vmap/libs/mathlib/m4x4.c

/*
   Copyright (C) 2001-2006, William Joseph.
   All Rights Reserved.

   This file is part of GtkRadiant.

   GtkRadiant 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 2 of the License, or
   (at your option) any later version.

   GtkRadiant 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.

   You should have received a copy of the GNU General Public License
   along with GtkRadiant; if not, write to the Free Software
   Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
 */

#include "mathlib.h"

const m4x4_t g_m4x4_identity = {
	1, 0, 0, 0,
	0, 1, 0, 0,
	0, 0, 1, 0,
	0, 0, 0, 1,
};

void m4x4_identity( m4x4_t matrix ){
	matrix[1] = matrix[2] = matrix[3] =
		matrix[4] = matrix[6] = matrix[7] =
			matrix[8] = matrix[9] = matrix[11] =
				matrix[12] = matrix[13] = matrix[14] = 0;

	matrix[0] = matrix[5] = matrix[10] = matrix[15] = 1;
}

m4x4Handedness_t m4x4_handedness( const m4x4_t matrix ){
	vec3_t cross;
	CrossProduct( matrix + 0, matrix + 4, cross );
	return ( DotProduct( matrix + 8, cross ) < 0 ) ? eLeftHanded : eRightHanded;
}

void m4x4_assign( m4x4_t matrix, const m4x4_t other ){
	M4X4_COPY( matrix, other );
}

void m4x4_translation_for_vec3( m4x4_t matrix, const vec3_t translation ){
	matrix[1] = matrix[2] = matrix[3] =
		matrix[4] = matrix[6] = matrix[7] =
			matrix[8] = matrix[9] = matrix[11] = 0;

	matrix[0] = matrix[5] = matrix[10] = matrix[15] = 1;

	matrix[12] = translation[0];
	matrix[13] = translation[1];
	matrix[14] = translation[2];
}

/*
   clockwise rotation around X, Y, Z, facing along axis
   1  0   0    cy 0  sy   cz  sz 0
   0  cx  sx   0  1  0   -sz  cz 0
   0 -sx  cx  -sy 0  cy   0   0  1

   rows of Z by cols of Y
   cy*cz -sy*cz+sz -sy*sz+cz
   -sz*cy -sz*sy+cz

   .. or something like that..

   final rotation is Z * Y * X
   cy*cz -sx*-sy*cz+cx*sz  cx*-sy*sz+sx*cz
   -cy*sz  sx*sy*sz+cx*cz  -cx*-sy*sz+sx*cz
   sy    -sx*cy            cx*cy
 */

/* transposed
 |  cy.cz + 0.sz + sy.0            cy.-sz + 0 .cz +  sy.0          cy.0  + 0 .0  +   sy.1       |
 |  sx.sy.cz + cx.sz + -sx.cy.0    sx.sy.-sz + cx.cz + -sx.cy.0    sx.sy.0  + cx.0  + -sx.cy.1  |
 | -cx.sy.cz + sx.sz +  cx.cy.0   -cx.sy.-sz + sx.cz +  cx.cy.0   -cx.sy.0  + 0 .0  +  cx.cy.1  |
 */
void m4x4_rotation_for_vec3( m4x4_t matrix, const vec3_t euler, eulerOrder_t order ){
	double cx, sx, cy, sy, cz, sz;

	cx = cos( DEG2RAD( euler[0] ) );
	sx = sin( DEG2RAD( euler[0] ) );
	cy = cos( DEG2RAD( euler[1] ) );
	sy = sin( DEG2RAD( euler[1] ) );
	cz = cos( DEG2RAD( euler[2] ) );
	sz = sin( DEG2RAD( euler[2] ) );

	switch ( order )
	{
	case eXYZ:

#if 1

	{
		matrix[0]  = (vec_t)( cy * cz );
		matrix[1]  = (vec_t)( cy * sz );
		matrix[2]  = (vec_t)-sy;
		matrix[4]  = (vec_t)( sx * sy * cz + cx * -sz );
		matrix[5]  = (vec_t)( sx * sy * sz + cx * cz );
		matrix[6]  = (vec_t)( sx * cy );
		matrix[8]  = (vec_t)( cx * sy * cz + sx * sz );
		matrix[9]  = (vec_t)( cx * sy * sz + -sx * cz );
		matrix[10] = (vec_t)( cx * cy );
	}

		matrix[12]  =  matrix[13] = matrix[14] = matrix[3] = matrix[7] = matrix[11] = 0;
		matrix[15] =  1;

#else

		m4x4_identity( matrix );
		matrix[5] = (vec_t) cx; matrix[6] = (vec_t) sx;
		matrix[9] = (vec_t)-sx; matrix[10] = (vec_t) cx;

		{
			m4x4_t temp;
			m4x4_identity( temp );
			temp[0] = (vec_t) cy; temp[2] = (vec_t)-sy;
			temp[8] = (vec_t) sy; temp[10] = (vec_t) cy;
			m4x4_premultiply_by_m4x4( matrix, temp );
			m4x4_identity( temp );
			temp[0] = (vec_t) cz; temp[1] = (vec_t) sz;
			temp[4] = (vec_t)-sz; temp[5] = (vec_t) cz;
			m4x4_premultiply_by_m4x4( matrix, temp );
		}
#endif

		break;

	case eYZX:
		m4x4_identity( matrix );
		matrix[0] = (vec_t) cy; matrix[2] = (vec_t)-sy;
		matrix[8] = (vec_t) sy; matrix[10] = (vec_t) cy;

		{
			m4x4_t temp;
			m4x4_identity( temp );
			temp[5] = (vec_t) cx; temp[6] = (vec_t) sx;
			temp[9] = (vec_t)-sx; temp[10] = (vec_t) cx;
			m4x4_premultiply_by_m4x4( matrix, temp );
			m4x4_identity( temp );
			temp[0] = (vec_t) cz; temp[1] = (vec_t) sz;
			temp[4] = (vec_t)-sz; temp[5] = (vec_t) cz;
			m4x4_premultiply_by_m4x4( matrix, temp );
		}
		break;

	case eZXY:
		m4x4_identity( matrix );
		matrix[0] = (vec_t) cz; matrix[1] = (vec_t) sz;
		matrix[4] = (vec_t)-sz; matrix[5] = (vec_t) cz;

		{
			m4x4_t temp;
			m4x4_identity( temp );
			temp[5] = (vec_t) cx; temp[6] = (vec_t) sx;
			temp[9] = (vec_t)-sx; temp[10] = (vec_t) cx;
			m4x4_premultiply_by_m4x4( matrix, temp );
			m4x4_identity( temp );
			temp[0] = (vec_t) cy; temp[2] = (vec_t)-sy;
			temp[8] = (vec_t) sy; temp[10] = (vec_t) cy;
			m4x4_premultiply_by_m4x4( matrix, temp );
		}
		break;

	case eXZY:
		m4x4_identity( matrix );
		matrix[5] = (vec_t) cx; matrix[6] = (vec_t) sx;
		matrix[9] = (vec_t)-sx; matrix[10] = (vec_t) cx;

		{
			m4x4_t temp;
			m4x4_identity( temp );
			temp[0] = (vec_t) cz; temp[1] = (vec_t) sz;
			temp[4] = (vec_t)-sz; temp[5] = (vec_t) cz;
			m4x4_premultiply_by_m4x4( matrix, temp );
			m4x4_identity( temp );
			temp[0] = (vec_t) cy; temp[2] = (vec_t)-sy;
			temp[8] = (vec_t) sy; temp[10] = (vec_t) cy;
			m4x4_premultiply_by_m4x4( matrix, temp );
		}
		break;

	case eYXZ:

/* transposed
 |  cy.cz + sx.sy.-sz + -cx.sy.0   0.cz + cx.-sz + sx.0   sy.cz + -sx.cy.-sz + cx.cy.0 |
 |  cy.sz + sx.sy.cz + -cx.sy.0    0.sz + cx.cz + sx.0    sy.sz + -sx.cy.cz + cx.cy.0  |
 |  cy.0 + sx.sy.0 + -cx.sy.1      0.0 + cx.0 + sx.1      sy.0 + -sx.cy.0 + cx.cy.1    |
 */

#if 1

	{
		matrix[0]  = (vec_t)( cy * cz + sx * sy * -sz );
		matrix[1]  = (vec_t)( cy * sz + sx * sy * cz );
		matrix[2]  = (vec_t)( -cx * sy );
		matrix[4]  = (vec_t)( cx * -sz );
		matrix[5]  = (vec_t)( cx * cz );
		matrix[6]  = (vec_t)( sx );
		matrix[8]  = (vec_t)( sy * cz + -sx * cy * -sz );
		matrix[9]  = (vec_t)( sy * sz + -sx * cy * cz );
		matrix[10] = (vec_t)( cx * cy );
	}

		matrix[12]  =  matrix[13] = matrix[14] = matrix[3] = matrix[7] = matrix[11] = 0;
		matrix[15] =  1;

#else

		m4x4_identity( matrix );
		matrix[0] = (vec_t) cy; matrix[2] = (vec_t)-sy;
		matrix[8] = (vec_t) sy; matrix[10] = (vec_t) cy;

		{
			m4x4_t temp;
			m4x4_identity( temp );
			temp[5] = (vec_t) cx; temp[6] = (vec_t) sx;
			temp[9] = (vec_t)-sx; temp[10] = (vec_t) cx;
			m4x4_premultiply_by_m4x4( matrix, temp );
			m4x4_identity( temp );
			temp[0] = (vec_t) cz; temp[1] = (vec_t) sz;
			temp[4] = (vec_t)-sz; temp[5] = (vec_t) cz;
			m4x4_premultiply_by_m4x4( matrix, temp );
		}
#endif
		break;

	case eZYX:
#if 1

	{
		matrix[0]  = (vec_t)( cy * cz );
		matrix[4]  = (vec_t)( cy * -sz );
		matrix[8]  = (vec_t)sy;
		matrix[1]  = (vec_t)( sx * sy * cz + cx * sz );
		matrix[5]  = (vec_t)( sx * sy * -sz + cx * cz );
		matrix[9]  = (vec_t)( -sx * cy );
		matrix[2]  = (vec_t)( cx * -sy * cz + sx * sz );
		matrix[6]  = (vec_t)( cx * -sy * -sz + sx * cz );
		matrix[10] = (vec_t)( cx * cy );
	}

		matrix[12]  =  matrix[13] = matrix[14] = matrix[3] = matrix[7] = matrix[11] = 0;
		matrix[15] =  1;

#else

		m4x4_identity( matrix );
		matrix[0] = (vec_t) cz; matrix[1] = (vec_t) sz;
		matrix[4] = (vec_t)-sz; matrix[5] = (vec_t) cz;
		{
			m4x4_t temp;
			m4x4_identity( temp );
			temp[0] = (vec_t) cy; temp[2] = (vec_t)-sy;
			temp[8] = (vec_t) sy; temp[10] = (vec_t) cy;
			m4x4_premultiply_by_m4x4( matrix, temp );
			m4x4_identity( temp );
			temp[5] = (vec_t) cx; temp[6] = (vec_t) sx;
			temp[9] = (vec_t)-sx; temp[10] = (vec_t) cx;
			m4x4_premultiply_by_m4x4( matrix, temp );
		}

#endif
		break;

	}
}

void m4x4_scale_for_vec3( m4x4_t matrix, const vec3_t scale ){
	matrix[1] = matrix[2] = matrix[3] =
		matrix[4] = matrix[6] = matrix[7] =
			matrix[8] = matrix[9] = matrix[11] =
				matrix[12] = matrix[13] = matrix[14] = 0;

	matrix[15] = 1;

	matrix[0] = scale[0];
	matrix[5] = scale[1];
	matrix[10] = scale[2];
}

void m4x4_rotation_for_quat( m4x4_t matrix, const vec4_t quat ){
#if 0
	const double xx = quat[0] * quat[0];
	const double xy = quat[0] * quat[1];
	const double xz = quat[0] * quat[2];
	const double xw = quat[0] * quat[3];

	const double yy = quat[1] * quat[1];
	const double yz = quat[1] * quat[2];
	const double yw = quat[1] * quat[3];

	const double zz = quat[2] * quat[2];
	const double zw = quat[2] * quat[3];

	matrix[0]  = 1 - 2 * ( yy + zz );
	matrix[4]  =     2 * ( xy - zw );
	matrix[8]  =     2 * ( xz + yw );

	matrix[1]  =     2 * ( xy + zw );
	matrix[5]  = 1 - 2 * ( xx + zz );
	matrix[9]  =     2 * ( yz - xw );

	matrix[2]  =     2 * ( xz - yw );
	matrix[6]  =     2 * ( yz + xw );
	matrix[10] = 1 - 2 * ( xx + yy );
#else
	const double x2 = quat[0] + quat[0];
	const double y2 = quat[1] + quat[1];
	const double z2 = quat[2] + quat[2];
	const double xx = quat[0] * x2;
	const double xy = quat[0] * y2;
	const double xz = quat[0] * z2;
	const double yy = quat[1] * y2;
	const double yz = quat[1] * z2;
	const double zz = quat[2] * z2;
	const double wx = quat[3] * x2;
	const double wy = quat[3] * y2;
	const double wz = quat[3] * z2;

	matrix[0] = (vec_t)( 1.0 - ( yy + zz ) );
	matrix[4] = (vec_t)( xy - wz );
	matrix[8] = (vec_t)( xz + wy );

	matrix[1] = (vec_t)( xy + wz );
	matrix[5] = (vec_t)( 1.0 - ( xx + zz ) );
	matrix[9] = (vec_t)( yz - wx );

	matrix[2] = (vec_t)( xz - wy );
	matrix[6] = (vec_t)( yz + wx );
	matrix[10] = (vec_t)( 1.0 - ( xx + yy ) );
#endif

	matrix[3]  = matrix[7] = matrix[11] = matrix[12] = matrix[13] = matrix[14] = 0;
	matrix[15] = 1;
}

void m4x4_rotation_for_axisangle( m4x4_t matrix, const vec3_t axis, double angle ){
	vec4_t quat;
	quat_for_axisangle( quat, axis, angle );
	m4x4_rotation_for_quat( matrix, quat );
}

void m4x4_frustum( m4x4_t matrix,
                   vec_t left, vec_t right,
                   vec_t bottom, vec_t top,
                   vec_t nearval, vec_t farval ){
	matrix[0] = (vec_t)( ( 2 * nearval ) / ( right - left ) );
	matrix[1] = 0;
	matrix[2] = 0;
	matrix[3] = 0;

	matrix[4] = 0;
	matrix[5] = (vec_t)( ( 2 * nearval ) / ( top - bottom ) );
	matrix[6] = 0;
	matrix[7] = 0;

	matrix[8] = (vec_t)( ( right + left ) / ( right - left ) );
	matrix[9] = (vec_t)( ( top + bottom ) / ( top - bottom ) );
	matrix[10] = (vec_t)( -( farval + nearval ) / ( farval - nearval ) );
	matrix[11] = -1;

	matrix[12] = 0;
	matrix[13] = 0;
	matrix[14] = (vec_t)( -( 2 * farval * nearval ) / ( farval - nearval ) );
	matrix[15] = 0;
}


void m4x4_get_translation_vec3( const m4x4_t matrix, vec3_t translation ){
	translation[0] = matrix[12];
	translation[1] = matrix[13];
	translation[2] = matrix[14];
}

void m4x4_get_rotation_vec3( const m4x4_t matrix, vec3_t euler, eulerOrder_t order ){
	double a, ca;

	switch ( order )
	{
	case eXYZ:
		a = asin( -matrix[2] );
		ca = cos( a );
		euler[1] = (vec_t)RAD2DEG( a ); /* Calculate Y-axis angle */

		if ( fabs( ca ) > 0.005 ) { /* Gimbal lock? */
			/* No, so get Z-axis angle */
			euler[2] = (vec_t)RAD2DEG( atan2( matrix[1] / ca, matrix[0] / ca ) );

			/* Get X-axis angle */
			euler[0] = (vec_t)RAD2DEG( atan2( matrix[6] / ca, matrix[10] / ca ) );
		}
		else /* Gimbal lock has occurred */
		{
			/* Set Z-axis angle to zero */
			euler[2]  = 0;

			/* And calculate X-axis angle */
			euler[0] = (vec_t)RAD2DEG( atan2( -matrix[9], matrix[5] ) );
		}
		break;
	case eYZX:
		/* NOT IMPLEMENTED */
		break;
	case eZXY:
		/* NOT IMPLEMENTED */
		break;
	case eXZY:
		/* NOT IMPLEMENTED */
		break;
	case eYXZ:
		a = asin( matrix[6] );
		ca = cos( a );
		euler[0] = (vec_t)RAD2DEG( a ); /* Calculate X-axis angle */

		if ( fabs( ca ) > 0.005 ) { /* Gimbal lock? */
			/* No, so get Y-axis angle */
			euler[1] = (vec_t)RAD2DEG( atan2( -matrix[2] / ca, matrix[10] / ca ) );

			/* Get Z-axis angle */
			euler[2] = (vec_t)RAD2DEG( atan2( -matrix[4] / ca, matrix[5] / ca ) );
		}
		else /* Gimbal lock has occurred */
		{
			/* Set Z-axis angle to zero */
			euler[2]  = 0;

			/* And calculate Y-axis angle */
			euler[1] = (vec_t)RAD2DEG( atan2( matrix[8], matrix[0] ) );
		}
		break;
	case eZYX:
		a = asin( matrix[8] );
		ca = cos( a );
		euler[1] = (vec_t)RAD2DEG( a ); /* Calculate Y-axis angle */

		if ( fabs( ca ) > 0.005 ) { /* Gimbal lock? */
			/* No, so get X-axis angle */
			euler[0] = (vec_t)RAD2DEG( atan2( -matrix[9] / ca, matrix[10] / ca ) );

			/* Get Z-axis angle */
			euler[2] = (vec_t)RAD2DEG( atan2( -matrix[4] / ca, matrix[0] / ca ) );
		}
		else /* Gimbal lock has occurred */
		{
			/* Set X-axis angle to zero */
			euler[0]  = 0;

			/* And calculate Z-axis angle */
			euler[2] = (vec_t)RAD2DEG( atan2( matrix[1], matrix[5] ) );
		}
		break;
	}

	/* return only positive angles in [0,360] */
	if ( euler[0] < 0 ) {
		euler[0] += 360;
	}
	if ( euler[1] < 0 ) {
		euler[1] += 360;
	}
	if ( euler[2] < 0 ) {
		euler[2] += 360;
	}
}

void m4x4_get_scale_vec3( const m4x4_t matrix, vec3_t scale ){
	scale[0] = VectorLength( matrix + 0 );
	scale[1] = VectorLength( matrix + 4 );
	scale[2] = VectorLength( matrix + 8 );
}

void m4x4_get_transform_vec3( const m4x4_t matrix, vec3_t translation, vec3_t euler, eulerOrder_t order, vec3_t scale ){
	m4x4_t normalised;
	m4x4_assign( normalised, matrix );
	scale[0] = VectorNormalize( normalised + 0, normalised + 0 );
	scale[1] = VectorNormalize( normalised + 4, normalised + 4 );
	scale[2] = VectorNormalize( normalised + 8, normalised + 8 );
	if ( m4x4_handedness( normalised ) == eLeftHanded ) {
		VectorNegate( normalised + 0, normalised + 0 );
		VectorNegate( normalised + 4, normalised + 4 );
		VectorNegate( normalised + 8, normalised + 8 );
		scale[0] = -scale[0];
		scale[1] = -scale[1];
		scale[2] = -scale[2];
	}
	m4x4_get_rotation_vec3( normalised, euler, order );
	m4x4_get_translation_vec3( matrix, translation );
}

void m4x4_translate_by_vec3( m4x4_t matrix, const vec3_t translation ){
	m4x4_t temp;
	m4x4_translation_for_vec3( temp, translation );
	m4x4_multiply_by_m4x4( matrix, temp );
}

void m4x4_rotate_by_vec3( m4x4_t matrix, const vec3_t euler, eulerOrder_t order ){
	m4x4_t temp;
	m4x4_rotation_for_vec3( temp, euler, order );
	m4x4_multiply_by_m4x4( matrix, temp );
}

void m4x4_scale_by_vec3( m4x4_t matrix, const vec3_t scale ){
	m4x4_t temp;
	m4x4_scale_for_vec3( temp, scale );
	m4x4_multiply_by_m4x4( matrix, temp );
}

void m4x4_rotate_by_quat( m4x4_t matrix, const vec4_t rotation ){
	m4x4_t temp;
	m4x4_rotation_for_quat( temp, rotation );
	m4x4_multiply_by_m4x4( matrix, temp );
}

void m4x4_rotate_by_axisangle( m4x4_t matrix, const vec3_t axis, double angle ){
	m4x4_t temp;
	m4x4_rotation_for_axisangle( temp, axis, angle );
	m4x4_multiply_by_m4x4( matrix, temp );
}

void m4x4_transform_by_vec3( m4x4_t matrix, const vec3_t translation, const vec3_t euler, eulerOrder_t order, const vec3_t scale ){
	m4x4_translate_by_vec3( matrix, translation );
	m4x4_rotate_by_vec3( matrix, euler, order );
	m4x4_scale_by_vec3( matrix, scale );
}

void m4x4_pivoted_rotate_by_vec3( m4x4_t matrix, const vec3_t euler, eulerOrder_t order, const vec3_t pivotpoint ){
	vec3_t vec3_temp;
	VectorNegate( pivotpoint, vec3_temp );

	m4x4_translate_by_vec3( matrix, pivotpoint );
	m4x4_rotate_by_vec3( matrix, euler, order );
	m4x4_translate_by_vec3( matrix, vec3_temp );
}

void m4x4_pivoted_scale_by_vec3( m4x4_t matrix, const vec3_t scale, const vec3_t pivotpoint ){
	vec3_t vec3_temp;
	VectorNegate( pivotpoint, vec3_temp );

	m4x4_translate_by_vec3( matrix, pivotpoint );
	m4x4_scale_by_vec3( matrix, scale );
	m4x4_translate_by_vec3( matrix, vec3_temp );
}

void m4x4_pivoted_transform_by_vec3( m4x4_t matrix, const vec3_t translation, const vec3_t euler, eulerOrder_t order, const vec3_t scale, const vec3_t pivotpoint ){
	vec3_t vec3_temp;

	VectorAdd( pivotpoint, translation, vec3_temp );
	m4x4_translate_by_vec3( matrix, vec3_temp );
	m4x4_rotate_by_vec3( matrix, euler, order );
	m4x4_scale_by_vec3( matrix, scale );
	VectorNegate( pivotpoint, vec3_temp );
	m4x4_translate_by_vec3( matrix, vec3_temp );
}

void m4x4_pivoted_transform_by_rotation( m4x4_t matrix, const vec3_t translation, const m4x4_t rotation, const vec3_t scale, const vec3_t pivotpoint ){
	vec3_t vec3_temp;

	VectorAdd( pivotpoint, translation, vec3_temp );
	m4x4_translate_by_vec3( matrix, vec3_temp );
	m4x4_multiply_by_m4x4( matrix, rotation );
	m4x4_scale_by_vec3( matrix, scale );
	VectorNegate( pivotpoint, vec3_temp );
	m4x4_translate_by_vec3( matrix, vec3_temp );
}

void m4x4_pivoted_rotate_by_quat( m4x4_t matrix, const vec4_t rotation, const vec3_t pivotpoint ){
	vec3_t vec3_temp;
	VectorNegate( pivotpoint, vec3_temp );

	m4x4_translate_by_vec3( matrix, pivotpoint );
	m4x4_rotate_by_quat( matrix, rotation );
	m4x4_translate_by_vec3( matrix, vec3_temp );
}

void m4x4_pivoted_rotate_by_axisangle( m4x4_t matrix, const vec3_t axis, double angle, const vec3_t pivotpoint ){
	vec3_t vec3_temp;
	VectorNegate( pivotpoint, vec3_temp );

	m4x4_translate_by_vec3( matrix, pivotpoint );
	m4x4_rotate_by_axisangle( matrix, axis, angle );
	m4x4_translate_by_vec3( matrix, vec3_temp );
}

/*
   A = A.B

   A0 = B0 * A0 + B1 * A4 + B2 * A8 + B3 * A12
   A4 = B4 * A0 + B5 * A4 + B6 * A8 + B7 * A12
   A8 = B8 * A0 + B9 * A4 + B10* A8 + B11* A12
   A12= B12* A0 + B13* A4 + B14* A8 + B15* A12

   A1 = B0 * A1 + B1 * A5 + B2 * A9 + B3 * A13
   A5 = B4 * A1 + B5 * A5 + B6 * A9 + B7 * A13
   A9 = B8 * A1 + B9 * A5 + B10* A9 + B11* A13
   A13= B12* A1 + B13* A5 + B14* A9 + B15* A13

   A2 = B0 * A2 + B1 * A6 + B2 * A10+ B3 * A14
   A6 = B4 * A2 + B5 * A6 + B6 * A10+ B7 * A14
   A10= B8 * A2 + B9 * A6 + B10* A10+ B11* A14
   A14= B12* A2 + B13* A6 + B14* A10+ B15* A14

   A3 = B0 * A3 + B1 * A7 + B2 * A11+ B3 * A15
   A7 = B4 * A3 + B5 * A7 + B6 * A11+ B7 * A15
   A11= B8 * A3 + B9 * A7 + B10* A11+ B11* A15
   A15= B12* A3 + B13* A7 + B14* A11+ B15* A15
 */

void m4x4_multiply_by_m4x4( m4x4_t dst, const m4x4_t src ){
	vec_t dst0, dst1, dst2, dst3;

#if 1

	dst0 = src[0] * dst[0] + src[1] * dst[4] + src[2] * dst[8] + src[3] * dst[12];
	dst1 = src[4] * dst[0] + src[5] * dst[4] + src[6] * dst[8] + src[7] * dst[12];
	dst2 = src[8] * dst[0] + src[9] * dst[4] + src[10] * dst[8] + src[11] * dst[12];
	dst3 = src[12] * dst[0] + src[13] * dst[4] + src[14] * dst[8] + src[15] * dst[12];
	dst[0] = dst0; dst[4] = dst1; dst[8] = dst2; dst[12] = dst3;

	dst0 = src[0] * dst[1] + src[1] * dst[5] + src[2] * dst[9] + src[3] * dst[13];
	dst1 = src[4] * dst[1] + src[5] * dst[5] + src[6] * dst[9] + src[7] * dst[13];
	dst2 = src[8] * dst[1] + src[9] * dst[5] + src[10] * dst[9] + src[11] * dst[13];
	dst3 = src[12] * dst[1] + src[13] * dst[5] + src[14] * dst[9] + src[15] * dst[13];
	dst[1] = dst0; dst[5] = dst1; dst[9] = dst2; dst[13] = dst3;

	dst0 = src[0] * dst[2] + src[1] * dst[6] + src[2] * dst[10] + src[3] * dst[14];
	dst1 = src[4] * dst[2] + src[5] * dst[6] + src[6] * dst[10] + src[7] * dst[14];
	dst2 = src[8] * dst[2] + src[9] * dst[6] + src[10] * dst[10] + src[11] * dst[14];
	dst3 = src[12] * dst[2] + src[13] * dst[6] + src[14] * dst[10] + src[15] * dst[14];
	dst[2] = dst0; dst[6] = dst1; dst[10] = dst2; dst[14] = dst3;

	dst0 = src[0] * dst[3] + src[1] * dst[7] + src[2] * dst[11] + src[3] * dst[15];
	dst1 = src[4] * dst[3] + src[5] * dst[7] + src[6] * dst[11] + src[7] * dst[15];
	dst2 = src[8] * dst[3] + src[9] * dst[7] + src[10] * dst[11] + src[11] * dst[15];
	dst3 = src[12] * dst[3] + src[13] * dst[7] + src[14] * dst[11] + src[15] * dst[15];
	dst[3] = dst0; dst[7] = dst1; dst[11] = dst2; dst[15] = dst3;

#else

	vec_t * p = dst;
	for ( int i = 0; i < 4; i++ )
	{
		dst1 =  src[0]  * p[0];
		dst1 += src[1]  * p[4];
		dst1 += src[2]  * p[8];
		dst1 += src[3]  * p[12];
		dst2 =  src[4]  * p[0];
		dst2 += src[5]  * p[4];
		dst2 += src[6]  * p[8];
		dst2 += src[7]  * p[12];
		dst3 =  src[8]  * p[0];
		dst3 += src[9]  * p[4];
		dst3 += src[10] * p[8];
		dst3 += src[11] * p[12];
		dst4 =  src[12] * p[0];
		dst4 += src[13] * p[4];
		dst4 += src[14] * p[8];
		dst4 += src[15] * p[12];

		p[0] = dst1;
		p[4] = dst2;
		p[8] = dst3;
		p[12] = dst4;
		p++;
	}

#endif
}

/*
   A = B.A

   A0 = A0 * B0 + A1 * B4 + A2 * B8 + A3 * B12
   A1 = A0 * B1 + A1 * B5 + A2 * B9 + A3 * B13
   A2 = A0 * B2 + A1 * B6 + A2 * B10+ A3 * B14
   A3 = A0 * B3 + A1 * B7 + A2 * B11+ A3 * B15

   A4 = A4 * B0 + A5 * B4 + A6 * B8 + A7 * B12
   A5 = A4 * B1 + A5 * B5 + A6 * B9 + A7 * B13
   A6 = A4 * B2 + A5 * B6 + A6 * B10+ A7 * B14
   A7 = A4 * B3 + A5 * B7 + A6 * B11+ A7 * B15

   A8 = A8 * B0 + A9 * B4 + A10* B8 + A11* B12
   A9 = A8 * B1 + A9 * B5 + A10* B9 + A11* B13
   A10= A8 * B2 + A9 * B6 + A10* B10+ A11* B14
   A11= A8 * B3 + A9 * B7 + A10* B11+ A11* B15

   A12= A12* B0 + A13* B4 + A14* B8 + A15* B12
   A13= A12* B1 + A13* B5 + A14* B9 + A15* B13
   A14= A12* B2 + A13* B6 + A14* B10+ A15* B14
   A15= A12* B3 + A13* B7 + A14* B11+ A15* B15
 */

void m4x4_premultiply_by_m4x4( m4x4_t dst, const m4x4_t src ){
	vec_t dst0, dst1, dst2, dst3;

#if 1

	dst0 = dst[0] * src[0] + dst[1] * src[4] + dst[2] * src[8] + dst[3] * src[12];
	dst1 = dst[0] * src[1] + dst[1] * src[5] + dst[2] * src[9] + dst[3] * src[13];
	dst2 = dst[0] * src[2] + dst[1] * src[6] + dst[2] * src[10] + dst[3] * src[14];
	dst3 = dst[0] * src[3] + dst[1] * src[7] + dst[2] * src[11] + dst[3] * src[15];
	dst[0] = dst0; dst[1] = dst1; dst[2] = dst2; dst[3] = dst3;

	dst0 = dst[4] * src[0] + dst[5] * src[4] + dst[6] * src[8] + dst[7] * src[12];
	dst1 = dst[4] * src[1] + dst[5] * src[5] + dst[6] * src[9] + dst[7] * src[13];
	dst2 = dst[4] * src[2] + dst[5] * src[6] + dst[6] * src[10] + dst[7] * src[14];
	dst3 = dst[4] * src[3] + dst[5] * src[7] + dst[6] * src[11] + dst[7] * src[15];
	dst[4] = dst0; dst[5] = dst1; dst[6] = dst2; dst[7] = dst3;

	dst0 = dst[8] * src[0] + dst[9] * src[4] + dst[10] * src[8] + dst[11] * src[12];
	dst1 = dst[8] * src[1] + dst[9] * src[5] + dst[10] * src[9] + dst[11] * src[13];
	dst2 = dst[8] * src[2] + dst[9] * src[6] + dst[10] * src[10] + dst[11] * src[14];
	dst3 = dst[8] * src[3] + dst[9] * src[7] + dst[10] * src[11] + dst[11] * src[15];
	dst[8] = dst0; dst[9] = dst1; dst[10] = dst2; dst[11] = dst3;

	dst0 = dst[12] * src[0] + dst[13] * src[4] + dst[14] * src[8] + dst[15] * src[12];
	dst1 = dst[12] * src[1] + dst[13] * src[5] + dst[14] * src[9] + dst[15] * src[13];
	dst2 = dst[12] * src[2] + dst[13] * src[6] + dst[14] * src[10] + dst[15] * src[14];
	dst3 = dst[12] * src[3] + dst[13] * src[7] + dst[14] * src[11] + dst[15] * src[15];
	dst[12] = dst0; dst[13] = dst1; dst[14] = dst2; dst[15] = dst3;

#else

	vec_t* p = dst;
	for ( int i = 0; i < 4; i++ )
	{
		dst1 =  src[0]  * p[0];
		dst2 =  src[1]  * p[0];
		dst3 =  src[2]  * p[0];
		dst4 =  src[3]  * p[0];
		dst1 += src[4]  * p[1];
		dst2 += src[5]  * p[1];
		dst3 += src[6]  * p[1];
		dst4 += src[7]  * p[1];
		dst1 += src[8]  * p[2];
		dst2 += src[9]  * p[2];
		dst4 += src[11] * p[2];
		dst3 += src[10] * p[2];
		dst1 += src[12] * p[3];
		dst2 += src[13] * p[3];
		dst3 += src[14] * p[3];
		dst4 += src[15] * p[3];

		*p++ = dst1;
		*p++ = dst2;
		*p++ = dst3;
		*p++ = dst4;
	}

#endif
}

void m4x4_orthogonal_multiply_by_m4x4( m4x4_t dst, const m4x4_t src ){
	vec_t dst0, dst1, dst2, dst3;

	dst0 = src[0] * dst[0] + src[1] * dst[4] + src[2] * dst[8];
	dst1 = src[4] * dst[0] + src[5] * dst[4] + src[6] * dst[8];
	dst2 = src[8] * dst[0] + src[9] * dst[4] + src[10] * dst[8];
	dst3 = src[12] * dst[0] + src[13] * dst[4] + src[14] * dst[8] + dst[12];
	dst[0] = dst0; dst[4] = dst1; dst[8] = dst2; dst[12] = dst3;

	dst0 = src[0] * dst[1] + src[1] * dst[5] + src[2] * dst[9];
	dst1 = src[4] * dst[1] + src[5] * dst[5] + src[6] * dst[9];
	dst2 = src[8] * dst[1] + src[9] * dst[5] + src[10] * dst[9];
	dst3 = src[12] * dst[1] + src[13] * dst[5] + src[14] * dst[9] + dst[13];
	dst[1] = dst0; dst[5] = dst1; dst[9] = dst2; dst[13] = dst3;

	dst0 = src[0] * dst[2] + src[1] * dst[6] + src[2] * dst[10];
	dst1 = src[4] * dst[2] + src[5] * dst[6] + src[6] * dst[10];
	dst2 = src[8] * dst[2] + src[9] * dst[6] + src[10] * dst[10];
	dst3 = src[12] * dst[2] + src[13] * dst[6] + src[14] * dst[10] + dst[14];
	dst[2] = dst0; dst[6] = dst1; dst[10] = dst2; dst[14] = dst3;
}

void m4x4_orthogonal_premultiply_by_m4x4( m4x4_t dst, const m4x4_t src ){
	vec_t dst0, dst1, dst2;

	dst0 = dst[0] * src[0] + dst[1] * src[4] + dst[2] * src[8];
	dst1 = dst[0] * src[1] + dst[1] * src[5] + dst[2] * src[9];
	dst2 = dst[0] * src[2] + dst[1] * src[6] + dst[2] * src[10];
	dst[0] = dst0; dst[1] = dst1; dst[2] = dst2;

	dst0 = dst[4] * src[0] + dst[5] * src[4] + dst[6] * src[8];
	dst1 = dst[4] * src[1] + dst[5] * src[5] + dst[6] * src[9];
	dst2 = dst[4] * src[2] + dst[5] * src[6] + dst[6] * src[10];
	dst[4] = dst0; dst[5] = dst1; dst[6] = dst2;

	dst0 = dst[8] * src[0] + dst[9] * src[4] + dst[10] * src[8];
	dst1 = dst[8] * src[1] + dst[9] * src[5] + dst[10] * src[9];
	dst2 = dst[8] * src[2] + dst[9] * src[6] + dst[10] * src[10];
	dst[8] = dst0; dst[9] = dst1; dst[10] = dst2;

	dst0 = dst[12] * src[0] + dst[13] * src[4] + dst[14] * src[8] + dst[15] * src[12];
	dst1 = dst[12] * src[1] + dst[13] * src[5] + dst[14] * src[9] + dst[15] * src[13];
	dst2 = dst[12] * src[2] + dst[13] * src[6] + dst[14] * src[10] + dst[15] * src[14];
	dst[12] = dst0; dst[13] = dst1; dst[14] = dst2;
}

void m4x4_transform_point( const m4x4_t matrix, vec3_t point ){
	float out1, out2, out3;

	out1 =  matrix[0]  * point[0] + matrix[4]  * point[1] + matrix[8]  * point[2] + matrix[12];
	out2 =  matrix[1]  * point[0] + matrix[5]  * point[1] + matrix[9]  * point[2] + matrix[13];
	out3 =  matrix[2]  * point[0] + matrix[6]  * point[1] + matrix[10] * point[2] + matrix[14];

	point[0] = out1;
	point[1] = out2;
	point[2] = out3;
}

void m4x4_transform_normal( const m4x4_t matrix, vec3_t normal ){
	float out1, out2, out3;

	out1 =  matrix[0]  * normal[0] + matrix[4]  * normal[1] + matrix[8]  * normal[2];
	out2 =  matrix[1]  * normal[0] + matrix[5]  * normal[1] + matrix[9]  * normal[2];
	out3 =  matrix[2]  * normal[0] + matrix[6]  * normal[1] + matrix[10] * normal[2];

	normal[0] = out1;
	normal[1] = out2;
	normal[2] = out3;
}

void m4x4_transform_vec4( const m4x4_t matrix, vec4_t vector ){
	float out1, out2, out3, out4;

	out1 =  matrix[0]  * vector[0] + matrix[4]  * vector[1] + matrix[8]  * vector[2] + matrix[12] * vector[3];
	out2 =  matrix[1]  * vector[0] + matrix[5]  * vector[1] + matrix[9]  * vector[2] + matrix[13] * vector[3];
	out3 =  matrix[2]  * vector[0] + matrix[6]  * vector[1] + matrix[10] * vector[2] + matrix[14] * vector[3];
	out4 =  matrix[3]  * vector[0] + matrix[7]  * vector[1] + matrix[11] * vector[2] + matrix[15] * vector[3];

	vector[0] = out1;
	vector[1] = out2;
	vector[2] = out3;
	vector[3] = out4;
}

#define CLIP_X_LT_W( p ) ( ( p )[0] < ( p )[3] )
#define CLIP_X_GT_W( p ) ( ( p )[0] > -( p )[3] )
#define CLIP_Y_LT_W( p ) ( ( p )[1] < ( p )[3] )
#define CLIP_Y_GT_W( p ) ( ( p )[1] > -( p )[3] )
#define CLIP_Z_LT_W( p ) ( ( p )[2] < ( p )[3] )
#define CLIP_Z_GT_W( p ) ( ( p )[2] > -( p )[3] )

clipmask_t homogenous_clip_point( const vec4_t clipped ){
	clipmask_t result = CLIP_FAIL;
	if ( CLIP_X_LT_W( clipped ) ) {
		result &= ~CLIP_LT_X;                    // X < W
	}
	if ( CLIP_X_GT_W( clipped ) ) {
		result &= ~CLIP_GT_X;                    // X > -W
	}
	if ( CLIP_Y_LT_W( clipped ) ) {
		result &= ~CLIP_LT_Y;                    // Y < W
	}
	if ( CLIP_Y_GT_W( clipped ) ) {
		result &= ~CLIP_GT_Y;                    // Y > -W
	}
	if ( CLIP_Z_LT_W( clipped ) ) {
		result &= ~CLIP_LT_Z;                    // Z < W
	}
	if ( CLIP_Z_GT_W( clipped ) ) {
		result &= ~CLIP_GT_Z;                    // Z > -W
	}
	return result;
}

clipmask_t m4x4_clip_point( const m4x4_t matrix, const vec3_t point, vec4_t clipped ){
	clipped[0] = point[0];
	clipped[1] = point[1];
	clipped[2] = point[2];
	clipped[3] = 1;
	m4x4_transform_vec4( matrix, clipped );
	return homogenous_clip_point( clipped );
}


unsigned int homogenous_clip_triangle( vec4_t clipped[9] ){
	vec4_t buffer[9];
	unsigned int rcount = 3;
	unsigned int wcount = 0;
	vec_t const* rptr = clipped[0];
	vec_t* wptr = buffer[0];
	const vec_t* p0;
	const vec_t* p1;
	unsigned char b0, b1;

	unsigned int i;
	double scale;

	p0 = rptr;
	b0 = CLIP_X_LT_W( p0 );
	for ( i = 0; i < rcount; ++i )
	{
		p1 = ( i + 1 != rcount ) ? p0 + 4 : rptr;
		b1 = CLIP_X_LT_W( p1 );
		if ( b0 ^ b1 ) {
			wptr[0] = p1[0] - p0[0];
			wptr[1] = p1[1] - p0[1];
			wptr[2] = p1[2] - p0[2];
			wptr[3] = p1[3] - p0[3];

			scale = ( p0[0] - p0[3] ) / ( wptr[3] - wptr[0] );

			wptr[0] = (vec_t)( p0[0] + scale * ( wptr[0] ) );
			wptr[1] = (vec_t)( p0[1] + scale * ( wptr[1] ) );
			wptr[2] = (vec_t)( p0[2] + scale * ( wptr[2] ) );
			wptr[3] = (vec_t)( p0[3] + scale * ( wptr[3] ) );

			wptr += 4;
			++wcount;
		}

		if ( b1 ) {
			wptr[0] = p1[0];
			wptr[1] = p1[1];
			wptr[2] = p1[2];
			wptr[3] = p1[3];

			wptr += 4;
			++wcount;
		}

		p0 = p1;
		b0 = b1;
	}

	rcount = wcount;
	wcount = 0;
	rptr = buffer[0];
	wptr = clipped[0];
	p0 = rptr;
	b0 = CLIP_X_GT_W( p0 );

	for ( i = 0; i < rcount; ++i )
	{
		p1 = ( i + 1 != rcount ) ? p0 + 4 : rptr;
		b1 = CLIP_X_GT_W( p1 );
		if ( b0 ^ b1 ) {
			wptr[0] = p1[0] - p0[0];
			wptr[1] = p1[1] - p0[1];
			wptr[2] = p1[2] - p0[2];
			wptr[3] = p1[3] - p0[3];

			scale = ( p0[0] + p0[3] ) / ( -wptr[3] - wptr[0] );

			wptr[0] = (vec_t)( p0[0] + scale * ( wptr[0] ) );
			wptr[1] = (vec_t)( p0[1] + scale * ( wptr[1] ) );
			wptr[2] = (vec_t)( p0[2] + scale * ( wptr[2] ) );
			wptr[3] = (vec_t)( p0[3] + scale * ( wptr[3] ) );

			wptr += 4;
			++wcount;
		}

		if ( b1 ) {
			wptr[0] = p1[0];
			wptr[1] = p1[1];
			wptr[2] = p1[2];
			wptr[3] = p1[3];

			wptr += 4;
			++wcount;
		}

		p0 = p1;
		b0 = b1;
	}

	rcount = wcount;
	wcount = 0;
	rptr = clipped[0];
	wptr = buffer[0];
	p0 = rptr;
	b0 = CLIP_Y_LT_W( p0 );

	for ( i = 0; i < rcount; ++i )
	{
		p1 = ( i + 1 != rcount ) ? p0 + 4 : rptr;
		b1 = CLIP_Y_LT_W( p1 );
		if ( b0 ^ b1 ) {
			wptr[0] = p1[0] - p0[0];
			wptr[1] = p1[1] - p0[1];
			wptr[2] = p1[2] - p0[2];
			wptr[3] = p1[3] - p0[3];

			scale = ( p0[1] - p0[3] ) / ( wptr[3] - wptr[1] );

			wptr[0] = (vec_t)( p0[0] + scale * ( wptr[0] ) );
			wptr[1] = (vec_t)( p0[1] + scale * ( wptr[1] ) );
			wptr[2] = (vec_t)( p0[2] + scale * ( wptr[2] ) );
			wptr[3] = (vec_t)( p0[3] + scale * ( wptr[3] ) );

			wptr += 4;
			++wcount;
		}

		if ( b1 ) {
			wptr[0] = p1[0];
			wptr[1] = p1[1];
			wptr[2] = p1[2];
			wptr[3] = p1[3];

			wptr += 4;
			++wcount;
		}

		p0 = p1;
		b0 = b1;
	}

	rcount = wcount;
	wcount = 0;
	rptr = buffer[0];
	wptr = clipped[0];
	p0 = rptr;
	b0 = CLIP_Y_GT_W( p0 );

	for ( i = 0; i < rcount; ++i )
	{
		p1 = ( i + 1 != rcount ) ? p0 + 4 : rptr;
		b1 = CLIP_Y_GT_W( p1 );
		if ( b0 ^ b1 ) {
			wptr[0] = p1[0] - p0[0];
			wptr[1] = p1[1] - p0[1];
			wptr[2] = p1[2] - p0[2];
			wptr[3] = p1[3] - p0[3];

			scale = ( p0[1] + p0[3] ) / ( -wptr[3] - wptr[1] );

			wptr[0] = (vec_t)( p0[0] + scale * ( wptr[0] ) );
			wptr[1] = (vec_t)( p0[1] + scale * ( wptr[1] ) );
			wptr[2] = (vec_t)( p0[2] + scale * ( wptr[2] ) );
			wptr[3] = (vec_t)( p0[3] + scale * ( wptr[3] ) );

			wptr += 4;
			++wcount;
		}

		if ( b1 ) {
			wptr[0] = p1[0];
			wptr[1] = p1[1];
			wptr[2] = p1[2];
			wptr[3] = p1[3];

			wptr += 4;
			++wcount;
		}

		p0 = p1;
		b0 = b1;
	}

	rcount = wcount;
	wcount = 0;
	rptr = clipped[0];
	wptr = buffer[0];
	p0 = rptr;
	b0 = CLIP_Z_LT_W( p0 );

	for ( i = 0; i < rcount; ++i )
	{
		p1 = ( i + 1 != rcount ) ? p0 + 4 : rptr;
		b1 = CLIP_Z_LT_W( p1 );
		if ( b0 ^ b1 ) {
			wptr[0] = p1[0] - p0[0];
			wptr[1] = p1[1] - p0[1];
			wptr[2] = p1[2] - p0[2];
			wptr[3] = p1[3] - p0[3];

			scale = ( p0[2] - p0[3] ) / ( wptr[3] - wptr[2] );

			wptr[0] = (vec_t)( p0[0] + scale * ( wptr[0] ) );
			wptr[1] = (vec_t)( p0[1] + scale * ( wptr[1] ) );
			wptr[2] = (vec_t)( p0[2] + scale * ( wptr[2] ) );
			wptr[3] = (vec_t)( p0[3] + scale * ( wptr[3] ) );

			wptr += 4;
			++wcount;
		}

		if ( b1 ) {
			wptr[0] = p1[0];
			wptr[1] = p1[1];
			wptr[2] = p1[2];
			wptr[3] = p1[3];

			wptr += 4;
			++wcount;
		}

		p0 = p1;
		b0 = b1;
	}

	rcount = wcount;
	wcount = 0;
	rptr = buffer[0];
	wptr = clipped[0];
	p0 = rptr;
	b0 = CLIP_Z_GT_W( p0 );

	for ( i = 0; i < rcount; ++i )
	{
		p1 = ( i + 1 != rcount ) ? p0 + 4 : rptr;
		b1 = CLIP_Z_GT_W( p1 );
		if ( b0 ^ b1 ) {
			wptr[0] = p1[0] - p0[0];
			wptr[1] = p1[1] - p0[1];
			wptr[2] = p1[2] - p0[2];
			wptr[3] = p1[3] - p0[3];

			scale = ( p0[2] + p0[3] ) / ( -wptr[3] - wptr[2] );

			wptr[0] = (vec_t)( p0[0] + scale * ( wptr[0] ) );
			wptr[1] = (vec_t)( p0[1] + scale * ( wptr[1] ) );
			wptr[2] = (vec_t)( p0[2] + scale * ( wptr[2] ) );
			wptr[3] = (vec_t)( p0[3] + scale * ( wptr[3] ) );

			wptr += 4;
			++wcount;
		}

		if ( b1 ) {
			wptr[0] = p1[0];
			wptr[1] = p1[1];
			wptr[2] = p1[2];
			wptr[3] = p1[3];

			wptr += 4;
			++wcount;
		}

		p0 = p1;
		b0 = b1;
	}

	return wcount;
}

unsigned int m4x4_clip_triangle( const m4x4_t matrix, const vec3_t p0, const vec3_t p1, const vec3_t p2, vec4_t clipped[9] ){
	clipped[0][0] = p0[0];
	clipped[0][1] = p0[1];
	clipped[0][2] = p0[2];
	clipped[0][3] = 1;
	clipped[1][0] = p1[0];
	clipped[1][1] = p1[1];
	clipped[1][2] = p1[2];
	clipped[1][3] = 1;
	clipped[2][0] = p2[0];
	clipped[2][1] = p2[1];
	clipped[2][2] = p2[2];
	clipped[2][3] = 1;

	m4x4_transform_vec4( matrix, clipped[0] );
	m4x4_transform_vec4( matrix, clipped[1] );
	m4x4_transform_vec4( matrix, clipped[2] );

	return homogenous_clip_triangle( clipped );
}

unsigned int homogenous_clip_line( vec4_t clipped[2] ){
	vec4_t clip;
	double scale;
	const vec_t* const p0 = clipped[0];
	const vec_t* const p1 = clipped[1];

	// early out
	{
		clipmask_t mask0 = homogenous_clip_point( clipped[0] );
		clipmask_t mask1 = homogenous_clip_point( clipped[1] );

		if ( ( mask0 | mask1 ) == CLIP_PASS ) { // both points passed all planes
			return 2;
		}

		if ( mask0 & mask1 ) { // both points failed any one plane
			return 0;
		}
	}

	{
		const unsigned int index = CLIP_X_LT_W( p0 );
		if ( index ^ CLIP_X_LT_W( p1 ) ) {
			clip[0] = p1[0] - p0[0];
			clip[1] = p1[1] - p0[1];
			clip[2] = p1[2] - p0[2];
			clip[3] = p1[3] - p0[3];

			scale = ( p0[0] - p0[3] ) / ( clip[3] - clip[0] );

			clip[0] = (vec_t)( p0[0] + scale * ( clip[0] ) );
			clip[1] = (vec_t)( p0[1] + scale * ( clip[1] ) );
			clip[2] = (vec_t)( p0[2] + scale * ( clip[2] ) );
			clip[3] = (vec_t)( p0[3] + scale * ( clip[3] ) );

			clipped[index][0] = clip[0];
			clipped[index][1] = clip[1];
			clipped[index][2] = clip[2];
			clipped[index][3] = clip[3];
		}
		else if ( index == 0 ) {
			return 0;
		}
	}

	{
		const unsigned int index = CLIP_X_GT_W( p0 );
		if ( index ^ CLIP_X_GT_W( p1 ) ) {
			clip[0] = p1[0] - p0[0];
			clip[1] = p1[1] - p0[1];
			clip[2] = p1[2] - p0[2];
			clip[3] = p1[3] - p0[3];

			scale = ( p0[0] + p0[3] ) / ( -clip[3] - clip[0] );

			clip[0] = (vec_t)( p0[0] + scale * ( clip[0] ) );
			clip[1] = (vec_t)( p0[1] + scale * ( clip[1] ) );
			clip[2] = (vec_t)( p0[2] + scale * ( clip[2] ) );
			clip[3] = (vec_t)( p0[3] + scale * ( clip[3] ) );

			clipped[index][0] = clip[0];
			clipped[index][1] = clip[1];
			clipped[index][2] = clip[2];
			clipped[index][3] = clip[3];
		}
		else if ( index == 0 ) {
			return 0;
		}
	}

	{
		const unsigned int index = CLIP_Y_LT_W( p0 );
		if ( index ^ CLIP_Y_LT_W( p1 ) ) {
			clip[0] = p1[0] - p0[0];
			clip[1] = p1[1] - p0[1];
			clip[2] = p1[2] - p0[2];
			clip[3] = p1[3] - p0[3];

			scale = ( p0[1] - p0[3] ) / ( clip[3] - clip[1] );

			clip[0] = (vec_t)( p0[0] + scale * ( clip[0] ) );
			clip[1] = (vec_t)( p0[1] + scale * ( clip[1] ) );
			clip[2] = (vec_t)( p0[2] + scale * ( clip[2] ) );
			clip[3] = (vec_t)( p0[3] + scale * ( clip[3] ) );

			clipped[index][0] = clip[0];
			clipped[index][1] = clip[1];
			clipped[index][2] = clip[2];
			clipped[index][3] = clip[3];
		}
		else if ( index == 0 ) {
			return 0;
		}
	}

	{
		const unsigned int index = CLIP_Y_GT_W( p0 );
		if ( index ^ CLIP_Y_GT_W( p1 ) ) {
			clip[0] = p1[0] - p0[0];
			clip[1] = p1[1] - p0[1];
			clip[2] = p1[2] - p0[2];
			clip[3] = p1[3] - p0[3];

			scale = ( p0[1] + p0[3] ) / ( -clip[3] - clip[1] );

			clip[0] = (vec_t)( p0[0] + scale * ( clip[0] ) );
			clip[1] = (vec_t)( p0[1] + scale * ( clip[1] ) );
			clip[2] = (vec_t)( p0[2] + scale * ( clip[2] ) );
			clip[3] = (vec_t)( p0[3] + scale * ( clip[3] ) );

			clipped[index][0] = clip[0];
			clipped[index][1] = clip[1];
			clipped[index][2] = clip[2];
			clipped[index][3] = clip[3];
		}
		else if ( index == 0 ) {
			return 0;
		}
	}

	{
		const unsigned int index = CLIP_Z_LT_W( p0 );
		if ( index ^ CLIP_Z_LT_W( p1 ) ) {
			clip[0] = p1[0] - p0[0];
			clip[1] = p1[1] - p0[1];
			clip[2] = p1[2] - p0[2];
			clip[3] = p1[3] - p0[3];

			scale = ( p0[2] - p0[3] ) / ( clip[3] - clip[2] );

			clip[0] = (vec_t)( p0[0] + scale * ( clip[0] ) );
			clip[1] = (vec_t)( p0[1] + scale * ( clip[1] ) );
			clip[2] = (vec_t)( p0[2] + scale * ( clip[2] ) );
			clip[3] = (vec_t)( p0[3] + scale * ( clip[3] ) );

			clipped[index][0] = clip[0];
			clipped[index][1] = clip[1];
			clipped[index][2] = clip[2];
			clipped[index][3] = clip[3];
		}
		else if ( index == 0 ) {
			return 0;
		}
	}

	{
		const unsigned int index = CLIP_Z_GT_W( p0 );
		if ( index ^ CLIP_Z_GT_W( p1 ) ) {
			clip[0] = p1[0] - p0[0];
			clip[1] = p1[1] - p0[1];
			clip[2] = p1[2] - p0[2];
			clip[3] = p1[3] - p0[3];

			scale = ( p0[2] + p0[3] ) / ( -clip[3] - clip[2] );

			clip[0] = (vec_t)( p0[0] + scale * ( clip[0] ) );
			clip[1] = (vec_t)( p0[1] + scale * ( clip[1] ) );
			clip[2] = (vec_t)( p0[2] + scale * ( clip[2] ) );
			clip[3] = (vec_t)( p0[3] + scale * ( clip[3] ) );

			clipped[index][0] = clip[0];
			clipped[index][1] = clip[1];
			clipped[index][2] = clip[2];
			clipped[index][3] = clip[3];
		}
		else if ( index == 0 ) {
			return 0;
		}
	}

	return 2;
}

unsigned int m4x4_clip_line( const m4x4_t matrix, const vec3_t p0, const vec3_t p1, vec4_t clipped[2] ){
	clipped[0][0] = p0[0];
	clipped[0][1] = p0[1];
	clipped[0][2] = p0[2];
	clipped[0][3] = 1;
	clipped[1][0] = p1[0];
	clipped[1][1] = p1[1];
	clipped[1][2] = p1[2];
	clipped[1][3] = 1;

	m4x4_transform_vec4( matrix, clipped[0] );
	m4x4_transform_vec4( matrix, clipped[1] );

	return homogenous_clip_line( clipped );
}

void m4x4_transpose( m4x4_t matrix ){
	int i, j;
	float temp, *p1, *p2;

	for ( i = 1; i < 4; i++ ) {
		for ( j = 0; j < i; j++ ) {
			p1 = matrix + ( j * 4 + i );
			p2 = matrix + ( i * 4 + j );
			temp = *p1;
			*p1 = *p2;
			*p2 = temp;
		}
	}
}

/* adapted from Graphics Gems 2
   invert a 3d matrix (4x3) */
int m4x4_orthogonal_invert( m4x4_t matrix ){
	m4x4_t temp;
	vec_t* src = temp;

	m4x4_assign( src, matrix );

	/* Calculate the determinant of upper left 3x3 submatrix and
	 * determine if the matrix is singular.
	 */
	{
#if 0
		float pos = 0.0f;
		float neg = 0.0f;
		float det = src[0] * src[5] * src[10];
		if ( det >= 0.0 ) {
			pos += det;
		}
		else{ neg += det; }

		det = src[1] * src[6] * src[8];
		if ( det >= 0.0 ) {
			pos += det;
		}
		else{ neg += det; }

		det = src[2] * src[4] * src[9];
		if ( det >= 0.0 ) {
			pos += det;
		}
		else{ neg += det; }

		det = -src[2] * src[5] * src[8];
		if ( det >= 0.0 ) {
			pos += det;
		}
		else{ neg += det; }

		det = -src[1] * src[4] * src[10];
		if ( det >= 0.0 ) {
			pos += det;
		}
		else{ neg += det; }

		det = -src[0] * src[6] * src[9];
		if ( det >= 0.0 ) {
			pos += det;
		}
		else{ neg += det; }

		det = pos + neg;
#elif 0
		float det
		        = ( src[0] * src[5] * src[10] )
		          + ( src[1] * src[6] * src[8] )
		          + ( src[2] * src[4] * src[9] )
		          - ( src[2] * src[5] * src[8] )
		          - ( src[1] * src[4] * src[10] )
		          - ( src[0] * src[6] * src[9] );
#else
		float det
		        = src[0] * ( src[5] * src[10] - src[9] * src[6] )
		          - src[1] * ( src[4] * src[10] - src[8] * src[6] )
		          + src[2] * ( src[4] * src[9] - src[8] * src[5] );

#endif

		if ( det * det < 1e-25 ) {
			return 1;
		}

		det = 1.0f / det;
		matrix[0] = (  ( src[5] * src[10] - src[6] * src[9] ) * det );
		matrix[1] = ( -( src[1] * src[10] - src[2] * src[9] ) * det );
		matrix[2] = (  ( src[1] * src[6] - src[2] * src[5] ) * det );
		matrix[4] = ( -( src[4] * src[10] - src[6] * src[8] ) * det );
		matrix[5] = (  ( src[0] * src[10] - src[2] * src[8] ) * det );
		matrix[6] = ( -( src[0] * src[6] - src[2] * src[4] ) * det );
		matrix[8] = (  ( src[4] * src[9] - src[5] * src[8] ) * det );
		matrix[9] = ( -( src[0] * src[9] - src[1] * src[8] ) * det );
		matrix[10] = (  ( src[0] * src[5] - src[1] * src[4] ) * det );
	}

	/* Do the translation part */
	matrix[12] = -( src[12] * matrix[0] +
	                src[13] * matrix[4] +
	                src[14] * matrix[8] );
	matrix[13] = -( src[12] * matrix[1] +
	                src[13] * matrix[5] +
	                src[14] * matrix[9] );
	matrix[14] = -( src[12] * matrix[2] +
	                src[13] * matrix[6] +
	                src[14] * matrix[10] );

	return 0;
}

void quat_identity( vec4_t quat ){
	quat[0] = quat[1] = quat[2] = 0;
	quat[3] = 1;
}

void quat_multiply_by_quat( vec4_t quat, const vec4_t other ){
	const vec_t x = quat[3] * other[0] + quat[0] * other[3] + quat[1] * other[2] - quat[2] * other[1];
	const vec_t y = quat[3] * other[1] + quat[1] * other[3] + quat[2] * other[0] - quat[0] * other[2];
	const vec_t z = quat[3] * other[2] + quat[2] * other[3] + quat[0] * other[1] - quat[1] * other[0];
	const vec_t w = quat[3] * other[3] - quat[0] * other[0] - quat[1] * other[1] - quat[2] * other[2];
	quat[0] = x;
	quat[1] = y;
	quat[2] = z;
	quat[3] = w;
}

void quat_conjugate( vec4_t quat ){
	VectorNegate( quat, quat );
}

//! quaternion from two unit vectors
void quat_for_unit_vectors( vec4_t quat, const vec3_t from, const vec3_t to ){
	CrossProduct( from, to, quat );
	quat[3] = DotProduct( from, to );
}

void quat_normalise( vec4_t quat ){
	const vec_t n = 1 / ( quat[0] * quat[0] +  quat[1] * quat[1] +  quat[2] * quat[2] +  quat[3] *  quat[3] );
	quat[0] *= n;
	quat[1] *= n;
	quat[2] *= n;
	quat[3] *= n;
}

void quat_for_axisangle( vec4_t quat, const vec3_t axis, double angle ){
	angle *= 0.5;

	quat[3] = (float)sin( angle );

	quat[0] = axis[0] * quat[3];
	quat[1] = axis[1] * quat[3];
	quat[2] = axis[2] * quat[3];
	quat[3] = (float)cos( angle );
}

void m3x3_multiply_by_m3x3( m3x3_t matrix, const m3x3_t matrix_src ){
	float *pDest = matrix;
	float out1, out2, out3;
	int i;

	for ( i = 0; i < 3; i++ )
	{
		out1 =  matrix_src[0] * pDest[0];
		out1 += matrix_src[1] * pDest[3];
		out1 += matrix_src[2] * pDest[6];
		out2 =  matrix_src[3] * pDest[0];
		out2 += matrix_src[4] * pDest[3];
		out2 += matrix_src[5] * pDest[6];
		out3 =  matrix_src[6] * pDest[0];
		out3 += matrix_src[7] * pDest[3];
		out3 += matrix_src[8] * pDest[6];

		pDest[0] = out1;
		pDest[3] = out2;
		pDest[6] = out3;

		pDest++;
	}
}

void m3x3_transform_vec3( const m3x3_t matrix, vec3_t vector ){
	float out1, out2, out3;

	out1 =  matrix[0]  * vector[0];
	out1 += matrix[3]  * vector[1];
	out1 += matrix[6]  * vector[2];
	out2 =  matrix[1]  * vector[0];
	out2 += matrix[4]  * vector[1];
	out2 += matrix[7]  * vector[2];
	out3 =  matrix[2]  * vector[0];
	out3 += matrix[5]  * vector[1];
	out3 += matrix[8] * vector[2];

	vector[0] = out1;
	vector[1] = out2;
	vector[2] = out3;
}

float m3_det( m3x3_t mat ){
	float det;

	det = mat[0] * ( mat[4] * mat[8] - mat[7] * mat[5] )
	      - mat[1] * ( mat[3] * mat[8] - mat[6] * mat[5] )
	      + mat[2] * ( mat[3] * mat[7] - mat[6] * mat[4] );

	return( det );
}

int m3_inverse( m3x3_t mr, m3x3_t ma ){
	float det = m3_det( ma );

	if ( det == 0 ) {
		return 1;
	}


	mr[0] =    ma[4] * ma[8] - ma[5] * ma[7]   / det;
	mr[1] = -( ma[1] * ma[8] - ma[7] * ma[2] ) / det;
	mr[2] =    ma[1] * ma[5] - ma[4] * ma[2]   / det;

	mr[3] = -( ma[3] * ma[8] - ma[5] * ma[6] ) / det;
	mr[4] =    ma[0] * ma[8] - ma[6] * ma[2]   / det;
	mr[5] = -( ma[0] * ma[5] - ma[3] * ma[2] ) / det;

	mr[6] =    ma[3] * ma[7] - ma[6] * ma[4]   / det;
	mr[7] = -( ma[0] * ma[7] - ma[6] * ma[1] ) / det;
	mr[8] =    ma[0] * ma[4] - ma[1] * ma[3]   / det;

	return 0;
}

void m4_submat( m4x4_t mr, m3x3_t mb, int i, int j ){
	int ti, tj, idst, jdst;

	for ( ti = 0; ti < 4; ti++ )
	{
		if ( ti < i ) {
			idst = ti;
		}
		else if ( ti > i ) {
			idst = ti - 1;
		}
		else{
			continue;
		}

		for ( tj = 0; tj < 4; tj++ )
		{
			if ( tj < j ) {
				jdst = tj;
			}
			else if ( tj > j ) {
				jdst = tj - 1;
			}
			else{
				continue;
			}

			mb[idst * 3 + jdst] = mr[ti * 4 + tj ];
		}
	}
}

float m4_det( m4x4_t mr ){
	float det, result = 0, i = 1;
	m3x3_t msub3;
	int n;

	for ( n = 0; n < 4; n++, i *= -1 )
	{
		m4_submat( mr, msub3, 0, n );

		det     = m3_det( msub3 );
		result += mr[n] * det * i;
	}

	return result;
}

int m4x4_invert( m4x4_t matrix ){
	float mdet = m4_det( matrix );
	m3x3_t mtemp;
	int i, j, sign;
	m4x4_t m4x4_temp;

#if 0
	if ( fabs( mdet ) < 0.0000000001 ) {
		return 1;
	}
#endif

	m4x4_assign( m4x4_temp, matrix );

	for ( i = 0; i < 4; i++ )
		for ( j = 0; j < 4; j++ )
		{
			sign = 1 - ( ( i + j ) % 2 ) * 2;

			m4_submat( m4x4_temp, mtemp, i, j );

			matrix[i + j * 4] = ( m3_det( mtemp ) * sign ) / mdet; /*  FIXME: try using * inverse det and see if speed/accuracy are good enough */
		}

	return 0;
}
#if 0
void m4x4_solve_ge( m4x4_t matrix, vec4_t x ){
	int indx[4];
	int c,r;
	int i;
	int best;
	float scale[4];
	float f, pivot;
	float aug[4];
	float recip, ratio;
	float* p;

	for ( r = 0; r < 4; r++ )
	{
		aug[r] = 0;
		indx[r] = r;
	}

	for ( r = 0; r < 4; r++ )
	{
		scale[r] = 0;
		for ( c = 0; c < 4; c++, p++ )
		{
			if ( fabs( *p ) > scale[r] ) {
				scale[r] = (float)fabs( *p );
			}
		}
	}

	for ( c = 0; c < 3; c++ )
	{
		pivot = 0;
		for ( r = c; r < 4; r++ )
		{
			f = (float)fabs( matrix[( indx[r] << 2 ) + c] ) / scale[indx[r]];
			if ( f > pivot ) {
				pivot = f;
				best = r;
			}
		}

		i = indx[c];
		indx[c] = indx[best];
		indx[best] = i;

		recip = 1 / matrix[( indx[c] << 2 ) + c];

		for ( r = c + 1; r < 4; r++ )
		{
			p = matrix + ( indx[r] << 2 );
			ratio = p[c] * recip;

			for ( i = c + 1; i < 4; i++ )
				p[i] -= ratio * matrix[( indx[c] << 2 ) + i];
			aug[indx[r]] -= ratio * aug[indx[c]];
		}
	}

	x[indx[3]] = aug[indx[3]] / matrix[( indx[3] << 2 ) + 3];
	for ( r = 2; r >= 0; r-- )
	{
		f = aug[indx[r]];
		p = matrix + ( indx[r] << 2 );
		recip = 1 / p[r];
		for ( c = ( r + 1 ); c < 4; c++ )
		{
			f -= ( p[c] * x[indx[c]] );
		}
		x[indx[r]] = f * recip;
	}
}
#endif

int matrix_solve_ge( vec_t* matrix, vec_t* aug, vec3_t x ){
	const int N = 3;
	int indx[N];
	int c,r;
	int i;
	int best;
	float scale[N];
	float f, pivot;
	float ratio;
	float* p;

	for ( r = 0; r < N; r++ )
	{
		indx[r] = r;
	}

	for ( r = 0; r < N; r++ )
	{
		p = matrix + r;
		scale[r] = 0;
		for ( c = 0; c < N; c++, p++ )
		{
			if ( fabs( *p ) > scale[r] ) {
				scale[r] = (float)fabs( *p );
			}
		}
	}

	for ( c = 0; c < N; c++ )
	{
		pivot = 0;
		best = -1;
		for ( r = c; r < N; r++ )
		{
			f = (float)fabs( matrix[( indx[r] * N ) + c] ) / scale[indx[r]];
			if ( f > pivot ) {
				pivot = f;
				best = r;
			}
		}

		if ( best == -1 ) {
			return 1;
		}

		i = indx[c];
		indx[c] = indx[best];
		indx[best] = i;

		for ( r = c + 1; r < N; r++ )
		{
			p = matrix + ( indx[r] * N );
			ratio = p[c] / matrix[( indx[c] * N ) + c];

			for ( i = c + 1; i < N; i++ ) p[i] -= ratio * matrix[( indx[c] * N ) + i];
			aug[indx[r]] -= ratio * aug[indx[c]];
		}
	}

	x[N - 1] = aug[indx[N - 1]] / matrix[( indx[N - 1] * N ) + N - 1];
	for ( r = 1; r >= 0; r-- )
	{
		f = aug[indx[r]];
		p = matrix + ( indx[r] * N );
		for ( c = ( r + 1 ); c < N; c++ ) f -= ( p[c] * x[c] );
		x[r] = f / p[r];
	}
	return 0;
}

#ifdef YOU_WANT_IT_TO_BORK
/* Gaussian elimination */
for ( i = 0; i < 4; i++ )
{
	for ( j = ( i + 1 ); j < 4; j++ )
	{
		ratio = matrix[j][i] / matrix[i][i];
		for ( count = i; count < n; count++ ) {
			matrix[j][count] -= ( ratio * matrix[i][count] );
		}
		b[j] -= ( ratio * b[i] );
	}
}

/* Back substitution */
x[n - 1] = b[n - 1] / matrix[n - 1][n - 1];
for ( i = ( n - 2 ); i >= 0; i-- )
{
	temp = b[i];
	for ( j = ( i + 1 ); j < n; j++ )
	{
		temp -= ( matrix[i][j] * x[j] );
	}
	x[i] = temp / matrix[i][i];
}
#endif

int plane_intersect_planes( const vec4_t plane1, const vec4_t plane2, const vec4_t plane3, vec3_t intersection ){
	m3x3_t planes;
	vec3_t b;
	VectorCopy( plane1, planes + 0 );
	b[0] = plane1[3];
	VectorCopy( plane2, planes + 3 );
	b[1] = plane2[3];
	VectorCopy( plane3, planes + 6 );
	b[2] = plane3[3];

	return matrix_solve_ge( planes, b, intersection );
}