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vmap/libs/mathlib/m4x4.c

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2020-11-17 11:16:16 +00:00
/*
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 );
}