text: /*<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) 1993-2018 The Geometry Center.
     $Id: //main/2015/qhull/src/libqhull/geom.h#3 $$Change: 2549 $
     $DateTime: 2018/12/28 22:24:20 $$Author: bbarber $
  */
  
  #ifndef qhDEFgeom
  #define qhDEFgeom 1
  
  #include "libqhull.h"
  
  /* ============ -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, const char *string, realT **rows, int numrow, int numcol);
  void    qh_printpoints(FILE *fp, const 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);
  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 */
  
  
  
  