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 dVALIDMAT(m) (!(dIsNan(m[0]) | dIsNan(m[2]) | 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 
00047 
00048 /*
00049  * 3-way dot product. dDOTpq means that elements of `a' and `b' are spaced
00050  * p and q indexes apart respectively. dDOT() means dDOT11.
00051  * in C++ we could use function templates to get all the versions of these
00052  * functions - but on some compilers this will result in sub-optimal code.
00053  */
00054 
00055 #define dDOTpq(a,b,p,q) ((a)[0]*(b)[0] + (a)[p]*(b)[q] + (a)[2*(p)]*(b)[2*(q)])
00056 
00057 #ifdef __cplusplus
00058 
00059 PURE_INLINE dReal dDOT   (const dReal *a, const dReal *b) { return dDOTpq(a,b,1,1); }
00060 PURE_INLINE dReal dDOT13 (const dReal *a, const dReal *b) { return dDOTpq(a,b,1,3); }
00061 PURE_INLINE dReal dDOT31 (const dReal *a, const dReal *b) { return dDOTpq(a,b,3,1); }
00062 PURE_INLINE dReal dDOT33 (const dReal *a, const dReal *b) { return dDOTpq(a,b,3,3); }
00063 PURE_INLINE dReal dDOT14 (const dReal *a, const dReal *b) { return dDOTpq(a,b,1,4); }
00064 PURE_INLINE dReal dDOT41 (const dReal *a, const dReal *b) { return dDOTpq(a,b,4,1); }
00065 PURE_INLINE dReal dDOT44 (const dReal *a, const dReal *b) { return dDOTpq(a,b,4,4); }
00066 
00067 #else
00068 
00069 #define dDOT(a,b)   dDOTpq(a,b,1,1)
00070 #define dDOT13(a,b) dDOTpq(a,b,1,3)
00071 #define dDOT31(a,b) dDOTpq(a,b,3,1)
00072 #define dDOT33(a,b) dDOTpq(a,b,3,3)
00073 #define dDOT14(a,b) dDOTpq(a,b,1,4)
00074 #define dDOT41(a,b) dDOTpq(a,b,4,1)
00075 #define dDOT44(a,b) dDOTpq(a,b,4,4)
00076 
00077 #endif /* __cplusplus */
00078 
00079 
00080 /*
00081  * cross product, set a = b x c. dCROSSpqr means that elements of `a', `b'
00082  * and `c' are spaced p, q and r indexes apart respectively.
00083  * dCROSS() means dCROSS111. `op' is normally `=', but you can set it to
00084  * +=, -= etc to get other effects.
00085  */
00086 
00087 #define dCROSS(a,op,b,c) \
00088 do { \
00089   (a)[0] op ((b)[1]*(c)[2] - (b)[2]*(c)[1]); \
00090   (a)[1] op ((b)[2]*(c)[0] - (b)[0]*(c)[2]); \
00091   (a)[2] op ((b)[0]*(c)[1] - (b)[1]*(c)[0]); \
00092 } while(0)
00093 #define dCROSSpqr(a,op,b,c,p,q,r) \
00094 do { \
00095   (a)[  0] op ((b)[  q]*(c)[2*r] - (b)[2*q]*(c)[  r]); \
00096   (a)[  p] op ((b)[2*q]*(c)[  0] - (b)[  0]*(c)[2*r]); \
00097   (a)[2*p] op ((b)[  0]*(c)[  r] - (b)[  q]*(c)[  0]); \
00098 } while(0)
00099 #define dCROSS114(a,op,b,c) dCROSSpqr(a,op,b,c,1,1,4)
00100 #define dCROSS141(a,op,b,c) dCROSSpqr(a,op,b,c,1,4,1)
00101 #define dCROSS144(a,op,b,c) dCROSSpqr(a,op,b,c,1,4,4)
00102 #define dCROSS411(a,op,b,c) dCROSSpqr(a,op,b,c,4,1,1)
00103 #define dCROSS414(a,op,b,c) dCROSSpqr(a,op,b,c,4,1,4)
00104 #define dCROSS441(a,op,b,c) dCROSSpqr(a,op,b,c,4,4,1)
00105 #define dCROSS444(a,op,b,c) dCROSSpqr(a,op,b,c,4,4,4)
00106 
00107 
00108 /*
00109  * set a 3x3 submatrix of A to a matrix such that submatrix(A)*b = a x b.
00110  * A is stored by rows, and has `skip' elements per row. the matrix is
00111  * assumed to be already zero, so this does not write zero elements!
00112  * if (plus,minus) is (+,-) then a positive version will be written.
00113  * if (plus,minus) is (-,+) then a negative version will be written.
00114  */
00115 
00116 #define dCROSSMAT(A,a,skip,plus,minus) \
00117 do { \
00118   (A)[1] = minus (a)[2]; \
00119   (A)[2] = plus (a)[1]; \
00120   (A)[(skip)+0] = plus (a)[2]; \
00121   (A)[(skip)+2] = minus (a)[0]; \
00122   (A)[2*(skip)+0] = minus (a)[1]; \
00123   (A)[2*(skip)+1] = plus (a)[0]; \
00124 } while(0)
00125 
00126 
00127 /*
00128  * compute the distance between two 3D-vectors
00129  */
00130 
00131 #ifdef __cplusplus
00132 PURE_INLINE dReal dDISTANCE (const dVector3 a, const dVector3 b)
00133    { 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]) ); }
00134 #else
00135 #define dDISTANCE(a,b) \
00136    (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]) ))
00137 #endif
00138 
00139 
00140 /*
00141  * special case matrix multipication, with operator selection
00142  */
00143 
00144 #define dMULTIPLYOP0_331(A,op,B,C) \
00145 do { \
00146   (A)[0] op dDOT((B),(C)); \
00147   (A)[1] op dDOT((B+4),(C)); \
00148   (A)[2] op dDOT((B+8),(C)); \
00149 } while(0)
00150 #define dMULTIPLYOP1_331(A,op,B,C) \
00151 do { \
00152   (A)[0] op dDOT41((B),(C)); \
00153   (A)[1] op dDOT41((B+1),(C)); \
00154   (A)[2] op dDOT41((B+2),(C)); \
00155 } while(0)
00156 #define dMULTIPLYOP0_133(A,op,B,C) \
00157 do { \
00158   (A)[0] op dDOT14((B),(C)); \
00159   (A)[1] op dDOT14((B),(C+1)); \
00160   (A)[2] op dDOT14((B),(C+2)); \
00161 } while(0)
00162 #define dMULTIPLYOP0_333(A,op,B,C) \
00163 do { \
00164   (A)[0] op dDOT14((B),(C)); \
00165   (A)[1] op dDOT14((B),(C+1)); \
00166   (A)[2] op dDOT14((B),(C+2)); \
00167   (A)[4] op dDOT14((B+4),(C)); \
00168   (A)[5] op dDOT14((B+4),(C+1)); \
00169   (A)[6] op dDOT14((B+4),(C+2)); \
00170   (A)[8] op dDOT14((B+8),(C)); \
00171   (A)[9] op dDOT14((B+8),(C+1)); \
00172   (A)[10] op dDOT14((B+8),(C+2)); \
00173 } while(0)
00174 #define dMULTIPLYOP1_333(A,op,B,C) \
00175 do { \
00176   (A)[0] op dDOT44((B),(C)); \
00177   (A)[1] op dDOT44((B),(C+1)); \
00178   (A)[2] op dDOT44((B),(C+2)); \
00179   (A)[4] op dDOT44((B+1),(C)); \
00180   (A)[5] op dDOT44((B+1),(C+1)); \
00181   (A)[6] op dDOT44((B+1),(C+2)); \
00182   (A)[8] op dDOT44((B+2),(C)); \
00183   (A)[9] op dDOT44((B+2),(C+1)); \
00184   (A)[10] op dDOT44((B+2),(C+2)); \
00185 } while(0)
00186 #define dMULTIPLYOP2_333(A,op,B,C) \
00187 do { \
00188   (A)[0] op dDOT((B),(C)); \
00189   (A)[1] op dDOT((B),(C+4)); \
00190   (A)[2] op dDOT((B),(C+8)); \
00191   (A)[4] op dDOT((B+4),(C)); \
00192   (A)[5] op dDOT((B+4),(C+4)); \
00193   (A)[6] op dDOT((B+4),(C+8)); \
00194   (A)[8] op dDOT((B+8),(C)); \
00195   (A)[9] op dDOT((B+8),(C+4)); \
00196   (A)[10] op dDOT((B+8),(C+8)); \
00197 } while(0)
00198 
00199 #ifdef __cplusplus
00200 
00201 #define DECL template <class TA, class TB, class TC> PURE_INLINE void
00202 
00203 DECL dMULTIPLY0_331(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_331(A,=,B,C); }
00204 DECL dMULTIPLY1_331(TA *A, const TB *B, const TC *C) { dMULTIPLYOP1_331(A,=,B,C); }
00205 DECL dMULTIPLY0_133(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_133(A,=,B,C); }
00206 DECL dMULTIPLY0_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_333(A,=,B,C); }
00207 DECL dMULTIPLY1_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP1_333(A,=,B,C); }
00208 DECL dMULTIPLY2_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP2_333(A,=,B,C); }
00209 
00210 DECL dMULTIPLYADD0_331(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_331(A,+=,B,C); }
00211 DECL dMULTIPLYADD1_331(TA *A, const TB *B, const TC *C) { dMULTIPLYOP1_331(A,+=,B,C); }
00212 DECL dMULTIPLYADD0_133(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_133(A,+=,B,C); }
00213 DECL dMULTIPLYADD0_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_333(A,+=,B,C); }
00214 DECL dMULTIPLYADD1_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP1_333(A,+=,B,C); }
00215 DECL dMULTIPLYADD2_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP2_333(A,+=,B,C); }
00216 
00217 #undef DECL
00218 
00219 #else
00220 
00221 #define dMULTIPLY0_331(A,B,C) dMULTIPLYOP0_331(A,=,B,C)
00222 #define dMULTIPLY1_331(A,B,C) dMULTIPLYOP1_331(A,=,B,C)
00223 #define dMULTIPLY0_133(A,B,C) dMULTIPLYOP0_133(A,=,B,C)
00224 #define dMULTIPLY0_333(A,B,C) dMULTIPLYOP0_333(A,=,B,C)
00225 #define dMULTIPLY1_333(A,B,C) dMULTIPLYOP1_333(A,=,B,C)
00226 #define dMULTIPLY2_333(A,B,C) dMULTIPLYOP2_333(A,=,B,C)
00227 
00228 #define dMULTIPLYADD0_331(A,B,C) dMULTIPLYOP0_331(A,+=,B,C)
00229 #define dMULTIPLYADD1_331(A,B,C) dMULTIPLYOP1_331(A,+=,B,C)
00230 #define dMULTIPLYADD0_133(A,B,C) dMULTIPLYOP0_133(A,+=,B,C)
00231 #define dMULTIPLYADD0_333(A,B,C) dMULTIPLYOP0_333(A,+=,B,C)
00232 #define dMULTIPLYADD1_333(A,B,C) dMULTIPLYOP1_333(A,+=,B,C)
00233 #define dMULTIPLYADD2_333(A,B,C) dMULTIPLYOP2_333(A,+=,B,C)
00234 
00235 #endif
00236 
00237 
00238 #ifdef __cplusplus
00239 extern "C" {
00240 #endif
00241 
00242 /*
00243  * normalize 3x1 and 4x1 vectors (i.e. scale them to unit length)
00244  */
00245 ODE_API void dNormalize3 (dVector3 a);
00246 ODE_API void dNormalize4 (dVector4 a);
00247 
00248 
00249 /*
00250  * given a unit length "normal" vector n, generate vectors p and q vectors
00251  * that are an orthonormal basis for the plane space perpendicular to n.
00252  * i.e. this makes p,q such that n,p,q are all perpendicular to each other.
00253  * q will equal n x p. if n is not unit length then p will be unit length but
00254  * q wont be.
00255  */
00256 
00257 ODE_API void dPlaneSpace (const dVector3 n, dVector3 p, dVector3 q);
00258 
00259 #ifdef __cplusplus
00260 }
00261 #endif
00262 
00263 #endif

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