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+#ifndef GIM_LINEAR_H_INCLUDED
+#define GIM_LINEAR_H_INCLUDED
+
+/*! \file gim_linear_math.h
+*\author Francisco Leon Najera
+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"
+
+
+
+
+//! 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; \
+}\
+
+
+
+
+
+
+/// 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
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