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diff --git a/extern/bullet2/src/BulletCollision/Gimpact/gim_linear_math.h b/extern/bullet2/src/BulletCollision/Gimpact/gim_linear_math.h new file mode 100644 index 00000000000..7bfd50409db --- /dev/null +++ b/extern/bullet2/src/BulletCollision/Gimpact/gim_linear_math.h @@ -0,0 +1,1584 @@ +#ifndef GIM_LINEAR_H_INCLUDED +#define GIM_LINEAR_H_INCLUDED + +/*! \file gim_linear_math.h +*\author Francisco León Nájera +Type Independant Vector and matrix operations. +*/ +/* +----------------------------------------------------------------------------- +This source file is part of GIMPACT Library. + +For the latest info, see http://gimpact.sourceforge.net/ + +Copyright (c) 2006 Francisco Leon Najera. C.C. 80087371. +email: projectileman@yahoo.com + + This library is free software; you can redistribute it and/or + modify it under the terms of EITHER: + (1) The GNU Lesser General Public License as published by the Free + Software Foundation; either version 2.1 of the License, or (at + your option) any later version. The text of the GNU Lesser + General Public License is included with this library in the + file GIMPACT-LICENSE-LGPL.TXT. + (2) The BSD-style license that is included with this library in + the file GIMPACT-LICENSE-BSD.TXT. + (3) The zlib/libpng license that is included with this library in + the file GIMPACT-LICENSE-ZLIB.TXT. + + This library 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 files + GIMPACT-LICENSE-LGPL.TXT, GIMPACT-LICENSE-ZLIB.TXT and GIMPACT-LICENSE-BSD.TXT for more details. + +----------------------------------------------------------------------------- +*/ + + +#include "gim_math.h" +#include "gim_geom_types.h" + + + +/*! \defgroup VECTOR_OPERATIONS +T +Operations for vectors : vec2f,vec3f and vec4f +*/ +//! @{ + +//! Zero out a 2D vector +#define VEC_ZERO_2(a) \ +{ \ + (a)[0] = (a)[1] = 0.0f; \ +}\ + + +//! Zero out a 3D vector +#define VEC_ZERO(a) \ +{ \ + (a)[0] = (a)[1] = (a)[2] = 0.0f; \ +}\ + + +/// Zero out a 4D vector +#define VEC_ZERO_4(a) \ +{ \ + (a)[0] = (a)[1] = (a)[2] = (a)[3] = 0.0f; \ +}\ + + +/// Vector copy +#define VEC_COPY_2(b,a) \ +{ \ + (b)[0] = (a)[0]; \ + (b)[1] = (a)[1]; \ +}\ + + +/// Copy 3D vector +#define VEC_COPY(b,a) \ +{ \ + (b)[0] = (a)[0]; \ + (b)[1] = (a)[1]; \ + (b)[2] = (a)[2]; \ +}\ + + +/// Copy 4D vector +#define VEC_COPY_4(b,a) \ +{ \ + (b)[0] = (a)[0]; \ + (b)[1] = (a)[1]; \ + (b)[2] = (a)[2]; \ + (b)[3] = (a)[3]; \ +}\ + +/// VECTOR SWAP +#define VEC_SWAP(b,a) \ +{ \ + GIM_SWAP_NUMBERS((b)[0],(a)[0]);\ + GIM_SWAP_NUMBERS((b)[1],(a)[1]);\ + GIM_SWAP_NUMBERS((b)[2],(a)[2]);\ +}\ + +/// Vector difference +#define VEC_DIFF_2(v21,v2,v1) \ +{ \ + (v21)[0] = (v2)[0] - (v1)[0]; \ + (v21)[1] = (v2)[1] - (v1)[1]; \ +}\ + + +/// Vector difference +#define VEC_DIFF(v21,v2,v1) \ +{ \ + (v21)[0] = (v2)[0] - (v1)[0]; \ + (v21)[1] = (v2)[1] - (v1)[1]; \ + (v21)[2] = (v2)[2] - (v1)[2]; \ +}\ + + +/// Vector difference +#define VEC_DIFF_4(v21,v2,v1) \ +{ \ + (v21)[0] = (v2)[0] - (v1)[0]; \ + (v21)[1] = (v2)[1] - (v1)[1]; \ + (v21)[2] = (v2)[2] - (v1)[2]; \ + (v21)[3] = (v2)[3] - (v1)[3]; \ +}\ + + +/// Vector sum +#define VEC_SUM_2(v21,v2,v1) \ +{ \ + (v21)[0] = (v2)[0] + (v1)[0]; \ + (v21)[1] = (v2)[1] + (v1)[1]; \ +}\ + + +/// Vector sum +#define VEC_SUM(v21,v2,v1) \ +{ \ + (v21)[0] = (v2)[0] + (v1)[0]; \ + (v21)[1] = (v2)[1] + (v1)[1]; \ + (v21)[2] = (v2)[2] + (v1)[2]; \ +}\ + + +/// Vector sum +#define VEC_SUM_4(v21,v2,v1) \ +{ \ + (v21)[0] = (v2)[0] + (v1)[0]; \ + (v21)[1] = (v2)[1] + (v1)[1]; \ + (v21)[2] = (v2)[2] + (v1)[2]; \ + (v21)[3] = (v2)[3] + (v1)[3]; \ +}\ + + +/// scalar times vector +#define VEC_SCALE_2(c,a,b) \ +{ \ + (c)[0] = (a)*(b)[0]; \ + (c)[1] = (a)*(b)[1]; \ +}\ + + +/// scalar times vector +#define VEC_SCALE(c,a,b) \ +{ \ + (c)[0] = (a)*(b)[0]; \ + (c)[1] = (a)*(b)[1]; \ + (c)[2] = (a)*(b)[2]; \ +}\ + + +/// scalar times vector +#define VEC_SCALE_4(c,a,b) \ +{ \ + (c)[0] = (a)*(b)[0]; \ + (c)[1] = (a)*(b)[1]; \ + (c)[2] = (a)*(b)[2]; \ + (c)[3] = (a)*(b)[3]; \ +}\ + + +/// accumulate scaled vector +#define VEC_ACCUM_2(c,a,b) \ +{ \ + (c)[0] += (a)*(b)[0]; \ + (c)[1] += (a)*(b)[1]; \ +}\ + + +/// accumulate scaled vector +#define VEC_ACCUM(c,a,b) \ +{ \ + (c)[0] += (a)*(b)[0]; \ + (c)[1] += (a)*(b)[1]; \ + (c)[2] += (a)*(b)[2]; \ +}\ + + +/// accumulate scaled vector +#define VEC_ACCUM_4(c,a,b) \ +{ \ + (c)[0] += (a)*(b)[0]; \ + (c)[1] += (a)*(b)[1]; \ + (c)[2] += (a)*(b)[2]; \ + (c)[3] += (a)*(b)[3]; \ +}\ + + +/// Vector dot product +#define VEC_DOT_2(a,b) ((a)[0]*(b)[0] + (a)[1]*(b)[1]) + + +/// Vector dot product +#define VEC_DOT(a,b) ((a)[0]*(b)[0] + (a)[1]*(b)[1] + (a)[2]*(b)[2]) + +/// Vector dot product +#define VEC_DOT_4(a,b) ((a)[0]*(b)[0] + (a)[1]*(b)[1] + (a)[2]*(b)[2] + (a)[3]*(b)[3]) + +/// vector impact parameter (squared) +#define VEC_IMPACT_SQ(bsq,direction,position) {\ + GREAL _llel_ = VEC_DOT(direction, position);\ + bsq = VEC_DOT(position, position) - _llel_*_llel_;\ +}\ + + +/// vector impact parameter +#define VEC_IMPACT(bsq,direction,position) {\ + VEC_IMPACT_SQ(bsq,direction,position); \ + GIM_SQRT(bsq,bsq); \ +}\ + +/// Vector length +#define VEC_LENGTH_2(a,l)\ +{\ + GREAL _pp = VEC_DOT_2(a,a);\ + GIM_SQRT(_pp,l);\ +}\ + + +/// Vector length +#define VEC_LENGTH(a,l)\ +{\ + GREAL _pp = VEC_DOT(a,a);\ + GIM_SQRT(_pp,l);\ +}\ + + +/// Vector length +#define VEC_LENGTH_4(a,l)\ +{\ + GREAL _pp = VEC_DOT_4(a,a);\ + GIM_SQRT(_pp,l);\ +}\ + +/// Vector inv length +#define VEC_INV_LENGTH_2(a,l)\ +{\ + GREAL _pp = VEC_DOT_2(a,a);\ + GIM_INV_SQRT(_pp,l);\ +}\ + + +/// Vector inv length +#define VEC_INV_LENGTH(a,l)\ +{\ + GREAL _pp = VEC_DOT(a,a);\ + GIM_INV_SQRT(_pp,l);\ +}\ + + +/// Vector inv length +#define VEC_INV_LENGTH_4(a,l)\ +{\ + GREAL _pp = VEC_DOT_4(a,a);\ + GIM_INV_SQRT(_pp,l);\ +}\ + + + +/// distance between two points +#define VEC_DISTANCE(_len,_va,_vb) {\ + vec3f _tmp_; \ + VEC_DIFF(_tmp_, _vb, _va); \ + VEC_LENGTH(_tmp_,_len); \ +}\ + + +/// Vector length +#define VEC_CONJUGATE_LENGTH(a,l)\ +{\ + GREAL _pp = 1.0 - a[0]*a[0] - a[1]*a[1] - a[2]*a[2];\ + GIM_SQRT(_pp,l);\ +}\ + + +/// Vector length +#define VEC_NORMALIZE(a) { \ + GREAL len;\ + VEC_INV_LENGTH(a,len); \ + if(len<G_REAL_INFINITY)\ + {\ + a[0] *= len; \ + a[1] *= len; \ + a[2] *= len; \ + } \ +}\ + +/// Set Vector size +#define VEC_RENORMALIZE(a,newlen) { \ + GREAL len;\ + VEC_INV_LENGTH(a,len); \ + if(len<G_REAL_INFINITY)\ + {\ + len *= newlen;\ + a[0] *= len; \ + a[1] *= len; \ + a[2] *= len; \ + } \ +}\ + +/// Vector cross +#define VEC_CROSS(c,a,b) \ +{ \ + c[0] = (a)[1] * (b)[2] - (a)[2] * (b)[1]; \ + c[1] = (a)[2] * (b)[0] - (a)[0] * (b)[2]; \ + c[2] = (a)[0] * (b)[1] - (a)[1] * (b)[0]; \ +}\ + + +/*! Vector perp -- assumes that n is of unit length + * accepts vector v, subtracts out any component parallel to n */ +#define VEC_PERPENDICULAR(vp,v,n) \ +{ \ + GREAL dot = VEC_DOT(v, n); \ + vp[0] = (v)[0] - dot*(n)[0]; \ + vp[1] = (v)[1] - dot*(n)[1]; \ + vp[2] = (v)[2] - dot*(n)[2]; \ +}\ + + +/*! Vector parallel -- assumes that n is of unit length */ +#define VEC_PARALLEL(vp,v,n) \ +{ \ + GREAL dot = VEC_DOT(v, n); \ + vp[0] = (dot) * (n)[0]; \ + vp[1] = (dot) * (n)[1]; \ + vp[2] = (dot) * (n)[2]; \ +}\ + +/*! Same as Vector parallel -- n can have any length + * accepts vector v, subtracts out any component perpendicular to n */ +#define VEC_PROJECT(vp,v,n) \ +{ \ + GREAL scalar = VEC_DOT(v, n); \ + scalar/= VEC_DOT(n, n); \ + vp[0] = (scalar) * (n)[0]; \ + vp[1] = (scalar) * (n)[1]; \ + vp[2] = (scalar) * (n)[2]; \ +}\ + + +/*! accepts vector v*/ +#define VEC_UNPROJECT(vp,v,n) \ +{ \ + GREAL scalar = VEC_DOT(v, n); \ + scalar = VEC_DOT(n, n)/scalar; \ + vp[0] = (scalar) * (n)[0]; \ + vp[1] = (scalar) * (n)[1]; \ + vp[2] = (scalar) * (n)[2]; \ +}\ + + +/*! Vector reflection -- assumes n is of unit length + Takes vector v, reflects it against reflector n, and returns vr */ +#define VEC_REFLECT(vr,v,n) \ +{ \ + GREAL dot = VEC_DOT(v, n); \ + vr[0] = (v)[0] - 2.0 * (dot) * (n)[0]; \ + vr[1] = (v)[1] - 2.0 * (dot) * (n)[1]; \ + vr[2] = (v)[2] - 2.0 * (dot) * (n)[2]; \ +}\ + + +/*! Vector blending +Takes two vectors a, b, blends them together with two scalars */ +#define VEC_BLEND_AB(vr,sa,a,sb,b) \ +{ \ + vr[0] = (sa) * (a)[0] + (sb) * (b)[0]; \ + vr[1] = (sa) * (a)[1] + (sb) * (b)[1]; \ + vr[2] = (sa) * (a)[2] + (sb) * (b)[2]; \ +}\ + +/*! Vector blending +Takes two vectors a, b, blends them together with s <=1 */ +#define VEC_BLEND(vr,a,b,s) VEC_BLEND_AB(vr,(1-s),a,s,b) + +#define VEC_SET3(a,b,op,c) a[0]=b[0] op c[0]; a[1]=b[1] op c[1]; a[2]=b[2] op c[2]; + +//! Finds the bigger cartesian coordinate from a vector +#define VEC_MAYOR_COORD(vec, maxc)\ +{\ + GREAL A[] = {fabs(vec[0]),fabs(vec[1]),fabs(vec[2])};\ + maxc = A[0]>A[1]?(A[0]>A[2]?0:2):(A[1]>A[2]?1:2);\ +}\ + +//! Finds the 2 smallest cartesian coordinates from a vector +#define VEC_MINOR_AXES(vec, i0, i1)\ +{\ + VEC_MAYOR_COORD(vec,i0);\ + i0 = (i0+1)%3;\ + i1 = (i0+1)%3;\ +}\ + + + + +#define VEC_EQUAL(v1,v2) (v1[0]==v2[0]&&v1[1]==v2[1]&&v1[2]==v2[2]) + +#define VEC_NEAR_EQUAL(v1,v2) (GIM_NEAR_EQUAL(v1[0],v2[0])&&GIM_NEAR_EQUAL(v1[1],v2[1])&&GIM_NEAR_EQUAL(v1[2],v2[2])) + + +/// Vector cross +#define X_AXIS_CROSS_VEC(dst,src)\ +{ \ + dst[0] = 0.0f; \ + dst[1] = -src[2]; \ + dst[2] = src[1]; \ +}\ + +#define Y_AXIS_CROSS_VEC(dst,src)\ +{ \ + dst[0] = src[2]; \ + dst[1] = 0.0f; \ + dst[2] = -src[0]; \ +}\ + +#define Z_AXIS_CROSS_VEC(dst,src)\ +{ \ + dst[0] = -src[1]; \ + dst[1] = src[0]; \ + dst[2] = 0.0f; \ +}\ + + + +//! @} + + +/*! \defgroup MATRIX_OPERATIONS +Operations for matrices : mat2f, mat3f and mat4f +*/ +//! @{ + +/// initialize matrix +#define IDENTIFY_MATRIX_3X3(m) \ +{ \ + m[0][0] = 1.0; \ + m[0][1] = 0.0; \ + m[0][2] = 0.0; \ + \ + m[1][0] = 0.0; \ + m[1][1] = 1.0; \ + m[1][2] = 0.0; \ + \ + m[2][0] = 0.0; \ + m[2][1] = 0.0; \ + m[2][2] = 1.0; \ +}\ + +/*! initialize matrix */ +#define IDENTIFY_MATRIX_4X4(m) \ +{ \ + m[0][0] = 1.0; \ + m[0][1] = 0.0; \ + m[0][2] = 0.0; \ + m[0][3] = 0.0; \ + \ + m[1][0] = 0.0; \ + m[1][1] = 1.0; \ + m[1][2] = 0.0; \ + m[1][3] = 0.0; \ + \ + m[2][0] = 0.0; \ + m[2][1] = 0.0; \ + m[2][2] = 1.0; \ + m[2][3] = 0.0; \ + \ + m[3][0] = 0.0; \ + m[3][1] = 0.0; \ + m[3][2] = 0.0; \ + m[3][3] = 1.0; \ +}\ + +/*! initialize matrix */ +#define ZERO_MATRIX_4X4(m) \ +{ \ + m[0][0] = 0.0; \ + m[0][1] = 0.0; \ + m[0][2] = 0.0; \ + m[0][3] = 0.0; \ + \ + m[1][0] = 0.0; \ + m[1][1] = 0.0; \ + m[1][2] = 0.0; \ + m[1][3] = 0.0; \ + \ + m[2][0] = 0.0; \ + m[2][1] = 0.0; \ + m[2][2] = 0.0; \ + m[2][3] = 0.0; \ + \ + m[3][0] = 0.0; \ + m[3][1] = 0.0; \ + m[3][2] = 0.0; \ + m[3][3] = 0.0; \ +}\ + +/*! matrix rotation X */ +#define ROTX_CS(m,cosine,sine) \ +{ \ + /* rotation about the x-axis */ \ + \ + m[0][0] = 1.0; \ + m[0][1] = 0.0; \ + m[0][2] = 0.0; \ + m[0][3] = 0.0; \ + \ + m[1][0] = 0.0; \ + m[1][1] = (cosine); \ + m[1][2] = (sine); \ + m[1][3] = 0.0; \ + \ + m[2][0] = 0.0; \ + m[2][1] = -(sine); \ + m[2][2] = (cosine); \ + m[2][3] = 0.0; \ + \ + m[3][0] = 0.0; \ + m[3][1] = 0.0; \ + m[3][2] = 0.0; \ + m[3][3] = 1.0; \ +}\ + +/*! matrix rotation Y */ +#define ROTY_CS(m,cosine,sine) \ +{ \ + /* rotation about the y-axis */ \ + \ + m[0][0] = (cosine); \ + m[0][1] = 0.0; \ + m[0][2] = -(sine); \ + m[0][3] = 0.0; \ + \ + m[1][0] = 0.0; \ + m[1][1] = 1.0; \ + m[1][2] = 0.0; \ + m[1][3] = 0.0; \ + \ + m[2][0] = (sine); \ + m[2][1] = 0.0; \ + m[2][2] = (cosine); \ + m[2][3] = 0.0; \ + \ + m[3][0] = 0.0; \ + m[3][1] = 0.0; \ + m[3][2] = 0.0; \ + m[3][3] = 1.0; \ +}\ + +/*! matrix rotation Z */ +#define ROTZ_CS(m,cosine,sine) \ +{ \ + /* rotation about the z-axis */ \ + \ + m[0][0] = (cosine); \ + m[0][1] = (sine); \ + m[0][2] = 0.0; \ + m[0][3] = 0.0; \ + \ + m[1][0] = -(sine); \ + m[1][1] = (cosine); \ + m[1][2] = 0.0; \ + m[1][3] = 0.0; \ + \ + m[2][0] = 0.0; \ + m[2][1] = 0.0; \ + m[2][2] = 1.0; \ + m[2][3] = 0.0; \ + \ + m[3][0] = 0.0; \ + m[3][1] = 0.0; \ + m[3][2] = 0.0; \ + m[3][3] = 1.0; \ +}\ + +/*! matrix copy */ +#define COPY_MATRIX_2X2(b,a) \ +{ \ + b[0][0] = a[0][0]; \ + b[0][1] = a[0][1]; \ + \ + b[1][0] = a[1][0]; \ + b[1][1] = a[1][1]; \ + \ +}\ + + +/*! matrix copy */ +#define COPY_MATRIX_2X3(b,a) \ +{ \ + b[0][0] = a[0][0]; \ + b[0][1] = a[0][1]; \ + b[0][2] = a[0][2]; \ + \ + b[1][0] = a[1][0]; \ + b[1][1] = a[1][1]; \ + b[1][2] = a[1][2]; \ +}\ + + +/*! matrix copy */ +#define COPY_MATRIX_3X3(b,a) \ +{ \ + b[0][0] = a[0][0]; \ + b[0][1] = a[0][1]; \ + b[0][2] = a[0][2]; \ + \ + b[1][0] = a[1][0]; \ + b[1][1] = a[1][1]; \ + b[1][2] = a[1][2]; \ + \ + b[2][0] = a[2][0]; \ + b[2][1] = a[2][1]; \ + b[2][2] = a[2][2]; \ +}\ + + +/*! matrix copy */ +#define COPY_MATRIX_4X4(b,a) \ +{ \ + b[0][0] = a[0][0]; \ + b[0][1] = a[0][1]; \ + b[0][2] = a[0][2]; \ + b[0][3] = a[0][3]; \ + \ + b[1][0] = a[1][0]; \ + b[1][1] = a[1][1]; \ + b[1][2] = a[1][2]; \ + b[1][3] = a[1][3]; \ + \ + b[2][0] = a[2][0]; \ + b[2][1] = a[2][1]; \ + b[2][2] = a[2][2]; \ + b[2][3] = a[2][3]; \ + \ + b[3][0] = a[3][0]; \ + b[3][1] = a[3][1]; \ + b[3][2] = a[3][2]; \ + b[3][3] = a[3][3]; \ +}\ + + +/*! matrix transpose */ +#define TRANSPOSE_MATRIX_2X2(b,a) \ +{ \ + b[0][0] = a[0][0]; \ + b[0][1] = a[1][0]; \ + \ + b[1][0] = a[0][1]; \ + b[1][1] = a[1][1]; \ +}\ + + +/*! matrix transpose */ +#define TRANSPOSE_MATRIX_3X3(b,a) \ +{ \ + b[0][0] = a[0][0]; \ + b[0][1] = a[1][0]; \ + b[0][2] = a[2][0]; \ + \ + b[1][0] = a[0][1]; \ + b[1][1] = a[1][1]; \ + b[1][2] = a[2][1]; \ + \ + b[2][0] = a[0][2]; \ + b[2][1] = a[1][2]; \ + b[2][2] = a[2][2]; \ +}\ + + +/*! matrix transpose */ +#define TRANSPOSE_MATRIX_4X4(b,a) \ +{ \ + b[0][0] = a[0][0]; \ + b[0][1] = a[1][0]; \ + b[0][2] = a[2][0]; \ + b[0][3] = a[3][0]; \ + \ + b[1][0] = a[0][1]; \ + b[1][1] = a[1][1]; \ + b[1][2] = a[2][1]; \ + b[1][3] = a[3][1]; \ + \ + b[2][0] = a[0][2]; \ + b[2][1] = a[1][2]; \ + b[2][2] = a[2][2]; \ + b[2][3] = a[3][2]; \ + \ + b[3][0] = a[0][3]; \ + b[3][1] = a[1][3]; \ + b[3][2] = a[2][3]; \ + b[3][3] = a[3][3]; \ +}\ + + +/*! multiply matrix by scalar */ +#define SCALE_MATRIX_2X2(b,s,a) \ +{ \ + b[0][0] = (s) * a[0][0]; \ + b[0][1] = (s) * a[0][1]; \ + \ + b[1][0] = (s) * a[1][0]; \ + b[1][1] = (s) * a[1][1]; \ +}\ + + +/*! multiply matrix by scalar */ +#define SCALE_MATRIX_3X3(b,s,a) \ +{ \ + b[0][0] = (s) * a[0][0]; \ + b[0][1] = (s) * a[0][1]; \ + b[0][2] = (s) * a[0][2]; \ + \ + b[1][0] = (s) * a[1][0]; \ + b[1][1] = (s) * a[1][1]; \ + b[1][2] = (s) * a[1][2]; \ + \ + b[2][0] = (s) * a[2][0]; \ + b[2][1] = (s) * a[2][1]; \ + b[2][2] = (s) * a[2][2]; \ +}\ + + +/*! multiply matrix by scalar */ +#define SCALE_MATRIX_4X4(b,s,a) \ +{ \ + b[0][0] = (s) * a[0][0]; \ + b[0][1] = (s) * a[0][1]; \ + b[0][2] = (s) * a[0][2]; \ + b[0][3] = (s) * a[0][3]; \ + \ + b[1][0] = (s) * a[1][0]; \ + b[1][1] = (s) * a[1][1]; \ + b[1][2] = (s) * a[1][2]; \ + b[1][3] = (s) * a[1][3]; \ + \ + b[2][0] = (s) * a[2][0]; \ + b[2][1] = (s) * a[2][1]; \ + b[2][2] = (s) * a[2][2]; \ + b[2][3] = (s) * a[2][3]; \ + \ + b[3][0] = s * a[3][0]; \ + b[3][1] = s * a[3][1]; \ + b[3][2] = s * a[3][2]; \ + b[3][3] = s * a[3][3]; \ +}\ + + +/*! multiply matrix by scalar */ +#define SCALE_VEC_MATRIX_2X2(b,svec,a) \ +{ \ + b[0][0] = svec[0] * a[0][0]; \ + b[1][0] = svec[0] * a[1][0]; \ + \ + b[0][1] = svec[1] * a[0][1]; \ + b[1][1] = svec[1] * a[1][1]; \ +}\ + + +/*! multiply matrix by scalar. Each columns is scaled by each scalar vector component */ +#define SCALE_VEC_MATRIX_3X3(b,svec,a) \ +{ \ + b[0][0] = svec[0] * a[0][0]; \ + b[1][0] = svec[0] * a[1][0]; \ + b[2][0] = svec[0] * a[2][0]; \ + \ + b[0][1] = svec[1] * a[0][1]; \ + b[1][1] = svec[1] * a[1][1]; \ + b[2][1] = svec[1] * a[2][1]; \ + \ + b[0][2] = svec[2] * a[0][2]; \ + b[1][2] = svec[2] * a[1][2]; \ + b[2][2] = svec[2] * a[2][2]; \ +}\ + + +/*! multiply matrix by scalar */ +#define SCALE_VEC_MATRIX_4X4(b,svec,a) \ +{ \ + b[0][0] = svec[0] * a[0][0]; \ + b[1][0] = svec[0] * a[1][0]; \ + b[2][0] = svec[0] * a[2][0]; \ + b[3][0] = svec[0] * a[3][0]; \ + \ + b[0][1] = svec[1] * a[0][1]; \ + b[1][1] = svec[1] * a[1][1]; \ + b[2][1] = svec[1] * a[2][1]; \ + b[3][1] = svec[1] * a[3][1]; \ + \ + b[0][2] = svec[2] * a[0][2]; \ + b[1][2] = svec[2] * a[1][2]; \ + b[2][2] = svec[2] * a[2][2]; \ + b[3][2] = svec[2] * a[3][2]; \ + \ + b[0][3] = svec[3] * a[0][3]; \ + b[1][3] = svec[3] * a[1][3]; \ + b[2][3] = svec[3] * a[2][3]; \ + b[3][3] = svec[3] * a[3][3]; \ +}\ + + +/*! multiply matrix by scalar */ +#define ACCUM_SCALE_MATRIX_2X2(b,s,a) \ +{ \ + b[0][0] += (s) * a[0][0]; \ + b[0][1] += (s) * a[0][1]; \ + \ + b[1][0] += (s) * a[1][0]; \ + b[1][1] += (s) * a[1][1]; \ +}\ + + +/*! multiply matrix by scalar */ +#define ACCUM_SCALE_MATRIX_3X3(b,s,a) \ +{ \ + b[0][0] += (s) * a[0][0]; \ + b[0][1] += (s) * a[0][1]; \ + b[0][2] += (s) * a[0][2]; \ + \ + b[1][0] += (s) * a[1][0]; \ + b[1][1] += (s) * a[1][1]; \ + b[1][2] += (s) * a[1][2]; \ + \ + b[2][0] += (s) * a[2][0]; \ + b[2][1] += (s) * a[2][1]; \ + b[2][2] += (s) * a[2][2]; \ +}\ + + +/*! multiply matrix by scalar */ +#define ACCUM_SCALE_MATRIX_4X4(b,s,a) \ +{ \ + b[0][0] += (s) * a[0][0]; \ + b[0][1] += (s) * a[0][1]; \ + b[0][2] += (s) * a[0][2]; \ + b[0][3] += (s) * a[0][3]; \ + \ + b[1][0] += (s) * a[1][0]; \ + b[1][1] += (s) * a[1][1]; \ + b[1][2] += (s) * a[1][2]; \ + b[1][3] += (s) * a[1][3]; \ + \ + b[2][0] += (s) * a[2][0]; \ + b[2][1] += (s) * a[2][1]; \ + b[2][2] += (s) * a[2][2]; \ + b[2][3] += (s) * a[2][3]; \ + \ + b[3][0] += (s) * a[3][0]; \ + b[3][1] += (s) * a[3][1]; \ + b[3][2] += (s) * a[3][2]; \ + b[3][3] += (s) * a[3][3]; \ +}\ + +/*! matrix product */ +/*! c[x][y] = a[x][0]*b[0][y]+a[x][1]*b[1][y]+a[x][2]*b[2][y]+a[x][3]*b[3][y];*/ +#define MATRIX_PRODUCT_2X2(c,a,b) \ +{ \ + c[0][0] = a[0][0]*b[0][0]+a[0][1]*b[1][0]; \ + c[0][1] = a[0][0]*b[0][1]+a[0][1]*b[1][1]; \ + \ + c[1][0] = a[1][0]*b[0][0]+a[1][1]*b[1][0]; \ + c[1][1] = a[1][0]*b[0][1]+a[1][1]*b[1][1]; \ + \ +}\ + +/*! matrix product */ +/*! c[x][y] = a[x][0]*b[0][y]+a[x][1]*b[1][y]+a[x][2]*b[2][y]+a[x][3]*b[3][y];*/ +#define MATRIX_PRODUCT_3X3(c,a,b) \ +{ \ + c[0][0] = a[0][0]*b[0][0]+a[0][1]*b[1][0]+a[0][2]*b[2][0]; \ + c[0][1] = a[0][0]*b[0][1]+a[0][1]*b[1][1]+a[0][2]*b[2][1]; \ + c[0][2] = a[0][0]*b[0][2]+a[0][1]*b[1][2]+a[0][2]*b[2][2]; \ + \ + c[1][0] = a[1][0]*b[0][0]+a[1][1]*b[1][0]+a[1][2]*b[2][0]; \ + c[1][1] = a[1][0]*b[0][1]+a[1][1]*b[1][1]+a[1][2]*b[2][1]; \ + c[1][2] = a[1][0]*b[0][2]+a[1][1]*b[1][2]+a[1][2]*b[2][2]; \ + \ + c[2][0] = a[2][0]*b[0][0]+a[2][1]*b[1][0]+a[2][2]*b[2][0]; \ + c[2][1] = a[2][0]*b[0][1]+a[2][1]*b[1][1]+a[2][2]*b[2][1]; \ + c[2][2] = a[2][0]*b[0][2]+a[2][1]*b[1][2]+a[2][2]*b[2][2]; \ +}\ + + +/*! matrix product */ +/*! c[x][y] = a[x][0]*b[0][y]+a[x][1]*b[1][y]+a[x][2]*b[2][y]+a[x][3]*b[3][y];*/ +#define MATRIX_PRODUCT_4X4(c,a,b) \ +{ \ + c[0][0] = a[0][0]*b[0][0]+a[0][1]*b[1][0]+a[0][2]*b[2][0]+a[0][3]*b[3][0];\ + c[0][1] = a[0][0]*b[0][1]+a[0][1]*b[1][1]+a[0][2]*b[2][1]+a[0][3]*b[3][1];\ + c[0][2] = a[0][0]*b[0][2]+a[0][1]*b[1][2]+a[0][2]*b[2][2]+a[0][3]*b[3][2];\ + c[0][3] = a[0][0]*b[0][3]+a[0][1]*b[1][3]+a[0][2]*b[2][3]+a[0][3]*b[3][3];\ + \ + c[1][0] = a[1][0]*b[0][0]+a[1][1]*b[1][0]+a[1][2]*b[2][0]+a[1][3]*b[3][0];\ + c[1][1] = a[1][0]*b[0][1]+a[1][1]*b[1][1]+a[1][2]*b[2][1]+a[1][3]*b[3][1];\ + c[1][2] = a[1][0]*b[0][2]+a[1][1]*b[1][2]+a[1][2]*b[2][2]+a[1][3]*b[3][2];\ + c[1][3] = a[1][0]*b[0][3]+a[1][1]*b[1][3]+a[1][2]*b[2][3]+a[1][3]*b[3][3];\ + \ + c[2][0] = a[2][0]*b[0][0]+a[2][1]*b[1][0]+a[2][2]*b[2][0]+a[2][3]*b[3][0];\ + c[2][1] = a[2][0]*b[0][1]+a[2][1]*b[1][1]+a[2][2]*b[2][1]+a[2][3]*b[3][1];\ + c[2][2] = a[2][0]*b[0][2]+a[2][1]*b[1][2]+a[2][2]*b[2][2]+a[2][3]*b[3][2];\ + c[2][3] = a[2][0]*b[0][3]+a[2][1]*b[1][3]+a[2][2]*b[2][3]+a[2][3]*b[3][3];\ + \ + c[3][0] = a[3][0]*b[0][0]+a[3][1]*b[1][0]+a[3][2]*b[2][0]+a[3][3]*b[3][0];\ + c[3][1] = a[3][0]*b[0][1]+a[3][1]*b[1][1]+a[3][2]*b[2][1]+a[3][3]*b[3][1];\ + c[3][2] = a[3][0]*b[0][2]+a[3][1]*b[1][2]+a[3][2]*b[2][2]+a[3][3]*b[3][2];\ + c[3][3] = a[3][0]*b[0][3]+a[3][1]*b[1][3]+a[3][2]*b[2][3]+a[3][3]*b[3][3];\ +}\ + + +/*! matrix times vector */ +#define MAT_DOT_VEC_2X2(p,m,v) \ +{ \ + p[0] = m[0][0]*v[0] + m[0][1]*v[1]; \ + p[1] = m[1][0]*v[0] + m[1][1]*v[1]; \ +}\ + + +/*! matrix times vector */ +#define MAT_DOT_VEC_3X3(p,m,v) \ +{ \ + p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2]; \ + p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2]; \ + p[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2]; \ +}\ + + +/*! matrix times vector +v is a vec4f +*/ +#define MAT_DOT_VEC_4X4(p,m,v) \ +{ \ + p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2] + m[0][3]*v[3]; \ + p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2] + m[1][3]*v[3]; \ + p[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2] + m[2][3]*v[3]; \ + p[3] = m[3][0]*v[0] + m[3][1]*v[1] + m[3][2]*v[2] + m[3][3]*v[3]; \ +}\ + +/*! matrix times vector +v is a vec3f +and m is a mat4f<br> +Last column is added as the position +*/ +#define MAT_DOT_VEC_3X4(p,m,v) \ +{ \ + p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2] + m[0][3]; \ + p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2] + m[1][3]; \ + p[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2] + m[2][3]; \ +}\ + + +/*! vector transpose times matrix */ +/*! p[j] = v[0]*m[0][j] + v[1]*m[1][j] + v[2]*m[2][j]; */ +#define VEC_DOT_MAT_3X3(p,v,m) \ +{ \ + p[0] = v[0]*m[0][0] + v[1]*m[1][0] + v[2]*m[2][0]; \ + p[1] = v[0]*m[0][1] + v[1]*m[1][1] + v[2]*m[2][1]; \ + p[2] = v[0]*m[0][2] + v[1]*m[1][2] + v[2]*m[2][2]; \ +}\ + + +/*! affine matrix times vector */ +/** The matrix is assumed to be an affine matrix, with last two + * entries representing a translation */ +#define MAT_DOT_VEC_2X3(p,m,v) \ +{ \ + p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]; \ + p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]; \ +}\ + +//! Transform a plane +#define MAT_TRANSFORM_PLANE_4X4(pout,m,plane)\ +{ \ + pout[0] = m[0][0]*plane[0] + m[0][1]*plane[1] + m[0][2]*plane[2];\ + pout[1] = m[1][0]*plane[0] + m[1][1]*plane[1] + m[1][2]*plane[2];\ + pout[2] = m[2][0]*plane[0] + m[2][1]*plane[1] + m[2][2]*plane[2];\ + pout[3] = m[0][3]*pout[0] + m[1][3]*pout[1] + m[2][3]*pout[2] + plane[3];\ +}\ + + + +/** inverse transpose of matrix times vector + * + * This macro computes inverse transpose of matrix m, + * and multiplies vector v into it, to yeild vector p + * + * DANGER !!! Do Not use this on normal vectors!!! + * It will leave normals the wrong length !!! + * See macro below for use on normals. + */ +#define INV_TRANSP_MAT_DOT_VEC_2X2(p,m,v) \ +{ \ + GREAL det; \ + \ + det = m[0][0]*m[1][1] - m[0][1]*m[1][0]; \ + p[0] = m[1][1]*v[0] - m[1][0]*v[1]; \ + p[1] = - m[0][1]*v[0] + m[0][0]*v[1]; \ + \ + /* if matrix not singular, and not orthonormal, then renormalize */ \ + if ((det!=1.0f) && (det != 0.0f)) { \ + det = 1.0f / det; \ + p[0] *= det; \ + p[1] *= det; \ + } \ +}\ + + +/** transform normal vector by inverse transpose of matrix + * and then renormalize the vector + * + * This macro computes inverse transpose of matrix m, + * and multiplies vector v into it, to yeild vector p + * Vector p is then normalized. + */ +#define NORM_XFORM_2X2(p,m,v) \ +{ \ + GREAL len; \ + \ + /* do nothing if off-diagonals are zero and diagonals are \ + * equal */ \ + if ((m[0][1] != 0.0) || (m[1][0] != 0.0) || (m[0][0] != m[1][1])) { \ + p[0] = m[1][1]*v[0] - m[1][0]*v[1]; \ + p[1] = - m[0][1]*v[0] + m[0][0]*v[1]; \ + \ + len = p[0]*p[0] + p[1]*p[1]; \ + GIM_INV_SQRT(len,len); \ + p[0] *= len; \ + p[1] *= len; \ + } else { \ + VEC_COPY_2 (p, v); \ + } \ +}\ + + +/** outer product of vector times vector transpose + * + * The outer product of vector v and vector transpose t yeilds + * dyadic matrix m. + */ +#define OUTER_PRODUCT_2X2(m,v,t) \ +{ \ + m[0][0] = v[0] * t[0]; \ + m[0][1] = v[0] * t[1]; \ + \ + m[1][0] = v[1] * t[0]; \ + m[1][1] = v[1] * t[1]; \ +}\ + + +/** outer product of vector times vector transpose + * + * The outer product of vector v and vector transpose t yeilds + * dyadic matrix m. + */ +#define OUTER_PRODUCT_3X3(m,v,t) \ +{ \ + m[0][0] = v[0] * t[0]; \ + m[0][1] = v[0] * t[1]; \ + m[0][2] = v[0] * t[2]; \ + \ + m[1][0] = v[1] * t[0]; \ + m[1][1] = v[1] * t[1]; \ + m[1][2] = v[1] * t[2]; \ + \ + m[2][0] = v[2] * t[0]; \ + m[2][1] = v[2] * t[1]; \ + m[2][2] = v[2] * t[2]; \ +}\ + + +/** outer product of vector times vector transpose + * + * The outer product of vector v and vector transpose t yeilds + * dyadic matrix m. + */ +#define OUTER_PRODUCT_4X4(m,v,t) \ +{ \ + m[0][0] = v[0] * t[0]; \ + m[0][1] = v[0] * t[1]; \ + m[0][2] = v[0] * t[2]; \ + m[0][3] = v[0] * t[3]; \ + \ + m[1][0] = v[1] * t[0]; \ + m[1][1] = v[1] * t[1]; \ + m[1][2] = v[1] * t[2]; \ + m[1][3] = v[1] * t[3]; \ + \ + m[2][0] = v[2] * t[0]; \ + m[2][1] = v[2] * t[1]; \ + m[2][2] = v[2] * t[2]; \ + m[2][3] = v[2] * t[3]; \ + \ + m[3][0] = v[3] * t[0]; \ + m[3][1] = v[3] * t[1]; \ + m[3][2] = v[3] * t[2]; \ + m[3][3] = v[3] * t[3]; \ +}\ + + +/** outer product of vector times vector transpose + * + * The outer product of vector v and vector transpose t yeilds + * dyadic matrix m. + */ +#define ACCUM_OUTER_PRODUCT_2X2(m,v,t) \ +{ \ + m[0][0] += v[0] * t[0]; \ + m[0][1] += v[0] * t[1]; \ + \ + m[1][0] += v[1] * t[0]; \ + m[1][1] += v[1] * t[1]; \ +}\ + + +/** outer product of vector times vector transpose + * + * The outer product of vector v and vector transpose t yeilds + * dyadic matrix m. + */ +#define ACCUM_OUTER_PRODUCT_3X3(m,v,t) \ +{ \ + m[0][0] += v[0] * t[0]; \ + m[0][1] += v[0] * t[1]; \ + m[0][2] += v[0] * t[2]; \ + \ + m[1][0] += v[1] * t[0]; \ + m[1][1] += v[1] * t[1]; \ + m[1][2] += v[1] * t[2]; \ + \ + m[2][0] += v[2] * t[0]; \ + m[2][1] += v[2] * t[1]; \ + m[2][2] += v[2] * t[2]; \ +}\ + + +/** outer product of vector times vector transpose + * + * The outer product of vector v and vector transpose t yeilds + * dyadic matrix m. + */ +#define ACCUM_OUTER_PRODUCT_4X4(m,v,t) \ +{ \ + m[0][0] += v[0] * t[0]; \ + m[0][1] += v[0] * t[1]; \ + m[0][2] += v[0] * t[2]; \ + m[0][3] += v[0] * t[3]; \ + \ + m[1][0] += v[1] * t[0]; \ + m[1][1] += v[1] * t[1]; \ + m[1][2] += v[1] * t[2]; \ + m[1][3] += v[1] * t[3]; \ + \ + m[2][0] += v[2] * t[0]; \ + m[2][1] += v[2] * t[1]; \ + m[2][2] += v[2] * t[2]; \ + m[2][3] += v[2] * t[3]; \ + \ + m[3][0] += v[3] * t[0]; \ + m[3][1] += v[3] * t[1]; \ + m[3][2] += v[3] * t[2]; \ + m[3][3] += v[3] * t[3]; \ +}\ + + +/** determinant of matrix + * + * Computes determinant of matrix m, returning d + */ +#define DETERMINANT_2X2(d,m) \ +{ \ + d = m[0][0] * m[1][1] - m[0][1] * m[1][0]; \ +}\ + + +/** determinant of matrix + * + * Computes determinant of matrix m, returning d + */ +#define DETERMINANT_3X3(d,m) \ +{ \ + d = m[0][0] * (m[1][1]*m[2][2] - m[1][2] * m[2][1]); \ + d -= m[0][1] * (m[1][0]*m[2][2] - m[1][2] * m[2][0]); \ + d += m[0][2] * (m[1][0]*m[2][1] - m[1][1] * m[2][0]); \ +}\ + + +/** i,j,th cofactor of a 4x4 matrix + * + */ +#define COFACTOR_4X4_IJ(fac,m,i,j) \ +{ \ + GUINT __ii[4], __jj[4], __k; \ + \ + for (__k=0; __k<i; __k++) __ii[__k] = __k; \ + for (__k=i; __k<3; __k++) __ii[__k] = __k+1; \ + for (__k=0; __k<j; __k++) __jj[__k] = __k; \ + for (__k=j; __k<3; __k++) __jj[__k] = __k+1; \ + \ + (fac) = m[__ii[0]][__jj[0]] * (m[__ii[1]][__jj[1]]*m[__ii[2]][__jj[2]] \ + - m[__ii[1]][__jj[2]]*m[__ii[2]][__jj[1]]); \ + (fac) -= m[__ii[0]][__jj[1]] * (m[__ii[1]][__jj[0]]*m[__ii[2]][__jj[2]] \ + - m[__ii[1]][__jj[2]]*m[__ii[2]][__jj[0]]);\ + (fac) += m[__ii[0]][__jj[2]] * (m[__ii[1]][__jj[0]]*m[__ii[2]][__jj[1]] \ + - m[__ii[1]][__jj[1]]*m[__ii[2]][__jj[0]]);\ + \ + __k = i+j; \ + if ( __k != (__k/2)*2) { \ + (fac) = -(fac); \ + } \ +}\ + + +/** determinant of matrix + * + * Computes determinant of matrix m, returning d + */ +#define DETERMINANT_4X4(d,m) \ +{ \ + GREAL cofac; \ + COFACTOR_4X4_IJ (cofac, m, 0, 0); \ + d = m[0][0] * cofac; \ + COFACTOR_4X4_IJ (cofac, m, 0, 1); \ + d += m[0][1] * cofac; \ + COFACTOR_4X4_IJ (cofac, m, 0, 2); \ + d += m[0][2] * cofac; \ + COFACTOR_4X4_IJ (cofac, m, 0, 3); \ + d += m[0][3] * cofac; \ +}\ + + +/** cofactor of matrix + * + * Computes cofactor of matrix m, returning a + */ +#define COFACTOR_2X2(a,m) \ +{ \ + a[0][0] = (m)[1][1]; \ + a[0][1] = - (m)[1][0]; \ + a[1][0] = - (m)[0][1]; \ + a[1][1] = (m)[0][0]; \ +}\ + + +/** cofactor of matrix + * + * Computes cofactor of matrix m, returning a + */ +#define COFACTOR_3X3(a,m) \ +{ \ + a[0][0] = m[1][1]*m[2][2] - m[1][2]*m[2][1]; \ + a[0][1] = - (m[1][0]*m[2][2] - m[2][0]*m[1][2]); \ + a[0][2] = m[1][0]*m[2][1] - m[1][1]*m[2][0]; \ + a[1][0] = - (m[0][1]*m[2][2] - m[0][2]*m[2][1]); \ + a[1][1] = m[0][0]*m[2][2] - m[0][2]*m[2][0]; \ + a[1][2] = - (m[0][0]*m[2][1] - m[0][1]*m[2][0]); \ + a[2][0] = m[0][1]*m[1][2] - m[0][2]*m[1][1]; \ + a[2][1] = - (m[0][0]*m[1][2] - m[0][2]*m[1][0]); \ + a[2][2] = m[0][0]*m[1][1] - m[0][1]*m[1][0]); \ +}\ + + +/** cofactor of matrix + * + * Computes cofactor of matrix m, returning a + */ +#define COFACTOR_4X4(a,m) \ +{ \ + int i,j; \ + \ + for (i=0; i<4; i++) { \ + for (j=0; j<4; j++) { \ + COFACTOR_4X4_IJ (a[i][j], m, i, j); \ + } \ + } \ +}\ + + +/** adjoint of matrix + * + * Computes adjoint of matrix m, returning a + * (Note that adjoint is just the transpose of the cofactor matrix) + */ +#define ADJOINT_2X2(a,m) \ +{ \ + a[0][0] = (m)[1][1]; \ + a[1][0] = - (m)[1][0]; \ + a[0][1] = - (m)[0][1]; \ + a[1][1] = (m)[0][0]; \ +}\ + + +/** adjoint of matrix + * + * Computes adjoint of matrix m, returning a + * (Note that adjoint is just the transpose of the cofactor matrix) + */ +#define ADJOINT_3X3(a,m) \ +{ \ + a[0][0] = m[1][1]*m[2][2] - m[1][2]*m[2][1]; \ + a[1][0] = - (m[1][0]*m[2][2] - m[2][0]*m[1][2]); \ + a[2][0] = m[1][0]*m[2][1] - m[1][1]*m[2][0]; \ + a[0][1] = - (m[0][1]*m[2][2] - m[0][2]*m[2][1]); \ + a[1][1] = m[0][0]*m[2][2] - m[0][2]*m[2][0]; \ + a[2][1] = - (m[0][0]*m[2][1] - m[0][1]*m[2][0]); \ + a[0][2] = m[0][1]*m[1][2] - m[0][2]*m[1][1]; \ + a[1][2] = - (m[0][0]*m[1][2] - m[0][2]*m[1][0]); \ + a[2][2] = m[0][0]*m[1][1] - m[0][1]*m[1][0]); \ +}\ + + +/** adjoint of matrix + * + * Computes adjoint of matrix m, returning a + * (Note that adjoint is just the transpose of the cofactor matrix) + */ +#define ADJOINT_4X4(a,m) \ +{ \ + char _i_,_j_; \ + \ + for (_i_=0; _i_<4; _i_++) { \ + for (_j_=0; _j_<4; _j_++) { \ + COFACTOR_4X4_IJ (a[_j_][_i_], m, _i_, _j_); \ + } \ + } \ +}\ + + +/** compute adjoint of matrix and scale + * + * Computes adjoint of matrix m, scales it by s, returning a + */ +#define SCALE_ADJOINT_2X2(a,s,m) \ +{ \ + a[0][0] = (s) * m[1][1]; \ + a[1][0] = - (s) * m[1][0]; \ + a[0][1] = - (s) * m[0][1]; \ + a[1][1] = (s) * m[0][0]; \ +}\ + + +/** compute adjoint of matrix and scale + * + * Computes adjoint of matrix m, scales it by s, returning a + */ +#define SCALE_ADJOINT_3X3(a,s,m) \ +{ \ + a[0][0] = (s) * (m[1][1] * m[2][2] - m[1][2] * m[2][1]); \ + a[1][0] = (s) * (m[1][2] * m[2][0] - m[1][0] * m[2][2]); \ + a[2][0] = (s) * (m[1][0] * m[2][1] - m[1][1] * m[2][0]); \ + \ + a[0][1] = (s) * (m[0][2] * m[2][1] - m[0][1] * m[2][2]); \ + a[1][1] = (s) * (m[0][0] * m[2][2] - m[0][2] * m[2][0]); \ + a[2][1] = (s) * (m[0][1] * m[2][0] - m[0][0] * m[2][1]); \ + \ + a[0][2] = (s) * (m[0][1] * m[1][2] - m[0][2] * m[1][1]); \ + a[1][2] = (s) * (m[0][2] * m[1][0] - m[0][0] * m[1][2]); \ + a[2][2] = (s) * (m[0][0] * m[1][1] - m[0][1] * m[1][0]); \ +}\ + + +/** compute adjoint of matrix and scale + * + * Computes adjoint of matrix m, scales it by s, returning a + */ +#define SCALE_ADJOINT_4X4(a,s,m) \ +{ \ + char _i_,_j_; \ + for (_i_=0; _i_<4; _i_++) { \ + for (_j_=0; _j_<4; _j_++) { \ + COFACTOR_4X4_IJ (a[_j_][_i_], m, _i_, _j_); \ + a[_j_][_i_] *= s; \ + } \ + } \ +}\ + +/** inverse of matrix + * + * Compute inverse of matrix a, returning determinant m and + * inverse b + */ +#define INVERT_2X2(b,det,a) \ +{ \ + GREAL _tmp_; \ + DETERMINANT_2X2 (det, a); \ + _tmp_ = 1.0 / (det); \ + SCALE_ADJOINT_2X2 (b, _tmp_, a); \ +}\ + + +/** inverse of matrix + * + * Compute inverse of matrix a, returning determinant m and + * inverse b + */ +#define INVERT_3X3(b,det,a) \ +{ \ + GREAL _tmp_; \ + DETERMINANT_3X3 (det, a); \ + _tmp_ = 1.0 / (det); \ + SCALE_ADJOINT_3X3 (b, _tmp_, a); \ +}\ + + +/** inverse of matrix + * + * Compute inverse of matrix a, returning determinant m and + * inverse b + */ +#define INVERT_4X4(b,det,a) \ +{ \ + GREAL _tmp_; \ + DETERMINANT_4X4 (det, a); \ + _tmp_ = 1.0 / (det); \ + SCALE_ADJOINT_4X4 (b, _tmp_, a); \ +}\ + +//! Get the triple(3) row of a transform matrix +#define MAT_GET_ROW(mat,vec3,rowindex)\ +{\ + vec3[0] = mat[rowindex][0];\ + vec3[1] = mat[rowindex][1];\ + vec3[2] = mat[rowindex][2]; \ +}\ + +//! Get the tuple(2) row of a transform matrix +#define MAT_GET_ROW2(mat,vec2,rowindex)\ +{\ + vec2[0] = mat[rowindex][0];\ + vec2[1] = mat[rowindex][1];\ +}\ + + +//! Get the quad (4) row of a transform matrix +#define MAT_GET_ROW4(mat,vec4,rowindex)\ +{\ + vec4[0] = mat[rowindex][0];\ + vec4[1] = mat[rowindex][1];\ + vec4[2] = mat[rowindex][2];\ + vec4[3] = mat[rowindex][3];\ +}\ + +//! Get the triple(3) col of a transform matrix +#define MAT_GET_COL(mat,vec3,colindex)\ +{\ + vec3[0] = mat[0][colindex];\ + vec3[1] = mat[1][colindex];\ + vec3[2] = mat[2][colindex]; \ +}\ + +//! Get the tuple(2) col of a transform matrix +#define MAT_GET_COL2(mat,vec2,colindex)\ +{\ + vec2[0] = mat[0][colindex];\ + vec2[1] = mat[1][colindex];\ +}\ + + +//! Get the quad (4) col of a transform matrix +#define MAT_GET_COL4(mat,vec4,colindex)\ +{\ + vec4[0] = mat[0][colindex];\ + vec4[1] = mat[1][colindex];\ + vec4[2] = mat[2][colindex];\ + vec4[3] = mat[3][colindex];\ +}\ + +//! Get the triple(3) col of a transform matrix +#define MAT_GET_X(mat,vec3)\ +{\ + MAT_GET_COL(mat,vec3,0);\ +}\ + +//! Get the triple(3) col of a transform matrix +#define MAT_GET_Y(mat,vec3)\ +{\ + MAT_GET_COL(mat,vec3,1);\ +}\ + +//! Get the triple(3) col of a transform matrix +#define MAT_GET_Z(mat,vec3)\ +{\ + MAT_GET_COL(mat,vec3,2);\ +}\ + + +//! Get the triple(3) col of a transform matrix +#define MAT_SET_X(mat,vec3)\ +{\ + mat[0][0] = vec3[0];\ + mat[1][0] = vec3[1];\ + mat[2][0] = vec3[2];\ +}\ + +//! Get the triple(3) col of a transform matrix +#define MAT_SET_Y(mat,vec3)\ +{\ + mat[0][1] = vec3[0];\ + mat[1][1] = vec3[1];\ + mat[2][1] = vec3[2];\ +}\ + +//! Get the triple(3) col of a transform matrix +#define MAT_SET_Z(mat,vec3)\ +{\ + mat[0][2] = vec3[0];\ + mat[1][2] = vec3[1];\ + mat[2][2] = vec3[2];\ +}\ + + +//! Get the triple(3) col of a transform matrix +#define MAT_GET_TRANSLATION(mat,vec3)\ +{\ + vec3[0] = mat[0][3];\ + vec3[1] = mat[1][3];\ + vec3[2] = mat[2][3]; \ +}\ + +//! Set the triple(3) col of a transform matrix +#define MAT_SET_TRANSLATION(mat,vec3)\ +{\ + mat[0][3] = vec3[0];\ + mat[1][3] = vec3[1];\ + mat[2][3] = vec3[2]; \ +}\ + + + +//! Returns the dot product between a vec3f and the row of a matrix +#define MAT_DOT_ROW(mat,vec3,rowindex) (vec3[0]*mat[rowindex][0] + vec3[1]*mat[rowindex][1] + vec3[2]*mat[rowindex][2]) + +//! Returns the dot product between a vec2f and the row of a matrix +#define MAT_DOT_ROW2(mat,vec2,rowindex) (vec2[0]*mat[rowindex][0] + vec2[1]*mat[rowindex][1]) + +//! Returns the dot product between a vec4f and the row of a matrix +#define MAT_DOT_ROW4(mat,vec4,rowindex) (vec4[0]*mat[rowindex][0] + vec4[1]*mat[rowindex][1] + vec4[2]*mat[rowindex][2] + vec4[3]*mat[rowindex][3]) + + +//! Returns the dot product between a vec3f and the col of a matrix +#define MAT_DOT_COL(mat,vec3,colindex) (vec3[0]*mat[0][colindex] + vec3[1]*mat[1][colindex] + vec3[2]*mat[2][colindex]) + +//! Returns the dot product between a vec2f and the col of a matrix +#define MAT_DOT_COL2(mat,vec2,colindex) (vec2[0]*mat[0][colindex] + vec2[1]*mat[1][colindex]) + +//! Returns the dot product between a vec4f and the col of a matrix +#define MAT_DOT_COL4(mat,vec4,colindex) (vec4[0]*mat[0][colindex] + vec4[1]*mat[1][colindex] + vec4[2]*mat[2][colindex] + vec4[3]*mat[3][colindex]) + +/*!Transpose matrix times vector +v is a vec3f +and m is a mat4f<br> +*/ +#define INV_MAT_DOT_VEC_3X3(p,m,v) \ +{ \ + p[0] = MAT_DOT_COL(m,v,0); \ + p[1] = MAT_DOT_COL(m,v,1); \ + p[2] = MAT_DOT_COL(m,v,2); \ +}\ + + +//! @} + +#endif // GIM_VECTOR_H_INCLUDED |