/usr/include/ug/evm.h is in libug-dev 3.12.1-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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* \ingroup gm
*/
/****************************************************************************/
/* */
/* File: evm.h */
/* */
/* Purpose: elementary vector manipulations, header for evm.c */
/* */
/* Author: Klaus Johannsen */
/* Institut fuer Computeranwendungen */
/* Universitaet Stuttgart */
/* Pfaffenwaldring 27 */
/* 70569 Stuttgart */
/* internet: ug@ica3.uni-stuttgart.de */
/* */
/* History: 8.12.94 begin, ug3-version */
/* */
/* Remarks: */
/* */
/****************************************************************************/
/****************************************************************************/
/* */
/* auto include mechanism and other include files */
/* */
/****************************************************************************/
#ifndef __EVM__
#define __EVM__
#include "ugtypes.h"
#include "gm.h"
#include "debug.h"
#include "namespace.h"
START_UGDIM_NAMESPACE
/****************************************************************************/
/* */
/* defines in the following order */
/* */
/* compile time constants defining static data size (i.e. arrays) */
/* other constants */
/* macros */
/* */
/****************************************************************************/
/****************************************************************************/
/* */
/* macros */
/* */
/****************************************************************************/
/* space dimension indices */
#define _X_ 0
#define _Y_ 1
#define _Z_ 2
/* misc macros */
#define SQRT(a) sqrt((double)(a))
#define POW(a,b) pow((double)(a),(double)(b))
#define ISNaN(x) (!((x)-(x)==0) || ((x)-(x)!=0))
/* macros for coord points */
#define COPY_SC_TO_SH(p1,p2) (p2).x=(short)((p1).x);(p2).y=(short)((p1).y)
#define CP_SUBTRACT(A,B,C) {(C).x = (A).x - (B).x;\
(C).y = (A).y - (B).y;}
#define CP_LIMCOMB(a,A,b,B,C) {(C).x = (DOUBLE)(a)*(A).x + (DOUBLE)(b)*(B).x;\
(C).y = (DOUBLE)(a)*(A).y + (DOUBLE)(b)*(B).y;}
#define CP_SCALARPRODUCT(A,B,c) (c) = (A).x*(B).x + (A).y*(B).y;
#define CP_EUKLIDNORM(A,b) (b) = (DOUBLE)sqrt((double)((A).x*(A).x+(A).y*(A).y));
/* macros for 1D vector operations */
#define V1_LINCOMB(a,A,b,B,C) {(C)[0] = (a)*(A)[0] + (b)*(B)[0];}
#define V1_SET(a,A) {(A)[0] = a;}
#define V1_COPY(A,C) {(C)[0] = (A)[0];}
#define V1_SUBTRACT(A,B,C) {(C)[0] = (A)[0] - (B)[0];}
#define V1_ADD(A,B,C) {(C)[0] = (A)[0] + (B)[0];}
#define V1_ADD1(A,C) {(C)[0] += (A)[0];}
#define V1_AVG2(p1,p2,p) {(p)[0] = 0.5*((p1)[0]+(p2)[0]);}
#define V1_AVG3(p1,p2,p3,p) {(p)[0] = ((p1)[0]+(p2)[0]+(p3)[0])/3.0;
#define V1_AVG4(p1,p2,p3,p4,p) {(p)[0] = 0.25*((p1)[0]+(p2)[0]+(p3)[0]+(p4)[0]);}
#define V1_SCALE(c,C) {(C)[0] = (c)*(C)[0];}
#define V1_SCALEADD1(c,A,C) {(C)[0] += (c)*(A)[0];}
#define V1_SCALESET(c,A,C) {(C)[0] = (c)*(A)[0];}
#define V1_VECTOR_PRODUCT(A,B,c) (c) = (A)[0]*(B)[1];
#define V1_COMPARE(A,B,c) (c) = (ABS((A)[0]-(B)[0])<SMALL_C);
#define V1_ISEQUAL(A,B) (ABS((A)[0]-(B)[0])<SMALL_C)
#define V1_EUKLIDNORM(A,b) (b) = (A)[0]);
#define V1_EUKLIDNORM_OF_DIFF(A,B,b) (b) = sqrt((double)(((A)[0]-(B)[0])*((A)[0]-(B)[0])));
#define V1_CLEAR(A) {(A)[0] = 0.0;}
#define V1_SCALAR_PRODUCT(A,B,c) (c) = (A)[0]*(B)[0];
#define V1_SCAL_PROD(A,B) ((A)[0]*(B)[0])
#define V1_ISZERO(A) (ABS((A)[0])<SMALL_C)
#define V1_SUP(v,s) {s = v[0]);}
#define V1_NORMAL(s,n) {(n)[0] = (s)[0];}
#define M1_INVERT(M,IM,det) {det = (IM)[0]; \
if (ABS((det))<SMALL_D*SMALL_D) \
return (1); \
(M)[0] = 1./det;}
#define MT1_TIMES_V1(M,A,B) {(B)[0] = (M)[0][0]*(A)[0];}
/* macros for 2D vector operations */
#define V2_LINCOMB(a,A,b,B,C) {(C)[0] = (a)*(A)[0] + (b)*(B)[0];\
(C)[1] = (a)*(A)[1] + (b)*(B)[1];}
#define V2_SET(a,A) {(A)[0] = a;\
(A)[1] = a;}
#define V2_COPY(A,C) {(C)[0] = (A)[0];\
(C)[1] = (A)[1];}
#define V2_SUBTRACT(A,B,C) {(C)[0] = (A)[0] - (B)[0];\
(C)[1] = (A)[1] - (B)[1];}
#define V2_ADD(A,B,C) {(C)[0] = (A)[0] + (B)[0];\
(C)[1] = (A)[1] + (B)[1];}
#define V2_ADD1(A,C) {(C)[0] += (A)[0];\
(C)[1] += (A)[1];}
#define V2_AVG2(p1,p2,p) {(p)[0] = 0.5*((p1)[0]+(p2)[0]); \
(p)[1] = 0.5*((p1)[1]+(p2)[1]);}
#define V2_AVG3(p1,p2,p3,p) {(p)[0] = ((p1)[0]+(p2)[0]+(p3)[0])/3.0; \
(p)[1] = ((p1)[1]+(p2)[1]+(p3)[1])/3.0;}
#define V2_AVG4(p1,p2,p3,p4,p) {(p)[0] = 0.25*((p1)[0]+(p2)[0]+(p3)[0]+(p4)[0]); \
(p)[1] = 0.25*((p1)[1]+(p2)[1]+(p3)[1]+(p4)[1]);}
#define V2_SCALE(c,C) {(C)[0] = (c)*(C)[0];\
(C)[1] = (c)*(C)[1];}
#define V2_SCALEADD1(c,A,C) {(C)[0] += (c)*(A)[0];\
(C)[1] += (c)*(A)[1];}
#define V2_SCALESET(c,A,C) {(C)[0] = (c)*(A)[0];\
(C)[1] = (c)*(A)[1];}
#define V2_VECTOR_PRODUCT(A,B,c) (c) = (A)[0]*(B)[1] - (A)[1]*(B)[0];
#define V2_COMPARE(A,B,c) (c) = (((ABS((A)[0]-(B)[0])<SMALL_C)&&(ABS((A)[1]-(B)[1])<SMALL_C)) ? (0) : (1));
#define V2_ISEQUAL(A,B) ((ABS((A)[0]-(B)[0])<SMALL_C)&&(ABS((A)[1]-(B)[1])<SMALL_C))
#define V2_EUKLIDNORM(A,b) (b) = sqrt((double)((A)[0]*(A)[0]+(A)[1]*(A)[1]));
#define V2_EUKLIDNORM_OF_DIFF(A,B,b) (b) = sqrt((double)(((A)[0]-(B)[0])*((A)[0]-(B)[0])+((A)[1]-(B)[1])*((A)[1]-(B)[1])));
#define V2_CLEAR(A) {(A)[0] = 0.0; (A)[1]= 0.0;}
#define V2_SCALAR_PRODUCT(A,B,c) (c) = (A)[0]*(B)[0]+(A)[1]*(B)[1];
#define V2_SCAL_PROD(A,B) ((A)[0]*(B)[0]+(A)[1]*(B)[1])
#define V2_ISZERO(A) (ABS((A)[0])<SMALL_C && ABS((A)[1])<SMALL_C)
#define V2_SUP(v,s) {s = MAX(ABS(v[0]),ABS(v[1]));}
#define V2_NORMAL(s,n) {(n)[0] = (s)[1]; (n)[1] = -(s)[0];}
/* macros for 2D matrix-vector operations */
#define M2_TIMES_V2(M,A,B) {(B)[0] = (M)[0]*(A)[0] + (M)[2]*(A)[1];\
(B)[1] = (M)[1]*(A)[0] + (M)[3]*(A)[1];}
#define MM2_TIMES_V2(M,A,B) {(B)[0] = (M)[0][0]*(A)[0] + (M)[0][1]*(A)[1];\
(B)[1] = (M)[1][0]*(A)[0] + (M)[1][1]*(A)[1];}
#define MT2_TIMES_V2(M,A,B) {(B)[0] = (M)[0][0]*(A)[0] + (M)[1][0]*(A)[1];\
(B)[1] = (M)[0][1]*(A)[0] + (M)[1][1]*(A)[1];}
#define MD2_TIMES_V2(M,A,B) {(B)[0] = (M)[0]*(A)[0];\
(B)[1] = (M)[1]*(A)[1];}
/* macros for matrix operations */
#define M2_SCALE(c,M) {(M)[0] = (c)*(M)[0];\
(M)[1] = (c)*(M)[1];\
(M)[2] = (c)*(M)[2];\
(M)[3] = (c)*(M)[3];}
#define M2_ADD(A,B,C) {(C)[0] = (A)[0]+(B)[0];\
(C)[1] = (A)[1]+(B)[1];\
(C)[2] = (A)[2]+(B)[2];\
(C)[3] = (A)[3]+(B)[3];}
#define M2_COPY(A,C) {(C)[0] = (A)[0];\
(C)[1] = (A)[1];\
(C)[2] = (A)[2];\
(C)[3] = (A)[3];}
#define MM2_COPY(A,C) {(C)[0][0] = (A)[0][0];\
(C)[0][1] = (A)[0][1];\
(C)[1][0] = (A)[1][0];\
(C)[1][1] = (A)[1][1];}
#define M2_DET(M) ((M)[0]*(M)[3] - (M)[1]*(M)[2])
#define MM2_DET(M) ((M)[0][0]*(M)[1][1] - (M)[1][0]*(M)[0][1])
#define M2_LINCOMB(a,A,b,B,C) {(C)[0] = (a)*(A)[0]+(b)*(B)[0];\
(C)[1] = (a)*(A)[1]+(b)*(B)[1]);\
(C)[2] = (a)*(A)[2]+(b)*(B)[2]);\
(C)[3] = (a)*(A)[3]+(b)*(B)[3]);}
#define M2_TIMES_M2(A,B,C) {(C)[0] = (A)[0]*(B)[0]+(A)[2]*(B)[1];\
(C)[1] = (A)[1]*(B)[0]+(A)[3]*(B)[1];\
(C)[2] = (A)[0]*(B)[2]+(A)[2]*(B)[3];\
(C)[3] = (A)[1]*(B)[2]+(A)[3]*(B)[3];}
#define M2_INVERT_STD(M,IM,det) \
{ DOUBLE invdet; \
det = (M)[0]*(M)[3]-(M)[1]*(M)[2]; \
if (ABS((det))<SMALL_D*SMALL_D) det= 0.; \
else { \
invdet = 1.0 / (det); \
(IM)[0] = (M)[3]*invdet; \
(IM)[1] = -(M)[1]*invdet; \
(IM)[2] = -(M)[2]*invdet; \
(IM)[3] = (M)[0]*invdet;}}
#define M2_INVERT(M,IM,det) \
{ DOUBLE invdet; \
det = (M)[0][0]*(M)[1][1]-(M)[1][0]*(M)[0][1]; \
if (ABS((det))<SMALL_D*SMALL_D) det= 0.; \
else { \
invdet = 1.0 / (det); \
(IM)[0][0] = (M)[1][1]*invdet; \
(IM)[1][0] = -(M)[1][0]*invdet; \
(IM)[0][1] = -(M)[0][1]*invdet; \
(IM)[1][1] = (M)[0][0]*invdet;}}
#define M2_MAXNORM(M,n) (n)=MAX(ABS((M)[0])+ABS((M)[2]),ABS((M)[1])+ABS((M)[3]))
/* macros for vector operations */
#define V3_LINCOMB(a,A,b,B,C) {(C)[0] = (a)*(A)[0] + (b)*(B)[0];\
(C)[1] = (a)*(A)[1] + (b)*(B)[1];\
(C)[2] = (a)*(A)[2] + (b)*(B)[2];}
#define V3_SET(a,A) {(A)[0] = a;\
(A)[1] = a;\
(A)[2] = a;}
#define V3_COPY(A,C) {(C)[0] = (A)[0];\
(C)[1] = (A)[1];\
(C)[2] = (A)[2];}
#define V3_SUBTRACT(A,B,C) {(C)[0] = (A)[0] - (B)[0];\
(C)[1] = (A)[1] - (B)[1];\
(C)[2] = (A)[2] - (B)[2];}
#define V3_ADD(A,B,C) {(C)[0] = (A)[0] + (B)[0];\
(C)[1] = (A)[1] + (B)[1];\
(C)[2] = (A)[2] + (B)[2];}
#define V3_ADD1(A,C) {(C)[0] += (A)[0];\
(C)[1] += (A)[1];\
(C)[2] += (A)[2];}
#define V3_AVG2(p1,p2,p) {(p)[0] = 0.5*((p1)[0]+(p2)[0]); \
(p)[1] = 0.5*((p1)[1]+(p2)[1]); \
(p)[2] = 0.5*((p1)[2]+(p2)[2]);}
#define V3_AVG3(p1,p2,p3,p) {(p)[0] = ((p1)[0]+(p2)[0]+(p3)[0])/3.0; \
(p)[1] = ((p1)[1]+(p2)[1]+(p3)[1])/3.0; \
(p)[2] = ((p1)[2]+(p2)[2]+(p3)[2])/3.0;}
#define V3_AVG4(p1,p2,p3,p4,p) {(p)[0] = 0.25*((p1)[0]+(p2)[0]+(p3)[0]+(p4)[0]); \
(p)[1] = 0.25*((p1)[1]+(p2)[1]+(p3)[1]+(p4)[1]); \
(p)[2] = 0.25*((p1)[2]+(p2)[2]+(p3)[2]+(p4)[2]);}
#define V3_SCALE(c,C) {(C)[0] = (c)*(C)[0];\
(C)[1] = (c)*(C)[1];\
(C)[2] = (c)*(C)[2];}
#define V3_SCALEADD1(c,A,C) {(C)[0] += (c)*(A)[0];\
(C)[1] += (c)*(A)[1];\
(C)[2] += (c)*(A)[2];}
#define V3_SCALESET(c,A,C) {(C)[0] = (c)*(A)[0];\
(C)[1] = (c)*(A)[1];\
(C)[2] = (c)*(A)[2];}
#define V3_VECTOR_PRODUCT(A,B,C) {(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];}
#define V3_EUKLIDNORM(A,b) (b) = (sqrt((double)((A)[0]*(A)[0]+(A)[1]*(A)[1]+(A)[2]*(A)[2])));
#define V3_COMPARE(A,B,c) (c) = (((ABS((A)[0]-(B)[0])<SMALL_C)&&(ABS((A)[1]-(B)[1])<SMALL_C)&&(ABS((A)[2]-(B)[2])<SMALL_C)) ? (0) : (1));
#define V3_ISEQUAL(A,B) ((ABS((A)[0]-(B)[0])<SMALL_C)&&(ABS((A)[1]-(B)[1])<SMALL_C)&&(ABS((A)[2]-(B)[2])<SMALL_C))
#define V3_EUKLIDNORM_OF_DIFF(A,B,b) (b) = (sqrt((double)(((A)[0]-(B)[0])*((A)[0]-(B)[0])+((A)[1]-(B)[1])*((A)[1]-(B)[1])+((A)[2]-(B)[2])*((A)[2]-(B)[2]))));
#define V3_CLEAR(A) {(A)[0] = 0.0; (A)[1]= 0.0; (A)[2] = 0.0;}
#define V3_SCALAR_PRODUCT(A,B,c) (c) = ((A)[0]*(B)[0]+(A)[1]*(B)[1]+(A)[2]*(B)[2]);
#define V3_SCAL_PROD(A,B) ((A)[0]*(B)[0]+(A)[1]*(B)[1]+(A)[2]*(B)[2])
#define V3_ISZERO(A) ((A)[0]==0.0 && (A)[1]==0.0 && (A)[2]==0.0)
#define V3_SUP(v,s) {s = MAX(ABS(v[0]),MAX(ABS(v[1]),ABS(v[2])));}
/* macros for matrix-vector operations */
#define M3_TIMES_V3(M,A,B) {(B)[0] = (M)[0]*(A)[0] + (M)[3]*(A)[1] + (M)[6]*(A)[2];\
(B)[1] = (M)[1]*(A)[0] + (M)[4]*(A)[1] + (M)[7]*(A)[2];\
(B)[2] = (M)[2]*(A)[0] + (M)[5]*(A)[1] + (M)[8]*(A)[2];}
#define MM3_TIMES_V3(M,A,B) {(B)[0] = (M)[0][0]*(A)[0] + (M)[0][1]*(A)[1] + (M)[0][2]*(A)[2];\
(B)[1] = (M)[1][0]*(A)[0] + (M)[1][1]*(A)[1] + (M)[1][2]*(A)[2];\
(B)[2] = (M)[2][0]*(A)[0] + (M)[2][1]*(A)[1] + (M)[2][2]*(A)[2];}
#define MT3_TIMES_V3(M,A,B) {(B)[0] = (M)[0][0]*(A)[0] + (M)[1][0]*(A)[1] + (M)[2][0]*(A)[2];\
(B)[1] = (M)[0][1]*(A)[0] + (M)[1][1]*(A)[1] + (M)[2][1]*(A)[2];\
(B)[2] = (M)[0][2]*(A)[0] + (M)[1][2]*(A)[1] + (M)[2][2]*(A)[2];}
#define MD3_TIMES_V3(M,A,B) {(B)[0] = (M)[0]*(A)[0];\
(B)[1] = (M)[1]*(A)[1];\
(B)[2] = (M)[2]*(A)[2];}
/* macros for matrix operations */
#define M3_SCALE(c,M) {(M)[0] = (c)*(M)[0];\
(M)[1] = (c)*(M)[1];\
(M)[2] = (c)*(M)[2];\
(M)[3] = (c)*(M)[3];\
(M)[4] = (c)*(M)[4];\
(M)[5] = (c)*(M)[5];\
(M)[6] = (c)*(M)[6];\
(M)[7] = (c)*(M)[7];\
(M)[8] = (c)*(M)[8];}
#define M3_COPY(A,C) {(C)[0] = (A)[0];\
(C)[1] = (A)[1];\
(C)[2] = (A)[2];\
(C)[3] = (A)[3];\
(C)[4] = (A)[4];\
(C)[5] = (A)[5];\
(C)[6] = (A)[6];\
(C)[7] = (A)[7];\
(C)[8] = (A)[8];}
#define MM3_COPY(A,C) {(C)[0][0] = (A)[0][0]; \
(C)[0][1] = (A)[0][1]; \
(C)[0][2] = (A)[0][2]; \
(C)[1][0] = (A)[1][0]; \
(C)[1][1] = (A)[1][1]; \
(C)[1][2] = (A)[1][2]; \
(C)[2][0] = (A)[2][0]; \
(C)[2][1] = (A)[2][1]; \
(C)[2][2] = (A)[2][2];}
#define M3_DET(M) ((M)[0]*(M)[4]*(M)[8] + (M)[1]*(M)[5]*(M)[6] + (M)[2]*(M)[3]*(M)[7] \
-(M)[2]*(M)[4]*(M)[6] - (M)[0]*(M)[5]*(M)[7] - (M)[1]*(M)[3]*(M)[8])
#define MM3_DET(M) ((M)[0][0]*(M)[1][1]*(M)[2][2] + (M)[0][1]*(M)[1][2]*(M)[2][0] + (M)[0][2]*(M)[1][0]*(M)[2][1] \
-(M)[0][2]*(M)[1][1]*(M)[2][0] - (M)[0][0]*(M)[1][2]*(M)[2][1] - (M)[0][1]*(M)[1][0]*(M)[2][2])
#define M3_ADD(A,B,C) {(C)[0] = (A)[0]+(B)[0];\
(C)[1] = (A)[1]+(B)[1];\
(C)[2] = (A)[2]+(B)[2];\
(C)[3] = (A)[3]+(B)[3];\
(C)[4] = (A)[4]+(B)[4];\
(C)[5] = (A)[5]+(B)[5];\
(C)[6] = (A)[6]+(B)[6];\
(C)[7] = (A)[7]+(B)[7];\
(C)[8] = (A)[8]+(B)[8];}
#define M3_ADDMATRIX(A,B,C) M3_ADD(A,B,C)
#define M3_LINCOMB(a,A,b,B,C) {(C)[0] = (a)*(A)[0]+(b)*(B)[0];\
(C)[1] = (a)*(A)[1]+(b)*(B)[1];\
(C)[2] = (a)*(A)[2]+(b)*(B)[2];\
(C)[3] = (a)*(A)[3]+(b)*(B)[3];\
(C)[4] = (a)*(A)[4]+(b)*(B)[4];\
(C)[5] = (a)*(A)[5]+(b)*(B)[5];\
(C)[6] = (a)*(A)[6]+(b)*(B)[6];\
(C)[7] = (a)*(A)[7]+(b)*(B)[7];\
(C)[8] = (a)*(A)[8]+(b)*(B)[8];}
#define M3_TIMES_M3(A,B,C) {(C)[0] = (A)[0]*(B)[0]+(A)[3]*(B)[1]+(A)[6]*(B)[2];\
(C)[1] = (A)[1]*(B)[0]+(A)[4]*(B)[1]+(A)[7]*(B)[2];\
(C)[2] = (A)[2]*(B)[0]+(A)[5]*(B)[1]+(A)[8]*(B)[2];\
(C)[3] = (A)[0]*(B)[3]+(A)[3]*(B)[4]+(A)[6]*(B)[5];\
(C)[4] = (A)[1]*(B)[3]+(A)[4]*(B)[4]+(A)[7]*(B)[5];\
(C)[5] = (A)[2]*(B)[3]+(A)[5]*(B)[4]+(A)[8]*(B)[5];\
(C)[6] = (A)[0]*(B)[6]+(A)[3]*(B)[7]+(A)[6]*(B)[8];\
(C)[7] = (A)[1]*(B)[6]+(A)[4]*(B)[7]+(A)[7]*(B)[8];\
(C)[8] = (A)[2]*(B)[6]+(A)[5]*(B)[7]+(A)[8]*(B)[8];}
#define M3_INVERT(M,IM,det) \
{ DOUBLE invdet; \
(det) = (M)[0][0]*(M)[1][1]*(M)[2][2] \
+ (M)[0][1]*(M)[1][2]*(M)[2][0] \
+ (M)[0][2]*(M)[1][0]*(M)[2][1] \
- (M)[0][2]*(M)[1][1]*(M)[2][0] \
- (M)[0][0]*(M)[1][2]*(M)[2][1] \
- (M)[0][1]*(M)[1][0]*(M)[2][2]; \
if (ABS((det))<SMALL_D*SMALL_D) \
return (1); \
invdet = 1.0 / (det); \
(IM)[0][0] = ( (M)[1][1]*(M)[2][2] - (M)[1][2]*(M)[2][1]) * invdet; \
(IM)[0][1] = (-(M)[0][1]*(M)[2][2] + (M)[0][2]*(M)[2][1]) * invdet; \
(IM)[0][2] = ( (M)[0][1]*(M)[1][2] - (M)[0][2]*(M)[1][1]) * invdet; \
(IM)[1][0] = (-(M)[1][0]*(M)[2][2] + (M)[1][2]*(M)[2][0]) * invdet; \
(IM)[1][1] = ( (M)[0][0]*(M)[2][2] - (M)[0][2]*(M)[2][0]) * invdet; \
(IM)[1][2] = (-(M)[0][0]*(M)[1][2] + (M)[0][2]*(M)[1][0]) * invdet; \
(IM)[2][0] = ( (M)[1][0]*(M)[2][1] - (M)[1][1]*(M)[2][0]) * invdet; \
(IM)[2][1] = (-(M)[0][0]*(M)[2][1] + (M)[0][1]*(M)[2][0]) * invdet; \
(IM)[2][2] = ( (M)[0][0]*(M)[1][1] - (M)[0][1]*(M)[1][0]) * invdet;}
#ifdef __MPW32__
#define M4_TIMES_M4(A,B,C) {int i,j,k; for (i=0; i<4; i++) for (j=0; j<4; j++) for (k=0; k<4; k++) \
(C)[i+4*j] = (A)[i+4*k] * (B)[k+4*j];}
#else
#define M4_TIMES_M4(A,B,C) {(C)[0] = (A)[ 0]*(B)[ 0]+(A)[ 4]*(B)[ 1]+(A)[ 8]*(B)[ 2]+(A)[12]*(B)[ 3];\
(C)[1] = (A)[ 1]*(B)[ 0]+(A)[ 5]*(B)[ 1]+(A)[ 9]*(B)[ 2]+(A)[13]*(B)[ 3];\
(C)[2] = (A)[ 2]*(B)[ 0]+(A)[ 6]*(B)[ 1]+(A)[10]*(B)[ 2]+(A)[14]*(B)[ 3];\
(C)[3] = (A)[ 3]*(B)[ 0]+(A)[ 7]*(B)[ 1]+(A)[11]*(B)[ 2]+(A)[15]*(B)[ 3];\
(C)[4] = (A)[ 0]*(B)[ 4]+(A)[ 4]*(B)[ 5]+(A)[ 8]*(B)[ 6]+(A)[12]*(B)[ 7];\
(C)[5] = (A)[ 1]*(B)[ 4]+(A)[ 5]*(B)[ 5]+(A)[ 9]*(B)[ 6]+(A)[13]*(B)[ 7];\
(C)[6] = (A)[ 2]*(B)[ 4]+(A)[ 6]*(B)[ 5]+(A)[10]*(B)[ 6]+(A)[14]*(B)[ 7];\
(C)[7] = (A)[ 3]*(B)[ 4]+(A)[ 7]*(B)[ 5]+(A)[11]*(B)[ 6]+(A)[15]*(B)[ 7];\
(C)[8] = (A)[ 0]*(B)[ 8]+(A)[ 4]*(B)[ 9]+(A)[ 8]*(B)[10]+(A)[12]*(B)[11];\
(C)[9] = (A)[ 1]*(B)[ 8]+(A)[ 5]*(B)[ 9]+(A)[ 9]*(B)[10]+(A)[13]*(B)[11];\
(C)[10] = (A)[ 2]*(B)[ 8]+(A)[ 6]*(B)[ 9]+(A)[10]*(B)[10]+(A)[14]*(B)[11];\
(C)[11] = (A)[ 3]*(B)[ 8]+(A)[ 7]*(B)[ 9]+(A)[11]*(B)[10]+(A)[15]*(B)[11];\
(C)[12] = (A)[ 0]*(B)[12]+(A)[ 4]*(B)[13]+(A)[ 8]*(B)[14]+(A)[12]*(B)[15];\
(C)[13] = (A)[ 1]*(B)[12]+(A)[ 5]*(B)[13]+(A)[ 9]*(B)[14]+(A)[13]*(B)[15];\
(C)[14] = (A)[ 2]*(B)[12]+(A)[ 6]*(B)[13]+(A)[10]*(B)[14]+(A)[14]*(B)[15];\
(C)[15] = (A)[ 3]*(B)[12]+(A)[ 7]*(B)[13]+(A)[11]*(B)[14]+(A)[15]*(B)[15];}
#endif
#define M4_COPY(A,B) {(B)[0] = (A)[0]; (B)[1] = (A)[1]; (B)[2] = (A)[2]; (B)[3] = (A)[3]; \
(B)[4] = (A)[4]; (B)[5] = (A)[5]; (B)[6] = (A)[6]; (B)[7] = (A)[7]; \
(B)[8] = (A)[8]; (B)[9] = (A)[9]; (B)[10] = (A)[10]; (B)[11] = (A)[11]; \
(B)[12] = (A)[12]; (B)[13] = (A)[13]; (B)[14] = (A)[14]; (B)[15] = (A)[15];}
#define M4_CLEAR(B) {(B)[0] = 0.0; (B)[1] = 0.0; (B)[2] = 0.0; (B)[3] = 0.0; \
(B)[4] = 0.0; (B)[5] = 0.0; (B)[6] = 0.0; (B)[7] = 0.0; \
(B)[8] = 0.0; (B)[9] = 0.0; (B)[10] = 0.0; (B)[11] = 0.0; \
(B)[12] = 0.0; (B)[13] = 0.0; (B)[14] = 0.0; (B)[15] = 0.0;}
/* macros for exact solver (EX) */
#define EX_MAT(m,b,i,j) ((m)[2*(b)*(i) + (j)])
/****************************************************************************/
/* */
/* typedef of DIM-routines */
/* */
/****************************************************************************/
#ifdef __TWODIM__
#define V_BDIM_LINCOMB(a,A,b,B,C) V1_LINCOMB(a,A,b,B,C)
#define V_BDIM_SET(a,A) V1_SET(a,A)
#define V_BDIM_COPY(A,C) V1_COPY(A,C)
#define V_BDIM_SUBTRACT(A,B,C) V1_SUBTRACT(A,B,C)
#define V_BDIM_ADD(A,B,C) V1_ADD(A,B,C)
#define V_BDIM_ADD1(A,C) V1_ADD1(A,C)
#define V_BDIM_AVG2(A,B,X) V1_AVG2(A,B,X)
#define V_BDIM_AVG3(A,B,C,X) V1_AVG3(A,B,C,X)
#define V_BDIM_AVG4(A,B,C,D,X) V1_AVG4(A,B,C,D,X)
#define V_BDIM_SCALE(c,C) V1_SCALE(c,C)
#define V_BDIM_SCALEADD1(c,A,C) V1_SCALEADD1(c,A,C)
#define V_BDIM_SCALESET(c,A,C) V1_SCALESET(c,A,C)
#define V_BDIM_VECTOR_PRODUCT(A,B,c) V1_VECTOR_PRODUCT(A,B,c)
#define V_BDIM_COMPARE(A,B,c) V1_COMPARE(A,B,c)
#define V_BDIM_ISEQUAL(A,B) V1_ISEQUAL(A,B)
#define V_BDIM_EUKLIDNORM(A,b) V1_EUKLIDNORM(A,b)
#define V_BDIM_EUKLIDNORM_OF_DIFF(A,B,b) V1_EUKLIDNORM_OF_DIFF(A,B,b)
#define V_BDIM_CLEAR(A) V1_CLEAR(A)
#define V_BDIM_SCALAR_PRODUCT(A,B,c) V1_SCALAR_PRODUCT(A,B,c)
#define V_BDIM_SCAL_PROD(A,B) V1_SCAL_PROD(A,B)
#define V_BDIM_ISZERO(A) V1_ISZERO(A)
#define V_BDIM_SUP(v,s) V1_SUP(v,s)
#define V_BDIM_Normalize(a) V1_Normalize(a)
#define M_BDIM_INVERT(M,IM,det) M1_INVERT(M,IM,det)
#define MT_TIMES_V_BDIM(M,A,B) MT1_TIMES_V1(M,A,B)
#define V_DIM_LINCOMB(a,A,b,B,C) V2_LINCOMB(a,A,b,B,C)
#define V_DIM_SET(a,A) V2_SET(a,A)
#define V_DIM_COPY(A,C) V2_COPY(A,C)
#define V_DIM_SUBTRACT(A,B,C) V2_SUBTRACT(A,B,C)
#define V_DIM_ADD(A,B,C) V2_ADD(A,B,C)
#define V_DIM_ADD1(A,C) V2_ADD1(A,C)
#define V_DIM_AVG2(A,B,X) V2_AVG2(A,B,X)
#define V_DIM_AVG3(A,B,C,X) V2_AVG3(A,B,C,X)
#define V_DIM_AVG4(A,B,C,D,X) V2_AVG4(A,B,C,D,X)
#define V_DIM_SCALE(c,C) V2_SCALE(c,C)
#define V_DIM_SCALEADD1(c,A,C) V2_SCALEADD1(c,A,C)
#define V_DIM_SCALESET(c,A,C) V2_SCALESET(c,A,C)
#define V_DIM_VECTOR_PRODUCT(A,B,c) V2_VECTOR_PRODUCT(A,B,c)
#define V_DIM_COMPARE(A,B,c) V2_COMPARE(A,B,c)
#define V_DIM_ISEQUAL(A,B) V2_ISEQUAL(A,B)
#define V_DIM_EUKLIDNORM(A,b) V2_EUKLIDNORM(A,b)
#define V_DIM_EUKLIDNORM_OF_DIFF(A,B,b) V2_EUKLIDNORM_OF_DIFF(A,B,b)
#define V_DIM_CLEAR(A) V2_CLEAR(A)
#define V_DIM_SCALAR_PRODUCT(A,B,c) V2_SCALAR_PRODUCT(A,B,c)
#define V_DIM_SCAL_PROD(A,B) V2_SCAL_PROD(A,B)
#define V_DIM_SP(A,B) V2_SCAL_PROD(A,B)
#define V_DIM_ISZERO(A) V2_ISZERO(A)
#define V_DIM_SUP(v,s) V2_SUP(v,s)
#define V_DIM_Normalize(a) V2_Normalize(a)
#define V_DIM_NORMAL(a) V2_NORMAL(a)
#define M_TIMES_V_DIM(M,A,B) M2_TIMES_V2(M,A,B)
#define MM_TIMES_V_DIM(M,A,B) MM2_TIMES_V2(M,A,B)
#define MT_TIMES_V_DIM(M,A,B) MT2_TIMES_V2(M,A,B)
#define MD_TIMES_V_DIM(M,A,B) MD2_TIMES_V2(M,A,B)
#define M_DIM_ADD(A,B,C) M2_ADD(A,B,C)
#define M_DIM_COPY(A,C) M2_COPY(A,C)
#define MM_DIM_COPY(A,C) MM2_COPY(A,C)
#define M_DIM_DET(M) M2_DET(M)
#define MM_DIM_DET(M) MM2_DET(M)
#define M_DIM_SCALE(c,M) M2_SCALE(c,M)
#define M_DIM_INVERT(M,IM,det) M2_INVERT(M,IM,det)
#endif
#ifdef __THREEDIM__
#define V_BDIM_LINCOMB(a,A,b,B,C) V2_LINCOMB(a,A,b,B,C)
#define V_BDIM_SET(a,A) V2_SET(a,A)
#define V_BDIM_COPY(A,C) V2_COPY(A,C)
#define V_BDIM_SUBTRACT(A,B,C) V2_SUBTRACT(A,B,C)
#define V_BDIM_ADD(A,B,C) V2_ADD(A,B,C)
#define V_BDIM_ADD1(A,C) V2_ADD1(A,C)
#define V_BDIM_AVG2(A,B,X) V2_AVG2(A,B,X)
#define V_BDIM_AVG3(A,B,C,X) V2_AVG3(A,B,C,X)
#define V_BDIM_AVG4(A,B,C,D,X) V2_AVG4(A,B,C,D,X)
#define V_BDIM_SCALE(c,C) V2_SCALE(c,C)
#define V_BDIM_SCALEADD1(c,A,C) V2_SCALEADD1(c,A,C)
#define V_BDIM_SCALESET(c,A,C) V2_SCALESET(c,A,C)
#define V_BDIM_VECTOR_PRODUCT(A,B,c) V2_VECTOR_PRODUCT(A,B,c)
#define V_BDIM_COMPARE(A,B,c) V2_COMPARE(A,B,c)
#define V_BDIM_ISEQUAL(A,B) V2_ISEQUAL(A,B)
#define V_BDIM_EUKLIDNORM(A,b) V2_EUKLIDNORM(A,b)
#define V_BDIM_EUKLIDNORM_OF_DIFF(A,B,b) V2_EUKLIDNORM_OF_DIFF(A,B,b)
#define V_BDIM_CLEAR(A) V2_CLEAR(A)
#define V_BDIM_SCALAR_PRODUCT(A,B,c) V2_SCALAR_PRODUCT(A,B,c)
#define V_BDIM_SCAL_PROD(A,B) V2_SCAL_PROD(A,B)
#define V_BDIM_ISZERO(A) V2_ISZERO(A)
#define V_BDIM_SUP(v,s) V2_SUP(v,s)
#define V_BDIM_Normalize(a) V2_Normalize(a)
#define M_BDIM_INVERT(M,IM,det) M2_INVERT(M,IM,det)
#define MT_TIMES_V_BDIM(M,A,B) MT2_TIMES_V2(M,A,B)
#define V_DIM_LINCOMB(a,A,b,B,C) V3_LINCOMB(a,A,b,B,C)
#define V_DIM_SET(a,A) V3_SET(a,A)
#define V_DIM_COPY(A,C) V3_COPY(A,C)
#define V_DIM_SUBTRACT(A,B,C) V3_SUBTRACT(A,B,C)
#define V_DIM_ADD(A,B,C) V3_ADD(A,B,C)
#define V_DIM_ADD1(A,C) V3_ADD1(A,C)
#define V_DIM_AVG2(A,B,X) V3_AVG2(A,B,X)
#define V_DIM_AVG3(A,B,C,X) V3_AVG3(A,B,C,X)
#define V_DIM_AVG4(A,B,C,D,X) V3_AVG4(A,B,C,D,X)
#define V_DIM_SCALE(c,C) V3_SCALE(c,C)
#define V_DIM_SCALEADD1(c,A,C) V3_SCALEADD1(c,A,C)
#define V_DIM_SCALESET(c,A,C) V3_SCALESET(c,A,C)
#define V_DIM_VECTOR_PRODUCT(A,B,c) V3_VECTOR_PRODUCT(A,B,c)
#define V_DIM_COMPARE(A,B,c) V3_COMPARE(A,B,c)
#define V_DIM_ISEQUAL(A,B) V3_ISEQUAL(A,B)
#define V_DIM_EUKLIDNORM(A,b) V3_EUKLIDNORM(A,b)
#define V_DIM_EUKLIDNORM_OF_DIFF(A,B,b) V3_EUKLIDNORM_OF_DIFF(A,B,b)
#define V_DIM_CLEAR(A) V3_CLEAR(A)
#define V_DIM_SCALAR_PRODUCT(A,B,c) V3_SCALAR_PRODUCT(A,B,c)
#define V_DIM_SCAL_PROD(A,B) V3_SCAL_PROD(A,B)
#define V_DIM_SP(A,B) V3_SCAL_PROD(A,B)
#define V_DIM_ISZERO(A) V3_ISZERO(A)
#define M_TIMES_V_DIM(M,A,B) M3_TIMES_V3(M,A,B)
#define MM_TIMES_V_DIM(M,A,B) MM3_TIMES_V3(M,A,B)
#define MT_TIMES_V_DIM(M,A,B) MT3_TIMES_V3(M,A,B)
#define MD_TIMES_V_DIM(M,A,B) MD3_TIMES_V3(M,A,B)
#define M_DIM_ADD(A,B,C) M3_ADD(A,B,C)
#define M_DIM_COPY(A,C) M3_COPY(A,C)
#define MM_DIM_COPY(A,C) MM3_COPY(A,C)
#define M_DIM_DET(M) M3_DET(M)
#define MM_DIM_DET(M) MM3_DET(M)
#define M_DIM_SCALE(c,M) M3_SCALE(c,M)
#define V_DIM_Normalize(a) V3_Normalize(a)
#define V_DIM_NORMAL(a) V3_NORMAL(a)
#define M_DIM_INVERT(M,IM,det) M3_INVERT(M,IM,det)
#define V_DIM_SUP(v,s) V3_SUP(v,s)
#endif
/****************************************************************************/
/* */
/* typedef of 2d points for screen coordinates */
/* */
/****************************************************************************/
struct coord_point
{
DOUBLE x;
DOUBLE y;
};
typedef struct coord_point COORD_POINT;
/****************************************************************************/
/* */
/* definition of exported global variables */
/* */
/****************************************************************************/
extern const DOUBLE unit_vec[DIM][DIM];
/****************************************************************************/
/* */
/* function declarations */
/* */
/****************************************************************************/
/* general routines */
INT ClipRectangleAgainstRectangle (const DOUBLE *r1min, const DOUBLE *r1max, DOUBLE *r2min, DOUBLE *r2max);
INT CheckRectagleIntersection (const DOUBLE *r1min, const DOUBLE *r1max, const DOUBLE *r2min, const DOUBLE *r2max);
INT CheckRectangle (const DOUBLE *rmin, const DOUBLE *rmax, const DOUBLE minsize);
INT PointInTriangle (const COORD_POINT *Points, const COORD_POINT Point);
INT PointInPolygon (const COORD_POINT *Points, INT n, COORD_POINT Point);
INT PointInPolygonC (const DOUBLE_VECTOR_2D *Points, INT n, const DOUBLE_VECTOR_2D Point);
INT PolyArea (INT n, DOUBLE_VECTOR_2D *Polygon, DOUBLE *Area);
INT QuadraticFittedMin (DOUBLE *x, DOUBLE *y, INT n, DOUBLE *minx);
INT EXDecomposeMatrixFLOAT (FLOAT *Mat, INT bw, INT n);
INT EXDecomposeMatrixDOUBLE (DOUBLE *Mat, INT bw, INT n);
INT EXApplyLUFLOAT (FLOAT *Mat, INT bw, INT n, DOUBLE *Vec);
INT EXApplyLUDOUBLE (DOUBLE *Mat, INT bw, INT n, DOUBLE *Vec);
INT LineISTriangle3D (const DOUBLE *c1, const DOUBLE *c2, const DOUBLE *c3, const DOUBLE *p1, const DOUBLE *p2, DOUBLE *lambda);
INT Yams (INT n, DOUBLE *sol, DOUBLE *mat, DOUBLE *rhs);
/* 2D routines */
INT M2_Invert (DOUBLE *Inverse, const DOUBLE *Matrix);
DOUBLE vp (const DOUBLE x1, const DOUBLE y1, const DOUBLE x2, const DOUBLE y2);
INT V2_Normalize (DOUBLE *a);
INT V2_Rotate (DOUBLE *vector, DOUBLE alpha);
INT V2_IntersectLineSegments (const DOUBLE_VECTOR a0, const DOUBLE_VECTOR a1, const DOUBLE_VECTOR b0, const DOUBLE_VECTOR b1, DOUBLE *lambda);
INT V2_apbmin2c (const DOUBLE *a, const DOUBLE *b, const DOUBLE *c, DOUBLE *d, DOUBLE *r);
DOUBLE tarea (DOUBLE x0,DOUBLE y0,DOUBLE x1,DOUBLE y1,DOUBLE x2,DOUBLE y2);
DOUBLE qarea (DOUBLE x0,DOUBLE y0,DOUBLE x1,DOUBLE y1,DOUBLE x2,DOUBLE y2,DOUBLE x3,DOUBLE y3);
DOUBLE c_tarea (const DOUBLE *x0, const DOUBLE *x1, const DOUBLE *x2);
DOUBLE c_qarea (const DOUBLE *x0, const DOUBLE *x1, const DOUBLE *x2, const DOUBLE *x3);
DOUBLE ctarea (DOUBLE x0,DOUBLE y0,DOUBLE x1,DOUBLE y1,DOUBLE x2,DOUBLE y2);
DOUBLE cqarea (DOUBLE x0,DOUBLE y0,DOUBLE x1,DOUBLE y1,DOUBLE x2,DOUBLE y2,DOUBLE x3,DOUBLE y3);
DOUBLE V_te (const DOUBLE *x0, const DOUBLE *x1,
const DOUBLE *x2, const DOUBLE *x3);
DOUBLE V_py (const DOUBLE *x0, const DOUBLE *x1, const DOUBLE *x2,
const DOUBLE *x3, const DOUBLE *x4);
DOUBLE V_pr (const DOUBLE *x0, const DOUBLE *x1, const DOUBLE *x2,
const DOUBLE *x3, const DOUBLE *x4, const DOUBLE *x5);
DOUBLE V_he (const DOUBLE *x0, const DOUBLE *x1, const DOUBLE *x2, const DOUBLE *x3,
const DOUBLE *x4, const DOUBLE *x5, const DOUBLE *x6, const DOUBLE *x7);
/* 3D routines */
INT M3_Invert (DOUBLE *Inverse, const DOUBLE *Matrix);
INT V3_Normalize (DOUBLE *a);
INT V3_NormVectorProduct (const DOUBLE *a, const DOUBLE *b, DOUBLE *result);
INT V3_Rotate (DOUBLE *vector, const DOUBLE *axis, DOUBLE alpha);
INT V3_Angle (const DOUBLE *a, const DOUBLE *b, DOUBLE *result);
INT V3_Orthogonalize (const DOUBLE *a, const DOUBLE *b, DOUBLE *r);
INT V3_Project (const DOUBLE *a, const DOUBLE *b, DOUBLE *r);
/* 4D routines */
INT M4_Invert (DOUBLE *Inverse, const DOUBLE *Matrix);
/* volume calculations*/
DOUBLE GeneralElementVolume (INT tag, DOUBLE *x_co[]);
DOUBLE ElementVolume (const ELEMENT *elem);
END_UGDIM_NAMESPACE
#endif
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