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- ======================== */

    returns the absolute value of a
#define fabs_( a ) ((( a ) < 0 ) ? -( a ):( a ))
    returns the maximum value of a and b
#define fmax_( a,b )  ( ( a ) < ( b ) ? ( b ) : ( a ) )


    returns the minimum value of a and b
#define fmin_( a,b )  ( ( a ) > ( b ) ? ( b ) : ( a ) )


  maximize_(maxval, val)
    set maxval to val if val is greater than maxval
#define maximize_( maxval, val ) {if (( maxval ) < ( val )) ( maxval )= ( val );}


  minimize_(minval, val)
    set minval to val if val is less than minval
#define minimize_( minval, val ) {if (( minval ) > ( val )) ( minval )= ( val );}


  det2_(a1, a2,     
        b1, b2)
    compute a 2-d determinate
#define det2_( a1,a2,b1,b2 ) (( a1 )*( b2 ) - ( a2 )*( b1 ))

  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 ) )

  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 */