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/*<html><pre> -<a href="qh-geom.htm"
>-------------------------------</a><a name="TOP">-</a>
geom.h
header file for geometric routines
see qh-geom.htm and geom.c
copyright (c) 1993-2002 The Geometry Center
*/
#ifndef qhDEFgeom
#define qhDEFgeom 1
/* ============ -macros- ======================== */
/*-<a href="qh-geom.htm#TOC"
>--------------------------------</a><a name="fabs_">-</a>
fabs_(a)
returns the absolute value of a
*/
#define fabs_( a ) ((( a ) < 0 ) ? -( a ):( a ))
/*-<a href="qh-geom.htm#TOC"
>--------------------------------</a><a name="fmax_">-</a>
fmax_(a,b)
returns the maximum value of a and b
*/
#define fmax_( a,b ) ( ( a ) < ( b ) ? ( b ) : ( a ) )
/*-<a href="qh-geom.htm#TOC"
>--------------------------------</a><a name="fmin_">-</a>
fmin_(a,b)
returns the minimum value of a and b
*/
#define fmin_( a,b ) ( ( a ) > ( b ) ? ( b ) : ( a ) )
/*-<a href="qh-geom.htm#TOC"
>--------------------------------</a><a name="maximize_">-</a>
maximize_(maxval, val)
set maxval to val if val is greater than maxval
*/
#define maximize_( maxval, val ) {if (( maxval ) < ( val )) ( maxval )= ( val );}
/*-<a href="qh-geom.htm#TOC"
>--------------------------------</a><a name="minimize_">-</a>
minimize_(minval, val)
set minval to val if val is less than minval
*/
#define minimize_( minval, val ) {if (( minval ) > ( val )) ( minval )= ( val );}
/*-<a href="qh-geom.htm#TOC"
>--------------------------------</a><a name="det2_">-</a>
det2_(a1, a2,
b1, b2)
compute a 2-d determinate
*/
#define det2_( a1,a2,b1,b2 ) (( a1 )*( b2 ) - ( a2 )*( b1 ))
/*-<a href="qh-geom.htm#TOC"
>--------------------------------</a><a name="det3_">-</a>
det3_(a1, a2, a3,
b1, b2, b3,
c1, c2, c3)
compute a 3-d determinate
*/
#define det3_( a1,a2,a3,b1,b2,b3,c1,c2,c3 ) ( ( a1 )*det2_( b2,b3,c2,c3 ) \
- ( b1 )*det2_( a2,a3,c2,c3 ) + ( c1 )*det2_( a2,a3,b2,b3 ) )
/*-<a href="qh-geom.htm#TOC"
>--------------------------------</a><a name="dX">-</a>
dX( p1, p2 )
dY( p1, p2 )
dZ( p1, p2 )
given two indices into rows[],
compute the difference between X, Y, or Z coordinates
*/
#define dX( p1,p2 ) ( *( rows[p1] ) - *( rows[p2] ))
#define dY( p1,p2 ) ( *( rows[p1]+1 ) - *( rows[p2]+1 ))
#define dZ( p1,p2 ) ( *( rows[p1]+2 ) - *( rows[p2]+2 ))
#define dW( p1,p2 ) ( *( rows[p1]+3 ) - *( rows[p2]+3 ))
/*============= prototypes in alphabetical order, infrequent at end ======= */
void qh_backnormal (realT **rows, int numrow, int numcol, boolT sign, coordT *normal, boolT *nearzero);
void qh_distplane (pointT *point, facetT *facet, realT *dist);
facetT *qh_findbest (pointT *point, facetT *startfacet,
boolT bestoutside, boolT isnewfacets, boolT noupper,
realT *dist, boolT *isoutside, int *numpart);
facetT *qh_findbesthorizon (boolT ischeckmax, pointT *point,
facetT *startfacet, boolT noupper, realT *bestdist, int *numpart);
facetT *qh_findbestnew (pointT *point, facetT *startfacet, realT *dist,
boolT bestoutside, boolT *isoutside, int *numpart);
void qh_gausselim(realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero);
realT qh_getangle(pointT *vect1, pointT *vect2);
pointT *qh_getcenter(setT *vertices);
pointT *qh_getcentrum(facetT *facet);
realT qh_getdistance(facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist);
void qh_normalize (coordT *normal, int dim, boolT toporient);
void qh_normalize2 (coordT *normal, int dim, boolT toporient,
realT *minnorm, boolT *ismin);
pointT *qh_projectpoint(pointT *point, facetT *facet, realT dist);
void qh_setfacetplane(facetT *newfacets);
void qh_sethyperplane_det (int dim, coordT **rows, coordT *point0,
boolT toporient, coordT *normal, realT *offset, boolT *nearzero);
void qh_sethyperplane_gauss (int dim, coordT **rows, pointT *point0,
boolT toporient, coordT *normal, coordT *offset, boolT *nearzero);
boolT qh_sharpnewfacets (void);
/*========= infrequently used code in geom2.c =============*/
coordT *qh_copypoints (coordT *points, int numpoints, int dimension);
void qh_crossproduct (int dim, realT vecA[3], realT vecB[3], realT vecC[3]);
realT qh_determinant (realT **rows, int dim, boolT *nearzero);
realT qh_detjoggle (pointT *points, int numpoints, int dimension);
void qh_detroundoff (void);
realT qh_detsimplex(pointT *apex, setT *points, int dim, boolT *nearzero);
realT qh_distnorm (int dim, pointT *point, pointT *normal, realT *offsetp);
realT qh_distround (int dimension, realT maxabs, realT maxsumabs);
realT qh_divzero(realT numer, realT denom, realT mindenom1, boolT *zerodiv);
realT qh_facetarea (facetT *facet);
realT qh_facetarea_simplex (int dim, coordT *apex, setT *vertices,
vertexT *notvertex, boolT toporient, coordT *normal, realT *offset);
pointT *qh_facetcenter (setT *vertices);
facetT *qh_findgooddist (pointT *point, facetT *facetA, realT *distp, facetT **facetlist);
void qh_getarea (facetT *facetlist);
boolT qh_gram_schmidt(int dim, realT **rows);
boolT qh_inthresholds (coordT *normal, realT *angle);
void qh_joggleinput (void);
realT *qh_maxabsval (realT *normal, int dim);
setT *qh_maxmin(pointT *points, int numpoints, int dimension);
realT qh_maxouter (void);
void qh_maxsimplex (int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex);
realT qh_minabsval (realT *normal, int dim);
int qh_mindiff (realT *vecA, realT *vecB, int dim);
boolT qh_orientoutside (facetT *facet);
void qh_outerinner (facetT *facet, realT *outerplane, realT *innerplane);
coordT qh_pointdist(pointT *point1, pointT *point2, int dim);
void qh_printmatrix (FILE *fp, char *string, realT **rows, int numrow, int numcol);
void qh_printpoints (FILE *fp, char *string, setT *points);
void qh_projectinput (void);
void qh_projectpoints (signed char *project, int n, realT *points,
int numpoints, int dim, realT *newpoints, int newdim);
int qh_rand( void);
void qh_srand( int seed);
realT qh_randomfactor (void);
void qh_randommatrix (realT *buffer, int dim, realT **row);
void qh_rotateinput (realT **rows);
void qh_rotatepoints (realT *points, int numpoints, int dim, realT **rows);
void qh_scaleinput (void);
void qh_scalelast (coordT *points, int numpoints, int dim, coordT low,
coordT high, coordT newhigh);
void qh_scalepoints (pointT *points, int numpoints, int dim,
realT *newlows, realT *newhighs);
boolT qh_sethalfspace (int dim, coordT *coords, coordT **nextp,
coordT *normal, coordT *offset, coordT *feasible);
coordT *qh_sethalfspace_all (int dim, int count, coordT *halfspaces, pointT *feasible);
pointT *qh_voronoi_center (int dim, setT *points);
#endif /* qhDEFgeom */
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