++) {
|
|
tempmat[j][k] -= (float)(tempmat[i][k]*temp);
|
|
inverse[j][k] -= (float)(inverse[i][k]*temp);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
/****************************** Linear Algebra *******************************/
|
|
|
|
void transpose_m3(float mat[][3])
|
|
{
|
|
float t;
|
|
|
|
t = mat[0][1] ;
|
|
mat[0][1] = mat[1][0] ;
|
|
mat[1][0] = t;
|
|
t = mat[0][2] ;
|
|
mat[0][2] = mat[2][0] ;
|
|
mat[2][0] = t;
|
|
t = mat[1][2] ;
|
|
mat[1][2] = mat[2][1] ;
|
|
mat[2][1] = t;
|
|
}
|
|
|
|
void transpose_m4(float mat[][4])
|
|
{
|
|
float t;
|
|
|
|
t = mat[0][1] ;
|
|
mat[0][1] = mat[1][0] ;
|
|
mat[1][0] = t;
|
|
t = mat[0][2] ;
|
|
mat[0][2] = mat[2][0] ;
|
|
mat[2][0] = t;
|
|
t = mat[0][3] ;
|
|
mat[0][3] = mat[3][0] ;
|
|
mat[3][0] = t;
|
|
|
|
t = mat[1][2] ;
|
|
mat[1][2] = mat[2][1] ;
|
|
mat[2][1] = t;
|
|
t = mat[1][3] ;
|
|
mat[1][3] = mat[3][1] ;
|
|
mat[3][1] = t;
|
|
|
|
t = mat[2][3] ;
|
|
mat[2][3] = mat[3][2] ;
|
|
mat[3][2] = t;
|
|
}
|
|
|
|
void orthogonalize_m3(float mat[][3], int axis)
|
|
{
|
|
float size[3];
|
|
mat3_to_size(size, mat);
|
|
normalize_v3(mat[axis]);
|
|
switch(axis)
|
|
{
|
|
case 0:
|
|
if (dot_v3v3(mat[0], mat[1]) < 1) {
|
|
cross_v3_v3v3(mat[2], mat[0], mat[1]);
|
|
normalize_v3(mat[2]);
|
|
cross_v3_v3v3(mat[1], mat[2], mat[0]);
|
|
} else if (dot_v3v3(mat[0], mat[2]) < 1) {
|
|
cross_v3_v3v3(mat[1], mat[2], mat[0]);
|
|
normalize_v3(mat[1]);
|
|
cross_v3_v3v3(mat[2], mat[0], mat[1]);
|
|
} else {
|
|
float vec[3];
|
|
|
|
vec[0]= mat[0][1];
|
|
vec[1]= mat[0][2];
|
|
vec[2]= mat[0][0];
|
|
|
|
cross_v3_v3v3(mat[2], mat[0], vec);
|
|
normalize_v3(mat[2]);
|
|
cross_v3_v3v3(mat[1], mat[2], mat[0]);
|
|
}
|
|
case 1:
|
|
if (dot_v3v3(mat[1], mat[0]) < 1) {
|
|
cross_v3_v3v3(mat[2], mat[0], mat[1]);
|
|
normalize_v3(mat[2]);
|
|
cross_v3_v3v3(mat[0], mat[1], mat[2]);
|
|
} else if (dot_v3v3(mat[0], mat[2]) < 1) {
|
|
cross_v3_v3v3(mat[0], mat[1], mat[2]);
|
|
normalize_v3(mat[0]);
|
|
cross_v3_v3v3(mat[2], mat[0], mat[1]);
|
|
} else {
|
|
float vec[3];
|
|
|
|
vec[0]= mat[1][1];
|
|
vec[1]= mat[1][2];
|
|
vec[2]= mat[1][0];
|
|
|
|
cross_v3_v3v3(mat[0], mat[1], vec);
|
|
normalize_v3(mat[0]);
|
|
cross_v3_v3v3(mat[2], mat[0], mat[1]);
|
|
}
|
|
case 2:
|
|
if (dot_v3v3(mat[2], mat[0]) < 1) {
|
|
cross_v3_v3v3(mat[1], mat[2], mat[0]);
|
|
normalize_v3(mat[1]);
|
|
cross_v3_v3v3(mat[0], mat[1], mat[2]);
|
|
} else if (dot_v3v3(mat[2], mat[1]) < 1) {
|
|
cross_v3_v3v3(mat[0], mat[1], mat[2]);
|
|
normalize_v3(mat[0]);
|
|
cross_v3_v3v3(mat[1], mat[2], mat[0]);
|
|
} else {
|
|
float vec[3];
|
|
|
|
vec[0]= mat[2][1];
|
|
vec[1]= mat[2][2];
|
|
vec[2]= mat[2][0];
|
|
|
|
cross_v3_v3v3(mat[0], vec, mat[2]);
|
|
normalize_v3(mat[0]);
|
|
cross_v3_v3v3(mat[1], mat[2], mat[0]);
|
|
}
|
|
}
|
|
mul_v3_fl(mat[0], size[0]);
|
|
mul_v3_fl(mat[1], size[1]);
|
|
mul_v3_fl(mat[2], size[2]);
|
|
}
|
|
|
|
void orthogonalize_m4(float mat[][4], int axis)
|
|
{
|
|
float size[3];
|
|
mat4_to_size(size, mat);
|
|
normalize_v3(mat[axis]);
|
|
switch(axis)
|
|
{
|
|
case 0:
|
|
if (dot_v3v3(mat[0], mat[1]) < 1) {
|
|
cross_v3_v3v3(mat[2], mat[0], mat[1]);
|
|
normalize_v3(mat[2]);
|
|
cross_v3_v3v3(mat[1], mat[2], mat[0]);
|
|
} else if (dot_v3v3(mat[0], mat[2]) < 1) {
|
|
cross_v3_v3v3(mat[1], mat[2], mat[0]);
|
|
normalize_v3(mat[1]);
|
|
cross_v3_v3v3(mat[2], mat[0], mat[1]);
|
|
} else {
|
|
float vec[3];
|
|
|
|
vec[0]= mat[0][1];
|
|
vec[1]= mat[0][2];
|
|
vec[2]= mat[0][0];
|
|
|
|
cross_v3_v3v3(mat[2], mat[0], vec);
|
|
normalize_v3(mat[2]);
|
|
cross_v3_v3v3(mat[1], mat[2], mat[0]);
|
|
}
|
|
case 1:
|
|
normalize_v3(mat[0]);
|
|
if (dot_v3v3(mat[1], mat[0]) < 1) {
|
|
cross_v3_v3v3(mat[2], mat[0], mat[1]);
|
|
normalize_v3(mat[2]);
|
|
cross_v3_v3v3(mat[0], mat[1], mat[2]);
|
|
} else if (dot_v3v3(mat[0], mat[2]) < 1) {
|
|
cross_v3_v3v3(mat[0], mat[1], mat[2]);
|
|
normalize_v3(mat[0]);
|
|
cross_v3_v3v3(mat[2], mat[0], mat[1]);
|
|
} else {
|
|
float vec[3];
|
|
|
|
vec[0]= mat[1][1];
|
|
vec[1]= mat[1][2];
|
|
vec[2]= mat[1][0];
|
|
|
|
cross_v3_v3v3(mat[0], mat[1], vec);
|
|
normalize_v3(mat[0]);
|
|
cross_v3_v3v3(mat[2], mat[0], mat[1]);
|
|
}
|
|
case 2:
|
|
if (dot_v3v3(mat[2], mat[0]) < 1) {
|
|
cross_v3_v3v3(mat[1], mat[2], mat[0]);
|
|
normalize_v3(mat[1]);
|
|
cross_v3_v3v3(mat[0], mat[1], mat[2]);
|
|
} else if (dot_v3v3(mat[2], mat[1]) < 1) {
|
|
cross_v3_v3v3(mat[0], mat[1], mat[2]);
|
|
normalize_v3(mat[0]);
|
|
cross_v3_v3v3(mat[1], mat[2], mat[0]);
|
|
} else {
|
|
float vec[3];
|
|
|
|
vec[0]= mat[2][1];
|
|
vec[1]= mat[2][2];
|
|
vec[2]= mat[2][0];
|
|
|
|
cross_v3_v3v3(mat[0], vec, mat[2]);
|
|
normalize_v3(mat[0]);
|
|
cross_v3_v3v3(mat[1], mat[2], mat[0]);
|
|
}
|
|
}
|
|
mul_v3_fl(mat[0], size[0]);
|
|
mul_v3_fl(mat[1], size[1]);
|
|
mul_v3_fl(mat[2], size[2]);
|
|
}
|
|
|
|
int is_orthogonal_m3(float mat[][3])
|
|
{
|
|
if (fabsf(dot_v3v3(mat[0], mat[1])) > 1.5f * FLT_EPSILON)
|
|
return 0;
|
|
|
|
if (fabsf(dot_v3v3(mat[1], mat[2])) > 1.5f * FLT_EPSILON)
|
|
return 0;
|
|
|
|
if (fabsf(dot_v3v3(mat[0], mat[2])) > 1.5f * FLT_EPSILON)
|
|
return 0;
|
|
|
|
return 1;
|
|
}
|
|
|
|
int is_orthogonal_m4(float mat[][4])
|
|
{
|
|
if (fabsf(dot_v3v3(mat[0], mat[1])) > 1.5f * FLT_EPSILON)
|
|
return 0;
|
|
|
|
if (fabsf(dot_v3v3(mat[1], mat[2])) > 1.5f * FLT_EPSILON)
|
|
return 0;
|
|
|
|
if (fabsf(dot_v3v3(mat[0], mat[2])) > 1.5f * FLT_EPSILON)
|
|
return 0;
|
|
|
|
return 1;
|
|
}
|
|
|
|
void normalize_m3(float mat[][3])
|
|
{
|
|
normalize_v3(mat[0]);
|
|
normalize_v3(mat[1]);
|
|
normalize_v3(mat[2]);
|
|
}
|
|
|
|
void normalize_m3_m3(float rmat[][3], float mat[][3])
|
|
{
|
|
normalize_v3_v3(rmat[0], mat[0]);
|
|
normalize_v3_v3(rmat[1], mat[1]);
|
|
normalize_v3_v3(rmat[2], mat[2]);
|
|
}
|
|
|
|
|
|
void normalize_m4(float mat[][4])
|
|
{
|
|
float len;
|
|
|
|
len= normalize_v3(mat[0]);
|
|
if(len!=0.0f) mat[0][3]/= len;
|
|
len= normalize_v3(mat[1]);
|
|
if(len!=0.0f) mat[1][3]/= len;
|
|
len= normalize_v3(mat[2]);
|
|
if(len!=0.0f) mat[2][3]/= len;
|
|
}
|
|
|
|
void normalize_m4_m4(float rmat[][4], float mat[][4])
|
|
{
|
|
float len;
|
|
|
|
len= normalize_v3_v3(rmat[0], mat[0]);
|
|
if(len!=0.0f) rmat[0][3]= mat[0][3] / len;
|
|
len= normalize_v3_v3(rmat[1], mat[1]);
|
|
if(len!=0.0f) rmat[1][3]= mat[1][3] / len;
|
|
len= normalize_v3_v3(rmat[2], mat[2]);
|
|
if(len!=0.0f) rmat[2][3]= mat[2][3] / len;
|
|
}
|
|
|
|
void adjoint_m3_m3(float m1[][3], float m[][3])
|
|
{
|
|
m1[0][0]=m[1][1]*m[2][2]-m[1][2]*m[2][1];
|
|
m1[0][1]= -m[0][1]*m[2][2]+m[0][2]*m[2][1];
|
|
m1[0][2]=m[0][1]*m[1][2]-m[0][2]*m[1][1];
|
|
|
|
m1[1][0]= -m[1][0]*m[2][2]+m[1][2]*m[2][0];
|
|
m1[1][1]=m[0][0]*m[2][2]-m[0][2]*m[2][0];
|
|
m1[1][2]= -m[0][0]*m[1][2]+m[0][2]*m[1][0];
|
|
|
|
m1[2][0]=m[1][0]*m[2][1]-m[1][1]*m[2][0];
|
|
m1[2][1]= -m[0][0]*m[2][1]+m[0][1]*m[2][0];
|
|
m1[2][2]=m[0][0]*m[1][1]-m[0][1]*m[1][0];
|
|
}
|
|
|
|
void adjoint_m4_m4(float out[][4], float in[][4]) /* out = ADJ(in) */
|
|
{
|
|
float a1, a2, a3, a4, b1, b2, b3, b4;
|
|
float c1, c2, c3, c4, d1, d2, d3, d4;
|
|
|
|
a1= in[0][0];
|
|
b1= in[0][1];
|
|
c1= in[0][2];
|
|
d1= in[0][3];
|
|
|
|
a2= in[1][0];
|
|
b2= in[1][1];
|
|
c2= in[1][2];
|
|
d2= in[1][3];
|
|
|
|
a3= in[2][0];
|
|
b3= in[2][1];
|
|
c3= in[2][2];
|
|
d3= in[2][3];
|
|
|
|
a4= in[3][0];
|
|
b4= in[3][1];
|
|
c4= in[3][2];
|
|
d4= in[3][3];
|
|
|
|
|
|
out[0][0] = determinant_m3(b2, b3, b4, c2, c3, c4, d2, d3, d4);
|
|
out[1][0] = - determinant_m3(a2, a3, a4, c2, c3, c4, d2, d3, d4);
|
|
out[2][0] = determinant_m3(a2, a3, a4, b2, b3, b4, d2, d3, d4);
|
|
out[3][0] = - determinant_m3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
|
|
|
|
out[0][1] = - determinant_m3(b1, b3, b4, c1, c3, c4, d1, d3, d4);
|
|
out[1][1] = determinant_m3(a1, a3, a4, c1, c3, c4, d1, d3, d4);
|
|
out[2][1] = - determinant_m3(a1, a3, a4, b1, b3, b4, d1, d3, d4);
|
|
out[3][1] = determinant_m3(a1, a3, a4, b1, b3, b4, c1, c3, c4);
|
|
|
|
out[0][2] = determinant_m3(b1, b2, b4, c1, c2, c4, d1, d2, d4);
|
|
out[1][2] = - determinant_m3(a1, a2, a4, c1, c2, c4, d1, d2, d4);
|
|
out[2][2] = determinant_m3(a1, a2, a4, b1, b2, b4, d1, d2, d4);
|
|
out[3][2] = - determinant_m3(a1, a2, a4, b1, b2, b4, c1, c2, c4);
|
|
|
|
out[0][3] = - determinant_m3(b1, b2, b3, c1, c2, c3, d1, d2, d3);
|
|
out[1][3] = determinant_m3(a1, a2, a3, c1, c2, c3, d1, d2, d3);
|
|
out[2][3] = - determinant_m3(a1, a2, a3, b1, b2, b3, d1, d2, d3);
|
|
out[3][3] = determinant_m3(a1, a2, a3, b1, b2, b3, c1, c2, c3);
|
|
}
|
|
|
|
float determinant_m2(float a,float b,float c,float d)
|
|
{
|
|
|
|
return a*d - b*c;
|
|
}
|
|
|
|
float determinant_m3(float a1, float a2, float a3,
|
|
float b1, float b2, float b3,
|
|
float c1, float c2, float c3)
|
|
{
|
|
float ans;
|
|
|
|
ans = a1 * determinant_m2(b2, b3, c2, c3)
|
|
- b1 * determinant_m2(a2, a3, c2, c3)
|
|
+ c1 * determinant_m2(a2, a3, b2, b3);
|
|
|
|
return ans;
|
|
}
|
|
|
|
float determinant_m4(float m[][4])
|
|
{
|
|
float ans;
|
|
float a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4,d1,d2,d3,d4;
|
|
|
|
a1= m[0][0];
|
|
b1= m[0][1];
|
|
c1= m[0][2];
|
|
d1= m[0][3];
|
|
|
|
a2= m[1][0];
|
|
b2= m[1][1];
|
|
c2= m[1][2];
|
|
d2= m[1][3];
|
|
|
|
a3= m[2][0];
|
|
b3= m[2][1];
|
|
c3= m[2][2];
|
|
d3= m[2][3];
|
|
|
|
a4= m[3][0];
|
|
b4= m[3][1];
|
|
c4= m[3][2];
|
|
d4= m[3][3];
|
|
|
|
ans = a1 * determinant_m3(b2, b3, b4, c2, c3, c4, d2, d3, d4)
|
|
- b1 * determinant_m3(a2, a3, a4, c2, c3, c4, d2, d3, d4)
|
|
+ c1 * determinant_m3(a2, a3, a4, b2, b3, b4, d2, d3, d4)
|
|
- d1 * determinant_m3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
|
|
|
|
return ans;
|
|
}
|
|
|
|
/****************************** Transformations ******************************/
|
|
|
|
void size_to_mat3(float mat[][3], const float size[3])
|
|
{
|
|
mat[0][0]= size[0];
|
|
mat[0][1]= 0.0f;
|
|
mat[0][2]= 0.0f;
|
|
mat[1][1]= size[1];
|
|
mat[1][0]= 0.0f;
|
|
mat[1][2]= 0.0f;
|
|
mat[2][2]= size[2];
|
|
mat[2][1]= 0.0f;
|
|
mat[2][0]= 0.0f;
|
|
}
|
|
|
|
void size_to_mat4(float mat[][4], const float size[3])
|
|
{
|
|
float tmat[3][3];
|
|
|
|
size_to_mat3(tmat,size);
|
|
unit_m4(mat);
|
|
copy_m4_m3(mat, tmat);
|
|
}
|
|
|
|
void mat3_to_size(float size[3], float mat[][3])
|
|
{
|
|
size[0]= len_v3(mat[0]);
|
|
size[1]= len_v3(mat[1]);
|
|
size[2]= len_v3(mat[2]);
|
|
}
|
|
|
|
void mat4_to_size(float size[3], float mat[][4])
|
|
{
|
|
size[0]= len_v3(mat[0]);
|
|
size[1]= len_v3(mat[1]);
|
|
size[2]= len_v3(mat[2]);
|
|
}
|
|
|
|
/* this gets the average scale of a matrix, only use when your scaling
|
|
* data that has no idea of scale axis, examples are bone-envelope-radius
|
|
* and curve radius */
|
|
float mat3_to_scale(float mat[][3])
|
|
{
|
|
/* unit length vector */
|
|
float unit_vec[3] = {0.577350269189626f, 0.577350269189626f, 0.577350269189626f};
|
|
mul_m3_v3(mat, unit_vec);
|
|
return len_v3(unit_vec);
|
|
}
|
|
|
|
float mat4_to_scale(float mat[][4])
|
|
{
|
|
float tmat[3][3];
|
|
copy_m3_m4(tmat, mat);
|
|
return mat3_to_scale(tmat);
|
|
}
|
|
|
|
|
|
void mat3_to_rot_size(float rot[3][3], float size[3], float mat3[3][3])
|
|
{
|
|
float mat3_n[3][3]; /* mat3 -> normalized, 3x3 */
|
|
float imat3_n[3][3]; /* mat3 -> normalized & inverted, 3x3 */
|
|
|
|
/* rotation & scale are linked, we need to create the mat's
|
|
* for these together since they are related. */
|
|
|
|
/* so scale doesnt interfear with rotation [#24291] */
|
|
/* note: this is a workaround for negative matrix not working for rotation conversion, FIXME */
|
|
normalize_m3_m3(mat3_n, mat3);
|
|
if(is_negative_m3(mat3)) {
|
|
negate_v3(mat3_n[0]);
|
|
negate_v3(mat3_n[1]);
|
|
negate_v3(mat3_n[2]);
|
|
}
|
|
|
|
/* rotation */
|
|
/* keep rot as a 3x3 matrix, the caller can convert into a quat or euler */
|
|
copy_m3_m3(rot, mat3_n);
|
|
|
|
/* scale */
|
|
/* note: mat4_to_size(ob->size, mat) fails for negative scale */
|
|
invert_m3_m3(imat3_n, mat3_n);
|
|
mul_m3_m3m3(mat3, imat3_n, mat3);
|
|
|
|
size[0]= mat3[0][0];
|
|
size[1]= mat3[1][1];
|
|
size[2]= mat3[2][2];
|
|
}
|
|
|
|
void mat4_to_loc_rot_size(float loc[3], float rot[3][3], float size[3], float wmat[][4])
|
|
{
|
|
float mat3[3][3]; /* wmat -> 3x3 */
|
|
|
|
copy_m3_m4(mat3, wmat);
|
|
mat3_to_rot_size(rot, size, mat3);
|
|
|
|
/* location */
|
|
copy_v3_v3(loc, wmat[3]);
|
|
}
|
|
|
|
void scale_m3_fl(float m[][3], float scale)
|
|
{
|
|
m[0][0]= m[1][1]= m[2][2]= scale;
|
|
m[0][1]= m[0][2]= 0.0;
|
|
m[1][0]= m[1][2]= 0.0;
|
|
m[2][0]= m[2][1]= 0.0;
|
|
}
|
|
|
|
void scale_m4_fl(float m[][4], float scale)
|
|
{
|
|
m[0][0]= m[1][1]= m[2][2]= scale;
|
|
m[3][3]= 1.0;
|
|
m[0][1]= m[0][2]= m[0][3]= 0.0;
|
|
m[1][0]= m[1][2]= m[1][3]= 0.0;
|
|
m[2][0]= m[2][1]= m[2][3]= 0.0;
|
|
m[3][0]= m[3][1]= m[3][2]= 0.0;
|
|
}
|
|
|
|
void translate_m4(float mat[][4],float Tx, float Ty, float Tz)
|
|
{
|
|
mat[3][0] += (Tx*mat[0][0] + Ty*mat[1][0] + Tz*mat[2][0]);
|
|
mat[3][1] += (Tx*mat[0][1] + Ty*mat[1][1] + Tz*mat[2][1]);
|
|
mat[3][2] += (Tx*mat[0][2] + Ty*mat[1][2] + Tz*mat[2][2]);
|
|
}
|
|
|
|
void rotate_m4(float mat[][4], const char axis, const float angle)
|
|
{
|
|
int col;
|
|
float temp[4]= {0.0f, 0.0f, 0.0f, 0.0f};
|
|
float cosine, sine;
|
|
|
|
assert(axis >= 'X' && axis <= 'Z');
|
|
|
|
cosine = (float)cos(angle);
|
|
sine = (float)sin(angle);
|
|
switch(axis){
|
|
case 'X':
|
|
for(col=0 ; col<4 ; col++)
|
|
temp[col] = cosine*mat[1][col] + sine*mat[2][col];
|
|
for(col=0 ; col<4 ; col++) {
|
|
mat[2][col] = - sine*mat[1][col] + cosine*mat[2][col];
|
|
mat[1][col] = temp[col];
|
|
}
|
|
break;
|
|
|
|
case 'Y':
|
|
for(col=0 ; col<4 ; col++)
|
|
temp[col] = cosine*mat[0][col] - sine*mat[2][col];
|
|
for(col=0 ; col<4 ; col++) {
|
|
mat[2][col] = sine*mat[0][col] + cosine*mat[2][col];
|
|
mat[0][col] = temp[col];
|
|
}
|
|
break;
|
|
|
|
case 'Z':
|
|
for(col=0 ; col<4 ; col++)
|
|
temp[col] = cosine*mat[0][col] + sine*mat[1][col];
|
|
for(col=0 ; col<4 ; col++) {
|
|
mat[1][col] = - sine*mat[0][col] + cosine*mat[1][col];
|
|
mat[0][col] = temp[col];
|
|
}
|
|
break;
|
|
}
|
|
}
|
|
|
|
void blend_m3_m3m3(float out[][3], float dst[][3], float src[][3], const float srcweight)
|
|
{
|
|
float srot[3][3], drot[3][3];
|
|
float squat[4], dquat[4], fquat[4];
|
|
float ssize[3], dsize[3], fsize[3];
|
|
float rmat[3][3], smat[3][3];
|
|
|
|
mat3_to_rot_size(drot, dsize, dst);
|
|
mat3_to_rot_size(srot, ssize, src);
|
|
|
|
mat3_to_quat(dquat, drot);
|
|
mat3_to_quat(squat, srot);
|
|
|
|
/* do blending */
|
|
interp_qt_qtqt(fquat, dquat, squat, srcweight);
|
|
interp_v3_v3v3(fsize, dsize, ssize, srcweight);
|
|
|
|
/* compose new matrix */
|
|
quat_to_mat3(rmat,fquat);
|
|
size_to_mat3(smat,fsize);
|
|
mul_m3_m3m3(out, rmat, smat);
|
|
}
|
|
|
|
void blend_m4_m4m4(float out[][4], float dst[][4], float src[][4], const float srcweight)
|
|
{
|
|
float sloc[3], dloc[3], floc[3];
|
|
float srot[3][3], drot[3][3];
|
|
float squat[4], dquat[4], fquat[4];
|
|
float ssize[3], dsize[3], fsize[3];
|
|
|
|
mat4_to_loc_rot_size(dloc, drot, dsize, dst);
|
|
mat4_to_loc_rot_size(sloc, srot, ssize, src);
|
|
|
|
mat3_to_quat(dquat, drot);
|
|
mat3_to_quat(squat, srot);
|
|
|
|
/* do blending */
|
|
interp_v3_v3v3(floc, dloc, sloc, srcweight);
|
|
interp_qt_qtqt(fquat, dquat, squat, srcweight);
|
|
interp_v3_v3v3(fsize, dsize, ssize, srcweight);
|
|
|
|
/* compose new matrix */
|
|
loc_quat_size_to_mat4(out, floc, fquat, fsize);
|
|
}
|
|
|
|
|
|
int is_negative_m3(float mat[][3])
|
|
{
|
|
float vec[3];
|
|
cross_v3_v3v3(vec, mat[0], mat[1]);
|
|
return (dot_v3v3(vec, mat[2]) < 0.0f);
|
|
}
|
|
|
|
int is_negative_m4(float mat[][4])
|
|
{
|
|
float vec[3];
|
|
cross_v3_v3v3(vec, mat[0], mat[1]);
|
|
return (dot_v3v3(vec, mat[2]) < 0.0f);
|
|
}
|
|
|
|
/* make a 4x4 matrix out of 3 transform components */
|
|
/* matrices are made in the order: scale * rot * loc */
|
|
// TODO: need to have a version that allows for rotation order...
|
|
void loc_eul_size_to_mat4(float mat[4][4], const float loc[3], const float eul[3], const float size[3])
|
|
{
|
|
float rmat[3][3], smat[3][3], tmat[3][3];
|
|
|
|
/* initialise new matrix */
|
|
unit_m4(mat);
|
|
|
|
/* make rotation + scaling part */
|
|
eul_to_mat3(rmat,eul);
|
|
size_to_mat3(smat,size);
|
|
mul_m3_m3m3(tmat, rmat, smat);
|
|
|
|
/* copy rot/scale part to output matrix*/
|
|
copy_m4_m3(mat, tmat);
|
|
|
|
/* copy location to matrix */
|
|
mat[3][0] = loc[0];
|
|
mat[3][1] = loc[1];
|
|
mat[3][2] = loc[2];
|
|
}
|
|
|
|
/* make a 4x4 matrix out of 3 transform components */
|
|
/* matrices are made in the order: scale * rot * loc */
|
|
void loc_eulO_size_to_mat4(float mat[4][4], const float loc[3], const float eul[3], const float size[3], const short rotOrder)
|
|
{
|
|
float rmat[3][3], smat[3][3], tmat[3][3];
|
|
|
|
/* initialise new matrix */
|
|
unit_m4(mat);
|
|
|
|
/* make rotation + scaling part */
|
|
eulO_to_mat3(rmat,eul, rotOrder);
|
|
size_to_mat3(smat,size);
|
|
mul_m3_m3m3(tmat, rmat, smat);
|
|
|
|
/* copy rot/scale part to output matrix*/
|
|
copy_m4_m3(mat, tmat);
|
|
|
|
/* copy location to matrix */
|
|
mat[3][0] = loc[0];
|
|
mat[3][1] = loc[1];
|
|
mat[3][2] = loc[2];
|
|
}
|
|
|
|
|
|
/* make a 4x4 matrix out of 3 transform components */
|
|
/* matrices are made in the order: scale * rot * loc */
|
|
void loc_quat_size_to_mat4(float mat[4][4], const float loc[3], const float quat[4], const float size[3])
|
|
{
|
|
float rmat[3][3], smat[3][3], tmat[3][3];
|
|
|
|
/* initialise new matrix */
|
|
unit_m4(mat);
|
|
|
|
/* make rotation + scaling part */
|
|
quat_to_mat3(rmat,quat);
|
|
size_to_mat3(smat,size);
|
|
mul_m3_m3m3(tmat, rmat, smat);
|
|
|
|
/* copy rot/scale part to output matrix*/
|
|
copy_m4_m3(mat, tmat);
|
|
|
|
/* copy location to matrix */
|
|
mat[3][0] = loc[0];
|
|
mat[3][1] = loc[1];
|
|
mat[3][2] = loc[2];
|
|
}
|
|
|
|
void loc_axisangle_size_to_mat4(float mat[4][4], const float loc[3], const float axis[3], const float angle, const float size[3])
|
|
{
|
|
float q[4];
|
|
axis_angle_to_quat(q, axis, angle);
|
|
loc_quat_size_to_mat4(mat, loc, q, size);
|
|
}
|
|
|
|
/*********************************** Other ***********************************/
|
|
|
|
void print_m3(const char *str, float m[][3])
|
|
{
|
|
printf("%s\n", str);
|
|
printf("%f %f %f\n",m[0][0],m[1][0],m[2][0]);
|
|
printf("%f %f %f\n",m[0][1],m[1][1],m[2][1]);
|
|
printf("%f %f %f\n",m[0][2],m[1][2],m[2][2]);
|
|
printf("\n");
|
|
}
|
|
|
|
void print_m4(const char *str, float m[][4])
|
|
{
|
|
printf("%s\n", str);
|
|
printf("%f %f %f %f\n",m[0][0],m[1][0],m[2][0],m[3][0]);
|
|
printf("%f %f %f %f\n",m[0][1],m[1][1],m[2][1],m[3][1]);
|
|
printf("%f %f %f %f\n",m[0][2],m[1][2],m[2][2],m[3][2]);
|
|
printf("%f %f %f %f\n",m[0][3],m[1][3],m[2][3],m[3][3]);
|
|
printf("\n");
|
|
}
|
|
|
|
/*********************************** SVD ************************************
|
|
* from TNT matrix library
|
|
|
|
* Compute the Single Value Decomposition of an arbitrary matrix A
|
|
* That is compute the 3 matrices U,W,V with U column orthogonal (m,n)
|
|
* ,W a diagonal matrix and V an orthogonal square matrix s.t.
|
|
* A = U.W.Vt. From this decomposition it is trivial to compute the
|
|
* (pseudo-inverse) of A as Ainv = V.Winv.tranpose(U).
|
|
*/
|
|
|
|
void svd_m4(float U[4][4], float s[4], float V[4][4], float A_[4][4])
|
|
{
|
|
float A[4][4];
|
|
float work1[4], work2[4];
|
|
int m = 4;
|
|
int n = 4;
|
|
int maxiter = 200;
|
|
int nu = minf(m,n);
|
|
|
|
float *work = work1;
|
|
float *e = work2;
|
|
float eps;
|
|
|
|
int i=0, j=0, k=0, p, pp, iter;
|
|
|
|
// Reduce A to bidiagonal form, storing the diagonal elements
|
|
// in s and the super-diagonal elements in e.
|
|
|
|
int nct = minf(m-1,n);
|
|
int nrt = maxf(0,minf(n-2,m));
|
|
|
|
copy_m4_m4(A, A_);
|
|
zero_m4(U);
|
|
zero_v4(s);
|
|
|
|
for (k = 0; k < maxf(nct,nrt); k++) {
|
|
if (k < nct) {
|
|
|
|
// Compute the transformation for the k-th column and
|
|
// place the k-th diagonal in s[k].
|
|
// Compute 2-norm of k-th column without under/overflow.
|
|
s[k] = 0;
|
|
for (i = k; i < m; i++) {
|
|
s[k] = hypotf(s[k],A[i][k]);
|
|
}
|
|
if (s[k] != 0.0f) {
|
|
float invsk;
|
|
if (A[k][k] < 0.0f) {
|
|
s[k] = -s[k];
|
|
}
|
|
invsk = 1.0f/s[k];
|
|
for (i = k; i < m; i++) {
|
|
A[i][k] *= invsk;
|
|
}
|
|
A[k][k] += 1.0f;
|
|
}
|
|
s[k] = -s[k];
|
|
}
|
|
for (j = k+1; j < n; j++) {
|
|
if ((k < nct) && (s[k] != 0.0f)) {
|
|
|
|
// Apply the transformation.
|
|
|
|
float t = 0;
|
|
for (i = k; i < m; i++) {
|
|
t += A[i][k]*A[i][j];
|
|
}
|
|
t = -t/A[k][k];
|
|
for (i = k; i < m; i++) {
|
|
A[i][j] += t*A[i][k];
|
|
}
|
|
}
|
|
|
|
// Place the k-th row of A into e for the
|
|
// subsequent calculation of the row transformation.
|
|
|
|
e[j] = A[k][j];
|
|
}
|
|
if (k < nct) {
|
|
|
|
// Place the transformation in U for subsequent back
|
|
// multiplication.
|
|
|
|
for (i = k; i < m; i++)
|
|
U[i][k] = A[i][k];
|
|
}
|
|
if (k < nrt) {
|
|
|
|
// Compute the k-th row transformation and place the
|
|
// k-th super-diagonal in e[k].
|
|
// Compute 2-norm without under/overflow.
|
|
e[k] = 0;
|
|
for (i = k+1; i < n; i++) {
|
|
e[k] = hypotf(e[k],e[i]);
|
|
}
|
|
if (e[k] != 0.0f) {
|
|
float invek;
|
|
if (e[k+1] < 0.0f) {
|
|
e[k] = -e[k];
|
|
}
|
|
invek = 1.0f/e[k];
|
|
for (i = k+1; i < n; i++) {
|
|
e[i] *= invek;
|
|
}
|
|
e[k+1] += 1.0f;
|
|
}
|
|
e[k] = -e[k];
|
|
if ((k+1 < m) & (e[k] != 0.0f)) {
|
|
float invek1;
|
|
|
|
// Apply the transformation.
|
|
|
|
for (i = k+1; i < m; i++) {
|
|
work[i] = 0.0f;
|
|
}
|
|
for (j = k+1; j < n; j++) {
|
|
for (i = k+1; i < m; i++) {
|
|
work[i] += e[j]*A[i][j];
|
|
}
|
|
}
|
|
invek1 = 1.0f/e[k+1];
|
|
for (j = k+1; j < n; j++) {
|
|
float t = -e[j]*invek1;
|
|
for (i = k+1; i < m; i++) {
|
|
A[i][j] += t*work[i];
|
|
}
|
|
}
|
|
}
|
|
|
|
// Place the transformation in V for subsequent
|
|
// back multiplication.
|
|
|
|
for (i = k+1; i < n; i++)
|
|
V[i][k] = e[i];
|
|
}
|
|
}
|
|
|
|
// Set up the final bidiagonal matrix or order p.
|
|
|
|
p = minf(n,m+1);
|
|
if (nct < n) {
|
|
s[nct] = A[nct][nct];
|
|
}
|
|
if (m < p) {
|
|
s[p-1] = 0.0f;
|
|
}
|
|
if (nrt+1 < p) {
|
|
e[nrt] = A[nrt][p-1];
|
|
}
|
|
e[p-1] = 0.0f;
|
|
|
|
// If required, generate U.
|
|
|
|
for (j = nct; j < nu; j++) {
|
|
for (i = 0; i < m; i++) {
|
|
U[i][j] = 0.0f;
|
|
}
|
|
U[j][j] = 1.0f;
|
|
}
|
|
for (k = nct-1; k >= 0; k--) {
|
|
if (s[k] != 0.0f) {
|
|
for (j = k+1; j < nu; j++) {
|
|
float t = 0;
|
|
for (i = k; i < m; i++) {
|
|
t += U[i][k]*U[i][j];
|
|
}
|
|
t = -t/U[k][k];
|
|
for (i = k; i < m; i++) {
|
|
U[i][j] += t*U[i][k];
|
|
}
|
|
}
|
|
for (i = k; i < m; i++ ) {
|
|
U[i][k] = -U[i][k];
|
|
}
|
|
U[k][k] = 1.0f + U[k][k];
|
|
for (i = 0; i < k-1; i++) {
|
|
U[i][k] = 0.0f;
|
|
}
|
|
} else {
|
|
for (i = 0; i < m; i++) {
|
|
U[i][k] = 0.0f;
|
|
}
|
|
U[k][k] = 1.0f;
|
|
}
|
|
}
|
|
|
|
// If required, generate V.
|
|
|
|
for (k = n-1; k >= 0; k--) {
|
|
if ((k < nrt) & (e[k] != 0.0f)) {
|
|
for (j = k+1; j < nu; j++) {
|
|
float t = 0;
|
|
for (i = k+1; i < n; i++) {
|
|
t += V[i][k]*V[i][j];
|
|
}
|
|
t = -t/V[k+1][k];
|
|
for (i = k+1; i < n; i++) {
|
|
V[i][j] += t*V[i][k];
|
|
}
|
|
}
|
|
}
|
|
for (i = 0; i < n; i++) {
|
|
V[i][k] = 0.0f;
|
|
}
|
|
V[k][k] = 1.0f;
|
|
}
|
|
|
|
// Main iteration loop for the singular values.
|
|
|
|
pp = p-1;
|
|
iter = 0;
|
|
eps = powf(2.0f,-52.0f);
|
|
while (p > 0) {
|
|
int kase=0;
|
|
|
|
// Test for maximum iterations to avoid infinite loop
|
|
if(maxiter == 0)
|
|
break;
|
|
maxiter--;
|
|
|
|
// This section of the program inspects for
|
|
// negligible elements in the s and e arrays. On
|
|
// completion the variables kase and k are set as follows.
|
|
|
|
// kase = 1 if s(p) and e[k-1] are negligible and k<p
|
|
// kase = 2 if s(k) is negligible and k<p
|
|
// kase = 3 if e[k-1] is negligible, k<p, and
|
|
// s(k), ..., s(p) are not negligible (qr step).
|
|
// kase = 4 if e(p-1) is negligible (convergence).
|
|
|
|
for (k = p-2; k >= -1; k--) {
|
|
if (k == -1) {
|
|
break;
|
|
}
|
|
if (fabsf(e[k]) <= eps*(fabsf(s[k]) + fabsf(s[k+1]))) {
|
|
e[k] = 0.0f;
|
|
break;
|
|
}
|
|
}
|
|
if (k == p-2) {
|
|
kase = 4;
|
|
} else {
|
|
int ks;
|
|
for (ks = p-1; ks >= k; ks--) {
|
|
float t;
|
|
if (ks == k) {
|
|
break;
|
|
}
|
|
t = (ks != p ? fabsf(e[ks]) : 0.f) +
|
|
(ks != k+1 ? fabsf(e[ks-1]) : 0.0f);
|
|
if (fabsf(s[ks]) <= eps*t) {
|
|
s[ks] = 0.0f;
|
|
break;
|
|
}
|
|
}
|
|
if (ks == k) {
|
|
kase = 3;
|
|
} else if (ks == p-1) {
|
|
kase = 1;
|
|
} else {
|
|
kase = 2;
|
|
k = ks;
|
|
}
|
|
}
|
|
k++;
|
|
|
|
// Perform the task indicated by kase.
|
|
|
|
switch (kase) {
|
|
|
|
// Deflate negligible s(p).
|
|
|
|
case 1: {
|
|
float f = e[p-2];
|
|
e[p-2] = 0.0f;
|
|
for (j = p-2; j >= k; j--) {
|
|
float t = hypotf(s[j],f);
|
|
float invt = 1.0f/t;
|
|
float cs = s[j]*invt;
|
|
float sn = f*invt;
|
|
s[j] = t;
|
|
if (j != k) {
|
|
f = -sn*e[j-1];
|
|
e[j-1] = cs*e[j-1];
|
|
}
|
|
|
|
for (i = 0; i < n; i++) {
|
|
t = cs*V[i][j] + sn*V[i][p-1];
|
|
V[i][p-1] = -sn*V[i][j] + cs*V[i][p-1];
|
|
V[i][j] = t;
|
|
}
|
|
}
|
|
}
|
|
break;
|
|
|
|
// Split at negligible s(k).
|
|
|
|
case 2: {
|
|
float f = e[k-1];
|
|
e[k-1] = 0.0f;
|
|
for (j = k; j < p; j++) {
|
|
float t = hypotf(s[j],f);
|
|
float invt = 1.0f/t;
|
|
float cs = s[j]*invt;
|
|
float sn = f*invt;
|
|
s[j] = t;
|
|
f = -sn*e[j];
|
|
e[j] = cs*e[j];
|
|
|
|
for (i = 0; i < m; i++) {
|
|
t = cs*U[i][j] + sn*U[i][k-1];
|
|
U[i][k-1] = -sn*U[i][j] + cs*U[i][k-1];
|
|
U[i][j] = t;
|
|
}
|
|
}
|
|
}
|
|
break;
|
|
|
|
// Perform one qr step.
|
|
|
|
case 3: {
|
|
|
|
// Calculate the shift.
|
|
|
|
float scale = maxf(maxf(maxf(maxf(
|
|
fabsf(s[p-1]),fabsf(s[p-2])),fabsf(e[p-2])),
|
|
fabsf(s[k])),fabsf(e[k]));
|
|
float invscale = 1.0f/scale;
|
|
float sp = s[p-1]*invscale;
|
|
float spm1 = s[p-2]*invscale;
|
|
float epm1 = e[p-2]*invscale;
|
|
float sk = s[k]*invscale;
|
|
float ek = e[k]*invscale;
|
|
float b = ((spm1 + sp)*(spm1 - sp) + epm1*epm1)*0.5f;
|
|
float c = (sp*epm1)*(sp*epm1);
|
|
float shift = 0.0f;
|
|
float f, g;
|
|
if ((b != 0.0f) || (c != 0.0f)) {
|
|
shift = sqrtf(b*b + c);
|
|
if (b < 0.0f) {
|
|
shift = -shift;
|
|
}
|
|
shift = c/(b + shift);
|
|
}
|
|
f = (sk + sp)*(sk - sp) + shift;
|
|
g = sk*ek;
|
|
|
|
// Chase zeros.
|
|
|
|
for (j = k; j < p-1; j++) {
|
|
float t = hypotf(f,g);
|
|
/* division by zero checks added to avoid NaN (brecht) */
|
|
float cs = (t == 0.0f)? 0.0f: f/t;
|
|
float sn = (t == 0.0f)? 0.0f: g/t;
|
|
if (j != k) {
|
|
e[j-1] = t;
|
|
}
|
|
f = cs*s[j] + sn*e[j];
|
|
e[j] = cs*e[j] - sn*s[j];
|
|
g = sn*s[j+1];
|
|
s[j+1] = cs*s[j+1];
|
|
|
|
for (i = 0; i < n; i++) {
|
|
t = cs*V[i][j] + sn*V[i][j+1];
|
|
V[i][j+1] = -sn*V[i][j] + cs*V[i][j+1];
|
|
V[i][j] = t;
|
|
}
|
|
|
|
t = hypotf(f,g);
|
|
/* division by zero checks added to avoid NaN (brecht) */
|
|
cs = (t == 0.0f)? 0.0f: f/t;
|
|
sn = (t == 0.0f)? 0.0f: g/t;
|
|
s[j] = t;
|
|
f = cs*e[j] + sn*s[j+1];
|
|
s[j+1] = -sn*e[j] + cs*s[j+1];
|
|
g = sn*e[j+1];
|
|
e[j+1] = cs*e[j+1];
|
|
if (j < m-1) {
|
|
for (i = 0; i < m; i++) {
|
|
t = cs*U[i][j] + sn*U[i][j+1];
|
|
U[i][j+1] = -sn*U[i][j] + cs*U[i][j+1];
|
|
U[i][j] = t;
|
|
}
|
|
}
|
|
}
|
|
e[p-2] = f;
|
|
iter = iter + 1;
|
|
}
|
|
break;
|
|
|
|
// Convergence.
|
|
|
|
case 4: {
|
|
|
|
// Make the singular values positive.
|
|
|
|
if (s[k] <= 0.0f) {
|
|
s[k] = (s[k] < 0.0f ? -s[k] : 0.0f);
|
|
|
|
for (i = 0; i <= pp; i++)
|
|
V[i][k] = -V[i][k];
|
|
}
|
|
|
|
// Order the singular values.
|
|
|
|
while (k < pp) {
|
|
float t;
|
|
if (s[k] >= s[k+1]) {
|
|
break;
|
|
}
|
|
t = s[k];
|
|
s[k] = s[k+1];
|
|
s[k+1] = t;
|
|
if (k < n-1) {
|
|
for (i = 0; i < n; i++) {
|
|
t = V[i][k+1]; V[i][k+1] = V[i][k]; V[i][k] = t;
|
|
}
|
|
}
|
|
if (k < m-1) {
|
|
for (i = 0; i < m; i++) {
|
|
t = U[i][k+1]; U[i][k+1] = U[i][k]; U[i][k] = t;
|
|
}
|
|
}
|
|
k++;
|
|
}
|
|
iter = 0;
|
|
p--;
|
|
}
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
|
|
void pseudoinverse_m4_m4(float Ainv[4][4], float A[4][4], float epsilon)
|
|
{
|
|
/* compute moon-penrose pseudo inverse of matrix, singular values
|
|
below epsilon are ignored for stability (truncated SVD) */
|
|
float V[4][4], W[4], Wm[4][4], U[4][4];
|
|
int i;
|
|
|
|
transpose_m4(A);
|
|
svd_m4(V, W, U, A);
|
|
transpose_m4(U);
|
|
transpose_m4(V);
|
|
|
|
zero_m4(Wm);
|
|
for(i=0; i<4; i++)
|
|
Wm[i][i]= (W[i] < epsilon)? 0.0f: 1.0f/W[i];
|
|
|
|
transpose_m4(V);
|
|
|
|
mul_serie_m4(Ainv, U, Wm, V, NULL, NULL, NULL, NULL, NULL);
|
|
}
|