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xash3d-fwgs/public/matrixlib.c

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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 "port.h"
#include "xash3d_types.h"
#include "const.h"
#include "com_model.h"
#include "mathlib.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_AnglesFromMatrix( const matrix3x4 in, vec3_t out )
{
float xyDist = sqrt( in[0][0] * in[0][0] + in[1][0] * in[1][0] );
if( xyDist > 0.001f )
{
// enough here to get angles?
out[0] = RAD2DEG( atan2( -in[2][0], xyDist ));
out[1] = RAD2DEG( atan2( in[1][0], in[0][0] ));
out[2] = RAD2DEG( atan2( in[2][1], in[2][2] ));
}
else
{
// forward is mostly Z, gimbal lock
out[0] = RAD2DEG( atan2( -in[2][0], xyDist ));
out[1] = RAD2DEG( atan2( -in[0][1], in[1][1] ));
out[2] = 0.0f;
}
}
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_PI2 / 360.0f);
SinCos( angle, &sy, &cy );
angle = angles[PITCH] * (M_PI2 / 360.0f);
SinCos( angle, &sp, &cp );
angle = angles[ROLL] * (M_PI2 / 360.0f);
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_PI2 / 360.0f);
SinCos( angle, &sy, &cy );
angle = angles[PITCH] * (M_PI2 / 360.0f);
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] = 0.0f;
out[2][2] = (cp) * scale;
out[2][3] = origin[2];
}
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];
}
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];
}
}
void Matrix3x4_TransformPositivePlane( const matrix3x4 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 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 = 1.0f / (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]);
}
void Matrix3x4_Transpose( matrix3x4 out, const matrix3x4 in1 )
{
// transpose only rotational component
out[0][0] = in1[0][0];
out[0][1] = in1[1][0];
out[0][2] = in1[2][0];
out[1][0] = in1[0][1];
out[1][1] = in1[1][1];
out[1][2] = in1[2][1];
out[2][0] = in1[0][2];
out[2][1] = in1[1][2];
out[2][2] = in1[2][2];
// copy origin
out[0][3] = in1[0][3];
out[1][3] = in1[1][3];
out[2][3] = in1[2][3];
}
/*
==================
Matrix3x4_TransformAABB
==================
*/
void Matrix3x4_TransformAABB( const matrix3x4 world, const vec3_t mins, const vec3_t maxs, vec3_t absmin, vec3_t absmax )
{
vec3_t localCenter, localExtents;
vec3_t worldCenter, worldExtents;
VectorAverage( mins, maxs, localCenter );
VectorSubtract( maxs, localCenter, localExtents );
Matrix3x4_VectorTransform( world, localCenter, worldCenter );
worldExtents[0] = DotProductAbs( localExtents, world[0] ); // auto-transposed!
worldExtents[1] = DotProductAbs( localExtents, world[1] );
worldExtents[2] = DotProductAbs( localExtents, world[2] );
VectorSubtract( worldCenter, worldExtents, absmin );
VectorAdd( worldCenter, worldExtents, absmax );
}
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] = 0.0f;
out[3][1] = 0.0f;
out[3][2] = 0.0f;
out[3][3] = 1.0f;
}
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_PI2 / 360.0f);
SinCos( angle, &sy, &cy );
angle = angles[PITCH] * (M_PI2 / 360.0f);
SinCos( angle, &sp, &cp );
angle = angles[ROLL] * (M_PI2 / 360.0f);
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] = 0.0f;
out[3][1] = 0.0f;
out[3][2] = 0.0f;
out[3][3] = 1.0f;
}
else if( angles[PITCH] )
{
angle = angles[YAW] * (M_PI2 / 360.0f);
SinCos( angle, &sy, &cy );
angle = angles[PITCH] * (M_PI2 / 360.0f);
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] = 0.0f;
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_TransformStandardPlane( 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;
}
void Matrix4x4_Transpose( matrix4x4 out, const matrix4x4 in1 )
{
out[0][0] = in1[0][0];
out[0][1] = in1[1][0];
out[0][2] = in1[2][0];
out[0][3] = in1[3][0];
out[1][0] = in1[0][1];
out[1][1] = in1[1][1];
out[1][2] = in1[2][1];
out[1][3] = in1[3][1];
out[2][0] = in1[0][2];
out[2][1] = in1[1][2];
out[2][2] = in1[2][2];
out[2][3] = in1[3][2];
out[3][0] = in1[0][3];
out[3][1] = in1[1][3];
out[3][2] = in1[2][3];
out[3][3] = in1[3][3];
}
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;
}
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