Voronoi.cc

//STARTHEADER
// $Id: Voronoi.cc 2767 2011-11-24 21:43:09Z salam $
//
// Copyright (c) 1994 by AT&T Bell Laboratories (see below)
//
//
//----------------------------------------------------------------------
// This file is included as part of FastJet but was mostly written by
// S. Fortune in C, put into C++ with memory management by S
// O'Sullivan, and with further interface and memory management
// modifications by Gregory Soyez.
//
// Permission to use, copy, modify, and distribute this software for
// any purpose without fee is hereby granted, provided that this
// entire notice is included in all copies of any software which is or
// includes a copy or modification of this software and in all copies
// of the supporting documentation for such software. THIS SOFTWARE IS
// BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED WARRANTY.
// IN PARTICULAR, NEITHER THE AUTHORS NOR AT&T MAKE ANY REPRESENTATION
// OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY OF THIS
// SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
//
//----------------------------------------------------------------------
//ENDHEADER


/*
 * The author of this software is Steven Fortune.  
 * Copyright (c) 1994 by AT&T Bell Laboratories.
 * Permission to use, copy, modify, and distribute this software for any
 * purpose without fee is hereby granted, provided that this entire notice
 * is included in all copies of any software which is or includes a copy
 * or modification of this software and in all copies of the supporting
 * documentation for such software.
 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
 * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHORS NOR AT&T MAKE ANY
 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
 */

/* 
 * This code was originally written by Stephan Fortune in C code.  I,
 * Shane O'Sullivan, have since modified it, encapsulating it in a C++
 * class and, fixing memory leaks and adding accessors to the Voronoi
 * Edges.  Permission to use, copy, modify, and distribute this
 * software for any purpose without fee is hereby granted, provided
 * that this entire notice is included in all copies of any software
 * which is or includes a copy or modification of this software and in
 * all copies of the supporting documentation for such software.  THIS
 * SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
 * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHORS NOR AT&T MAKE ANY
 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE
 * MERCHANTABILITY OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR
 * PURPOSE.
 */

/*
 * This code, included in the FastJet distribution, was originally
 * written by Stephan Fortune in C and adapted to C++ by Shane
 * O'Sullivan under the terms reported above.
 *
 * Below are the list of changes implemented by the FastJet authors:
 *
 * 2011-11-14  Gregory Soyez  <soyez@fastjet.fr>
 * 
 *      * removed 'plot' and 'triangulate' (were always 0)
 *      * removed unused plot functions (openpl, circle, range, 
 *        out_bisector, out_ep, out_vertex, out_site, out_triple)
 *      * removed unused 'VPoint p' in 'intersect'
 *
 *
 * 2011-07-22  Gregory Soyez  <soyez@fastjet.fr>
 * 
 *      * replaced Point by VPoint (to avoid any potential conflict
 *        with an already existing class Point in FastJet
 * 
 * 
 * 2011-06-28  Gregory Soyez  <soyez@fastjet.fr>
 * 
 *      * added support for situations with degenerate particles (we just
 *        discard the particles degenerate wiht an already existing
 *        one which is perfectly sufficient for our needs)
 *      * in 'VoronoiDiagramGenerator::intersect', improved the numerical
 *        precision in cases where the 2 parents are nearly degenerate
 * 
 * 
 * 2011-06-14  Gregory Soyez  <soyez@fastjet.fr>
 * 
 *      * fixed a potential overflow bug in VoronoiDiagramGenerator::PQbucket
 * 
 * 
 * 2007-05-07  Gregory Soyez  <soyez@fastjet.fr>
 * 
 *      * fied a few memory leaks
 *
 *      * put the code in the fastjet namespace
 * 
 *      * replaced float by double
 * 
 *      * generateVoronoi() takes a vector of Point instead of 2
 *        pointers
 * 
 *      * added info about the parent sites to GraphEdge (and clip_line)
 * 
 *      * removed condition on minimal distance between sites
 */

#include <stdio.h>
#include "fastjet/internal/Voronoi.hh"

using namespace std;

FASTJET_BEGIN_NAMESPACE

LimitedWarning VoronoiDiagramGenerator::_warning_degeneracy;

VoronoiDiagramGenerator::VoronoiDiagramGenerator(){
  siteidx = 0;
  sites = NULL;
  parent_sites = NULL;

  allMemoryList = new FreeNodeArrayList;
  allMemoryList->memory = NULL;
  allMemoryList->next = NULL;
  currentMemoryBlock = allMemoryList;
  allEdges = NULL;
  iteratorEdges = 0;
  minDistanceBetweenSites = 0;

  ELhash = NULL;
  PQhash = NULL;
}

VoronoiDiagramGenerator::~VoronoiDiagramGenerator(){
  cleanup();
  cleanupEdges();

  if (allMemoryList != NULL)
    delete allMemoryList;
}



bool VoronoiDiagramGenerator::generateVoronoi(vector<VPoint> *_parent_sites,
                                              double minX, double maxX, 
                                              double minY, double maxY, 
                                              double minDist){
  cleanup();
  cleanupEdges();
  int i;
  double x, y;

  minDistanceBetweenSites = minDist;

  parent_sites = _parent_sites;

  nsites = n_parent_sites = parent_sites->size();
  debug = 1;
  sorted = 0; 
  freeinit(&sfl, sizeof (Site));
                
  //sites = (Site *) myalloc(nsites*sizeof( *sites));
  sites = (Site *) myalloc(nsites*sizeof( Site));
  //parent_sites = (Site *) myalloc(nsites*sizeof( Site));
 
  if (sites == 0)
    return false;

  xmax = xmin = (*parent_sites)[0].x;
  ymax = ymin = (*parent_sites)[0].y;
  
  for(i=0;i<nsites;i++){
    x = (*parent_sites)[i].x;
    y = (*parent_sites)[i].y;
    sites[i].coord.x = x;
    sites[i].coord.y = y;
    sites[i].sitenbr = i;
    sites[i].refcnt  = 0;
    
    if (x<xmin)
      xmin=x;
    else if (x>xmax)
      xmax=x;
    
    if (y<ymin)
      ymin=y;
    else if (y>ymax)
      ymax=y;
  }
        
  qsort(sites, nsites, sizeof (*sites), scomp);

  // Gregory Soyez
  // 
  // check if some of the particles are degenerate to avoid a crash.
  //
  // At the moment, we work under the assumption that they will be
  // "clustered" later on, so we just keep the 1st one and discard the
  // others
  unsigned int offset=0;
  for (int is=1;is<nsites;is++){
    if (sites[is].coord.y==sites[is-1].coord.y && sites[is].coord.x==sites[is-1].coord.x){
      offset++;
    } else if (offset>0){
      sites[is-offset] = sites[is];
    }
  }

  if (offset>0){
    nsites-=offset;
    _warning_degeneracy.warn("VoronoiDiagramGenerator: two (or more) particles are degenerate in rapidity and azimuth, Voronoi cell assigned to the first of each set of degenerate particles.");
  }

  siteidx = 0;
  geominit();
  double temp = 0;
  if(minX > maxX){
    temp = minX;
    minX = maxX;
    maxX = temp;
  }
  if(minY > maxY){
    temp = minY;
    minY = maxY;
    maxY = temp;
  }
  borderMinX = minX;
  borderMinY = minY;
  borderMaxX = maxX;
  borderMaxY = maxY;
        
  siteidx = 0;
  voronoi();

  return true;
}

bool VoronoiDiagramGenerator::ELinitialize(){
  int i;
  freeinit(&hfl, sizeof(Halfedge));
  ELhashsize = 2 * sqrt_nsites;
  //ELhash = (Halfedge **) myalloc ( sizeof *ELhash * ELhashsize);
  ELhash = (Halfedge **) myalloc ( sizeof(Halfedge*)*ELhashsize);
  
  if(ELhash == 0)
    return false;
  
  for(i=0; i<ELhashsize; i +=1) ELhash[i] = (Halfedge *)NULL;
  ELleftend = HEcreate((Edge*) NULL, 0);
  ELrightend = HEcreate((Edge*) NULL, 0);
  ELleftend->ELleft = (Halfedge*) NULL;
  ELleftend->ELright = ELrightend;
  ELrightend->ELleft = ELleftend;
  ELrightend->ELright = (Halfedge*) NULL;
  ELhash[0] = ELleftend;
  ELhash[ELhashsize-1] = ELrightend;

  return true;
}


Halfedge* VoronoiDiagramGenerator::HEcreate(Edge *e,int pm){
  Halfedge *answer;
  answer = (Halfedge*) getfree(&hfl);
  answer->ELedge = e;
  answer->ELpm = pm;
  answer->PQnext = (Halfedge*) NULL;
  answer->vertex = (Site*) NULL;
  answer->ELrefcnt = 0;
  return answer;
}


void VoronoiDiagramGenerator::ELinsert(Halfedge *lb, Halfedge *newHe)
{
  newHe->ELleft = lb;
  newHe->ELright = lb->ELright;
  (lb->ELright)->ELleft = newHe;
  lb->ELright = newHe;
}


/* Get entry from hash table, pruning any deleted nodes */
Halfedge* VoronoiDiagramGenerator::ELgethash(int b){
  Halfedge *he;
        
  if ((b<0) || (b>=ELhashsize)) 
    return (Halfedge *) NULL;

  he = ELhash[b]; 
  if ((he==(Halfedge*) NULL) || (he->ELedge!=(Edge*) DELETED)) 
    return he;
        
  /* Hash table points to deleted half edge.  Patch as necessary. */
  ELhash[b] = (Halfedge*) NULL;
  if ((he->ELrefcnt -= 1) == 0) 
    makefree((Freenode*)he, &hfl);
  return (Halfedge*) NULL;
}       

Halfedge * VoronoiDiagramGenerator::ELleftbnd(VPoint *p){
  int i, bucket;
  Halfedge *he;
        
  /* Use hash table to get close to desired halfedge */
  // use the hash function to find the place in the hash map that this
  // HalfEdge should be
  // Gregory Soyez: the original code was 
  //
  //   bucket = (int)((p->x - xmin)/deltax * ELhashsize);       
  //   // make sure that the bucket position in within the range of the
  //   //hash array
  //   if (bucket<0) bucket =0;
  //   if (bucket>=ELhashsize) bucket = ELhashsize - 1;
  //
  // but this runs the risk of having a overflow which would 
  // cause bucket to be truncated at 0 instead of ELhashsize - 1
  // (or vice-versa)
  // We fix this by performing the test immediately on the double
  // We put in a extra bit of margin to be sure the conversion does
  // not play dirty tricks on us

  //const double &px = p->x;
  if (p->x < xmin){ bucket=0;}
  else if (p->x >= xmax){ bucket = ELhashsize - 1;}
  else{
    bucket= (int)((p->x - xmin)/deltax * ELhashsize);
    if (bucket>=ELhashsize) bucket = ELhashsize - 1;  // the lower cut should be robust
  }

  he = ELgethash(bucket);

  // if the HE isn't found, search backwards and forwards in the hash
  // map for the first non-null entry
  if (he == (Halfedge*) NULL){   
    for(i=1;1;i++){     
      if ((he=ELgethash(bucket-i)) != (Halfedge*) NULL) 
        break;
      if ((he=ELgethash(bucket+i)) != (Halfedge*) NULL) 
        break;
    };
    totalsearch += i;
  };
  ntry += 1;
  /* Now search linear list of halfedges for the correct one */
  if ((he==ELleftend)  || (he != ELrightend && right_of(he,p))){
    do{
      he = he->ELright;
    } while (he!=ELrightend && right_of(he,p));
      // keep going right on the list until either the end is reached,
      // or you find the 1st edge which the point
      he = he->ELleft;  //isn't to the right of
  } else 
    // if the point is to the left of the HalfEdge, then search left
    // for the HE just to the left of the point
    do{
      he = he->ELleft;
    } while ((he!=ELleftend )&& (!right_of(he,p)));
                
  /* Update hash table and reference counts */
  if ((bucket > 0) && (bucket <ELhashsize-1)){  
    if(ELhash[bucket] != (Halfedge *) NULL){
      ELhash[bucket]->ELrefcnt -= 1;
    }
    ELhash[bucket] = he;
    ELhash[bucket]->ELrefcnt += 1;
  };

  return he;
}


/* This delete routine can't reclaim node, since pointers from hash
   table may be present.   */
void VoronoiDiagramGenerator::ELdelete(Halfedge *he){
  (he->ELleft)->ELright = he->ELright;
  (he->ELright)->ELleft = he->ELleft;
  he->ELedge = (Edge*) DELETED;
}


Halfedge* VoronoiDiagramGenerator::ELright(Halfedge *he){
  return he->ELright;
}


Halfedge* VoronoiDiagramGenerator::ELleft(Halfedge *he){
  return he->ELleft;
}


Site * VoronoiDiagramGenerator::leftreg(Halfedge *he){
  if (he->ELedge == (Edge*) NULL) 
    return(bottomsite);
  return (he->ELpm == le) 
    ? he->ELedge->reg[le] 
    : he->ELedge->reg[re];
}

Site * VoronoiDiagramGenerator::rightreg(Halfedge *he){
  if (he->ELedge == (Edge*) NULL)
    // if this halfedge has no edge, return the bottom site (whatever
    // that is)
    return bottomsite;
  
  // if the ELpm field is zero, return the site 0 that this edge
  // bisects, otherwise return site number 1
  return (he->ELpm == le)
    ? he->ELedge->reg[re] 
    : he->ELedge->reg[le];
}

void VoronoiDiagramGenerator::geominit(){
  double sn;
  
  freeinit(&efl, sizeof(Edge));
  nvertices = 0;
  nedges = 0;
  sn = (double)nsites+4;
  sqrt_nsites = (int)sqrt(sn);
  deltay = ymax - ymin;
  deltax = xmax - xmin;
}


Edge * VoronoiDiagramGenerator::bisect(Site *s1, Site *s2){
  double dx,dy,adx,ady;
  Edge *newedge;        

  newedge = (Edge*) getfree(&efl);
        
  newedge->reg[0] = s1; //store the sites that this edge is bisecting
  newedge->reg[1] = s2;
  ref(s1); 
  ref(s2);

  // to begin with, there are no endpoints on the bisector - it goes
  // to infinity
  newedge->ep[0] = (Site*) NULL;
  newedge->ep[1] = (Site*) NULL;
  
  // get the difference in x dist between the sites
  dx = s2->coord.x - s1->coord.x;
  dy = s2->coord.y - s1->coord.y;

  // make sure that the difference is positive
  adx = dx>0 ? dx : -dx;
  ady = dy>0 ? dy : -dy;

  // get the slope of the line
  newedge->c = (double)(s1->coord.x * dx + s1->coord.y * dy
                        + (dx*dx + dy*dy)*0.5);

  if (adx>ady){ 
    //set formula of line, with x fixed to 1
    newedge->a = 1.0; newedge->b = dy/dx; newedge->c /= dx;
  } else {      
    //set formula of line, with y fixed to 1
    newedge->b = 1.0; newedge->a = dx/dy; newedge->c /= dy;
  }
        
  newedge->edgenbr = nedges;
  nedges++;

  return newedge;
}


// create a new site where the HalfEdges el1 and el2 intersect - note
// that the VPoint in the argument list is not used, don't know why
// it's there
//
// Gregory Soyez: removed the uinused point p
Site* VoronoiDiagramGenerator::intersect(Halfedge *el1, Halfedge *el2
                                         /*, VPoint *p*/){
  Edge *e1,*e2, *e;
  Halfedge *el;
  double d, xint, yint;
  int right_of_site;
  Site *v;
        
  e1 = el1->ELedge;
  e2 = el2->ELedge;
  if ((e1==(Edge*)NULL) || (e2==(Edge*)NULL)) 
    return ((Site*) NULL);

  // if the two edges bisect the same parent, return null
  if (e1->reg[1] == e2->reg[1]) 
    return (Site*) NULL;

  // Gregory Soyez:
  //    
  // if the 2 parents are too close, the intersection is going to be
  // computed from the "long edges" of the triangle which could causes
  // large rounding errors. In this case, use the bisector of the 2
  // parents to find the interaction point
  // 
  // The following replaces 
  //   d = e1->a * e2->b - e1->b * e2->a;
  //   if (-1.0e-10<d && d<1.0e-10) 
  //     return (Site*) NULL;
  //    
  //   xint = (e1->c*e2->b - e2->c*e1->b)/d;
  //   yint = (e2->c*e1->a - e1->c*e2->a)/d;

  double dx = e2->reg[1]->coord.x - e1->reg[1]->coord.x;
  double dy = e2->reg[1]->coord.y - e1->reg[1]->coord.y;
  double dxref = e1->reg[1]->coord.x - e1->reg[0]->coord.x;
  double dyref = e1->reg[1]->coord.y - e1->reg[0]->coord.y;

  if (dx*dx + dy*dy < 1e-14*(dxref*dxref+dyref*dyref)){
    // make sure that the difference is positive
    double adx = dx>0 ? dx : -dx;
    double ady = dy>0 ? dy : -dy;
    
    // get the slope of the line
    double a,b;
    double c = (double)(e1->reg[1]->coord.x * dx + e1->reg[1]->coord.y * dy
                        + (dx*dx + dy*dy)*0.5);
    
    if (adx>ady){
      a = 1.0; b = dy/dx; c /= dx;
    } else {
      b = 1.0; a = dx/dy; c /= dy;
    }

    d = e1->a * b - e1->b * a;
    if (-1.0e-10<d && d<1.0e-10) {
      return (Site*) NULL;
    }
        
    xint = (e1->c*b - c*e1->b)/d;
    yint = (c*e1->a - e1->c*a)/d;
    
  } else {      
    d = e1->a * e2->b - e1->b * e2->a;
    if (-1.0e-10<d && d<1.0e-10) {
      return (Site*) NULL;
    }
        
    xint = (e1->c*e2->b - e2->c*e1->b)/d;
    yint = (e2->c*e1->a - e1->c*e2->a)/d;
  }
  // end of Gregory Soyez's modifications

  volatile double local_y1 = e1->reg[1]->coord.y;
  volatile double local_y2 = e2->reg[1]->coord.y;
        
  if( (local_y1 < local_y2) ||
      ((local_y1 == local_y2) &&
       (e1->reg[1]->coord.x <  e2->reg[1]->coord.x)) ){ 
    el = el1; 
    e = e1;
  } else {      
    el = el2; 
    e = e2;
  }
        
  right_of_site = xint >= e->reg[1]->coord.x;
  if ((right_of_site && el->ELpm == le) || (!right_of_site && el->ELpm == re)) 
    return (Site*) NULL;
        
  // create a new site at the point of intersection - this is a new
  // vector event waiting to happen
  v = (Site*) getfree(&sfl);
  v->refcnt = 0;
  v->coord.x = xint;
  v->coord.y = yint;
  return v;
}

//HERE

/* returns 1 if p is to right of halfedge e */
int VoronoiDiagramGenerator::right_of(Halfedge *el,VPoint *p)
{
  Edge *e;
  Site *topsite;
  int right_of_site, above, fast;
  double dxp, dyp, dxs, t1, t2, t3, yl;
        
  e = el->ELedge;
  topsite = e->reg[1];
  right_of_site = p->x > topsite->coord.x;
  if(right_of_site && el->ELpm == le) return(1);
  if(!right_of_site && el->ELpm == re) return (0);
        
  if (e->a == 1.0)
    {   dyp = p->y - topsite->coord.y;
    dxp = p->x - topsite->coord.x;
    fast = 0;
    if ((!right_of_site & (e->b<0.0)) | (right_of_site & (e->b>=0.0)) )
      { above = dyp>= e->b*dxp; 
      fast = above;
      }
    else 
      { above = p->x + p->y*e->b > e-> c;
      if(e->b<0.0) above = !above;
      if (!above) fast = 1;
      };
    if (!fast)
      { dxs = topsite->coord.x - (e->reg[0])->coord.x;
      above = e->b * (dxp*dxp - dyp*dyp) <
        dxs*dyp*(1.0+2.0*dxp/dxs + e->b*e->b);
      if(e->b<0.0) above = !above;
      };
    }
  else  /*e->b==1.0 */
    {   yl = e->c - e->a*p->x;
    t1 = p->y - yl;
    t2 = p->x - topsite->coord.x;
    t3 = yl - topsite->coord.y;
    above = t1*t1 > t2*t2 + t3*t3;
    };
  return (el->ELpm==le ? above : !above);
}


void VoronoiDiagramGenerator::endpoint(Edge *e,int lr,Site * s)
{
  e->ep[lr] = s;
  ref(s);
  if(e->ep[re-lr]== (Site *) NULL) 
    return;

  clip_line(e);

  deref(e->reg[le]);
  deref(e->reg[re]);
  makefree((Freenode*)e, &efl);
}


double VoronoiDiagramGenerator::dist(Site *s,Site *t)
{
  double dx,dy;
  dx = s->coord.x - t->coord.x;
  dy = s->coord.y - t->coord.y;
  return (double)(sqrt(dx*dx + dy*dy));
}


void VoronoiDiagramGenerator::makevertex(Site *v)
{
  v->sitenbr = nvertices;
  nvertices += 1;
  //GS unused plot: out_vertex(v);
}


void VoronoiDiagramGenerator::deref(Site *v)
{
  v->refcnt -= 1;
  if (v->refcnt == 0 ) 
    makefree((Freenode*)v, &sfl);
}

void VoronoiDiagramGenerator::ref(Site *v)
{
  v->refcnt += 1;
}

//push the HalfEdge into the ordered linked list of vertices
void VoronoiDiagramGenerator::PQinsert(Halfedge *he,Site * v, double offset)
{
  Halfedge *last, *next;
        
  he->vertex = v;
  ref(v);
  he->ystar = (double)(v->coord.y + offset);
  last = &PQhash[PQbucket(he)];
  while ((next = last->PQnext) != (Halfedge *) NULL &&
         (he->ystar  > next->ystar  ||
          (he->ystar == next->ystar && v->coord.x > next->vertex->coord.x)))
    {   
      last = next;
    };
  he->PQnext = last->PQnext; 
  last->PQnext = he;
  PQcount += 1;
}

//remove the HalfEdge from the list of vertices 
void VoronoiDiagramGenerator::PQdelete(Halfedge *he)
{
  Halfedge *last;
        
  if(he->vertex != (Site *) NULL)
    {   
      last = &PQhash[PQbucket(he)];
      while (last->PQnext != he) 
        last = last->PQnext;

      last->PQnext = he->PQnext;
      PQcount -= 1;
      deref(he->vertex);
      he->vertex = (Site *) NULL;
    };
}

int VoronoiDiagramGenerator::PQbucket(Halfedge *he)
{
  // Gregory Soyez: the original code was 
  //
  //   bucket = (int)((he->ystar - ymin)/deltay * PQhashsize);
  //   if (bucket<0) bucket = 0;
  //   if (bucket>=PQhashsize) bucket = PQhashsize-1 ;
  //   if (bucket < PQmin) PQmin = bucket;
  //   return(bucket);
  //
  // but this runs the risk of having a overflow which would 
  // cause bucket to be truncated at 0 instead of PQhashsize-1
  // (or vice-versa)
  // We fix this by performing the test immediately on the double
  // We put in a extra bit of margin to be sure the conversion does
  // not play dirty tricks on us

  int bucket;
        
  double hey = he->ystar;
  if (hey < ymin){ bucket = 0;}
  else if (hey >= ymax){ bucket = PQhashsize-1;}
  else {
    bucket = (int)((hey - ymin)/deltay * PQhashsize);
    if (bucket>=PQhashsize) bucket = PQhashsize-1 ;
  }

  if (bucket < PQmin) PQmin = bucket;
  return(bucket);
}



int VoronoiDiagramGenerator::PQempty()
{
  return(PQcount==0);
}


VPoint VoronoiDiagramGenerator::PQ_min()
{
  VPoint answer;
        
  while(PQhash[PQmin].PQnext == (Halfedge *)NULL) {PQmin += 1;};
  answer.x = PQhash[PQmin].PQnext->vertex->coord.x;
  answer.y = PQhash[PQmin].PQnext->ystar;
  return (answer);
}

Halfedge * VoronoiDiagramGenerator::PQextractmin()
{
  Halfedge *curr;
        
  curr = PQhash[PQmin].PQnext;
  PQhash[PQmin].PQnext = curr->PQnext;
  PQcount -= 1;
  return(curr);
}


bool VoronoiDiagramGenerator::PQinitialize()
{
  int i; 
        
  PQcount = 0;
  PQmin = 0;
  PQhashsize = 4 * sqrt_nsites;
  //PQhash = (Halfedge *) myalloc(PQhashsize * sizeof *PQhash);
  PQhash = (Halfedge *) myalloc(PQhashsize * sizeof(Halfedge));

  if(PQhash == 0)
    return false;

  for(i=0; i<PQhashsize; i+=1) PQhash[i].PQnext = (Halfedge *)NULL;

  return true;
}


void VoronoiDiagramGenerator::freeinit(Freelist *fl,int size)
{
  fl->head = (Freenode *) NULL;
  fl->nodesize = size;
}

char * VoronoiDiagramGenerator::getfree(Freelist *fl)
{
  int i; 
  Freenode *t;

  if(fl->head == (Freenode *) NULL)
    {   
      t =  (Freenode *) myalloc(sqrt_nsites * fl->nodesize);

      if(t == 0)
        return 0;
                
      currentMemoryBlock->next = new FreeNodeArrayList;
      currentMemoryBlock = currentMemoryBlock->next;
      currentMemoryBlock->memory = t;
      currentMemoryBlock->next = 0;

      for(i=0; i<sqrt_nsites; i+=1)     
        makefree((Freenode *)((char *)t+i*fl->nodesize), fl);           
    };
  t = fl->head;
  fl->head = (fl->head)->nextfree;
  return((char *)t);
}



void VoronoiDiagramGenerator::makefree(Freenode *curr,Freelist *fl)
{
  curr->nextfree = fl->head;
  fl->head = curr;
}

void VoronoiDiagramGenerator::cleanup()
{
  if(sites != NULL){
    free(sites);
    sites = 0;
  }

  FreeNodeArrayList* current=NULL, *prev=NULL;

  current = prev = allMemoryList;

  while(current->next!=NULL){
    prev = current;
    current = current->next;
    free(prev->memory);
    delete prev;
    prev = NULL;
  }

  if(current!=NULL){
    if (current->memory!=NULL){
      free(current->memory);
    }
    delete current;
  }

  allMemoryList = new FreeNodeArrayList;
  allMemoryList->next = NULL;
  allMemoryList->memory = NULL;
  currentMemoryBlock = allMemoryList;

  if (ELhash!=NULL)
    free(ELhash);

  if (PQhash!=NULL)
    free(PQhash);
}

void VoronoiDiagramGenerator::cleanupEdges()
{
  GraphEdge* geCurrent = NULL, *gePrev = NULL;
  geCurrent = gePrev = allEdges;

  while(geCurrent!=NULL){
    gePrev = geCurrent;
    geCurrent = geCurrent->next;
    delete gePrev;
  }

  allEdges = 0;

}

void VoronoiDiagramGenerator::pushGraphEdge(double x1, double y1, double x2, double y2,
                                            Site *s1, Site *s2)
{
  GraphEdge* newEdge = new GraphEdge;
  newEdge->next = allEdges;
  allEdges = newEdge;
  newEdge->x1 = x1;
  newEdge->y1 = y1;
  newEdge->x2 = x2;
  newEdge->y2 = y2;

  newEdge->point1 = s1->sitenbr;
  newEdge->point2 = s2->sitenbr;
}


char * VoronoiDiagramGenerator::myalloc(unsigned n)
{
  char *t=0;    
  t=(char*)malloc(n);
  total_alloc += n;
  return(t);
}


// unused plot functions
//
// /* for those who don't have Cherry's plot */
// /* #include <plot.h> */
// void VoronoiDiagramGenerator::openpl(){}
// void VoronoiDiagramGenerator::circle(double x, double y, double radius){}
// void VoronoiDiagramGenerator::range(double minX, double minY, double maxX, double maxY){}
// 
// 
// 
// void VoronoiDiagramGenerator::out_bisector(Edge *e)
// {
//      
// 
// }
// 
// 
// void VoronoiDiagramGenerator::out_ep(Edge *e)
// {
//      
//      
// }
// 
// void VoronoiDiagramGenerator::out_vertex(Site *v)
// {
//      
// }
// 
// 
// void VoronoiDiagramGenerator::out_site(Site *s)
// {
//   // Gregory Soyez: 
//   //   plot was always 0 so the expression below was always false
//   //   and even if it was not, 'circle' does nothing!
//   //
//   // if(!triangulate & plot & !debug)
//   //   circle (s->coord.x, s->coord.y, cradius);
//      
// }
// 
// 
// void VoronoiDiagramGenerator::out_triple(Site *s1, Site *s2,Site * s3)
// {
//      
// }



void VoronoiDiagramGenerator::plotinit()
{
  double dx,dy,d;
        
  dy = ymax - ymin;
  dx = xmax - xmin;
  d = (double)(( dx > dy ? dx : dy) * 1.1);
  pxmin = (double)(xmin - (d-dx)/2.0);
  pxmax = (double)(xmax + (d-dx)/2.0);
  pymin = (double)(ymin - (d-dy)/2.0);
  pymax = (double)(ymax + (d-dy)/2.0);
  cradius = (double)((pxmax - pxmin)/350.0);
  //GS unused: openpl();
  //GS unused: range(pxmin, pymin, pxmax, pymax);
}


void VoronoiDiagramGenerator::clip_line(Edge *e)
{
  Site *s1, *s2;
  double x1=0,x2=0,y1=0,y2=0; //, temp = 0;

  x1 = e->reg[0]->coord.x;
  x2 = e->reg[1]->coord.x;
  y1 = e->reg[0]->coord.y;
  y2 = e->reg[1]->coord.y;

  //if the distance between the two points this line was created from is less than 
  //the square root of 2, then ignore it
  //TODO improve/remove
  //if(sqrt(((x2 - x1) * (x2 - x1)) + ((y2 - y1) * (y2 - y1))) < minDistanceBetweenSites)
  //  {
  //    return;
  //  }
  pxmin = borderMinX;
  pxmax = borderMaxX;
  pymin = borderMinY;
  pymax = borderMaxY;

  if(e->a == 1.0 && e ->b >= 0.0)
    {   
      s1 = e->ep[1];
      s2 = e->ep[0];
    }
  else 
    {
      s1 = e->ep[0];
      s2 = e->ep[1];
    };
        
  if(e->a == 1.0)
    {
      y1 = pymin;
      if (s1!=(Site *)NULL && s1->coord.y > pymin)
        {
          y1 = s1->coord.y;
        }
      if(y1>pymax) 
        {
          //    printf("\nClipped (1) y1 = %f to %f",y1,pymax);
          y1 = pymax;
          //return;
        }
      x1 = e->c - e->b * y1;
      y2 = pymax;
      if (s2!=(Site *)NULL && s2->coord.y < pymax) 
        y2 = s2->coord.y;

      if(y2<pymin) 
        {
          //printf("\nClipped (2) y2 = %f to %f",y2,pymin);
          y2 = pymin;
          //return;
        }
      x2 = (e->c) - (e->b) * y2;
      if (((x1> pxmax) & (x2>pxmax)) | ((x1<pxmin)&(x2<pxmin))) 
        {
          //printf("\nClipLine jumping out(3), x1 = %f, pxmin = %f, pxmax = %f",x1,pxmin,pxmax);
          return;
        }
      if(x1> pxmax)
        {       x1 = pxmax; y1 = (e->c - x1)/e->b;};
      if(x1<pxmin)
        {       x1 = pxmin; y1 = (e->c - x1)/e->b;};
      if(x2>pxmax)
        {       x2 = pxmax; y2 = (e->c - x2)/e->b;};
      if(x2<pxmin)
        {       x2 = pxmin; y2 = (e->c - x2)/e->b;};
    }
  else
    {
      x1 = pxmin;
      if (s1!=(Site *)NULL && s1->coord.x > pxmin) 
        x1 = s1->coord.x;
      if(x1>pxmax) 
        {
          //printf("\nClipped (3) x1 = %f to %f",x1,pxmin);
          //return;
          x1 = pxmax;
        }
      y1 = e->c - e->a * x1;
      x2 = pxmax;
      if (s2!=(Site *)NULL && s2->coord.x < pxmax) 
        x2 = s2->coord.x;
      if(x2<pxmin) 
        {
          //printf("\nClipped (4) x2 = %f to %f",x2,pxmin);
          //return;
          x2 = pxmin;
        }
      y2 = e->c - e->a * x2;
      if (((y1> pymax) & (y2>pymax)) | ((y1<pymin)&(y2<pymin))) 
        {
          //printf("\nClipLine jumping out(6), y1 = %f, pymin = %f, pymax = %f",y2,pymin,pymax);
          return;
        }
      if(y1> pymax)
        {       y1 = pymax; x1 = (e->c - y1)/e->a;};
      if(y1<pymin)
        {       y1 = pymin; x1 = (e->c - y1)/e->a;};
      if(y2>pymax)
        {       y2 = pymax; x2 = (e->c - y2)/e->a;};
      if(y2<pymin)
        {       y2 = pymin; x2 = (e->c - y2)/e->a;};
    };
        
  //printf("\nPushing line (%f,%f,%f,%f)",x1,y1,x2,y2);
  //fprintf(stdout, "Line with vertices (%f,%f) and (%f,%f)\n", 
  //    e->reg[0]->coord.x, e->reg[1]->coord.x, e->reg[0]->coord.y, e->reg[1]->coord.y);
  pushGraphEdge(x1,y1,x2,y2,e->reg[0],e->reg[1]);
}


/* implicit parameters: nsites, sqrt_nsites, xmin, xmax, ymin, ymax,
   deltax, deltay (can all be estimates).
   Performance suffers if they are wrong; better to make nsites,
   deltax, and deltay too big than too small.  (?) */

bool VoronoiDiagramGenerator::voronoi()
{
  Site *newsite, *bot, *top, *temp, *p;
  Site *v;
  VPoint newintstar;
  int pm;
  Halfedge *lbnd, *rbnd, *llbnd, *rrbnd, *bisector;
  Edge *e;
        
  PQinitialize();
  bottomsite = nextone();
  //GS unused plot: out_site(bottomsite);
  bool retval = ELinitialize();

  if(!retval)
    return false;
        
  newsite = nextone();
  while(1)
    {

      if(!PQempty()) 
        newintstar = PQ_min();
                
      //if the lowest site has a smaller y value than the lowest vector intersection, process the site
      //otherwise process the vector intersection               
      if (newsite != (Site *)NULL  && (PQempty() || newsite->coord.y < newintstar.y
                                       || (newsite->coord.y == newintstar.y && newsite->coord.x < newintstar.x)))
        {/* new site is smallest - this is a site event*/
          //GS unused plot: out_site(newsite);                                          //output the site
          lbnd = ELleftbnd(&(newsite->coord));                          //get the first HalfEdge to the LEFT of the new site
          rbnd = ELright(lbnd);                                         //get the first HalfEdge to the RIGHT of the new site
          bot = rightreg(lbnd);                                         //if this halfedge has no edge, , bot = bottom site (whatever that is)
          e = bisect(bot, newsite);                                     //create a new edge that bisects 
          bisector = HEcreate(e, le);                                   //create a new HalfEdge, setting its ELpm field to 0                    
          ELinsert(lbnd, bisector);                                     //insert this new bisector edge between the left and right vectors in a linked list     
            
          if ((p = intersect(lbnd, bisector)) != (Site *) NULL)         //if the new bisector intersects with the left edge, remove the left edge's vertex, and put in the new one
            {   
              PQdelete(lbnd);
              PQinsert(lbnd, p, dist(p,newsite));
            };
          lbnd = bisector;                                              
          bisector = HEcreate(e, re);                                   //create a new HalfEdge, setting its ELpm field to 1
          ELinsert(lbnd, bisector);                                     //insert the new HE to the right of the original bisector earlier in the IF stmt
            
          if ((p = intersect(bisector, rbnd)) != (Site *) NULL) //if this new bisector intersects with the
            {   
              PQinsert(bisector, p, dist(p,newsite));                   //push the HE into the ordered linked list of vertices
            };
          newsite = nextone();  
        }
      else if (!PQempty()) /* intersection is smallest - this is a vector event */                      
        {       
          lbnd = PQextractmin();                                                //pop the HalfEdge with the lowest vector off the ordered list of vectors                               
          llbnd = ELleft(lbnd);                                         //get the HalfEdge to the left of the above HE
          rbnd = ELright(lbnd);                                         //get the HalfEdge to the right of the above HE
          rrbnd = ELright(rbnd);                                                //get the HalfEdge to the right of the HE to the right of the lowest HE 
          bot = leftreg(lbnd);                                          //get the Site to the left of the left HE which it bisects
          top = rightreg(rbnd);                                         //get the Site to the right of the right HE which it bisects
            
          //GS unused plot: out_triple(bot, top, rightreg(lbnd));               //output the triple of sites, stating that a circle goes through them
            
          v = lbnd->vertex;                                             //get the vertex that caused this event
          makevertex(v);                                                        //set the vertex number - couldn't do this earlier since we didn't know when it would be processed
          endpoint(lbnd->ELedge,lbnd->ELpm,v);  //set the endpoint of the left HalfEdge to be this vector
          endpoint(rbnd->ELedge,rbnd->ELpm,v);  //set the endpoint of the right HalfEdge to be this vector
          ELdelete(lbnd);                                                       //mark the lowest HE for deletion - can't delete yet because there might be pointers to it in Hash Map  
          PQdelete(rbnd);                                                       //remove all vertex events to do with the  right HE
          ELdelete(rbnd);                                                       //mark the right HE for deletion - can't delete yet because there might be pointers to it in Hash Map   
          pm = le;                                                              //set the pm variable to zero
            
          if (bot->coord.y > top->coord.y)              //if the site to the left of the event is higher than the Site
            {                                                                           //to the right of it, then swap them and set the 'pm' variable to 1
              temp = bot; 
              bot = top; 
              top = temp; 
              pm = re;
            }
          e = bisect(bot, top);                                 //create an Edge (or line) that is between the two Sites. This creates
          //the formula of the line, and assigns a line number to it
          bisector = HEcreate(e, pm);                           //create a HE from the Edge 'e', and make it point to that edge with its ELedge field
          ELinsert(llbnd, bisector);                            //insert the new bisector to the right of the left HE
          endpoint(e, re-pm, v);                                        //set one endpoint to the new edge to be the vector point 'v'.
          //If the site to the left of this bisector is higher than the right
          //Site, then this endpoint is put in position 0; otherwise in pos 1
          deref(v);                                                             //delete the vector 'v'
            
          //if left HE and the new bisector don't intersect, then delete the left HE, and reinsert it 
          if((p = intersect(llbnd, bisector)) != (Site *) NULL)
            {   
              PQdelete(llbnd);
              PQinsert(llbnd, p, dist(p,bot));
            };
            
          //if right HE and the new bisector don't intersect, then reinsert it 
          if ((p = intersect(bisector, rrbnd)) != (Site *) NULL)
            {   
              PQinsert(bisector, p, dist(p,bot));
            };
        }
      else break;
    };

        


  for(lbnd=ELright(ELleftend); lbnd != ELrightend; lbnd=ELright(lbnd))
    {   
      e = lbnd->ELedge;

      clip_line(e);
    };

  //cleanup();

  return true;
        
}


int scomp(const void *p1,const void *p2)
{
  VPoint *s1 = (VPoint*)p1, *s2=(VPoint*)p2;
  if(s1->y < s2->y) return(-1);
  if(s1->y > s2->y) return(1);
  if(s1->x < s2->x) return(-1);
  if(s1->x > s2->x) return(1);
  return(0);
}

/* return a single in-storage site */
Site * VoronoiDiagramGenerator::nextone()
{
  Site *s;
  if(siteidx < nsites)
    {   
      s = &sites[siteidx];
      siteidx += 1;
      return(s);
    }
  else  
    return( (Site *)NULL);
}

FASTJET_END_NAMESPACE