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dquakeplus/source/matrixlib.c
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2022-02-08 16:49:56 -05:00

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/*
matrixlib.c - internal matrixlib
Copyright (C) 2010 Uncle Mike
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
*/
#include "quakedef.h"
const matrix3x4 matrix3x4_identity =
{
{ 1, 0, 0, 0 }, // PITCH [forward], org[0]
{ 0, 1, 0, 0 }, // YAW [right] , org[1]
{ 0, 0, 1, 0 }, // ROLL [up] , org[2]
};
/*
========================================================================
Matrix3x4 operations
========================================================================
*/
void Matrix3x4_VectorTransform( const matrix3x4 in, const float v[3], float out[3] )
{
out[0] = v[0] * in[0][0] + v[1] * in[0][1] + v[2] * in[0][2] + in[0][3];
out[1] = v[0] * in[1][0] + v[1] * in[1][1] + v[2] * in[1][2] + in[1][3];
out[2] = v[0] * in[2][0] + v[1] * in[2][1] + v[2] * in[2][2] + in[2][3];
}
void Matrix3x4_VectorITransform( const matrix3x4 in, const float v[3], float out[3] )
{
vec3_t dir;
dir[0] = v[0] - in[0][3];
dir[1] = v[1] - in[1][3];
dir[2] = v[2] - in[2][3];
out[0] = dir[0] * in[0][0] + dir[1] * in[1][0] + dir[2] * in[2][0];
out[1] = dir[0] * in[0][1] + dir[1] * in[1][1] + dir[2] * in[2][1];
out[2] = dir[0] * in[0][2] + dir[1] * in[1][2] + dir[2] * in[2][2];
}
void Matrix3x4_VectorRotate( const matrix3x4 in, const float v[3], float out[3] )
{
out[0] = v[0] * in[0][0] + v[1] * in[0][1] + v[2] * in[0][2];
out[1] = v[0] * in[1][0] + v[1] * in[1][1] + v[2] * in[1][2];
out[2] = v[0] * in[2][0] + v[1] * in[2][1] + v[2] * in[2][2];
}
void Matrix3x4_VectorIRotate( const matrix3x4 in, const float v[3], float out[3] )
{
out[0] = v[0] * in[0][0] + v[1] * in[1][0] + v[2] * in[2][0];
out[1] = v[0] * in[0][1] + v[1] * in[1][1] + v[2] * in[2][1];
out[2] = v[0] * in[0][2] + v[1] * in[1][2] + v[2] * in[2][2];
}
void Matrix3x4_ConcatTransforms( matrix3x4 out, const matrix3x4 in1, const matrix3x4 in2 )
{
out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] + in1[0][2] * in2[2][0];
out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] + in1[0][2] * in2[2][1];
out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] + in1[0][2] * in2[2][2];
out[0][3] = in1[0][0] * in2[0][3] + in1[0][1] * in2[1][3] + in1[0][2] * in2[2][3] + in1[0][3];
out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] + in1[1][2] * in2[2][0];
out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] + in1[1][2] * in2[2][1];
out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] + in1[1][2] * in2[2][2];
out[1][3] = in1[1][0] * in2[0][3] + in1[1][1] * in2[1][3] + in1[1][2] * in2[2][3] + in1[1][3];
out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] + in1[2][2] * in2[2][0];
out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] + in1[2][2] * in2[2][1];
out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] + in1[2][2] * in2[2][2];
out[2][3] = in1[2][0] * in2[0][3] + in1[2][1] * in2[1][3] + in1[2][2] * in2[2][3] + in1[2][3];
}
void Matrix3x4_SetOrigin( matrix3x4 out, float x, float y, float z )
{
out[0][3] = x;
out[1][3] = y;
out[2][3] = z;
}
void Matrix3x4_OriginFromMatrix( const matrix3x4 in, float *out )
{
out[0] = in[0][3];
out[1] = in[1][3];
out[2] = in[2][3];
}
void Matrix3x4_FromOriginQuat( matrix3x4 out, const vec4_t quaternion, const vec3_t origin )
{
out[0][0] = 1.0f - 2.0f * quaternion[1] * quaternion[1] - 2.0f * quaternion[2] * quaternion[2];
out[1][0] = 2.0f * quaternion[0] * quaternion[1] + 2.0f * quaternion[3] * quaternion[2];
out[2][0] = 2.0f * quaternion[0] * quaternion[2] - 2.0f * quaternion[3] * quaternion[1];
out[0][1] = 2.0f * quaternion[0] * quaternion[1] - 2.0f * quaternion[3] * quaternion[2];
out[1][1] = 1.0f - 2.0f * quaternion[0] * quaternion[0] - 2.0f * quaternion[2] * quaternion[2];
out[2][1] = 2.0f * quaternion[1] * quaternion[2] + 2.0f * quaternion[3] * quaternion[0];
out[0][2] = 2.0f * quaternion[0] * quaternion[2] + 2.0f * quaternion[3] * quaternion[1];
out[1][2] = 2.0f * quaternion[1] * quaternion[2] - 2.0f * quaternion[3] * quaternion[0];
out[2][2] = 1.0f - 2.0f * quaternion[0] * quaternion[0] - 2.0f * quaternion[1] * quaternion[1];
out[0][3] = origin[0];
out[1][3] = origin[1];
out[2][3] = origin[2];
}
void Matrix3x4_CreateFromEntity( matrix3x4 out, const vec3_t angles, const vec3_t origin, float scale )
{
float angle, sr, sp, sy, cr, cp, cy;
if( angles[ROLL] )
{
angle = angles[YAW] * (M_PI*2 / 360);
SinCos( angle, &sy, &cy );
angle = angles[PITCH] * (M_PI*2 / 360);
SinCos( angle, &sp, &cp );
angle = angles[ROLL] * (M_PI*2 / 360);
SinCos( angle, &sr, &cr );
out[0][0] = (cp*cy) * scale;
out[0][1] = (sr*sp*cy+cr*-sy) * scale;
out[0][2] = (cr*sp*cy+-sr*-sy) * scale;
out[0][3] = origin[0];
out[1][0] = (cp*sy) * scale;
out[1][1] = (sr*sp*sy+cr*cy) * scale;
out[1][2] = (cr*sp*sy+-sr*cy) * scale;
out[1][3] = origin[1];
out[2][0] = (-sp) * scale;
out[2][1] = (sr*cp) * scale;
out[2][2] = (cr*cp) * scale;
out[2][3] = origin[2];
}
else if( angles[PITCH] )
{
angle = angles[YAW] * (M_PI*2 / 360);
SinCos( angle, &sy, &cy );
angle = angles[PITCH] * (M_PI*2 / 360);
SinCos( angle, &sp, &cp );
out[0][0] = (cp*cy) * scale;
out[0][1] = (-sy) * scale;
out[0][2] = (sp*cy) * scale;
out[0][3] = origin[0];
out[1][0] = (cp*sy) * scale;
out[1][1] = (cy) * scale;
out[1][2] = (sp*sy) * scale;
out[1][3] = origin[1];
out[2][0] = (-sp) * scale;
out[2][1] = 0;
out[2][2] = (cp) * scale;
out[2][3] = origin[2];
}
else if( angles[YAW] )
{
angle = angles[YAW] * (M_PI*2 / 360);
SinCos( angle, &sy, &cy );
out[0][0] = (cy) * scale;
out[0][1] = (-sy) * scale;
out[0][2] = 0;
out[0][3] = origin[0];
out[1][0] = (sy) * scale;
out[1][1] = (cy) * scale;
out[1][2] = 0;
out[1][3] = origin[1];
out[2][0] = 0;
out[2][1] = 0;
out[2][2] = scale;
out[2][3] = origin[2];
}
else
{
out[0][0] = scale;
out[0][1] = 0;
out[0][2] = 0;
out[0][3] = origin[0];
out[1][0] = 0;
out[1][1] = scale;
out[1][2] = 0;
out[1][3] = origin[1];
out[2][0] = 0;
out[2][1] = 0;
out[2][2] = scale;
out[2][3] = origin[2];
}
}
void Matrix3x4_TransformPositivePlane( const matrix3x4 in, const vec3_t normal, float d, vec3_t out, float *dist )
{
#ifdef PSP_VFPU
float scale = vfpu_sqrtf( in[0][0] * in[0][0] + in[0][1] * in[0][1] + in[0][2] * in[0][2] );
#else
float scale = sqrtf( in[0][0] * in[0][0] + in[0][1] * in[0][1] + in[0][2] * in[0][2] );
#endif
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 Matrix3x4_Invert_Simple( matrix3x4 out, const matrix3x4 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 = 1.0 / (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]);
}
const matrix4x4 matrix4x4_identity =
{
{ 1, 0, 0, 0 }, // PITCH
{ 0, 1, 0, 0 }, // YAW
{ 0, 0, 1, 0 }, // ROLL
{ 0, 0, 0, 1 }, // ORIGIN
};
/*
========================================================================
Matrix4x4 operations
========================================================================
*/
void Matrix4x4_VectorTransform( const matrix4x4 in, const float v[3], float out[3] )
{
out[0] = v[0] * in[0][0] + v[1] * in[0][1] + v[2] * in[0][2] + in[0][3];
out[1] = v[0] * in[1][0] + v[1] * in[1][1] + v[2] * in[1][2] + in[1][3];
out[2] = v[0] * in[2][0] + v[1] * in[2][1] + v[2] * in[2][2] + in[2][3];
}
void Matrix4x4_VectorITransform( const matrix4x4 in, const float v[3], float out[3] )
{
vec3_t dir;
dir[0] = v[0] - in[0][3];
dir[1] = v[1] - in[1][3];
dir[2] = v[2] - in[2][3];
out[0] = dir[0] * in[0][0] + dir[1] * in[1][0] + dir[2] * in[2][0];
out[1] = dir[0] * in[0][1] + dir[1] * in[1][1] + dir[2] * in[2][1];
out[2] = dir[0] * in[0][2] + dir[1] * in[1][2] + dir[2] * in[2][2];
}
void Matrix4x4_VectorRotate( const matrix4x4 in, const float v[3], float out[3] )
{
out[0] = v[0] * in[0][0] + v[1] * in[0][1] + v[2] * in[0][2];
out[1] = v[0] * in[1][0] + v[1] * in[1][1] + v[2] * in[1][2];
out[2] = v[0] * in[2][0] + v[1] * in[2][1] + v[2] * in[2][2];
}
void Matrix4x4_VectorIRotate( const matrix4x4 in, const float v[3], float out[3] )
{
out[0] = v[0] * in[0][0] + v[1] * in[1][0] + v[2] * in[2][0];
out[1] = v[0] * in[0][1] + v[1] * in[1][1] + v[2] * in[2][1];
out[2] = v[0] * in[0][2] + v[1] * in[1][2] + v[2] * in[2][2];
}
void Matrix4x4_ConcatTransforms( matrix4x4 out, const matrix4x4 in1, const matrix4x4 in2 )
{
out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] + in1[0][2] * in2[2][0];
out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] + in1[0][2] * in2[2][1];
out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] + in1[0][2] * in2[2][2];
out[0][3] = in1[0][0] * in2[0][3] + in1[0][1] * in2[1][3] + in1[0][2] * in2[2][3] + in1[0][3];
out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] + in1[1][2] * in2[2][0];
out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] + in1[1][2] * in2[2][1];
out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] + in1[1][2] * in2[2][2];
out[1][3] = in1[1][0] * in2[0][3] + in1[1][1] * in2[1][3] + in1[1][2] * in2[2][3] + in1[1][3];
out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] + in1[2][2] * in2[2][0];
out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] + in1[2][2] * in2[2][1];
out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] + in1[2][2] * in2[2][2];
out[2][3] = in1[2][0] * in2[0][3] + in1[2][1] * in2[1][3] + in1[2][2] * in2[2][3] + in1[2][3];
}
void Matrix4x4_SetOrigin( matrix4x4 out, float x, float y, float z )
{
out[0][3] = x;
out[1][3] = y;
out[2][3] = z;
}
void Matrix4x4_OriginFromMatrix( const matrix4x4 in, float *out )
{
out[0] = in[0][3];
out[1] = in[1][3];
out[2] = in[2][3];
}
void Matrix4x4_FromOriginQuat( matrix4x4 out, const vec4_t quaternion, const vec3_t origin )
{
out[0][0] = 1.0f - 2.0f * quaternion[1] * quaternion[1] - 2.0f * quaternion[2] * quaternion[2];
out[1][0] = 2.0f * quaternion[0] * quaternion[1] + 2.0f * quaternion[3] * quaternion[2];
out[2][0] = 2.0f * quaternion[0] * quaternion[2] - 2.0f * quaternion[3] * quaternion[1];
out[0][3] = origin[0];
out[0][1] = 2.0f * quaternion[0] * quaternion[1] - 2.0f * quaternion[3] * quaternion[2];
out[1][1] = 1.0f - 2.0f * quaternion[0] * quaternion[0] - 2.0f * quaternion[2] * quaternion[2];
out[2][1] = 2.0f * quaternion[1] * quaternion[2] + 2.0f * quaternion[3] * quaternion[0];
out[1][3] = origin[1];
out[0][2] = 2.0f * quaternion[0] * quaternion[2] + 2.0f * quaternion[3] * quaternion[1];
out[1][2] = 2.0f * quaternion[1] * quaternion[2] - 2.0f * quaternion[3] * quaternion[0];
out[2][2] = 1.0f - 2.0f * quaternion[0] * quaternion[0] - 2.0f * quaternion[1] * quaternion[1];
out[2][3] = origin[2];
out[3][0] = 0;
out[3][1] = 0;
out[3][2] = 0;
out[3][3] = 1;
}
void Matrix4x4_CreateFromEntity( matrix4x4 out, const vec3_t angles, const vec3_t origin, float scale )
{
float angle, sr, sp, sy, cr, cp, cy;
if( angles[ROLL] )
{
angle = angles[YAW] * (M_PI*2 / 360);
SinCos( angle, &sy, &cy );
angle = angles[PITCH] * (M_PI*2 / 360);
SinCos( angle, &sp, &cp );
angle = angles[ROLL] * (M_PI*2 / 360);
SinCos( angle, &sr, &cr );
out[0][0] = (cp*cy) * scale;
out[0][1] = (sr*sp*cy+cr*-sy) * scale;
out[0][2] = (cr*sp*cy+-sr*-sy) * scale;
out[0][3] = origin[0];
out[1][0] = (cp*sy) * scale;
out[1][1] = (sr*sp*sy+cr*cy) * scale;
out[1][2] = (cr*sp*sy+-sr*cy) * scale;
out[1][3] = origin[1];
out[2][0] = (-sp) * scale;
out[2][1] = (sr*cp) * scale;
out[2][2] = (cr*cp) * scale;
out[2][3] = origin[2];
out[3][0] = 0;
out[3][1] = 0;
out[3][2] = 0;
out[3][3] = 1;
}
else if( angles[PITCH] )
{
angle = angles[YAW] * (M_PI*2 / 360);
SinCos( angle, &sy, &cy );
angle = angles[PITCH] * (M_PI*2 / 360);
SinCos( angle, &sp, &cp );
out[0][0] = (cp*cy) * scale;
out[0][1] = (-sy) * scale;
out[0][2] = (sp*cy) * scale;
out[0][3] = origin[0];
out[1][0] = (cp*sy) * scale;
out[1][1] = (cy) * scale;
out[1][2] = (sp*sy) * scale;
out[1][3] = origin[1];
out[2][0] = (-sp) * scale;
out[2][1] = 0;
out[2][2] = (cp) * scale;
out[2][3] = origin[2];
out[3][0] = 0;
out[3][1] = 0;
out[3][2] = 0;
out[3][3] = 1;
}
else if( angles[YAW] )
{
angle = angles[YAW] * (M_PI*2 / 360);
SinCos( angle, &sy, &cy );
out[0][0] = (cy) * scale;
out[0][1] = (-sy) * scale;
out[0][2] = 0;
out[0][3] = origin[0];
out[1][0] = (sy) * scale;
out[1][1] = (cy) * scale;
out[1][2] = 0;
out[1][3] = origin[1];
out[2][0] = 0;
out[2][1] = 0;
out[2][2] = scale;
out[2][3] = origin[2];
out[3][0] = 0;
out[3][1] = 0;
out[3][2] = 0;
out[3][3] = 1;
}
else
{
out[0][0] = scale;
out[0][1] = 0;
out[0][2] = 0;
out[0][3] = origin[0];
out[1][0] = 0;
out[1][1] = scale;
out[1][2] = 0;
out[1][3] = origin[1];
out[2][0] = 0;
out[2][1] = 0;
out[2][2] = scale;
out[2][3] = origin[2];
out[3][0] = 0;
out[3][1] = 0;
out[3][2] = 0;
out[3][3] = 1;
}
}
void Matrix4x4_ConvertToEntity( const matrix4x4 in, vec3_t angles, vec3_t origin )
{
#ifdef PSP_VFPU
float xyDist = vfpu_sqrtf( in[0][0] * in[0][0] + in[1][0] * in[1][0] );
#else
float xyDist = sqrtf( in[0][0] * in[0][0] + in[1][0] * in[1][0] );
#endif
// enough here to get angles?
if( xyDist > 0.001f )
{
#ifdef PSP_VFPU
angles[0] = RAD2DEG( vfpu_atan2f( -in[2][0], xyDist ) );
angles[1] = RAD2DEG( vfpu_atan2f( in[1][0], in[0][0] ) );
angles[2] = RAD2DEG( vfpu_atan2f( in[2][1], in[2][2] ) );
#else
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] ) );
#endif
}
else // forward is mostly Z, gimbal lock
{
#ifdef PSP_VFPU
angles[0] = RAD2DEG( vfpu_atan2f( -in[2][0], xyDist ) );
angles[1] = RAD2DEG( vfpu_atan2f( -in[0][1], in[1][1] ) );
#else
angles[0] = RAD2DEG( atan2( -in[2][0], xyDist ) );
angles[1] = RAD2DEG( atan2( -in[0][1], in[1][1] ) );
#endif
angles[2] = 0;
}
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 )
{
#ifdef PSP_VFPU
float scale = vfpu_sqrtf( in[0][0] * in[0][0] + in[0][1] * in[0][1] + in[0][2] * in[0][2] );
#else
float scale = sqrtf( in[0][0] * in[0][0] + in[0][1] * in[0][1] + in[0][2] * in[0][2] );
#endif
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_TransformStandardPlane( const matrix4x4 in, const vec3_t normal, float d, vec3_t out, float *dist )
{
#ifdef PSP_VFPU
float scale = vfpu_sqrtf( in[0][0] * in[0][0] + in[0][1] * in[0][1] + in[0][2] * in[0][2] );
#else
float scale = sqrtf( in[0][0] * in[0][0] + in[0][1] * in[0][1] + in[0][2] * in[0][2] );
#endif
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;
out[3][1] = 0;
out[3][2] = 0;
out[3][3] = 1;
}
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