/* * vec.h -- Vector macros for 2,3, and 4 dimensions, * for any combination of C scalar types. * * Author: Don Hatch (hatch@sgi.com) * Last modified: Fri Dec 15 01:57:07 PST 1995 * * General description: * * The macro name describes its arguments; e.g. * MXS3 is "matrix times scalar in 3 dimensions"; * VMV2 is "vector minus vector in 2 dimensions". * * If the result of an operation is a scalar, then the macro "returns" * the value; e.g. * result = DOT3(v,w); * result = DET4(m); * * If the result of an operation is a vector or matrix, then * the first argument is the destination; e.g. * SET2(tovec, fromvec); * MXM3(result, m1, m2); * * WARNING: For the operations that are not done "componentwise" * (e.g. vector cross products and matrix multiplies) * the destination should not be either of the arguments, * for obvious reasons. For example, the following is wrong: * VXM2(v,v,m); * For such "unsafe" macros, there are safe versions provided, * but you have to specify a type for the temporary * result vector or matrix. For example, the safe versions * of VXM2 are: * VXM2d(v,v,m) if v's scalar type is double or float * VXM2i(v,v,m) if v's scalar type is int or char * VXM2l(v,v,m) if v's scalar type is long * VXM2r(v,v,m) if v's scalar type is real * VXM2safe(type,v,v,m) for other scalar types. * * These "safe" macros and INVERTMAT do not evaluate to C expressions * (so, for example, they can't be used inside the parentheses of * a for(...)). * * Specific descriptions: * * The "?"'s in the following can be 2, 3, or 4. * * EXPAND?(v) comma-separated list of elements of v * * SET?(to,from) to = from * SETMAT?(to,from) to = from * ROUNDVEC?(to,from) to = from with entries rounded * to nearest integer * ROUNDMAT?(to,from) to = from with entries rounded * to nearest integer * FILLVEC?(v,s) set each entry of vector v to be s * FILLMAT?(m,s) set each entry of matrix m to be s * ZEROVEC?(v) v = 0 * ISZEROVEC?(v) v == 0 * EQVEC?(v,w) v == w * EQMAT?(m1,m2) m1 == m2 * ZEROMAT?(m) m = 0 * IDENTMAT?(m) m = 1 * TRANSPOSE?(to,from) (matrix to) = (transpose of matrix from) * ADJOINT?(to,from) (matrix to) = (adjoint of matrix from) * i.e. its determinant times its inverse * INVERTMAT?{d,i,l,r}(to,from) (matrix to) = (inverse of matrix from) * with temp adjoint and determinant type * double, int, long, or real respectively * * V{P,M}V?(to,v,w) to = v {+,-} w * M{P,M}M?(to,m1,m2) to = m1 {+,-} m2 * SX{V,M}?(to,s,from) to = s * from * VPSXV?(to,v,s,w) to = v + s*w * VPVXS?(to,v,w,s) to = v + w*s * M{V,M}?(to,from) to = -from * {V,M}{X,D}S?(to,from,s) to = from {*,/} s * MXM?(to,m1,m2) to = m1 * m2 * VXM?(to,v,m) (row vec to) = (row vec v) * m * MXV?(to,m,v) (column vec to) = m * (column vec v) * VMODS?(to,v,s) to = v mod s (always >= 0) * VMODV?(to,v0,v1) to = v0 mod v1 componentwise * VDIVS?(to,v,s) to = (v-(v mod s))/s * VDIVV?(to,v0,v1) to = (v0-(v0 mod v1))/v1 componentwise * V{MIN,MAX}S?(to,v,s) to = {MIN,MAX}(v, s) * V{MIN,MAX}V?(to,v0,v1) to = {MIN,MAX}(v0, v1) * LERP?(to,v0,v1,t) to = v0 + t*(v1-v0) * * DET?(m) determinant of m * TRACE?(m) trace (sum of diagonal entries) of m * DOT?(v,w) dot (scalar) product of v and w * NORMSQRD?(v) square of |v| * DISTSQRD?(v,w) square of |v-w| * * XV2(to,v) to = v rotated by 90 degrees * VXV3(to,v1,v2) to = cross (vector) product of v1 and v2 * VXVXV4(to,v1,v2,v3) to = 4-dimensional vector cross product * of v1,v2,v3 (a vector orthogonal to * v1,v2,v3 whose length equals the * volume of the spanned parallelotope) * VXV2(v0,v1) determinant of matrix with rows v0,v1 * VXVXV3(v0,v1,v2) determinant of matrix with rows v0,v1,v2 * VXVXVXV4(v0,v1,v2,v3) determinant of matrix with rows v0,..,v3 * * The following macros mix objects from different dimensions. * For example, V3XM4 would be used to apply a composite * 4x4 rotation-and-translation matrix to a 3d vector. * * SET3from2(to,from,pad) (3d vec to) = (2d vec from) with pad * SET4from3(to,from,pad) (4d vec to) = (3d vec from) with pad * SETMAT3from2(to,from,pad0,pad1) (3x3 mat to) = (2x2 mat from) * padded with pad0 on the sides * and pad1 in the corner * SETMAT4from3(to,from,pad0,pad1) (4x4 mat to) = (3x3 mat from) * padded with pad0 on the sides * and pad1 in the corner * V2XM3(to2,v2,m3) (2d row vec to2) = (2d row vec v2) * (3x3 mat m3) * V3XM4(to3,v3,m4) (3d row vec to3) = (3d row vec v2) * (4x4 mat m4) * M3XV2(to2,m3,v2) (2d col vec to2) = (3x3 mat m3) * (2d col vec v2) * M4XV3(to3,m4,v3) (3d col vec to3) = (4x4 mat m4) * (3d col vec v3) * M2XM3(to3,m2,m3) (3x3 mat to3) = (2x2 mat m2) * (3x3 mat m3) * M3XM4(to4,m3,m4) (4x4 mat to4) = (3x3 mat m3) * (4x4 mat m4) * M3XM2(to3,m3,m2) (3x3 mat to3) = (3x3 mat m3) * (2x2 mat m2) * M4XM3(to4,m4,m3) (4x4 mat to4) = (4x4 mat m4) * (3x3 mat m3) * * * This file is machine-generated and can be regenerated * for any number of dimensions. * The program that generated it is available upon request. */ #ifndef VEC_H #define VEC_H 4 #include /* for definition of floor() */ #define EXPAND2(v) (v)[0], (v)[1] #define EXPAND3(v) (v)[0], (v)[1], (v)[2] #define EXPAND4(v) (v)[0], (v)[1], (v)[2], (v)[3] #define SET2(to,from) \ ((to)[0] = (from)[0], \ (to)[1] = (from)[1]) #define SETMAT2(to,from) \ (SET2((to)[0], (from)[0]), \ SET2((to)[1], (from)[1])) #define ROUNDVEC2(to,from) \ ((to)[0] = floor((from)[0]+.5), \ (to)[1] = floor((from)[1]+.5)) #define ROUNDMAT2(to,from) \ (ROUNDVEC2((to)[0], (from)[0]), \ ROUNDVEC2((to)[1], (from)[1])) #define FILLVEC2(v,s) \ ((v)[0] = (s), \ (v)[1] = (s)) #define FILLMAT2(m,s) \ (FILLVEC2((m)[0], s), \ FILLVEC2((m)[1], s)) #define ZEROVEC2(v) \ ((v)[0] = 0, \ (v)[1] = 0) #define ISZEROVEC2(v) \ ((v)[0] == 0 && \ (v)[1] == 0) #define EQVEC2(v,w) \ ((v)[0] == (w)[0] && \ (v)[1] == (w)[1]) #define EQMAT2(m1,m2) \ (EQVEC2((m1)[0], (m2)[0]) && \ EQVEC2((m1)[1], (m2)[1])) #define ZEROMAT2(m) \ (ZEROVEC2((m)[0]), \ ZEROVEC2((m)[1])) #define IDENTMAT2(m) \ (ZEROVEC2((m)[0]), (m)[0][0]=1, \ ZEROVEC2((m)[1]), (m)[1][1]=1) #define TRANSPOSE2(to,from) \ (_SETcol2((to)[0], from, 0), \ _SETcol2((to)[1], from, 1)) #define VPSXV2(to,v,s,w) \ ((to)[0] = (v)[0] + (s) * (w)[0], \ (to)[1] = (v)[1] + (s) * (w)[1]) #define VPVXS2(to,v,w,s) \ ((to)[0] = (v)[0] + (w)[0] * (s), \ (to)[1] = (v)[1] + (w)[1] * (s)) #define VPV2(to,v,w) \ ((to)[0] = (v)[0] + (w)[0], \ (to)[1] = (v)[1] + (w)[1]) #define VMV2(to,v,w) \ ((to)[0] = (v)[0] - (w)[0], \ (to)[1] = (v)[1] - (w)[1]) #define MPM2(to,m1,m2) \ (VPV2((to)[0], (m1)[0], (m2)[0]), \ VPV2((to)[1], (m1)[1], (m2)[1])) #define MMM2(to,m1,m2) \ (VMV2((to)[0], (m1)[0], (m2)[0]), \ VMV2((to)[1], (m1)[1], (m2)[1])) #define SXV2(to,s,from) \ ((to)[0] = (s) * (from)[0], \ (to)[1] = (s) * (from)[1]) #define SXM2(to,s,from) \ (SXV2((to)[0], s, (from)[0]), \ SXV2((to)[1], s, (from)[1])) #define MV2(to,from) \ ((to)[0] = -(from)[0], \ (to)[1] = -(from)[1]) #define MM2(to,from) \ (MV2((to)[0], (from)[0]), \ MV2((to)[1], (from)[1])) #define VXS2(to,from,s) \ ((to)[0] = (from)[0] * (s), \ (to)[1] = (from)[1] * (s)) #define VDS2(to,from,s) \ ((to)[0] = (from)[0] / (s), \ (to)[1] = (from)[1] / (s)) #define MXS2(to,from,s) \ (VXS2((to)[0], (from)[0], s), \ VXS2((to)[1], (from)[1], s)) #define MDS2(to,from,s) \ (VDS2((to)[0], (from)[0], s), \ VDS2((to)[1], (from)[1], s)) #define MXM2(to,m1,m2) \ (VXM2((to)[0], (m1)[0], m2), \ VXM2((to)[1], (m1)[1], m2)) #define VXM2(to,v,m) \ ((to)[0] = _DOTcol2(v, m, 0), \ (to)[1] = _DOTcol2(v, m, 1)) #define MXV2(to,m,v) \ ((to)[0] = DOT2((m)[0], v), \ (to)[1] = DOT2((m)[1], v)) #define VMODS2(to,v,s) \ ((to)[0] = SMODS1((v)[0], s), \ (to)[1] = SMODS1((v)[1], s)) #define VMODV2(to,v0,v1) \ ((to)[0] = SMODS1((v0)[0], (v1)[0]), \ (to)[1] = SMODS1((v0)[1], (v1)[1])) #define VDIVS2(to,v,s) \ ((to)[0] = SDIVS1((v)[0], s), \ (to)[1] = SDIVS1((v)[1], s)) #define VDIVV2(to,v0,v1) \ ((to)[0] = SDIVS1((v0)[0], (v1)[0]), \ (to)[1] = SDIVS1((v0)[1], (v1)[1])) #define VMINS2(to,v,s) \ ((to)[0] = SMINS1((v)[0], s), \ (to)[1] = SMINS1((v)[1], s)) #define VMINV2(to,v0,v1) \ ((to)[0] = SMINS1((v0)[0], (v1)[0]), \ (to)[1] = SMINS1((v0)[1], (v1)[1])) #define VMAXS2(to,v,s) \ ((to)[0] = SMAXS1((v)[0], s), \ (to)[1] = SMAXS1((v)[1], s)) #define VMAXV2(to,v0,v1) \ ((to)[0] = SMAXS1((v0)[0], (v1)[0]), \ (to)[1] = SMAXS1((v0)[1], (v1)[1])) #define LERP2(to,v0,v1,t) \ ((to)[0]=(v0)[0]+(t)*((v1)[0]-(v0)[0]), \ (to)[1]=(v0)[1]+(t)*((v1)[1]-(v0)[1])) #define TRACE2(m) \ ((m)[0][0] + \ (m)[1][1]) #define DOT2(v,w) \ ((v)[0] * (w)[0] + \ (v)[1] * (w)[1]) #define NORMSQRD2(v) \ ((v)[0] * (v)[0] + \ (v)[1] * (v)[1]) #define DISTSQRD2(v,w) \ (((v)[0]-(w)[0])*((v)[0]-(w)[0]) + \ ((v)[1]-(w)[1])*((v)[1]-(w)[1])) #define _DOTcol2(v,m,j) \ ((v)[0] * (m)[0][j] + \ (v)[1] * (m)[1][j]) #define _SETcol2(v,m,j) \ ((v)[0] = (m)[0][j], \ (v)[1] = (m)[1][j]) #define _MXVcol2(to,m,M,j) \ ((to)[0][j] = _DOTcol2((m)[0],M,j), \ (to)[1][j] = _DOTcol2((m)[1],M,j)) #define _DET2(v0,v1,i0,i1) \ ((v0)[i0]* _DET1(v1,i1) + \ (v0)[i1]*-_DET1(v1,i0)) #define XV2(to,v1) \ ((to)[0] = -_DET1(v1, 1), \ (to)[1] = _DET1(v1, 0)) #define V2XM3(to2,v2,m3) \ ((to2)[0] = _DOTcol2(v2,m3,0) + (m3)[2][0], \ (to2)[1] = _DOTcol2(v2,m3,1) + (m3)[2][1]) #define M3XV2(to2,m3,v2) \ ((to2)[0] = DOT2((m3)[0],v2) + (m3)[0][2], \ (to2)[1] = DOT2((m3)[1],v2) + (m3)[1][2]) #define _DET1(v0,i0) \ ((v0)[i0]) #define VXV2(v0,v1) \ (_DET2(v0,v1,0,1)) #define DET2(m) \ (VXV2((m)[0],(m)[1])) #define SMODS1(a,b) \ ((((a)%(b)+(b))%(b))) #define SDIVS1(a,b) \ ((((a)-SMODS1(a,b))/(b))) #define SMINS1(a,b) \ (((a) < (b) ? (a) : (b))) #define SMAXS1(a,b) \ (((a) > (b) ? (a) : (b))) #define ADJOINT2(to,m) \ ( _ADJOINTcol2(to,0,m,1), \ __ADJOINTcol2(to,1,m,0)) #define _ADJOINTcol2(to,col,m,i1) \ ((to)[0][col] = _DET1(m[i1], 1), \ (to)[1][col] = -_DET1(m[i1], 0)) #define __ADJOINTcol2(to,col,m,i1) \ ((to)[0][col] = -_DET1(m[i1], 1), \ (to)[1][col] = _DET1(m[i1], 0)) #define SET3(to,from) \ ((to)[0] = (from)[0], \ (to)[1] = (from)[1], \ (to)[2] = (from)[2]) #define SETMAT3(to,from) \ (SET3((to)[0], (from)[0]), \ SET3((to)[1], (from)[1]), \ SET3((to)[2], (from)[2])) #define ROUNDVEC3(to,from) \ ((to)[0] = floor((from)[0]+.5), \ (to)[1] = floor((from)[1]+.5), \ (to)[2] = floor((from)[2]+.5)) #define ROUNDMAT3(to,from) \ (ROUNDVEC3((to)[0], (from)[0]), \ ROUNDVEC3((to)[1], (from)[1]), \ ROUNDVEC3((to)[2], (from)[2])) #define FILLVEC3(v,s) \ ((v)[0] = (s), \ (v)[1] = (s), \ (v)[2] = (s)) #define FILLMAT3(m,s) \ (FILLVEC3((m)[0], s), \ FILLVEC3((m)[1], s), \ FILLVEC3((m)[2], s)) #define ZEROVEC3(v) \ ((v)[0] = 0, \ (v)[1] = 0, \ (v)[2] = 0) #define ISZEROVEC3(v) \ ((v)[0] == 0 && \ (v)[1] == 0 && \ (v)[2] == 0) #define EQVEC3(v,w) \ ((v)[0] == (w)[0] && \ (v)[1] == (w)[1] && \ (v)[2] == (w)[2]) #define EQMAT3(m1,m2) \ (EQVEC3((m1)[0], (m2)[0]) && \ EQVEC3((m1)[1], (m2)[1]) && \ EQVEC3((m1)[2], (m2)[2])) #define ZEROMAT3(m) \ (ZEROVEC3((m)[0]), \ ZEROVEC3((m)[1]), \ ZEROVEC3((m)[2])) #define IDENTMAT3(m) \ (ZEROVEC3((m)[0]), (m)[0][0]=1, \ ZEROVEC3((m)[1]), (m)[1][1]=1, \ ZEROVEC3((m)[2]), (m)[2][2]=1) #define TRANSPOSE3(to,from) \ (_SETcol3((to)[0], from, 0), \ _SETcol3((to)[1], from, 1), \ _SETcol3((to)[2], from, 2)) #define VPSXV3(to,v,s,w) \ ((to)[0] = (v)[0] + (s) * (w)[0], \ (to)[1] = (v)[1] + (s) * (w)[1], \ (to)[2] = (v)[2] + (s) * (w)[2]) #define VPVXS3(to,v,w,s) \ ((to)[0] = (v)[0] + (w)[0] * (s), \ (to)[1] = (v)[1] + (w)[1] * (s), \ (to)[2] = (v)[2] + (w)[2] * (s)) #define VPV3(to,v,w) \ ((to)[0] = (v)[0] + (w)[0], \ (to)[1] = (v)[1] + (w)[1], \ (to)[2] = (v)[2] + (w)[2]) #define VMV3(to,v,w) \ ((to)[0] = (v)[0] - (w)[0], \ (to)[1] = (v)[1] - (w)[1], \ (to)[2] = (v)[2] - (w)[2]) #define MPM3(to,m1,m2) \ (VPV3((to)[0], (m1)[0], (m2)[0]), \ VPV3((to)[1], (m1)[1], (m2)[1]), \ VPV3((to)[2], (m1)[2], (m2)[2])) #define MMM3(to,m1,m2) \ (VMV3((to)[0], (m1)[0], (m2)[0]), \ VMV3((to)[1], (m1)[1], (m2)[1]), \ VMV3((to)[2], (m1)[2], (m2)[2])) #define SXV3(to,s,from) \ ((to)[0] = (s) * (from)[0], \ (to)[1] = (s) * (from)[1], \ (to)[2] = (s) * (from)[2]) #define SXM3(to,s,from) \ (SXV3((to)[0], s, (from)[0]), \ SXV3((to)[1], s, (from)[1]), \ SXV3((to)[2], s, (from)[2])) #define MV3(to,from) \ ((to)[0] = -(from)[0], \ (to)[1] = -(from)[1], \ (to)[2] = -(from)[2]) #define MM3(to,from) \ (MV3((to)[0], (from)[0]), \ MV3((to)[1], (from)[1]), \ MV3((to)[2], (from)[2])) #define VXS3(to,from,s) \ ((to)[0] = (from)[0] * (s), \ (to)[1] = (from)[1] * (s), \ (to)[2] = (from)[2] * (s)) #define VDS3(to,from,s) \ ((to)[0] = (from)[0] / (s), \ (to)[1] = (from)[1] / (s), \ (to)[2] = (from)[2] / (s)) #define MXS3(to,from,s) \ (VXS3((to)[0], (from)[0], s), \ VXS3((to)[1], (from)[1], s), \ VXS3((to)[2], (from)[2], s)) #define MDS3(to,from,s) \ (VDS3((to)[0], (from)[0], s), \ VDS3((to)[1], (from)[1], s), \ VDS3((to)[2], (from)[2], s)) #define MXM3(to,m1,m2) \ (VXM3((to)[0], (m1)[0], m2), \ VXM3((to)[1], (m1)[1], m2), \ VXM3((to)[2], (m1)[2], m2)) #define VXM3(to,v,m) \ ((to)[0] = _DOTcol3(v, m, 0), \ (to)[1] = _DOTcol3(v, m, 1), \ (to)[2] = _DOTcol3(v, m, 2)) #define MXV3(to,m,v) \ ((to)[0] = DOT3((m)[0], v), \ (to)[1] = DOT3((m)[1], v), \ (to)[2] = DOT3((m)[2], v)) #define VMODS3(to,v,s) \ ((to)[0] = SMODS1((v)[0], s), \ (to)[1] = SMODS1((v)[1], s), \ (to)[2] = SMODS1((v)[2], s)) #define VMODV3(to,v0,v1) \ ((to)[0] = SMODS1((v0)[0], (v1)[0]), \ (to)[1] = SMODS1((v0)[1], (v1)[1]), \ (to)[2] = SMODS1((v0)[2], (v1)[2])) #define VDIVS3(to,v,s) \ ((to)[0] = SDIVS1((v)[0], s), \ (to)[1] = SDIVS1((v)[1], s), \ (to)[2] = SDIVS1((v)[2], s)) #define VDIVV3(to,v0,v1) \ ((to)[0] = SDIVS1((v0)[0], (v1)[0]), \ (to)[1] = SDIVS1((v0)[1], (v1)[1]), \ (to)[2] = SDIVS1((v0)[2], (v1)[2])) #define VMINS3(to,v,s) \ ((to)[0] = SMINS1((v)[0], s), \ (to)[1] = SMINS1((v)[1], s), \ (to)[2] = SMINS1((v)[2], s)) #define VMINV3(to,v0,v1) \ ((to)[0] = SMINS1((v0)[0], (v1)[0]), \ (to)[1] = SMINS1((v0)[1], (v1)[1]), \ (to)[2] = SMINS1((v0)[2], (v1)[2])) #define VMAXS3(to,v,s) \ ((to)[0] = SMAXS1((v)[0], s), \ (to)[1] = SMAXS1((v)[1], s), \ (to)[2] = SMAXS1((v)[2], s)) #define VMAXV3(to,v0,v1) \ ((to)[0] = SMAXS1((v0)[0], (v1)[0]), \ (to)[1] = SMAXS1((v0)[1], (v1)[1]), \ (to)[2] = SMAXS1((v0)[2], (v1)[2])) #define LERP3(to,v0,v1,t) \ ((to)[0]=(v0)[0]+(t)*((v1)[0]-(v0)[0]), \ (to)[1]=(v0)[1]+(t)*((v1)[1]-(v0)[1]), \ (to)[2]=(v0)[2]+(t)*((v1)[2]-(v0)[2])) #define TRACE3(m) \ ((m)[0][0] + \ (m)[1][1] + \ (m)[2][2]) #define DOT3(v,w) \ ((v)[0] * (w)[0] + \ (v)[1] * (w)[1] + \ (v)[2] * (w)[2]) #define NORMSQRD3(v) \ ((v)[0] * (v)[0] + \ (v)[1] * (v)[1] + \ (v)[2] * (v)[2]) #define DISTSQRD3(v,w) \ (((v)[0]-(w)[0])*((v)[0]-(w)[0]) + \ ((v)[1]-(w)[1])*((v)[1]-(w)[1]) + \ ((v)[2]-(w)[2])*((v)[2]-(w)[2])) #define _DOTcol3(v,m,j) \ ((v)[0] * (m)[0][j] + \ (v)[1] * (m)[1][j] + \ (v)[2] * (m)[2][j]) #define _SETcol3(v,m,j) \ ((v)[0] = (m)[0][j], \ (v)[1] = (m)[1][j], \ (v)[2] = (m)[2][j]) #define _MXVcol3(to,m,M,j) \ ((to)[0][j] = _DOTcol3((m)[0],M,j), \ (to)[1][j] = _DOTcol3((m)[1],M,j), \ (to)[2][j] = _DOTcol3((m)[2],M,j)) #define _DET3(v0,v1,v2,i0,i1,i2) \ ((v0)[i0]* _DET2(v1,v2,i1,i2) + \ (v0)[i1]*-_DET2(v1,v2,i0,i2) + \ (v0)[i2]* _DET2(v1,v2,i0,i1)) #define VXV3(to,v1,v2) \ ((to)[0] = _DET2(v1,v2, 1,2), \ (to)[1] = -_DET2(v1,v2, 0,2), \ (to)[2] = _DET2(v1,v2, 0,1)) #define SET3from2(to,from,pad) \ ((to)[0] = (from)[0], \ (to)[1] = (from)[1], \ (to)[2] = (pad)) #define SETMAT3from2(to,from,pad0,pad1) \ (SET3from2((to)[0], (from)[0], pad0), \ SET3from2((to)[1], (from)[1], pad0), \ FILLVEC2((to)[2], (pad0)), (to)[2][2] = (pad1)) #define M2XM3(to3,m2,m3) \ (_MXVcol2(to3,m2,m3,0), (to3)[2][0]=(m3)[2][0], \ _MXVcol2(to3,m2,m3,1), (to3)[2][1]=(m3)[2][1], \ _MXVcol2(to3,m2,m3,2), (to3)[2][2]=(m3)[2][2]) #define M3XM2(to3,m3,m2) \ (VXM2((to3)[0],(m3)[0],m2), (to3)[0][2]=(m3)[0][2], \ VXM2((to3)[1],(m3)[1],m2), (to3)[1][2]=(m3)[1][2], \ VXM2((to3)[2],(m3)[2],m2), (to3)[2][2]=(m3)[2][2]) #define V3XM4(to3,v3,m4) \ ((to3)[0] = _DOTcol3(v3,m4,0) + (m4)[3][0], \ (to3)[1] = _DOTcol3(v3,m4,1) + (m4)[3][1], \ (to3)[2] = _DOTcol3(v3,m4,2) + (m4)[3][2]) #define M4XV3(to3,m4,v3) \ ((to3)[0] = DOT3((m4)[0],v3) + (m4)[0][3], \ (to3)[1] = DOT3((m4)[1],v3) + (m4)[1][3], \ (to3)[2] = DOT3((m4)[2],v3) + (m4)[2][3]) #define VXVXV3(v0,v1,v2) \ (_DET3(v0,v1,v2,0,1,2)) #define DET3(m) \ (VXVXV3((m)[0],(m)[1],(m)[2])) #define ADJOINT3(to,m) \ ( _ADJOINTcol3(to,0,m,1,2), \ __ADJOINTcol3(to,1,m,0,2), \ _ADJOINTcol3(to,2,m,0,1)) #define _ADJOINTcol3(to,col,m,i1,i2) \ ((to)[0][col] = _DET2(m[i1],m[i2], 1,2), \ (to)[1][col] = -_DET2(m[i1],m[i2], 0,2), \ (to)[2][col] = _DET2(m[i1],m[i2], 0,1)) #define __ADJOINTcol3(to,col,m,i1,i2) \ ((to)[0][col] = -_DET2(m[i1],m[i2], 1,2), \ (to)[1][col] = _DET2(m[i1],m[i2], 0,2), \ (to)[2][col] = -_DET2(m[i1],m[i2], 0,1)) #define SET4(to,from) \ ((to)[0] = (from)[0], \ (to)[1] = (from)[1], \ (to)[2] = (from)[2], \ (to)[3] = (from)[3]) #define SETMAT4(to,from) \ (SET4((to)[0], (from)[0]), \ SET4((to)[1], (from)[1]), \ SET4((to)[2], (from)[2]), \ SET4((to)[3], (from)[3])) #define ROUNDVEC4(to,from) \ ((to)[0] = floor((from)[0]+.5), \ (to)[1] = floor((from)[1]+.5), \ (to)[2] = floor((from)[2]+.5), \ (to)[3] = floor((from)[3]+.5)) #define ROUNDMAT4(to,from) \ (ROUNDVEC4((to)[0], (from)[0]), \ ROUNDVEC4((to)[1], (from)[1]), \ ROUNDVEC4((to)[2], (from)[2]), \ ROUNDVEC4((to)[3], (from)[3])) #define FILLVEC4(v,s) \ ((v)[0] = (s), \ (v)[1] = (s), \ (v)[2] = (s), \ (v)[3] = (s)) #define FILLMAT4(m,s) \ (FILLVEC4((m)[0], s), \ FILLVEC4((m)[1], s), \ FILLVEC4((m)[2], s), \ FILLVEC4((m)[3], s)) #define ZEROVEC4(v) \ ((v)[0] = 0, \ (v)[1] = 0, \ (v)[2] = 0, \ (v)[3] = 0) #define ISZEROVEC4(v) \ ((v)[0] == 0 && \ (v)[1] == 0 && \ (v)[2] == 0 && \ (v)[3] == 0) #define EQVEC4(v,w) \ ((v)[0] == (w)[0] && \ (v)[1] == (w)[1] && \ (v)[2] == (w)[2] && \ (v)[3] == (w)[3]) #define EQMAT4(m1,m2) \ (EQVEC4((m1)[0], (m2)[0]) && \ EQVEC4((m1)[1], (m2)[1]) && \ EQVEC4((m1)[2], (m2)[2]) && \ EQVEC4((m1)[3], (m2)[3])) #define ZEROMAT4(m) \ (ZEROVEC4((m)[0]), \ ZEROVEC4((m)[1]), \ ZEROVEC4((m)[2]), \ ZEROVEC4((m)[3])) #define IDENTMAT4(m) \ (ZEROVEC4((m)[0]), (m)[0][0]=1, \ ZEROVEC4((m)[1]), (m)[1][1]=1, \ ZEROVEC4((m)[2]), (m)[2][2]=1, \ ZEROVEC4((m)[3]), (m)[3][3]=1) #define TRANSPOSE4(to,from) \ (_SETcol4((to)[0], from, 0), \ _SETcol4((to)[1], from, 1), \ _SETcol4((to)[2], from, 2), \ _SETcol4((to)[3], from, 3)) #define VPSXV4(to,v,s,w) \ ((to)[0] = (v)[0] + (s) * (w)[0], \ (to)[1] = (v)[1] + (s) * (w)[1], \ (to)[2] = (v)[2] + (s) * (w)[2], \ (to)[3] = (v)[3] + (s) * (w)[3]) #define VPVXS4(to,v,w,s) \ ((to)[0] = (v)[0] + (w)[0] * (s), \ (to)[1] = (v)[1] + (w)[1] * (s), \ (to)[2] = (v)[2] + (w)[2] * (s), \ (to)[3] = (v)[3] + (w)[3] * (s)) #define VPV4(to,v,w) \ ((to)[0] = (v)[0] + (w)[0], \ (to)[1] = (v)[1] + (w)[1], \ (to)[2] = (v)[2] + (w)[2], \ (to)[3] = (v)[3] + (w)[3]) #define VMV4(to,v,w) \ ((to)[0] = (v)[0] - (w)[0], \ (to)[1] = (v)[1] - (w)[1], \ (to)[2] = (v)[2] - (w)[2], \ (to)[3] = (v)[3] - (w)[3]) #define MPM4(to,m1,m2) \ (VPV4((to)[0], (m1)[0], (m2)[0]), \ VPV4((to)[1], (m1)[1], (m2)[1]), \ VPV4((to)[2], (m1)[2], (m2)[2]), \ VPV4((to)[3], (m1)[3], (m2)[3])) #define MMM4(to,m1,m2) \ (VMV4((to)[0], (m1)[0], (m2)[0]), \ VMV4((to)[1], (m1)[1], (m2)[1]), \ VMV4((to)[2], (m1)[2], (m2)[2]), \ VMV4((to)[3], (m1)[3], (m2)[3])) #define SXV4(to,s,from) \ ((to)[0] = (s) * (from)[0], \ (to)[1] = (s) * (from)[1], \ (to)[2] = (s) * (from)[2], \ (to)[3] = (s) * (from)[3]) #define SXM4(to,s,from) \ (SXV4((to)[0], s, (from)[0]), \ SXV4((to)[1], s, (from)[1]), \ SXV4((to)[2], s, (from)[2]), \ SXV4((to)[3], s, (from)[3])) #define MV4(to,from) \ ((to)[0] = -(from)[0], \ (to)[1] = -(from)[1], \ (to)[2] = -(from)[2], \ (to)[3] = -(from)[3]) #define MM4(to,from) \ (MV4((to)[0], (from)[0]), \ MV4((to)[1], (from)[1]), \ MV4((to)[2], (from)[2]), \ MV4((to)[3], (from)[3])) #define VXS4(to,from,s) \ ((to)[0] = (from)[0] * (s), \ (to)[1] = (from)[1] * (s), \ (to)[2] = (from)[2] * (s), \ (to)[3] = (from)[3] * (s)) #define VDS4(to,from,s) \ ((to)[0] = (from)[0] / (s), \ (to)[1] = (from)[1] / (s), \ (to)[2] = (from)[2] / (s), \ (to)[3] = (from)[3] / (s)) #define MXS4(to,from,s) \ (VXS4((to)[0], (from)[0], s), \ VXS4((to)[1], (from)[1], s), \ VXS4((to)[2], (from)[2], s), \ VXS4((to)[3], (from)[3], s)) #define MDS4(to,from,s) \ (VDS4((to)[0], (from)[0], s), \ VDS4((to)[1], (from)[1], s), \ VDS4((to)[2], (from)[2], s), \ VDS4((to)[3], (from)[3], s)) #define MXM4(to,m1,m2) \ (VXM4((to)[0], (m1)[0], m2), \ VXM4((to)[1], (m1)[1], m2), \ VXM4((to)[2], (m1)[2], m2), \ VXM4((to)[3], (m1)[3], m2)) #define VXM4(to,v,m) \ ((to)[0] = _DOTcol4(v, m, 0), \ (to)[1] = _DOTcol4(v, m, 1), \ (to)[2] = _DOTcol4(v, m, 2), \ (to)[3] = _DOTcol4(v, m, 3)) #define MXV4(to,m,v) \ ((to)[0] = DOT4((m)[0], v), \ (to)[1] = DOT4((m)[1], v), \ (to)[2] = DOT4((m)[2], v), \ (to)[3] = DOT4((m)[3], v)) #define VMODS4(to,v,s) \ ((to)[0] = SMODS1((v)[0], s), \ (to)[1] = SMODS1((v)[1], s), \ (to)[2] = SMODS1((v)[2], s), \ (to)[3] = SMODS1((v)[3], s)) #define VMODV4(to,v0,v1) \ ((to)[0] = SMODS1((v0)[0], (v1)[0]), \ (to)[1] = SMODS1((v0)[1], (v1)[1]), \ (to)[2] = SMODS1((v0)[2], (v1)[2]), \ (to)[3] = SMODS1((v0)[3], (v1)[3])) #define VDIVS4(to,v,s) \ ((to)[0] = SDIVS1((v)[0], s), \ (to)[1] = SDIVS1((v)[1], s), \ (to)[2] = SDIVS1((v)[2], s), \ (to)[3] = SDIVS1((v)[3], s)) #define VDIVV4(to,v0,v1) \ ((to)[0] = SDIVS1((v0)[0], (v1)[0]), \ (to)[1] = SDIVS1((v0)[1], (v1)[1]), \ (to)[2] = SDIVS1((v0)[2], (v1)[2]), \ (to)[3] = SDIVS1((v0)[3], (v1)[3])) #define VMINS4(to,v,s) \ ((to)[0] = SMINS1((v)[0], s), \ (to)[1] = SMINS1((v)[1], s), \ (to)[2] = SMINS1((v)[2], s), \ (to)[3] = SMINS1((v)[3], s)) #define VMINV4(to,v0,v1) \ ((to)[0] = SMINS1((v0)[0], (v1)[0]), \ (to)[1] = SMINS1((v0)[1], (v1)[1]), \ (to)[2] = SMINS1((v0)[2], (v1)[2]), \ (to)[3] = SMINS1((v0)[3], (v1)[3])) #define VMAXS4(to,v,s) \ ((to)[0] = SMAXS1((v)[0], s), \ (to)[1] = SMAXS1((v)[1], s), \ (to)[2] = SMAXS1((v)[2], s), \ (to)[3] = SMAXS1((v)[3], s)) #define VMAXV4(to,v0,v1) \ ((to)[0] = SMAXS1((v0)[0], (v1)[0]), \ (to)[1] = SMAXS1((v0)[1], (v1)[1]), \ (to)[2] = SMAXS1((v0)[2], (v1)[2]), \ (to)[3] = SMAXS1((v0)[3], (v1)[3])) #define LERP4(to,v0,v1,t) \ ((to)[0]=(v0)[0]+(t)*((v1)[0]-(v0)[0]), \ (to)[1]=(v0)[1]+(t)*((v1)[1]-(v0)[1]), \ (to)[2]=(v0)[2]+(t)*((v1)[2]-(v0)[2]), \ (to)[3]=(v0)[3]+(t)*((v1)[3]-(v0)[3])) #define TRACE4(m) \ ((m)[0][0] + \ (m)[1][1] + \ (m)[2][2] + \ (m)[3][3]) #define DOT4(v,w) \ ((v)[0] * (w)[0] + \ (v)[1] * (w)[1] + \ (v)[2] * (w)[2] + \ (v)[3] * (w)[3]) #define NORMSQRD4(v) \ ((v)[0] * (v)[0] + \ (v)[1] * (v)[1] + \ (v)[2] * (v)[2] + \ (v)[3] * (v)[3]) #define DISTSQRD4(v,w) \ (((v)[0]-(w)[0])*((v)[0]-(w)[0]) + \ ((v)[1]-(w)[1])*((v)[1]-(w)[1]) + \ ((v)[2]-(w)[2])*((v)[2]-(w)[2]) + \ ((v)[3]-(w)[3])*((v)[3]-(w)[3])) #define _DOTcol4(v,m,j) \ ((v)[0] * (m)[0][j] + \ (v)[1] * (m)[1][j] + \ (v)[2] * (m)[2][j] + \ (v)[3] * (m)[3][j]) #define _SETcol4(v,m,j) \ ((v)[0] = (m)[0][j], \ (v)[1] = (m)[1][j], \ (v)[2] = (m)[2][j], \ (v)[3] = (m)[3][j]) #define _MXVcol4(to,m,M,j) \ ((to)[0][j] = _DOTcol4((m)[0],M,j), \ (to)[1][j] = _DOTcol4((m)[1],M,j), \ (to)[2][j] = _DOTcol4((m)[2],M,j), \ (to)[3][j] = _DOTcol4((m)[3],M,j)) #define _DET4(v0,v1,v2,v3,i0,i1,i2,i3) \ ((v0)[i0]* _DET3(v1,v2,v3,i1,i2,i3) + \ (v0)[i1]*-_DET3(v1,v2,v3,i0,i2,i3) + \ (v0)[i2]* _DET3(v1,v2,v3,i0,i1,i3) + \ (v0)[i3]*-_DET3(v1,v2,v3,i0,i1,i2)) #define VXVXV4(to,v1,v2,v3) \ ((to)[0] = -_DET3(v1,v2,v3, 1,2,3), \ (to)[1] = _DET3(v1,v2,v3, 0,2,3), \ (to)[2] = -_DET3(v1,v2,v3, 0,1,3), \ (to)[3] = _DET3(v1,v2,v3, 0,1,2)) #define SET4from3(to,from,pad) \ ((to)[0] = (from)[0], \ (to)[1] = (from)[1], \ (to)[2] = (from)[2], \ (to)[3] = (pad)) #define SETMAT4from3(to,from,pad0,pad1) \ (SET4from3((to)[0], (from)[0], pad0), \ SET4from3((to)[1], (from)[1], pad0), \ SET4from3((to)[2], (from)[2], pad0), \ FILLVEC3((to)[3], (pad0)), (to)[3][3] = (pad1)) #define M3XM4(to4,m3,m4) \ (_MXVcol3(to4,m3,m4,0), (to4)[3][0]=(m4)[3][0], \ _MXVcol3(to4,m3,m4,1), (to4)[3][1]=(m4)[3][1], \ _MXVcol3(to4,m3,m4,2), (to4)[3][2]=(m4)[3][2], \ _MXVcol3(to4,m3,m4,3), (to4)[3][3]=(m4)[3][3]) #define M4XM3(to4,m4,m3) \ (VXM3((to4)[0],(m4)[0],m3), (to4)[0][3]=(m4)[0][3], \ VXM3((to4)[1],(m4)[1],m3), (to4)[1][3]=(m4)[1][3], \ VXM3((to4)[2],(m4)[2],m3), (to4)[2][3]=(m4)[2][3], \ VXM3((to4)[3],(m4)[3],m3), (to4)[3][3]=(m4)[3][3]) #define VXVXVXV4(v0,v1,v2,v3) \ (_DET4(v0,v1,v2,v3,0,1,2,3)) #define DET4(m) \ (VXVXVXV4((m)[0],(m)[1],(m)[2],(m)[3])) #define ADJOINT4(to,m) \ ( _ADJOINTcol4(to,0,m,1,2,3), \ __ADJOINTcol4(to,1,m,0,2,3), \ _ADJOINTcol4(to,2,m,0,1,3), \ __ADJOINTcol4(to,3,m,0,1,2)) #define _ADJOINTcol4(to,col,m,i1,i2,i3) \ ((to)[0][col] = _DET3(m[i1],m[i2],m[i3], 1,2,3), \ (to)[1][col] = -_DET3(m[i1],m[i2],m[i3], 0,2,3), \ (to)[2][col] = _DET3(m[i1],m[i2],m[i3], 0,1,3), \ (to)[3][col] = -_DET3(m[i1],m[i2],m[i3], 0,1,2)) #define __ADJOINTcol4(to,col,m,i1,i2,i3) \ ((to)[0][col] = -_DET3(m[i1],m[i2],m[i3], 1,2,3), \ (to)[1][col] = _DET3(m[i1],m[i2],m[i3], 0,2,3), \ (to)[2][col] = -_DET3(m[i1],m[i2],m[i3], 0,1,3), \ (to)[3][col] = _DET3(m[i1],m[i2],m[i3], 0,1,2)) #define TRANSPOSE2safe(type,to,from) \ do {type _vec_h_temp_[2][2]; \ TRANSPOSE2(_vec_h_temp_,from); \ SETMAT2(to, _vec_h_temp_); \ } while (0) #define TRANSPOSE2d(to,from) TRANSPOSE2safe(double,to,from) #define TRANSPOSE2i(to,from) TRANSPOSE2safe(int,to,from) #define TRANSPOSE2l(to,from) TRANSPOSE2safe(long,to,from) #define TRANSPOSE2r(to,from) TRANSPOSE2safe(real,to,from) #define MXM2safe(type,to,m1,m2) \ do {type _vec_h_temp_[2][2]; \ MXM2(_vec_h_temp_,m1,m2); \ SETMAT2(to, _vec_h_temp_); \ } while (0) #define MXM2d(to,m1,m2) MXM2safe(double,to,m1,m2) #define MXM2i(to,m1,m2) MXM2safe(int,to,m1,m2) #define MXM2l(to,m1,m2) MXM2safe(long,to,m1,m2) #define MXM2r(to,m1,m2) MXM2safe(real,to,m1,m2) #define VXM2safe(type,to,v,m) \ do {type _vec_h_temp_[2]; \ VXM2(_vec_h_temp_,v,m); \ SET2(to, _vec_h_temp_); \ } while (0) #define VXM2d(to,v,m) VXM2safe(double,to,v,m) #define VXM2i(to,v,m) VXM2safe(int,to,v,m) #define VXM2l(to,v,m) VXM2safe(long,to,v,m) #define VXM2r(to,v,m) VXM2safe(real,to,v,m) #define MXV2safe(type,to,m,v) \ do {type _vec_h_temp_[2]; \ MXV2(_vec_h_temp_,m,v); \ SET2(to, _vec_h_temp_); \ } while (0) #define MXV2d(to,m,v) MXV2safe(double,to,m,v) #define MXV2i(to,m,v) MXV2safe(int,to,m,v) #define MXV2l(to,m,v) MXV2safe(long,to,m,v) #define MXV2r(to,m,v) MXV2safe(real,to,m,v) #define XV2safe(type,to,v1) \ do {type _vec_h_temp_[2]; \ XV2(_vec_h_temp_,v1); \ SET2(to, _vec_h_temp_); \ } while (0) #define XV2d(to,v1) XV2safe(double,to,v1) #define XV2i(to,v1) XV2safe(int,to,v1) #define XV2l(to,v1) XV2safe(long,to,v1) #define XV2r(to,v1) XV2safe(real,to,v1) #define V2XM3safe(type,to2,v2,m3) \ do {type _vec_h_temp_[2]; \ V2XM3(_vec_h_temp_,v2,m3); \ SET2(to2, _vec_h_temp_); \ } while (0) #define V2XM3d(to2,v2,m3) V2XM3safe(double,to2,v2,m3) #define V2XM3i(to2,v2,m3) V2XM3safe(int,to2,v2,m3) #define V2XM3l(to2,v2,m3) V2XM3safe(long,to2,v2,m3) #define V2XM3r(to2,v2,m3) V2XM3safe(real,to2,v2,m3) #define M3XV2safe(type,to2,m3,v2) \ do {type _vec_h_temp_[2]; \ M3XV2(_vec_h_temp_,m3,v2); \ SET2(to2, _vec_h_temp_); \ } while (0) #define M3XV2d(to2,m3,v2) M3XV2safe(double,to2,m3,v2) #define M3XV2i(to2,m3,v2) M3XV2safe(int,to2,m3,v2) #define M3XV2l(to2,m3,v2) M3XV2safe(long,to2,m3,v2) #define M3XV2r(to2,m3,v2) M3XV2safe(real,to2,m3,v2) #define ADJOINT2safe(type,to,m) \ do {type _vec_h_temp_[2][2]; \ ADJOINT2(_vec_h_temp_,m); \ SETMAT2(to, _vec_h_temp_); \ } while (0) #define ADJOINT2d(to,m) ADJOINT2safe(double,to,m) #define ADJOINT2i(to,m) ADJOINT2safe(int,to,m) #define ADJOINT2l(to,m) ADJOINT2safe(long,to,m) #define ADJOINT2r(to,m) ADJOINT2safe(real,to,m) #define INVERTMAT2safe(type,to,from) \ do {type _vec_h_temp_[2][2]; \ ADJOINT2(_vec_h_temp_, from); \ type _vec_h_temp_invdet_ = (type)1/(type)DET2(from); \ SXM2(to, _vec_h_temp_invdet_, _vec_h_temp_); \ } while (0) #define INVERTMAT2d(to,from) INVERTMAT2safe(double,to,from) #define INVERTMAT2i(to,from) INVERTMAT2safe(int,to,from) #define INVERTMAT2l(to,from) INVERTMAT2safe(long,to,from) #define INVERTMAT2r(to,from) INVERTMAT2safe(real,to,from) #define TRANSPOSE3safe(type,to,from) \ do {type _vec_h_temp_[3][3]; \ TRANSPOSE3(_vec_h_temp_,from); \ SETMAT3(to, _vec_h_temp_); \ } while (0) #define TRANSPOSE3d(to,from) TRANSPOSE3safe(double,to,from) #define TRANSPOSE3i(to,from) TRANSPOSE3safe(int,to,from) #define TRANSPOSE3l(to,from) TRANSPOSE3safe(long,to,from) #define TRANSPOSE3r(to,from) TRANSPOSE3safe(real,to,from) #define MXM3safe(type,to,m1,m2) \ do {type _vec_h_temp_[3][3]; \ MXM3(_vec_h_temp_,m1,m2); \ SETMAT3(to, _vec_h_temp_); \ } while (0) #define MXM3d(to,m1,m2) MXM3safe(double,to,m1,m2) #define MXM3i(to,m1,m2) MXM3safe(int,to,m1,m2) #define MXM3l(to,m1,m2) MXM3safe(long,to,m1,m2) #define MXM3r(to,m1,m2) MXM3safe(real,to,m1,m2) #define VXM3safe(type,to,v,m) \ do {type _vec_h_temp_[3]; \ VXM3(_vec_h_temp_,v,m); \ SET3(to, _vec_h_temp_); \ } while (0) #define VXM3d(to,v,m) VXM3safe(double,to,v,m) #define VXM3i(to,v,m) VXM3safe(int,to,v,m) #define VXM3l(to,v,m) VXM3safe(long,to,v,m) #define VXM3r(to,v,m) VXM3safe(real,to,v,m) #define MXV3safe(type,to,m,v) \ do {type _vec_h_temp_[3]; \ MXV3(_vec_h_temp_,m,v); \ SET3(to, _vec_h_temp_); \ } while (0) #define MXV3d(to,m,v) MXV3safe(double,to,m,v) #define MXV3i(to,m,v) MXV3safe(int,to,m,v) #define MXV3l(to,m,v) MXV3safe(long,to,m,v) #define MXV3r(to,m,v) MXV3safe(real,to,m,v) #define VXV3safe(type,to,v1,v2) \ do {type _vec_h_temp_[3]; \ VXV3(_vec_h_temp_,v1,v2); \ SET3(to, _vec_h_temp_); \ } while (0) #define VXV3d(to,v1,v2) VXV3safe(double,to,v1,v2) #define VXV3i(to,v1,v2) VXV3safe(int,to,v1,v2) #define VXV3l(to,v1,v2) VXV3safe(long,to,v1,v2) #define VXV3r(to,v1,v2) VXV3safe(real,to,v1,v2) #define M2XM3safe(type,to3,m2,m3) \ do {type _vec_h_temp_[3][3]; \ M2XM3(_vec_h_temp_,m2,m3); \ SETMAT3(to3, _vec_h_temp_); \ } while (0) #define M2XM3d(to3,m2,m3) M2XM3safe(double,to3,m2,m3) #define M2XM3i(to3,m2,m3) M2XM3safe(int,to3,m2,m3) #define M2XM3l(to3,m2,m3) M2XM3safe(long,to3,m2,m3) #define M2XM3r(to3,m2,m3) M2XM3safe(real,to3,m2,m3) #define M3XM2safe(type,to3,m3,m2) \ do {type _vec_h_temp_[3][3]; \ M3XM2(_vec_h_temp_,m3,m2); \ SETMAT3(to3, _vec_h_temp_); \ } while (0) #define M3XM2d(to3,m3,m2) M3XM2safe(double,to3,m3,m2) #define M3XM2i(to3,m3,m2) M3XM2safe(int,to3,m3,m2) #define M3XM2l(to3,m3,m2) M3XM2safe(long,to3,m3,m2) #define M3XM2r(to3,m3,m2) M3XM2safe(real,to3,m3,m2) #define V3XM4safe(type,to3,v3,m4) \ do {type _vec_h_temp_[3]; \ V3XM4(_vec_h_temp_,v3,m4); \ SET3(to3, _vec_h_temp_); \ } while (0) #define V3XM4d(to3,v3,m4) V3XM4safe(double,to3,v3,m4) #define V3XM4i(to3,v3,m4) V3XM4safe(int,to3,v3,m4) #define V3XM4l(to3,v3,m4) V3XM4safe(long,to3,v3,m4) #define V3XM4r(to3,v3,m4) V3XM4safe(real,to3,v3,m4) #define M4XV3safe(type,to3,m4,v3) \ do {type _vec_h_temp_[3]; \ M4XV3(_vec_h_temp_,m4,v3); \ SET3(to3, _vec_h_temp_); \ } while (0) #define M4XV3d(to3,m4,v3) M4XV3safe(double,to3,m4,v3) #define M4XV3i(to3,m4,v3) M4XV3safe(int,to3,m4,v3) #define M4XV3l(to3,m4,v3) M4XV3safe(long,to3,m4,v3) #define M4XV3r(to3,m4,v3) M4XV3safe(real,to3,m4,v3) #define ADJOINT3safe(type,to,m) \ do {type _vec_h_temp_[3][3]; \ ADJOINT3(_vec_h_temp_,m); \ SETMAT3(to, _vec_h_temp_); \ } while (0) #define ADJOINT3d(to,m) ADJOINT3safe(double,to,m) #define ADJOINT3i(to,m) ADJOINT3safe(int,to,m) #define ADJOINT3l(to,m) ADJOINT3safe(long,to,m) #define ADJOINT3r(to,m) ADJOINT3safe(real,to,m) #define INVERTMAT3safe(type,to,from) \ do {type _vec_h_temp_[3][3]; \ ADJOINT3(_vec_h_temp_, from); \ type _vec_h_temp_invdet_ = (type)1/(type)DET3(from); \ SXM3(to, _vec_h_temp_invdet_, _vec_h_temp_); \ } while (0) #define INVERTMAT3d(to,from) INVERTMAT3safe(double,to,from) #define INVERTMAT3i(to,from) INVERTMAT3safe(int,to,from) #define INVERTMAT3l(to,from) INVERTMAT3safe(long,to,from) #define INVERTMAT3r(to,from) INVERTMAT3safe(real,to,from) #define TRANSPOSE4safe(type,to,from) \ do {type _vec_h_temp_[4][4]; \ TRANSPOSE4(_vec_h_temp_,from); \ SETMAT4(to, _vec_h_temp_); \ } while (0) #define TRANSPOSE4d(to,from) TRANSPOSE4safe(double,to,from) #define TRANSPOSE4i(to,from) TRANSPOSE4safe(int,to,from) #define TRANSPOSE4l(to,from) TRANSPOSE4safe(long,to,from) #define TRANSPOSE4r(to,from) TRANSPOSE4safe(real,to,from) #define MXM4safe(type,to,m1,m2) \ do {type _vec_h_temp_[4][4]; \ MXM4(_vec_h_temp_,m1,m2); \ SETMAT4(to, _vec_h_temp_); \ } while (0) #define MXM4d(to,m1,m2) MXM4safe(double,to,m1,m2) #define MXM4i(to,m1,m2) MXM4safe(int,to,m1,m2) #define MXM4l(to,m1,m2) MXM4safe(long,to,m1,m2) #define MXM4r(to,m1,m2) MXM4safe(real,to,m1,m2) #define VXM4safe(type,to,v,m) \ do {type _vec_h_temp_[4]; \ VXM4(_vec_h_temp_,v,m); \ SET4(to, _vec_h_temp_); \ } while (0) #define VXM4d(to,v,m) VXM4safe(double,to,v,m) #define VXM4i(to,v,m) VXM4safe(int,to,v,m) #define VXM4l(to,v,m) VXM4safe(long,to,v,m) #define VXM4r(to,v,m) VXM4safe(real,to,v,m) #define MXV4safe(type,to,m,v) \ do {type _vec_h_temp_[4]; \ MXV4(_vec_h_temp_,m,v); \ SET4(to, _vec_h_temp_); \ } while (0) #define MXV4d(to,m,v) MXV4safe(double,to,m,v) #define MXV4i(to,m,v) MXV4safe(int,to,m,v) #define MXV4l(to,m,v) MXV4safe(long,to,m,v) #define MXV4r(to,m,v) MXV4safe(real,to,m,v) #define VXVXV4safe(type,to,v1,v2,v3) \ do {type _vec_h_temp_[4]; \ VXVXV4(_vec_h_temp_,v1,v2,v3); \ SET4(to, _vec_h_temp_); \ } while (0) #define VXVXV4d(to,v1,v2,v3) VXVXV4safe(double,to,v1,v2,v3) #define VXVXV4i(to,v1,v2,v3) VXVXV4safe(int,to,v1,v2,v3) #define VXVXV4l(to,v1,v2,v3) VXVXV4safe(long,to,v1,v2,v3) #define VXVXV4r(to,v1,v2,v3) VXVXV4safe(real,to,v1,v2,v3) #define M3XM4safe(type,to4,m3,m4) \ do {type _vec_h_temp_[4][4]; \ M3XM4(_vec_h_temp_,m3,m4); \ SETMAT4(to4, _vec_h_temp_); \ } while (0) #define M3XM4d(to4,m3,m4) M3XM4safe(double,to4,m3,m4) #define M3XM4i(to4,m3,m4) M3XM4safe(int,to4,m3,m4) #define M3XM4l(to4,m3,m4) M3XM4safe(long,to4,m3,m4) #define M3XM4r(to4,m3,m4) M3XM4safe(real,to4,m3,m4) #define M4XM3safe(type,to4,m4,m3) \ do {type _vec_h_temp_[4][4]; \ M4XM3(_vec_h_temp_,m4,m3); \ SETMAT4(to4, _vec_h_temp_); \ } while (0) #define M4XM3d(to4,m4,m3) M4XM3safe(double,to4,m4,m3) #define M4XM3i(to4,m4,m3) M4XM3safe(int,to4,m4,m3) #define M4XM3l(to4,m4,m3) M4XM3safe(long,to4,m4,m3) #define M4XM3r(to4,m4,m3) M4XM3safe(real,to4,m4,m3) #define ADJOINT4safe(type,to,m) \ do {type _vec_h_temp_[4][4]; \ ADJOINT4(_vec_h_temp_,m); \ SETMAT4(to, _vec_h_temp_); \ } while (0) #define ADJOINT4d(to,m) ADJOINT4safe(double,to,m) #define ADJOINT4i(to,m) ADJOINT4safe(int,to,m) #define ADJOINT4l(to,m) ADJOINT4safe(long,to,m) #define ADJOINT4r(to,m) ADJOINT4safe(real,to,m) #define INVERTMAT4safe(type,to,from) \ do {type _vec_h_temp_[4][4]; \ ADJOINT4(_vec_h_temp_, from); \ type _vec_h_temp_invdet_ = (type)1/(type)DET4(from); \ SXM4(to, _vec_h_temp_invdet_, _vec_h_temp_); \ } while (0) #define INVERTMAT4d(to,from) INVERTMAT4safe(double,to,from) #define INVERTMAT4i(to,from) INVERTMAT4safe(int,to,from) #define INVERTMAT4l(to,from) INVERTMAT4safe(long,to,from) #define INVERTMAT4r(to,from) INVERTMAT4safe(real,to,from) #endif /* VEC_H */