ioquake/gtkradiant
0
0
Fork 0
mirror of https://github.com/TTimo/GtkRadiant.git synced 2025-01-11 04:21:08 +00:00
Code Issues Projects Releases Packages Wiki Activity
gtkradiant/tools/urt/libs/mathlib/m4x4.c

1880 lines
49 KiB
C
Raw Blame History

/*
This code provided under the terms of the Id Software
LIMITED USE SOFTWARE LICENSE AGREEMENT, a copy of which is included with the
GtkRadiant sources (see LICENSE_ID). If you did not receive a copy of
LICENSE_ID, please contact Id Software immediately at info@idsoftware.com.
All changes and additions to the original source which have been developed by
other contributors (see CONTRIBUTORS) are provided under the terms of the
license the contributors choose (see LICENSE), to the extent permitted by the
LICENSE_ID. If you did not receive a copy of the contributor license,
please contact the GtkRadiant maintainers at info@gtkradiant.com immediately.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ``AS IS''
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#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);
}
Reference in a new issue View git blame Copy permalink