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gtkradiant/libs/mathlib/m4x4.c
TTimo 12b372f89c ok 
git-svn-id: svn://svn.icculus.org/gtkradiant/GtkRadiant@1 8a3a26a2-13c4-0310-b231-cf6edde360e5
2006-02-10 22:01:20 +00:00

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/*
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;
for ( tj = 0; tj < 4; tj++ )
{
if ( tj < j )
jdst = tj;
else
if ( tj > j )
jdst = tj-1;
if ( ti != i && tj != j )
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
#define N 3
int matrix_solve_ge(vec_t* matrix, vec_t* aug, vec3_t x)
{
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);
}
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