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# odemath.h

    00001 /*************************************************************************
    00002  *                                                                       *
    00003  * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith.       *
    00004  * All rights reserved.  Email: russ@q12.org   Web: www.q12.org          *
    00005  *                                                                       *
    00006  * This library is free software; you can redistribute it and/or         *
    00007  * modify it under the terms of EITHER:                                  *
    00008  *   (1) The GNU Lesser General Public License as published by the Free  *
    00009  *       Software Foundation; either version 2.1 of the License, or (at  *
    00010  *       your option) any later version. The text of the GNU Lesser      *
    00011  *       General Public License is included with this library in the     *
    00012  *       file LICENSE.TXT.                                               *
    00013  *   (2) The BSD-style license that is included with this library in     *
    00014  *       the file LICENSE-BSD.TXT.                                       *
    00015  *                                                                       *
    00016  * This library is distributed in the hope that it will be useful,       *
    00017  * but WITHOUT ANY WARRANTY; without even the implied warranty of        *
    00018  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files    *
    00019  * LICENSE.TXT and LICENSE-BSD.TXT for more details.                     *
    00020  *                                                                       *
    00021  *************************************************************************/
    00022
    00023 #ifndef _ODE_ODEMATH_H_
    00024 #define _ODE_ODEMATH_H_
    00025
    00026 #include <ode/common.h>
    00027
    00028 #ifdef __GNUC__
    00029 #define PURE_INLINE extern inline
    00030 #else
    00031 #define PURE_INLINE inline
    00032 #endif
    00033
    00034 /*
    00035  * macro to access elements i,j in an NxM matrix A, independent of the
    00036  * matrix storage convention.
    00037  */
    00038 #define dACCESS33(A,i,j) ((A)[(i)*4+(j)])
    00039
    00040 /*
    00041  * Macro to test for valid floating point values
    00042  */
    00043 #define dVALIDVEC3(v) (!(dIsNan(v[0]) || dIsNan(v[1]) || dIsNan(v[2])))
    00044 #define dVALIDVEC4(v) (!(dIsNan(v[0]) || dIsNan(v[2]) || dIsNan(v[2]) || dIsNan(v[3])))
    00045 #define dVALIDMAT3(m) (!(dIsNan(m[0]) || dIsNan(m[1]) || dIsNan(m[2]) || dIsNan(m[3]) || dIsNan(m[4]) || dIsNan(m[5]) || dIsNan(m[6]) || dIsNan(m[7]) || dIsNan(m[8]) || dIsNan(m[9]) || dIsNan(m[10]) || dIsNan(m[11])))
    00046 #define dVALIDMAT4(m) (!(dIsNan(m[0]) || dIsNan(m[1]) || dIsNan(m[2]) || dIsNan(m[3]) || dIsNan(m[4]) || dIsNan(m[5]) || dIsNan(m[6]) || dIsNan(m[7]) || dIsNan(m[8]) || dIsNan(m[9]) || dIsNan(m[10]) || dIsNan(m[11]) || dIsNan(m[12]) || dIsNan(m[13]) || dIsNan(m[14]) || dIsNan(m[15]) ))
    00047
    00048
    00049
    00050 /*
    00051  * General purpose vector operations with other vectors or constants.
    00052  */
    00053
    00054 #define dOP(a,op,b,c) \
    00055     (a)[0] = ((b)[0]) op ((c)[0]); \
    00056     (a)[1] = ((b)[1]) op ((c)[1]); \
    00057     (a)[2] = ((b)[2]) op ((c)[2]);
    00058 #define dOPC(a,op,b,c) \
    00059     (a)[0] = ((b)[0]) op (c); \
    00060     (a)[1] = ((b)[1]) op (c); \
    00061     (a)[2] = ((b)[2]) op (c);
    00062 #define dOPE(a,op,b) \
    00063     (a)[0] op ((b)[0]); \
    00064     (a)[1] op ((b)[1]); \
    00065     (a)[2] op ((b)[2]);
    00066 #define dOPEC(a,op,c) \
    00067     (a)[0] op (c); \
    00068     (a)[1] op (c); \
    00069     (a)[2] op (c);
    00070
    00071
    00072 /*
    00073  * Length, and squared length helpers. dLENGTH returns the length of a dVector3.
    00074  * dLENGTHSQUARED return the squared length of a dVector3.
    00075  */
    00076
    00077 #define dLENGTHSQUARED(a) (((a)[0])*((a)[0]) + ((a)[1])*((a)[1]) + ((a)[2])*((a)[2]))
    00078
    00079 #ifdef __cplusplus
    00080
    00081 PURE_INLINE dReal dLENGTH (const dReal *a) { return dSqrt(dLENGTHSQUARED(a)); }
    00082
    00083 #else
    00084
    00085 #define dLENGTH(a) ( dSqrt( ((a)[0])*((a)[0]) + ((a)[1])*((a)[1]) + ((a)[2])*((a)[2]) ) )
    00086
    00087 #endif /* __cplusplus */
    00088
    00089
    00090
    00091
    00092
    00093 /*
    00094  * 3-way dot product. dDOTpq means that elements of `a' and `b' are spaced
    00095  * p and q indexes apart respectively. dDOT() means dDOT11.
    00096  * in C++ we could use function templates to get all the versions of these
    00097  * functions - but on some compilers this will result in sub-optimal code.
    00098  */
    00099
    00100 #define dDOTpq(a,b,p,q) ((a)[0]*(b)[0] + (a)[p]*(b)[q] + (a)[2*(p)]*(b)[2*(q)])
    00101
    00102 #ifdef __cplusplus
    00103
    00104 PURE_INLINE dReal dDOT   (const dReal *a, const dReal *b) { return dDOTpq(a,b,1,1); }
    00105 PURE_INLINE dReal dDOT13 (const dReal *a, const dReal *b) { return dDOTpq(a,b,1,3); }
    00106 PURE_INLINE dReal dDOT31 (const dReal *a, const dReal *b) { return dDOTpq(a,b,3,1); }
    00107 PURE_INLINE dReal dDOT33 (const dReal *a, const dReal *b) { return dDOTpq(a,b,3,3); }
    00108 PURE_INLINE dReal dDOT14 (const dReal *a, const dReal *b) { return dDOTpq(a,b,1,4); }
    00109 PURE_INLINE dReal dDOT41 (const dReal *a, const dReal *b) { return dDOTpq(a,b,4,1); }
    00110 PURE_INLINE dReal dDOT44 (const dReal *a, const dReal *b) { return dDOTpq(a,b,4,4); }
    00111
    00112 #else
    00113
    00114 #define dDOT(a,b)   dDOTpq(a,b,1,1)
    00115 #define dDOT13(a,b) dDOTpq(a,b,1,3)
    00116 #define dDOT31(a,b) dDOTpq(a,b,3,1)
    00117 #define dDOT33(a,b) dDOTpq(a,b,3,3)
    00118 #define dDOT14(a,b) dDOTpq(a,b,1,4)
    00119 #define dDOT41(a,b) dDOTpq(a,b,4,1)
    00120 #define dDOT44(a,b) dDOTpq(a,b,4,4)
    00121
    00122 #endif /* __cplusplus */
    00123
    00124
    00125 /*
    00126  * cross product, set a = b x c. dCROSSpqr means that elements of `a', `b'
    00127  * and `c' are spaced p, q and r indexes apart respectively.
    00128  * dCROSS() means dCROSS111. `op' is normally `=', but you can set it to
    00129  * +=, -= etc to get other effects.
    00130  */
    00131
    00132 #define dCROSS(a,op,b,c) \
    00133 do { \
    00134   (a)[0] op ((b)[1]*(c)[2] - (b)[2]*(c)[1]); \
    00135   (a)[1] op ((b)[2]*(c)[0] - (b)[0]*(c)[2]); \
    00136   (a)[2] op ((b)[0]*(c)[1] - (b)[1]*(c)[0]); \
    00137 } while(0)
    00138 #define dCROSSpqr(a,op,b,c,p,q,r) \
    00139 do { \
    00140   (a)[  0] op ((b)[  q]*(c)[2*r] - (b)[2*q]*(c)[  r]); \
    00141   (a)[  p] op ((b)[2*q]*(c)[  0] - (b)[  0]*(c)[2*r]); \
    00142   (a)[2*p] op ((b)[  0]*(c)[  r] - (b)[  q]*(c)[  0]); \
    00143 } while(0)
    00144 #define dCROSS114(a,op,b,c) dCROSSpqr(a,op,b,c,1,1,4)
    00145 #define dCROSS141(a,op,b,c) dCROSSpqr(a,op,b,c,1,4,1)
    00146 #define dCROSS144(a,op,b,c) dCROSSpqr(a,op,b,c,1,4,4)
    00147 #define dCROSS411(a,op,b,c) dCROSSpqr(a,op,b,c,4,1,1)
    00148 #define dCROSS414(a,op,b,c) dCROSSpqr(a,op,b,c,4,1,4)
    00149 #define dCROSS441(a,op,b,c) dCROSSpqr(a,op,b,c,4,4,1)
    00150 #define dCROSS444(a,op,b,c) dCROSSpqr(a,op,b,c,4,4,4)
    00151
    00152
    00153 /*
    00154  * set a 3x3 submatrix of A to a matrix such that submatrix(A)*b = a x b.
    00155  * A is stored by rows, and has `skip' elements per row. the matrix is
    00156  * assumed to be already zero, so this does not write zero elements!
    00157  * if (plus,minus) is (+,-) then a positive version will be written.
    00158  * if (plus,minus) is (-,+) then a negative version will be written.
    00159  */
    00160
    00161 #define dCROSSMAT(A,a,skip,plus,minus) \
    00162 do { \
    00163   (A)[1] = minus (a)[2]; \
    00164   (A)[2] = plus (a)[1]; \
    00165   (A)[(skip)+0] = plus (a)[2]; \
    00166   (A)[(skip)+2] = minus (a)[0]; \
    00167   (A)[2*(skip)+0] = minus (a)[1]; \
    00168   (A)[2*(skip)+1] = plus (a)[0]; \
    00169 } while(0)
    00170
    00171
    00172 /*
    00173  * compute the distance between two 3D-vectors
    00174  */
    00175
    00176 #ifdef __cplusplus
    00177 PURE_INLINE dReal dDISTANCE (const dVector3 a, const dVector3 b)
    00178    { 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]) ); }
    00179 #else
    00180 #define dDISTANCE(a,b) \
    00181    (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]) ))
    00182 #endif
    00183
    00184
    00185 /*
    00186  * special case matrix multipication, with operator selection
    00187  */
    00188
    00189 #define dMULTIPLYOP0_331(A,op,B,C) \
    00190 do { \
    00191   (A)[0] op dDOT((B),(C)); \
    00192   (A)[1] op dDOT((B+4),(C)); \
    00193   (A)[2] op dDOT((B+8),(C)); \
    00194 } while(0)
    00195 #define dMULTIPLYOP1_331(A,op,B,C) \
    00196 do { \
    00197   (A)[0] op dDOT41((B),(C)); \
    00198   (A)[1] op dDOT41((B+1),(C)); \
    00199   (A)[2] op dDOT41((B+2),(C)); \
    00200 } while(0)
    00201 #define dMULTIPLYOP0_133(A,op,B,C) \
    00202 do { \
    00203   (A)[0] op dDOT14((B),(C)); \
    00204   (A)[1] op dDOT14((B),(C+1)); \
    00205   (A)[2] op dDOT14((B),(C+2)); \
    00206 } while(0)
    00207 #define dMULTIPLYOP0_333(A,op,B,C) \
    00208 do { \
    00209   (A)[0] op dDOT14((B),(C)); \
    00210   (A)[1] op dDOT14((B),(C+1)); \
    00211   (A)[2] op dDOT14((B),(C+2)); \
    00212   (A)[4] op dDOT14((B+4),(C)); \
    00213   (A)[5] op dDOT14((B+4),(C+1)); \
    00214   (A)[6] op dDOT14((B+4),(C+2)); \
    00215   (A)[8] op dDOT14((B+8),(C)); \
    00216   (A)[9] op dDOT14((B+8),(C+1)); \
    00217   (A)[10] op dDOT14((B+8),(C+2)); \
    00218 } while(0)
    00219 #define dMULTIPLYOP1_333(A,op,B,C) \
    00220 do { \
    00221   (A)[0] op dDOT44((B),(C)); \
    00222   (A)[1] op dDOT44((B),(C+1)); \
    00223   (A)[2] op dDOT44((B),(C+2)); \
    00224   (A)[4] op dDOT44((B+1),(C)); \
    00225   (A)[5] op dDOT44((B+1),(C+1)); \
    00226   (A)[6] op dDOT44((B+1),(C+2)); \
    00227   (A)[8] op dDOT44((B+2),(C)); \
    00228   (A)[9] op dDOT44((B+2),(C+1)); \
    00229   (A)[10] op dDOT44((B+2),(C+2)); \
    00230 } while(0)
    00231 #define dMULTIPLYOP2_333(A,op,B,C) \
    00232 do { \
    00233   (A)[0] op dDOT((B),(C)); \
    00234   (A)[1] op dDOT((B),(C+4)); \
    00235   (A)[2] op dDOT((B),(C+8)); \
    00236   (A)[4] op dDOT((B+4),(C)); \
    00237   (A)[5] op dDOT((B+4),(C+4)); \
    00238   (A)[6] op dDOT((B+4),(C+8)); \
    00239   (A)[8] op dDOT((B+8),(C)); \
    00240   (A)[9] op dDOT((B+8),(C+4)); \
    00241   (A)[10] op dDOT((B+8),(C+8)); \
    00242 } while(0)
    00243
    00244 #ifdef __cplusplus
    00245
    00246 #define DECL template <class TA, class TB, class TC> PURE_INLINE void
    00247
    00248 DECL dMULTIPLY0_331(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_331(A,=,B,C); }
    00249 DECL dMULTIPLY1_331(TA *A, const TB *B, const TC *C) { dMULTIPLYOP1_331(A,=,B,C); }
    00250 DECL dMULTIPLY0_133(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_133(A,=,B,C); }
    00251 DECL dMULTIPLY0_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_333(A,=,B,C); }
    00252 DECL dMULTIPLY1_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP1_333(A,=,B,C); }
    00253 DECL dMULTIPLY2_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP2_333(A,=,B,C); }
    00254
    00255 DECL dMULTIPLYADD0_331(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_331(A,+=,B,C); }
    00256 DECL dMULTIPLYADD1_331(TA *A, const TB *B, const TC *C) { dMULTIPLYOP1_331(A,+=,B,C); }
    00257 DECL dMULTIPLYADD0_133(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_133(A,+=,B,C); }
    00258 DECL dMULTIPLYADD0_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_333(A,+=,B,C); }
    00259 DECL dMULTIPLYADD1_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP1_333(A,+=,B,C); }
    00260 DECL dMULTIPLYADD2_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP2_333(A,+=,B,C); }
    00261
    00262 #undef DECL
    00263
    00264 #else
    00265
    00266 #define dMULTIPLY0_331(A,B,C) dMULTIPLYOP0_331(A,=,B,C)
    00267 #define dMULTIPLY1_331(A,B,C) dMULTIPLYOP1_331(A,=,B,C)
    00268 #define dMULTIPLY0_133(A,B,C) dMULTIPLYOP0_133(A,=,B,C)
    00269 #define dMULTIPLY0_333(A,B,C) dMULTIPLYOP0_333(A,=,B,C)
    00270 #define dMULTIPLY1_333(A,B,C) dMULTIPLYOP1_333(A,=,B,C)
    00271 #define dMULTIPLY2_333(A,B,C) dMULTIPLYOP2_333(A,=,B,C)
    00272
    00273 #define dMULTIPLYADD0_331(A,B,C) dMULTIPLYOP0_331(A,+=,B,C)
    00274 #define dMULTIPLYADD1_331(A,B,C) dMULTIPLYOP1_331(A,+=,B,C)
    00275 #define dMULTIPLYADD0_133(A,B,C) dMULTIPLYOP0_133(A,+=,B,C)
    00276 #define dMULTIPLYADD0_333(A,B,C) dMULTIPLYOP0_333(A,+=,B,C)
    00277 #define dMULTIPLYADD1_333(A,B,C) dMULTIPLYOP1_333(A,+=,B,C)
    00278 #define dMULTIPLYADD2_333(A,B,C) dMULTIPLYOP2_333(A,+=,B,C)
    00279
    00280 #endif
    00281
    00282
    00283 #ifdef __cplusplus
    00284 extern "C" {
    00285 #endif
    00286
    00287 /*
    00288  * normalize 3x1 and 4x1 vectors (i.e. scale them to unit length)
    00289  */
    00290 ODE_API void dNormalize3 (dVector3 a);
    00291 ODE_API void dNormalize4 (dVector4 a);
    00292
    00293
    00294 /*
    00295  * given a unit length "normal" vector n, generate vectors p and q vectors
    00296  * that are an orthonormal basis for the plane space perpendicular to n.
    00297  * i.e. this makes p,q such that n,p,q are all perpendicular to each other.
    00298  * q will equal n x p. if n is not unit length then p will be unit length but
    00299  * q wont be.
    00300  */
    00301
    00302 ODE_API void dPlaneSpace (const dVector3 n, dVector3 p, dVector3 q);
    00303
    00304 #ifdef __cplusplus
    00305 }
    00306 #endif
    00307
    00308 #endif