/************************************************************************* * * * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. * * All rights reserved. Email: russ@q12.org Web: www.q12.org * * * * 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 LICENSE.TXT. * * (2) The BSD-style license that is included with this library in * * the file LICENSE-BSD.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 * * LICENSE.TXT and LICENSE-BSD.TXT for more details. * * * *************************************************************************/ #ifndef _ODE_ODEMATH_H_ #define _ODE_ODEMATH_H_ #include #ifdef __cplusplus extern "C" { #endif /* 3-way dot product. dDOTpq means that elements of `a' and `b' are spaced * p and q indexes apart respectively. dDOT() means dDOT11. */ #ifdef __cplusplus inline dReal dDOT (const dReal *a, const dReal *b) { return ((a)[0]*(b)[0] + (a)[1]*(b)[1] + (a)[2]*(b)[2]); } inline dReal dDOT14(const dReal *a, const dReal *b) { return ((a)[0]*(b)[0] + (a)[1]*(b)[4] + (a)[2]*(b)[8]); } inline dReal dDOT41(const dReal *a, const dReal *b) { return ((a)[0]*(b)[0] + (a)[4]*(b)[1] + (a)[8]*(b)[2]); } inline dReal dDOT44(const dReal *a, const dReal *b) { return ((a)[0]*(b)[0] + (a)[4]*(b)[4] + (a)[8]*(b)[8]); } #else #define dDOT(a,b) ((a)[0]*(b)[0] + (a)[1]*(b)[1] + (a)[2]*(b)[2]) #define dDOT14(a,b) ((a)[0]*(b)[0] + (a)[1]*(b)[4] + (a)[2]*(b)[8]) #define dDOT41(a,b) ((a)[0]*(b)[0] + (a)[4]*(b)[1] + (a)[8]*(b)[2]) #define dDOT44(a,b) ((a)[0]*(b)[0] + (a)[4]*(b)[4] + (a)[8]*(b)[8]) #endif /* cross product, set a = b x c. dCROSSpqr means that elements of `a', `b' * and `c' are spaced p, q and r indexes apart respectively. * dCROSS() means dCROSS111. `op' is normally `=', but you can set it to * +=, -= etc to get other effects. */ #define dCROSS(a,op,b,c) \ (a)[0] op ((b)[1]*(c)[2] - (b)[2]*(c)[1]); \ (a)[1] op ((b)[2]*(c)[0] - (b)[0]*(c)[2]); \ (a)[2] op ((b)[0]*(c)[1] - (b)[1]*(c)[0]); #define dCROSSpqr(a,op,b,c,p,q,r) \ (a)[ 0] op ((b)[ q]*(c)[2*r] - (b)[2*q]*(c)[ r]); \ (a)[ p] op ((b)[2*q]*(c)[ 0] - (b)[ 0]*(c)[2*r]); \ (a)[2*p] op ((b)[ 0]*(c)[ r] - (b)[ q]*(c)[ 0]); #define dCROSS114(a,op,b,c) dCROSSpqr(a,op,b,c,1,1,4) #define dCROSS141(a,op,b,c) dCROSSpqr(a,op,b,c,1,4,1) #define dCROSS144(a,op,b,c) dCROSSpqr(a,op,b,c,1,4,4) #define dCROSS411(a,op,b,c) dCROSSpqr(a,op,b,c,4,1,1) #define dCROSS414(a,op,b,c) dCROSSpqr(a,op,b,c,4,1,4) #define dCROSS441(a,op,b,c) dCROSSpqr(a,op,b,c,4,4,1) #define dCROSS444(a,op,b,c) dCROSSpqr(a,op,b,c,4,4,4) /* set a 3x3 submatrix of A to a matrix such that submatrix(A)*b = a x b. * A is stored by rows, and has `skip' elements per row. the matrix is * assumed to be already zero, so this does not write zero elements! * if (plus,minus) is (+,-) then a positive version will be written. * if (plus,minus) is (-,+) then a negative version will be written. */ #define dCROSSMAT(A,a,skip,plus,minus) \ (A)[1] = minus (a)[2]; \ (A)[2] = plus (a)[1]; \ (A)[(skip)+0] = plus (a)[2]; \ (A)[(skip)+2] = minus (a)[0]; \ (A)[2*(skip)+0] = minus (a)[1]; \ (A)[2*(skip)+1] = plus (a)[0]; /* compute the distance between two 3-vectors (oops, C++!) */ #ifdef __cplusplus inline dReal dDISTANCE (const dVector3 a, const dVector3 b) { return dSqrt( (a[0]-b[0])*(a[0]-b[0]) + (a[1]-b[1])*(a[1]-b[1]) + (a[2]-b[2])*(a[2]-b[2]) ); } #else #define dDISTANCE(a,b) \ (dSqrt( ((a)[0]-(b)[0])*((a)[0]-(b)[0]) + ((a)[1]-(b)[1])*((a)[1]-(b)[1]) + \ ((a)[2]-(b)[2])*((a)[2]-(b)[2]) )) #endif /* normalize 3x1 and 4x1 vectors (i.e. scale them to unit length) */ void dNormalize3 (dVector3 a); void dNormalize4 (dVector4 a); /* given a unit length "normal" vector n, generate vectors p and q vectors * that are an orthonormal basis for the plane space perpendicular to n. * i.e. this makes p,q such that n,p,q are all perpendicular to each other. * q will equal n x p. if n is not unit length then p will be unit length but * q wont be. */ void dPlaneSpace (const dVector3 n, dVector3 p, dVector3 q); /* special case matrix multipication, with operator selection */ #define dMULTIPLYOP0_331(A,op,B,C) \ (A)[0] op dDOT((B),(C)); \ (A)[1] op dDOT((B+4),(C)); \ (A)[2] op dDOT((B+8),(C)); #define dMULTIPLYOP1_331(A,op,B,C) \ (A)[0] op dDOT41((B),(C)); \ (A)[1] op dDOT41((B+1),(C)); \ (A)[2] op dDOT41((B+2),(C)); #define dMULTIPLYOP0_133(A,op,B,C) \ (A)[0] op dDOT14((B),(C)); \ (A)[1] op dDOT14((B),(C+1)); \ (A)[2] op dDOT14((B),(C+2)); #define dMULTIPLYOP0_333(A,op,B,C) \ (A)[0] op dDOT14((B),(C)); \ (A)[1] op dDOT14((B),(C+1)); \ (A)[2] op dDOT14((B),(C+2)); \ (A)[4] op dDOT14((B+4),(C)); \ (A)[5] op dDOT14((B+4),(C+1)); \ (A)[6] op dDOT14((B+4),(C+2)); \ (A)[8] op dDOT14((B+8),(C)); \ (A)[9] op dDOT14((B+8),(C+1)); \ (A)[10] op dDOT14((B+8),(C+2)); #define dMULTIPLYOP1_333(A,op,B,C) \ (A)[0] op dDOT44((B),(C)); \ (A)[1] op dDOT44((B),(C+1)); \ (A)[2] op dDOT44((B),(C+2)); \ (A)[4] op dDOT44((B+1),(C)); \ (A)[5] op dDOT44((B+1),(C+1)); \ (A)[6] op dDOT44((B+1),(C+2)); \ (A)[8] op dDOT44((B+2),(C)); \ (A)[9] op dDOT44((B+2),(C+1)); \ (A)[10] op dDOT44((B+2),(C+2)); #define dMULTIPLYOP2_333(A,op,B,C) \ (A)[0] op dDOT((B),(C)); \ (A)[1] op dDOT((B),(C+4)); \ (A)[2] op dDOT((B),(C+8)); \ (A)[4] op dDOT((B+4),(C)); \ (A)[5] op dDOT((B+4),(C+4)); \ (A)[6] op dDOT((B+4),(C+8)); \ (A)[8] op dDOT((B+8),(C)); \ (A)[9] op dDOT((B+8),(C+4)); \ (A)[10] op dDOT((B+8),(C+8)); #ifdef __cplusplus inline void dMULTIPLY0_331(dReal *A, const dReal *B, const dReal *C) { dMULTIPLYOP0_331(A,=,B,C) } inline void dMULTIPLY1_331(dReal *A, const dReal *B, const dReal *C) { dMULTIPLYOP1_331(A,=,B,C) } inline void dMULTIPLY0_133(dReal *A, const dReal *B, const dReal *C) { dMULTIPLYOP0_133(A,=,B,C) } inline void dMULTIPLY0_333(dReal *A, const dReal *B, const dReal *C) { dMULTIPLYOP0_333(A,=,B,C) } inline void dMULTIPLY1_333(dReal *A, const dReal *B, const dReal *C) { dMULTIPLYOP1_333(A,=,B,C) } inline void dMULTIPLY2_333(dReal *A, const dReal *B, const dReal *C) { dMULTIPLYOP2_333(A,=,B,C) } inline void dMULTIPLYADD0_331(dReal *A, const dReal *B, const dReal *C) { dMULTIPLYOP0_331(A,+=,B,C) } inline void dMULTIPLYADD1_331(dReal *A, const dReal *B, const dReal *C) { dMULTIPLYOP1_331(A,+=,B,C) } inline void dMULTIPLYADD0_133(dReal *A, const dReal *B, const dReal *C) { dMULTIPLYOP0_133(A,+=,B,C) } inline void dMULTIPLYADD0_333(dReal *A, const dReal *B, const dReal *C) { dMULTIPLYOP0_333(A,+=,B,C) } inline void dMULTIPLYADD1_333(dReal *A, const dReal *B, const dReal *C) { dMULTIPLYOP1_333(A,+=,B,C) } inline void dMULTIPLYADD2_333(dReal *A, const dReal *B, const dReal *C) { dMULTIPLYOP2_333(A,+=,B,C) } #else #define dMULTIPLY0_331(A,B,C) dMULTIPLYOP0_331(A,=,B,C) #define dMULTIPLY1_331(A,B,C) dMULTIPLYOP1_331(A,=,B,C) #define dMULTIPLY0_133(A,B,C) dMULTIPLYOP0_133(A,=,B,C) #define dMULTIPLY0_333(A,B,C) dMULTIPLYOP0_333(A,=,B,C) #define dMULTIPLY1_333(A,B,C) dMULTIPLYOP1_333(A,=,B,C) #define dMULTIPLY2_333(A,B,C) dMULTIPLYOP2_333(A,=,B,C) #define dMULTIPLYADD0_331(A,B,C) dMULTIPLYOP0_331(A,+=,B,C) #define dMULTIPLYADD1_331(A,B,C) dMULTIPLYOP1_331(A,+=,B,C) #define dMULTIPLYADD0_133(A,B,C) dMULTIPLYOP0_133(A,+=,B,C) #define dMULTIPLYADD0_333(A,B,C) dMULTIPLYOP0_333(A,+=,B,C) #define dMULTIPLYADD1_333(A,B,C) dMULTIPLYOP1_333(A,+=,B,C) #define dMULTIPLYADD2_333(A,B,C) dMULTIPLYOP2_333(A,+=,B,C) #endif #ifdef __cplusplus } #endif #endif