724 lines
19 KiB
C
724 lines
19 KiB
C
/*
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matrixlib.c - internal matrixlib
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Copyright (C) 2010 Uncle Mike
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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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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#include "port.h"
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#include "xash3d_types.h"
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#include "const.h"
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#include "com_model.h"
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#include "xash3d_mathlib.h"
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const matrix3x4 m_matrix3x4_identity =
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{
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{ 1, 0, 0, 0 }, // PITCH [forward], org[0]
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{ 0, 1, 0, 0 }, // YAW [right] , org[1]
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{ 0, 0, 1, 0 }, // ROLL [up] , org[2]
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};
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/*
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========================================================================
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Matrix3x4 operations
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========================================================================
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*/
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void Matrix3x4_VectorTransform( const matrix3x4 in, const float v[3], float out[3] )
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{
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out[0] = v[0] * in[0][0] + v[1] * in[0][1] + v[2] * in[0][2] + in[0][3];
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out[1] = v[0] * in[1][0] + v[1] * in[1][1] + v[2] * in[1][2] + in[1][3];
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out[2] = v[0] * in[2][0] + v[1] * in[2][1] + v[2] * in[2][2] + in[2][3];
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}
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void Matrix3x4_VectorITransform( const matrix3x4 in, const float v[3], float out[3] )
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{
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vec3_t dir;
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dir[0] = v[0] - in[0][3];
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dir[1] = v[1] - in[1][3];
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dir[2] = v[2] - in[2][3];
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out[0] = dir[0] * in[0][0] + dir[1] * in[1][0] + dir[2] * in[2][0];
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out[1] = dir[0] * in[0][1] + dir[1] * in[1][1] + dir[2] * in[2][1];
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out[2] = dir[0] * in[0][2] + dir[1] * in[1][2] + dir[2] * in[2][2];
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}
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void Matrix3x4_VectorRotate( const matrix3x4 in, const float v[3], float out[3] )
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{
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out[0] = v[0] * in[0][0] + v[1] * in[0][1] + v[2] * in[0][2];
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out[1] = v[0] * in[1][0] + v[1] * in[1][1] + v[2] * in[1][2];
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out[2] = v[0] * in[2][0] + v[1] * in[2][1] + v[2] * in[2][2];
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}
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void Matrix3x4_VectorIRotate( const matrix3x4 in, const float v[3], float out[3] )
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{
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out[0] = v[0] * in[0][0] + v[1] * in[1][0] + v[2] * in[2][0];
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out[1] = v[0] * in[0][1] + v[1] * in[1][1] + v[2] * in[2][1];
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out[2] = v[0] * in[0][2] + v[1] * in[1][2] + v[2] * in[2][2];
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}
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void Matrix3x4_ConcatTransforms( matrix3x4 out, const matrix3x4 in1, const matrix3x4 in2 )
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{
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out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] + in1[0][2] * in2[2][0];
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out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] + in1[0][2] * in2[2][1];
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out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] + in1[0][2] * in2[2][2];
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out[0][3] = in1[0][0] * in2[0][3] + in1[0][1] * in2[1][3] + in1[0][2] * in2[2][3] + in1[0][3];
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out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] + in1[1][2] * in2[2][0];
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out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] + in1[1][2] * in2[2][1];
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out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] + in1[1][2] * in2[2][2];
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out[1][3] = in1[1][0] * in2[0][3] + in1[1][1] * in2[1][3] + in1[1][2] * in2[2][3] + in1[1][3];
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out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] + in1[2][2] * in2[2][0];
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out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] + in1[2][2] * in2[2][1];
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out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] + in1[2][2] * in2[2][2];
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out[2][3] = in1[2][0] * in2[0][3] + in1[2][1] * in2[1][3] + in1[2][2] * in2[2][3] + in1[2][3];
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}
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void Matrix3x4_AnglesFromMatrix( const matrix3x4 in, vec3_t out )
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{
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float xyDist = sqrt( in[0][0] * in[0][0] + in[1][0] * in[1][0] );
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if( xyDist > 0.001f )
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{
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// enough here to get angles?
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out[0] = RAD2DEG( atan2( -in[2][0], xyDist ));
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out[1] = RAD2DEG( atan2( in[1][0], in[0][0] ));
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out[2] = RAD2DEG( atan2( in[2][1], in[2][2] ));
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}
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else
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{
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// forward is mostly Z, gimbal lock
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out[0] = RAD2DEG( atan2( -in[2][0], xyDist ));
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out[1] = RAD2DEG( atan2( -in[0][1], in[1][1] ));
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out[2] = 0.0f;
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}
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}
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void Matrix3x4_FromOriginQuat( matrix3x4 out, const vec4_t quaternion, const vec3_t origin )
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{
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out[0][0] = 1.0f - 2.0f * quaternion[1] * quaternion[1] - 2.0f * quaternion[2] * quaternion[2];
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out[1][0] = 2.0f * quaternion[0] * quaternion[1] + 2.0f * quaternion[3] * quaternion[2];
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out[2][0] = 2.0f * quaternion[0] * quaternion[2] - 2.0f * quaternion[3] * quaternion[1];
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out[0][1] = 2.0f * quaternion[0] * quaternion[1] - 2.0f * quaternion[3] * quaternion[2];
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out[1][1] = 1.0f - 2.0f * quaternion[0] * quaternion[0] - 2.0f * quaternion[2] * quaternion[2];
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out[2][1] = 2.0f * quaternion[1] * quaternion[2] + 2.0f * quaternion[3] * quaternion[0];
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out[0][2] = 2.0f * quaternion[0] * quaternion[2] + 2.0f * quaternion[3] * quaternion[1];
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out[1][2] = 2.0f * quaternion[1] * quaternion[2] - 2.0f * quaternion[3] * quaternion[0];
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out[2][2] = 1.0f - 2.0f * quaternion[0] * quaternion[0] - 2.0f * quaternion[1] * quaternion[1];
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out[0][3] = origin[0];
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out[1][3] = origin[1];
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out[2][3] = origin[2];
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}
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void Matrix3x4_CreateFromEntity( matrix3x4 out, const vec3_t angles, const vec3_t origin, float scale )
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{
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float angle, sr, sp, sy, cr, cp, cy;
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if( angles[ROLL] )
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{
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angle = angles[YAW] * (M_PI2 / 360.0f);
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SinCos( angle, &sy, &cy );
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angle = angles[PITCH] * (M_PI2 / 360.0f);
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SinCos( angle, &sp, &cp );
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angle = angles[ROLL] * (M_PI2 / 360.0f);
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SinCos( angle, &sr, &cr );
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out[0][0] = (cp*cy) * scale;
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out[0][1] = (sr*sp*cy+cr*-sy) * scale;
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out[0][2] = (cr*sp*cy+-sr*-sy) * scale;
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out[0][3] = origin[0];
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out[1][0] = (cp*sy) * scale;
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out[1][1] = (sr*sp*sy+cr*cy) * scale;
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out[1][2] = (cr*sp*sy+-sr*cy) * scale;
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out[1][3] = origin[1];
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out[2][0] = (-sp) * scale;
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out[2][1] = (sr*cp) * scale;
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out[2][2] = (cr*cp) * scale;
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out[2][3] = origin[2];
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}
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else if( angles[PITCH] )
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{
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angle = angles[YAW] * (M_PI2 / 360.0f);
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SinCos( angle, &sy, &cy );
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angle = angles[PITCH] * (M_PI2 / 360.0f);
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SinCos( angle, &sp, &cp );
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out[0][0] = (cp*cy) * scale;
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out[0][1] = (-sy) * scale;
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out[0][2] = (sp*cy) * scale;
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out[0][3] = origin[0];
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out[1][0] = (cp*sy) * scale;
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out[1][1] = (cy) * scale;
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out[1][2] = (sp*sy) * scale;
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out[1][3] = origin[1];
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out[2][0] = (-sp) * scale;
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out[2][1] = 0.0f;
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out[2][2] = (cp) * scale;
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out[2][3] = origin[2];
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}
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else if( angles[YAW] )
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{
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angle = angles[YAW] * (M_PI2 / 360.0f);
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SinCos( angle, &sy, &cy );
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out[0][0] = (cy) * scale;
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out[0][1] = (-sy) * scale;
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out[0][2] = 0.0f;
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out[0][3] = origin[0];
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out[1][0] = (sy) * scale;
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out[1][1] = (cy) * scale;
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out[1][2] = 0.0f;
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out[1][3] = origin[1];
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out[2][0] = 0.0f;
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out[2][1] = 0.0f;
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out[2][2] = scale;
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out[2][3] = origin[2];
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}
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else
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{
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out[0][0] = scale;
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out[0][1] = 0.0f;
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out[0][2] = 0.0f;
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out[0][3] = origin[0];
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out[1][0] = 0.0f;
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out[1][1] = scale;
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out[1][2] = 0.0f;
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out[1][3] = origin[1];
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out[2][0] = 0.0f;
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out[2][1] = 0.0f;
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out[2][2] = scale;
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out[2][3] = origin[2];
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}
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}
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/*
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==================
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Matrix3x4_TransformAABB
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==================
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*/
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void Matrix3x4_TransformAABB( const matrix3x4 world, const vec3_t mins, const vec3_t maxs, vec3_t absmin, vec3_t absmax )
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{
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vec3_t localCenter, localExtents;
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vec3_t worldCenter, worldExtents;
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VectorAverage( mins, maxs, localCenter );
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VectorSubtract( maxs, localCenter, localExtents );
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Matrix3x4_VectorTransform( world, localCenter, worldCenter );
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worldExtents[0] = DotProductAbs( localExtents, world[0] ); // auto-transposed!
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worldExtents[1] = DotProductAbs( localExtents, world[1] );
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worldExtents[2] = DotProductAbs( localExtents, world[2] );
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VectorSubtract( worldCenter, worldExtents, absmin );
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VectorAdd( worldCenter, worldExtents, absmax );
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}
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const matrix4x4 m_matrix4x4_identity =
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{
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{ 1, 0, 0, 0 }, // PITCH
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{ 0, 1, 0, 0 }, // YAW
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{ 0, 0, 1, 0 }, // ROLL
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{ 0, 0, 0, 1 }, // ORIGIN
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};
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/*
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========================================================================
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Matrix4x4 operations
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========================================================================
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*/
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void Matrix4x4_VectorTransform( const matrix4x4 in, const float v[3], float out[3] )
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{
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out[0] = v[0] * in[0][0] + v[1] * in[0][1] + v[2] * in[0][2] + in[0][3];
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out[1] = v[0] * in[1][0] + v[1] * in[1][1] + v[2] * in[1][2] + in[1][3];
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out[2] = v[0] * in[2][0] + v[1] * in[2][1] + v[2] * in[2][2] + in[2][3];
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}
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void Matrix4x4_VectorITransform( const matrix4x4 in, const float v[3], float out[3] )
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{
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vec3_t dir;
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dir[0] = v[0] - in[0][3];
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dir[1] = v[1] - in[1][3];
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dir[2] = v[2] - in[2][3];
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out[0] = dir[0] * in[0][0] + dir[1] * in[1][0] + dir[2] * in[2][0];
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out[1] = dir[0] * in[0][1] + dir[1] * in[1][1] + dir[2] * in[2][1];
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out[2] = dir[0] * in[0][2] + dir[1] * in[1][2] + dir[2] * in[2][2];
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}
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void Matrix4x4_VectorRotate( const matrix4x4 in, const float v[3], float out[3] )
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{
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out[0] = v[0] * in[0][0] + v[1] * in[0][1] + v[2] * in[0][2];
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out[1] = v[0] * in[1][0] + v[1] * in[1][1] + v[2] * in[1][2];
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out[2] = v[0] * in[2][0] + v[1] * in[2][1] + v[2] * in[2][2];
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}
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void Matrix4x4_VectorIRotate( const matrix4x4 in, const float v[3], float out[3] )
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{
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out[0] = v[0] * in[0][0] + v[1] * in[1][0] + v[2] * in[2][0];
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out[1] = v[0] * in[0][1] + v[1] * in[1][1] + v[2] * in[2][1];
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out[2] = v[0] * in[0][2] + v[1] * in[1][2] + v[2] * in[2][2];
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}
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void Matrix4x4_ConcatTransforms( matrix4x4 out, const matrix4x4 in1, const matrix4x4 in2 )
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{
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out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] + in1[0][2] * in2[2][0];
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out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] + in1[0][2] * in2[2][1];
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out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] + in1[0][2] * in2[2][2];
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out[0][3] = in1[0][0] * in2[0][3] + in1[0][1] * in2[1][3] + in1[0][2] * in2[2][3] + in1[0][3];
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out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] + in1[1][2] * in2[2][0];
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out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] + in1[1][2] * in2[2][1];
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out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] + in1[1][2] * in2[2][2];
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out[1][3] = in1[1][0] * in2[0][3] + in1[1][1] * in2[1][3] + in1[1][2] * in2[2][3] + in1[1][3];
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out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] + in1[2][2] * in2[2][0];
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out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] + in1[2][2] * in2[2][1];
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out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] + in1[2][2] * in2[2][2];
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out[2][3] = in1[2][0] * in2[0][3] + in1[2][1] * in2[1][3] + in1[2][2] * in2[2][3] + in1[2][3];
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}
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void Matrix4x4_SetOrigin( matrix4x4 out, float x, float y, float z )
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{
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out[0][3] = x;
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out[1][3] = y;
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out[2][3] = z;
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}
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void Matrix4x4_CreateFromEntity( matrix4x4 out, const vec3_t angles, const vec3_t origin, float scale )
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{
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float angle, sr, sp, sy, cr, cp, cy;
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if( angles[ROLL] )
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{
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angle = angles[YAW] * (M_PI2 / 360.0f);
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SinCos( angle, &sy, &cy );
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angle = angles[PITCH] * (M_PI2 / 360.0f);
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SinCos( angle, &sp, &cp );
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angle = angles[ROLL] * (M_PI2 / 360.0f);
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SinCos( angle, &sr, &cr );
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out[0][0] = (cp*cy) * scale;
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out[0][1] = (sr*sp*cy+cr*-sy) * scale;
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out[0][2] = (cr*sp*cy+-sr*-sy) * scale;
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out[0][3] = origin[0];
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out[1][0] = (cp*sy) * scale;
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out[1][1] = (sr*sp*sy+cr*cy) * scale;
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out[1][2] = (cr*sp*sy+-sr*cy) * scale;
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out[1][3] = origin[1];
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out[2][0] = (-sp) * scale;
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out[2][1] = (sr*cp) * scale;
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out[2][2] = (cr*cp) * scale;
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out[2][3] = origin[2];
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out[3][0] = 0.0f;
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out[3][1] = 0.0f;
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out[3][2] = 0.0f;
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out[3][3] = 1.0f;
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}
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else if( angles[PITCH] )
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{
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angle = angles[YAW] * (M_PI2 / 360.0f);
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SinCos( angle, &sy, &cy );
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angle = angles[PITCH] * (M_PI2 / 360.0f);
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SinCos( angle, &sp, &cp );
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out[0][0] = (cp*cy) * scale;
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out[0][1] = (-sy) * scale;
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out[0][2] = (sp*cy) * scale;
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out[0][3] = origin[0];
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out[1][0] = (cp*sy) * scale;
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out[1][1] = (cy) * scale;
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out[1][2] = (sp*sy) * scale;
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out[1][3] = origin[1];
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|
out[2][0] = (-sp) * scale;
|
|
out[2][1] = 0.0f;
|
|
out[2][2] = (cp) * scale;
|
|
out[2][3] = origin[2];
|
|
out[3][0] = 0.0f;
|
|
out[3][1] = 0.0f;
|
|
out[3][2] = 0.0f;
|
|
out[3][3] = 1.0f;
|
|
}
|
|
else if( angles[YAW] )
|
|
{
|
|
angle = angles[YAW] * (M_PI2 / 360.0f);
|
|
SinCos( angle, &sy, &cy );
|
|
|
|
out[0][0] = (cy) * scale;
|
|
out[0][1] = (-sy) * scale;
|
|
out[0][2] = 0.0f;
|
|
out[0][3] = origin[0];
|
|
out[1][0] = (sy) * scale;
|
|
out[1][1] = (cy) * scale;
|
|
out[1][2] = 0.0f;
|
|
out[1][3] = origin[1];
|
|
out[2][0] = 0.0f;
|
|
out[2][1] = 0.0f;
|
|
out[2][2] = scale;
|
|
out[2][3] = origin[2];
|
|
out[3][0] = 0.0f;
|
|
out[3][1] = 0.0f;
|
|
out[3][2] = 0.0f;
|
|
out[3][3] = 1.0f;
|
|
}
|
|
else
|
|
{
|
|
out[0][0] = scale;
|
|
out[0][1] = 0.0f;
|
|
out[0][2] = 0.0f;
|
|
out[0][3] = origin[0];
|
|
out[1][0] = 0.0f;
|
|
out[1][1] = scale;
|
|
out[1][2] = 0.0f;
|
|
out[1][3] = origin[1];
|
|
out[2][0] = 0.0f;
|
|
out[2][1] = 0.0f;
|
|
out[2][2] = scale;
|
|
out[2][3] = origin[2];
|
|
out[3][0] = 0.0f;
|
|
out[3][1] = 0.0f;
|
|
out[3][2] = 0.0f;
|
|
out[3][3] = 1.0f;
|
|
}
|
|
}
|
|
|
|
void Matrix4x4_ConvertToEntity( const matrix4x4 in, vec3_t angles, vec3_t origin )
|
|
{
|
|
float xyDist = sqrt( in[0][0] * in[0][0] + in[1][0] * in[1][0] );
|
|
|
|
// enough here to get angles?
|
|
if( xyDist > 0.001f )
|
|
{
|
|
angles[0] = RAD2DEG( atan2( -in[2][0], xyDist ));
|
|
angles[1] = RAD2DEG( atan2( in[1][0], in[0][0] ));
|
|
angles[2] = RAD2DEG( atan2( in[2][1], in[2][2] ));
|
|
}
|
|
else // forward is mostly Z, gimbal lock
|
|
{
|
|
angles[0] = RAD2DEG( atan2( -in[2][0], xyDist ));
|
|
angles[1] = RAD2DEG( atan2( -in[0][1], in[1][1] ));
|
|
angles[2] = 0.0f;
|
|
}
|
|
|
|
origin[0] = in[0][3];
|
|
origin[1] = in[1][3];
|
|
origin[2] = in[2][3];
|
|
}
|
|
|
|
void Matrix4x4_TransformPositivePlane( const matrix4x4 in, const vec3_t normal, float d, vec3_t out, float *dist )
|
|
{
|
|
float scale = sqrt( in[0][0] * in[0][0] + in[0][1] * in[0][1] + in[0][2] * in[0][2] );
|
|
float iscale = 1.0f / scale;
|
|
|
|
out[0] = (normal[0] * in[0][0] + normal[1] * in[0][1] + normal[2] * in[0][2]) * iscale;
|
|
out[1] = (normal[0] * in[1][0] + normal[1] * in[1][1] + normal[2] * in[1][2]) * iscale;
|
|
out[2] = (normal[0] * in[2][0] + normal[1] * in[2][1] + normal[2] * in[2][2]) * iscale;
|
|
*dist = d * scale + ( out[0] * in[0][3] + out[1] * in[1][3] + out[2] * in[2][3] );
|
|
}
|
|
|
|
void Matrix4x4_Invert_Simple( matrix4x4 out, const matrix4x4 in1 )
|
|
{
|
|
// we only support uniform scaling, so assume the first row is enough
|
|
// (note the lack of sqrt here, because we're trying to undo the scaling,
|
|
// this means multiplying by the inverse scale twice - squaring it, which
|
|
// makes the sqrt a waste of time)
|
|
float scale = 1.0f / (in1[0][0] * in1[0][0] + in1[0][1] * in1[0][1] + in1[0][2] * in1[0][2]);
|
|
|
|
// invert the rotation by transposing and multiplying by the squared
|
|
// recipricol of the input matrix scale as described above
|
|
out[0][0] = in1[0][0] * scale;
|
|
out[0][1] = in1[1][0] * scale;
|
|
out[0][2] = in1[2][0] * scale;
|
|
out[1][0] = in1[0][1] * scale;
|
|
out[1][1] = in1[1][1] * scale;
|
|
out[1][2] = in1[2][1] * scale;
|
|
out[2][0] = in1[0][2] * scale;
|
|
out[2][1] = in1[1][2] * scale;
|
|
out[2][2] = in1[2][2] * scale;
|
|
|
|
// invert the translate
|
|
out[0][3] = -(in1[0][3] * out[0][0] + in1[1][3] * out[0][1] + in1[2][3] * out[0][2]);
|
|
out[1][3] = -(in1[0][3] * out[1][0] + in1[1][3] * out[1][1] + in1[2][3] * out[1][2]);
|
|
out[2][3] = -(in1[0][3] * out[2][0] + in1[1][3] * out[2][1] + in1[2][3] * out[2][2]);
|
|
|
|
// don't know if there's anything worth doing here
|
|
out[3][0] = 0.0f;
|
|
out[3][1] = 0.0f;
|
|
out[3][2] = 0.0f;
|
|
out[3][3] = 1.0f;
|
|
}
|
|
|
|
qboolean Matrix4x4_Invert_Full( matrix4x4 out, const matrix4x4 in1 )
|
|
{
|
|
float *temp;
|
|
float *r[4];
|
|
float rtemp[4][8];
|
|
float m[4];
|
|
float s;
|
|
|
|
r[0] = rtemp[0];
|
|
r[1] = rtemp[1];
|
|
r[2] = rtemp[2];
|
|
r[3] = rtemp[3];
|
|
|
|
r[0][0] = in1[0][0];
|
|
r[0][1] = in1[0][1];
|
|
r[0][2] = in1[0][2];
|
|
r[0][3] = in1[0][3];
|
|
r[0][4] = 1.0f;
|
|
r[0][5] = 0.0f;
|
|
r[0][6] = 0.0f;
|
|
r[0][7] = 0.0f;
|
|
|
|
r[1][0] = in1[1][0];
|
|
r[1][1] = in1[1][1];
|
|
r[1][2] = in1[1][2];
|
|
r[1][3] = in1[1][3];
|
|
r[1][5] = 1.0f;
|
|
r[1][4] = 0.0f;
|
|
r[1][6] = 0.0f;
|
|
r[1][7] = 0.0f;
|
|
|
|
r[2][0] = in1[2][0];
|
|
r[2][1] = in1[2][1];
|
|
r[2][2] = in1[2][2];
|
|
r[2][3] = in1[2][3];
|
|
r[2][6] = 1.0f;
|
|
r[2][4] = 0.0f;
|
|
r[2][5] = 0.0f;
|
|
r[2][7] = 0.0f;
|
|
|
|
r[3][0] = in1[3][0];
|
|
r[3][1] = in1[3][1];
|
|
r[3][2] = in1[3][2];
|
|
r[3][3] = in1[3][3];
|
|
r[3][4] = 0.0f;
|
|
r[3][5] = 0.0f;
|
|
r[3][6] = 0.0f;
|
|
r[3][7] = 1.0f;
|
|
|
|
if( fabs( r[3][0] ) > fabs( r[2][0] ))
|
|
{
|
|
temp = r[3];
|
|
r[3] = r[2];
|
|
r[2] = temp;
|
|
}
|
|
|
|
if( fabs( r[2][0] ) > fabs( r[1][0] ))
|
|
{
|
|
temp = r[2];
|
|
r[2] = r[1];
|
|
r[1] = temp;
|
|
}
|
|
|
|
if( fabs( r[1][0] ) > fabs( r[0][0] ))
|
|
{
|
|
temp = r[1];
|
|
r[1] = r[0];
|
|
r[0] = temp;
|
|
}
|
|
|
|
if( r[0][0] )
|
|
{
|
|
m[1] = r[1][0] / r[0][0];
|
|
m[2] = r[2][0] / r[0][0];
|
|
m[3] = r[3][0] / r[0][0];
|
|
|
|
s = r[0][1];
|
|
r[1][1] -= m[1] * s;
|
|
r[2][1] -= m[2] * s;
|
|
r[3][1] -= m[3] * s;
|
|
|
|
s = r[0][2];
|
|
r[1][2] -= m[1] * s;
|
|
r[2][2] -= m[2] * s;
|
|
r[3][2] -= m[3] * s;
|
|
|
|
s = r[0][3];
|
|
r[1][3] -= m[1] * s;
|
|
r[2][3] -= m[2] * s;
|
|
r[3][3] -= m[3] * s;
|
|
|
|
s = r[0][4];
|
|
if( s )
|
|
{
|
|
r[1][4] -= m[1] * s;
|
|
r[2][4] -= m[2] * s;
|
|
r[3][4] -= m[3] * s;
|
|
}
|
|
|
|
s = r[0][5];
|
|
if( s )
|
|
{
|
|
r[1][5] -= m[1] * s;
|
|
r[2][5] -= m[2] * s;
|
|
r[3][5] -= m[3] * s;
|
|
}
|
|
|
|
s = r[0][6];
|
|
if( s )
|
|
{
|
|
r[1][6] -= m[1] * s;
|
|
r[2][6] -= m[2] * s;
|
|
r[3][6] -= m[3] * s;
|
|
}
|
|
|
|
s = r[0][7];
|
|
if( s )
|
|
{
|
|
r[1][7] -= m[1] * s;
|
|
r[2][7] -= m[2] * s;
|
|
r[3][7] -= m[3] * s;
|
|
}
|
|
|
|
if( fabs( r[3][1] ) > fabs( r[2][1] ))
|
|
{
|
|
temp = r[3];
|
|
r[3] = r[2];
|
|
r[2] = temp;
|
|
}
|
|
|
|
if( fabs( r[2][1] ) > fabs( r[1][1] ))
|
|
{
|
|
temp = r[2];
|
|
r[2] = r[1];
|
|
r[1] = temp;
|
|
}
|
|
|
|
if( r[1][1] )
|
|
{
|
|
m[2] = r[2][1] / r[1][1];
|
|
m[3] = r[3][1] / r[1][1];
|
|
r[2][2] -= m[2] * r[1][2];
|
|
r[3][2] -= m[3] * r[1][2];
|
|
r[2][3] -= m[2] * r[1][3];
|
|
r[3][3] -= m[3] * r[1][3];
|
|
|
|
s = r[1][4];
|
|
if( s )
|
|
{
|
|
r[2][4] -= m[2] * s;
|
|
r[3][4] -= m[3] * s;
|
|
}
|
|
|
|
s = r[1][5];
|
|
if( s )
|
|
{
|
|
r[2][5] -= m[2] * s;
|
|
r[3][5] -= m[3] * s;
|
|
}
|
|
|
|
s = r[1][6];
|
|
if( s )
|
|
{
|
|
r[2][6] -= m[2] * s;
|
|
r[3][6] -= m[3] * s;
|
|
}
|
|
|
|
s = r[1][7];
|
|
if( s )
|
|
{
|
|
r[2][7] -= m[2] * s;
|
|
r[3][7] -= m[3] * s;
|
|
}
|
|
|
|
if( fabs( r[3][2] ) > fabs( r[2][2] ))
|
|
{
|
|
temp = r[3];
|
|
r[3] = r[2];
|
|
r[2] = temp;
|
|
}
|
|
|
|
if( r[2][2] )
|
|
{
|
|
m[3] = r[3][2] / r[2][2];
|
|
r[3][3] -= m[3] * r[2][3];
|
|
r[3][4] -= m[3] * r[2][4];
|
|
r[3][5] -= m[3] * r[2][5];
|
|
r[3][6] -= m[3] * r[2][6];
|
|
r[3][7] -= m[3] * r[2][7];
|
|
|
|
if( r[3][3] )
|
|
{
|
|
s = 1.0f / r[3][3];
|
|
r[3][4] *= s;
|
|
r[3][5] *= s;
|
|
r[3][6] *= s;
|
|
r[3][7] *= s;
|
|
|
|
m[2] = r[2][3];
|
|
s = 1.0f / r[2][2];
|
|
r[2][4] = s * (r[2][4] - r[3][4] * m[2]);
|
|
r[2][5] = s * (r[2][5] - r[3][5] * m[2]);
|
|
r[2][6] = s * (r[2][6] - r[3][6] * m[2]);
|
|
r[2][7] = s * (r[2][7] - r[3][7] * m[2]);
|
|
|
|
m[1] = r[1][3];
|
|
r[1][4] -= r[3][4] * m[1];
|
|
r[1][5] -= r[3][5] * m[1];
|
|
r[1][6] -= r[3][6] * m[1];
|
|
r[1][7] -= r[3][7] * m[1];
|
|
|
|
m[0] = r[0][3];
|
|
r[0][4] -= r[3][4] * m[0];
|
|
r[0][5] -= r[3][5] * m[0];
|
|
r[0][6] -= r[3][6] * m[0];
|
|
r[0][7] -= r[3][7] * m[0];
|
|
|
|
m[1] = r[1][2];
|
|
s = 1.0f / r[1][1];
|
|
r[1][4] = s * (r[1][4] - r[2][4] * m[1]);
|
|
r[1][5] = s * (r[1][5] - r[2][5] * m[1]);
|
|
r[1][6] = s * (r[1][6] - r[2][6] * m[1]);
|
|
r[1][7] = s * (r[1][7] - r[2][7] * m[1]);
|
|
|
|
m[0] = r[0][2];
|
|
r[0][4] -= r[2][4] * m[0];
|
|
r[0][5] -= r[2][5] * m[0];
|
|
r[0][6] -= r[2][6] * m[0];
|
|
r[0][7] -= r[2][7] * m[0];
|
|
|
|
m[0] = r[0][1];
|
|
s = 1.0f / r[0][0];
|
|
r[0][4] = s * (r[0][4] - r[1][4] * m[0]);
|
|
r[0][5] = s * (r[0][5] - r[1][5] * m[0]);
|
|
r[0][6] = s * (r[0][6] - r[1][6] * m[0]);
|
|
r[0][7] = s * (r[0][7] - r[1][7] * m[0]);
|
|
|
|
out[0][0] = r[0][4];
|
|
out[0][1] = r[0][5];
|
|
out[0][2] = r[0][6];
|
|
out[0][3] = r[0][7];
|
|
out[1][0] = r[1][4];
|
|
out[1][1] = r[1][5];
|
|
out[1][2] = r[1][6];
|
|
out[1][3] = r[1][7];
|
|
out[2][0] = r[2][4];
|
|
out[2][1] = r[2][5];
|
|
out[2][2] = r[2][6];
|
|
out[2][3] = r[2][7];
|
|
out[3][0] = r[3][4];
|
|
out[3][1] = r[3][5];
|
|
out[3][2] = r[3][6];
|
|
out[3][3] = r[3][7];
|
|
|
|
return true;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return false;
|
|
}
|