/*******************************************************************************
+
+  LEDA 7.2.2  
+
+
+  d3_complex.c
+
+
+  Copyright (c) 1995-2025
+  by Algorithmic Solutions Software GmbH
+  All rights reserved.
+ 
*******************************************************************************/


#include <LEDA/system/basic.h>
#include <LEDA/system/assert.h>

//using namespace leda;

#include "d3_complex.h"

using std::cout;
using std::cin;
using std::endl;
using std::ostream;
using std::istream;

LEDA_BEGIN_NAMESPACE

int compare(const sc_vertex& v1, const sc_vertex& v2)
{
	return int((char*)v2 - (char*)v1);
}


rational r_det(rational a11,rational a12,rational a13,
               rational a21,rational a22,rational a23,
               rational a31,rational a32,rational a33)
{
 return a11*a22*a33+a12*a23*a31+a13*a21*a32 -
        a13*a22*a31-a11*a23*a32-a12*a21*a33;
}

d3_rat_point intersect(rat_vector n1,rat_vector n2,rat_vector n3,
                                     rational D1,rational D2,rational D3)
{
 rational A1=n1.xcoord(); 
 rational B1=n1.ycoord(); 
 rational C1=n1.zcoord();
 rational A2=n2.xcoord(); 
 rational B2=n2.ycoord(); 
 rational C2=n2.zcoord();
 rational A3=n3.xcoord(); 
 rational B3=n3.ycoord(); 
 rational C3=n3.zcoord();

 rational det= r_det(A1,B1,C1,A2,B2,C2,A3,B3,C3);
 rational xdet=r_det(D1,B1,C1,D2,B2,C2,D3,B3,C3);
 rational ydet=r_det(A1,D1,C1,A2,D2,C2,A3,D3,C3);
 rational zdet=r_det(A1,B1,D1,A2,B2,D2,A3,B3,D3);

 if (det==0) error_handler(1,"intersec: determinant==0 .");

 rational xw=-xdet/det; 
 rational yw=-ydet/det; 
 rational zw=-zdet/det;

 return d3_rat_point(xw.normalize(),yw.normalize(),zw.normalize());
}
 

 D3_vertex::D3_vertex(d3_rat_point w,d3_simpl_complex* c)
 {
  stor=w;
  com_of=c;
  my=NULL;
  helper=NULL;
 }

 D3_vertex::D3_vertex(){
  my=NULL; helper=NULL;
 }

 D3_vertex::D3_vertex(const D3_vertex& S)
 {
  stor=S.stor;
  com_of=S.com_of;
  it=S.it;
  my=S.my;
  helper=S.helper;
 } 


 list<sc_simplex> Simplex::all_neighbours() const 
 {
  list<sc_simplex> all;
  if (abc != NULL) all.append(abc);
  if (abd != NULL) all.append(abd);
  if (acd != NULL) all.append(acd);
  if (bcd != NULL) all.append(bcd);
  return all;
 }

 list<sc_simplex> d3_simpl_complex::all_neighbours(sc_simplex sim) const
 {
  return sim->all_neighbours();
 }
 
 Simplex::Simplex(sc_vertex Ap,sc_vertex Bp,sc_vertex Cp)
 {
  HULL_TR=true; 
  a=Ap; 
  b=Bp; 
  c=Cp; 
  d=NULL;  
  Marker=-1; 
  helper=NULL;
  abc=NULL; 
  abd=NULL; 
  acd=NULL; 
  bcd=NULL;
  name="";
  Ap->my=this; 
  Bp->my=this; 
  Cp->my=this;
  abcdia=false; 
  abddia=false; 
  acddia=false; 
  bcddia=false;
 }

 Simplex::Simplex(sc_vertex Ap,sc_vertex Bp,sc_vertex Cp,sc_vertex Dp)
 {
  HULL_TR=false; 
  a=Ap; 
  b=Bp; 
  c=Cp; 
  d=Dp; 
  Marker=-1; 
  helper=NULL;
  abc=NULL; 
  abd=NULL; 
  acd=NULL; 
  bcd=NULL;  
  name="";
  Ap->my=this; 
  Bp->my=this; 
  Cp->my=this; 
  Dp->my=this;
  abcdia=false; 
  abddia=false; 
  acddia=false; 
  bcddia=false;
 }

 Simplex::Simplex(const Simplex& S)
 {
  HULL_TR=S.HULL_TR;
  a=S.a;
  b=S.b;
  c=S.c;
  d=S.d;
  abd=S.abd;
  bcd=S.bcd;
  acd=S.acd;
  abc=S.abc;
  name=S.name;
  helper=S.helper;
  Marker=S.Marker;
  abcdia=S.abcdia;
  abddia=S.abddia; 
  acddia=S.acddia; 
  bcddia=S.bcddia;
 }

 void Simplex::init(sc_simplex s1,sc_simplex s2,sc_simplex s3,sc_simplex s4)
 {
  abd=s1; 
  bcd=s2; 
  acd=s3; 
  abc=s4;
 }

 void Simplex::init(sc_simplex s1,sc_simplex s2,sc_simplex s3)
 {
  abd=s1; 
  bcd=s2; 
  acd=s3;
  helper=NULL;
 }

 void Simplex::update(sc_simplex old, sc_simplex neu)
 {
  if (old==abd) { abd=neu; return; }
  if (old==bcd) { bcd=neu; return; }
  if (old==acd) { acd=neu; return; }
  if (old==abc) { abc=neu; return; }  
 }

 void Simplex::change(sc_vertex k1,sc_vertex k2,sc_vertex k3,sc_vertex k4)
 {
  a=k1; 
  b=k2; 
  c=k3; 
  d=k4;
  a->my=this; 
  b->my=this; 
  c->my=this; 
  d->my=this;
 }

 void Simplex::change(sc_vertex k1,sc_vertex k2,sc_vertex k3)
 {
  a=k1; 
  b=k2; 
  c=k3;
  a->my=this; 
  b->my=this; 
  c->my=this;
 }

 void Simplex::clear_links()
 {
  abc=NULL; 
  abd=NULL; 
  acd=NULL; 
  bcd=NULL;
 }

 sc_vertex Simplex::find_other(sc_vertex p1,sc_vertex p2,sc_vertex p3)
 {
  if (p1!=a && p2!=a && p3!=a) return a;
  if (p1!=b && p2!=b && p3!=b) return b;
  if (p1!=c && p2!=c && p3!=c) return c;
  if (! HULL_TR && p1!=d && p2!=d && p3!=d) return d;
  return NULL;
 }

 int Simplex::index(sc_vertex p)
 {
  if (p==a) return 1;
  if (p==b) return 2;
  if (p==c) return 3;
  if (p==d) return 4;
  return 0;
 }

 sc_vertex Simplex::vertex(int i)
 {
   switch(i) {
   case 1: return a;
   case 2: return b;
   case 3: return c;
   case 4: return d;
   }
   return NULL;
 }

 void Simplex::set_link(sc_simplex S2,int i)
 // change link to a neighbour...
 {
   switch(i){
   case 1: /*a*/ bcd=S2; break;   
   case 2: /*b*/ acd=S2; break;
   case 3: /*c*/ abd=S2; break;
   case 4: /*d*/ abc=S2; break;
   }
 }

 bool Simplex::in_simplex(d3_rat_point p)
 {
   if (HULL_TR) 
    return in_sim(a->stor,b->stor,c->stor,p);
   else
    return contained_in_simplex(a->stor,b->stor,c->stor,d->stor,p);
 }

 bool Simplex::insphere(d3_rat_point p)
 {
   if (HULL_TR) return false;
   else return inside_sphere(a->stor,b->stor,c->stor,d->stor,p);
 }

 int Simplex::control_vert(sc_vertex v1,sc_vertex v2,sc_vertex v3)
 {
   //  3 vertices element { a,b,c,d } ?

  int i1=index(v1); 
  int i2=index(v2); 
  int i3=index(v3);

  if (i1==0 || i2==0 || i3==0) return 0;
  // zurueckgeben, ob abc,abd,acd,bcd
  if (i1!=4 && i2!=4 && i3!=4) return 1; //abc
  if (i1!=3 && i2!=3 && i3!=3) return 2; //abd 
  if (i1!=2 && i2!=2 && i3!=2) return 3; //acd
  return 4; //bcd
 }

 int Simplex::control_vert(sc_vertex v1,sc_vertex v2)
 {
  int i1=index(v1); 
  int i2=index(v2); 
  if (i1==0 || i2==0) return 0;
  if (i1!=3 && i2!=3) return 2; //ab
  if (i1!=2 && i2!=2) return 3; //ac
  if (i1!=1 && i1!=1) return 4; //bc 
  return 0;
 }

 int Simplex::link_new(sc_simplex ot)
 {
  if (ot==NULL) return 0;

  sc_vertex v1=NULL; 
  sc_vertex v2=NULL; 
  sc_vertex v3=NULL;

  int w=0;
  
  if (! HULL_TR) {
   if (ot->abc==NULL){ 
     v1=ot->a; 
     v2=ot->b; 
     v3=ot->c;
     w=control_vert(v1,v2,v3); 
     if (w !=0) ot->abc=this;
   }
   if (ot->abd==NULL && w==0){ 
     v1=ot->a; 
     v2=ot->b; 
     v3=ot->d;
     w=control_vert(v1,v2,v3); 
     if (w !=0) ot->abd=this; 
   }
   if (ot->acd==NULL && w==0){ 
     v1=ot->a; 
     v2=ot->c; 
     v3=ot->d;
     w=control_vert(v1,v2,v3); 
     if (w !=0) ot->acd=this;
   }
   if (ot->bcd==NULL && w==0){ 
     v1=ot->b; 
     v2=ot->c; 
     v3=ot->d;
     w=control_vert(v1,v2,v3); 
     if (w !=0) ot->bcd=this;
   } 
  }
  else { //abc-Verweis braucht nicht beachtet werden
   if (ot->abd==NULL && w==0){ 
     v1=ot->a; 
     v2=ot->b; 
     w=control_vert(v1,v2); 
     if (w !=0) ot->abd=this; 
   }
   if (ot->acd==NULL && w==0){ 
     v1=ot->a; 
     v2=ot->c; 
     w=control_vert(v1,v2); 
     if (w !=0) ot->acd=this; 
   }
   if (ot->bcd==NULL && w==0){ 
     v1=ot->b; 
     v2=ot->c;
     w=control_vert(v1,v2); 
     if (w !=0) ot->bcd=this; 
   } 
  }

  switch(w){
  case 1: abc=ot; break;
  case 2: abd=ot; break;
  case 3: acd=ot; break;
  case 4: bcd=ot; break;
  }
  
  if (w>0 && w<5) return w; else return 0;
 }
 
 d3_rat_point Simplex::circle_midpoint()
 // for hulltriangles
 {
  d3_rat_point pneu;
  d3_rat_point m1,m2;
  d3_rat_plane pl1(a->stor,b->stor,c->stor);
  d3_rat_point h=c->stor + pl1.normal();
  d3_rat_plane plh(a->stor,b->stor,h); 
  d3_rat_plane plh2(b->stor,c->stor,h);
  
  m1=midpoint(a->stor,b->stor);
  m2=midpoint(b->stor,c->stor);
 
  rat_vector r1=pl1.normal();
  rat_vector r2=plh.normal();
  rat_vector r3=plh2.normal();
  d3_rat_plane pl2(m1,m1+r1,m1+r2),pl3(m2,m2+r1,m2+r3);

  rat_vector n1,n2,n3;
  n1=pl1.normal(); n2=pl2.normal(); n3=pl3.normal();

  rational D1,D2,D3;
  D1=-(n1*m1.to_vector()); D2=-(n2*m1.to_vector()); D3=-(n3*m2.to_vector());

  //jetzt Schnittpunkt der 3 Ebenen ermitteln 
  pneu=intersect(n1,n2,n3,D1,D2,D3);
  return pneu;   
 }

 d3_rat_point Simplex::sphere_midpoint()
 {
  d3_rat_point pneu;
  d3_rat_point m1,m2,m3;
  d3_rat_plane pl1(a->stor,b->stor,d->stor),pl2(a->stor,c->stor,d->stor);
  d3_rat_plane pl3(a->stor,b->stor,c->stor);

  m1=midpoint(a->stor,b->stor);
  m2=midpoint(a->stor,c->stor);
  m3=midpoint(a->stor,d->stor);

  rat_vector r1,r2,r3;
  r1=pl1.normal(); r2=pl2.normal(); r3=pl3.normal();
  
  d3_rat_plane sr1(m1,m1+r1,m1+r3),sr2(m2,m2+r2,m2+r3),sr3(m3,m3+r1,m3+r2);
  rat_vector n1,n2,n3;
  n1=sr1.normal(); n2=sr2.normal(); n3=sr3.normal();

  rational D1,D2,D3;
  D1=-(n1*m1.to_vector()); D2=-(n2*m2.to_vector()); D3=-(n3*m3.to_vector());

  pneu=intersect(n1,n2,n3,D1,D2,D3);
  return pneu;
 }

 rational Simplex::vol()
 // simplex volume
 {
  if (HULL_TR) return 0; //HULLTRIANGLE is flat

  return volume(a->stor,b->stor,c->stor,d->stor);
 }


 Simpl_Triang::Simpl_Triang()
 {
  S1=NULL; S2=NULL;
  A=NULL; B=NULL; C=NULL;
 }

 Simpl_Triang::Simpl_Triang(sc_simplex sim1,sc_simplex sim2,sc_vertex Ap,sc_vertex Bp,sc_vertex Cp)
 {
  S1=sim1; S2=sim2; A=Ap; B=Bp; C=Cp;
 }
 Simpl_Triang::Simpl_Triang(const Simpl_Triang& S)
 {
  S1=S.S1; S2=S.S2; A=S.A; B=S.B; C=S.C;
 }


  void d3_simpl_complex::reset_flip_counters(){
   flk30=0; flk31=0; flk32=0; flk33=0; flk34=0; flk35=0;
   flk1=0; flk10=0; flk11=0; flk12=0;
  }

  void d3_simpl_complex::output_flip_counters(){
   cout << "Flips:\n";
   cout << "------\n";
   cout << "configuration 30/31/32/33/34/35:" << flk30 << " " << flk31 << " " << flk32 << " " << flk33 << " " 
        << flk34 << " " << flk35 << "\n";
   cout << "configuraton 1/10/11/12:" << flk1 << " " << flk10 << " " << flk11 << " " << flk12 << "\n";
  }

  d3_simpl_complex::d3_simpl_complex()
  {
    hull_last=NULL;
    reset_flip_counters();
  }

  d3_simpl_complex::~d3_simpl_complex()
  {
   sc_simplex z;
   forall(z,Sil) delete z;
   sc_vertex d;
   forall(d,Vert) delete d;
  }

  list<d3_rat_point> d3_simpl_complex::points()
  {
    list<d3_rat_point> L;
    sc_vertex v;

    forall(v,Vert) L.append(pos(v));

    return L;
  }
  
  void d3_simpl_complex::clear()
  {
    hull_last=NULL;
    sc_simplex z;
    forall(z,Sil) delete z;
    sc_vertex d;
    forall(d,Vert) delete d;
    Sil.clear();
    Vert.clear();
    reset_flip_counters();
  }

  void d3_simpl_complex::reset_markers()
  {
    sc_simplex akt;

    forall(akt,Sil) akt->Marker=-1;
  }

  sc_simplex d3_simpl_complex::get_simplex(sc_vertex v)
  {
    if (v->com_of != this) return NULL;
    return v->my;
  }

  sc_simplex d3_simpl_complex::opposite_simplex(sc_simplex S,int i)
  {
    if (S->com_of != this) return NULL; 
    if (i==1) return S->bcd;      
    if (i==2) return S->acd;
    if (i==3) return S->abd;
    if (i==4) return S->abc;
    return NULL;
  }

  sc_simplex d3_simpl_complex::opposite_simplex(sc_simplex S,sc_vertex v)
  {
   int i= S->index(v);
   if (i==0) return NULL;
   return opposite_simplex(S,i);
  }

  sc_vertex d3_simpl_complex::opposite_vertex(sc_simplex S,int i)
  {
   sc_simplex nb;
   sc_vertex v = 0;
   nb=opposite_simplex(S,i);
   if (nb==NULL) return NULL;
   else {
     switch(i) {
     case 1: v=nb->find_other(S->b,S->c,S->d);
             break;
     case 2: v=nb->find_other(S->a,S->c,S->d);
             break;
     case 3: v=nb->find_other(S->a,S->b,S->d);
             break;
     case 4: v=nb->find_other(S->a,S->b,S->c);
             break;
     }
     return v;
   }   
  }

  sc_vertex d3_simpl_complex::opposite_vertex(sc_simplex S,sc_vertex v)
  {
   int i= S->index(v);
   return (i==0) ? NULL : opposite_vertex(S,i);
  }

  sc_vertex d3_simpl_complex::add_vertex(d3_rat_point p)
  {
    sc_vertex z= new D3_vertex(p,this);
    z->it=Vert.append(z);
    return z;
  }

  sc_simplex d3_simpl_complex::add_simplex(sc_vertex a,sc_vertex b,sc_vertex c)
  { 
   if (a->com_of != this || b->com_of != this || c->com_of != this) return NULL;
   sc_simplex S= new Simplex(a,b,c); 
   S->com_of=this;
   S->it=Sil.append(S);
   hull_last=S;

   return S;      
  }

  sc_simplex d3_simpl_complex::add_simplex(sc_vertex a,sc_vertex b,sc_vertex c,sc_vertex d)
  { 
    if (a->com_of != this || b->com_of != this || 
        c->com_of != this || d->com_of != this) return NULL;   

    sc_simplex S= new Simplex(a,b,c,d);
    S->com_of=this;
    S->it = Sil.append(S);

    return S; 
  }

  sc_simplex d3_simpl_complex::search_simplex(d3_rat_point p) 
  {
   //should be improved ( "walk through" method or special data str.)
   sc_simplex akt;
   
   forall(akt,Sil){
     if (akt->in_simplex(p)) return akt;
   }

   return NULL;
  }

  sc_simplex d3_simpl_complex::search_simplex(sc_vertex v)
  {
   d3_rat_point p= v->stor;
   if (v->com_of != this) return NULL; // vertex has to be in the complex...
   return search_simplex(p);
  }

  sc_simplex d3_simpl_complex::wtsearch_simplex(d3_rat_point p)
  {
   if (Sil.empty()) return NULL; // no simplices in the complex...

   sc_simplex akt=Sil.head();

   do {
    if (akt->in_simplex(p)) return akt;
    else {
    // *akt verbessern...
    }
   } while (akt!=NULL);

   return akt;
  }

  sc_simplex d3_simpl_complex::wtsearch_simplex(sc_vertex v)
  {
   d3_rat_point p= v->stor;
   if (v->com_of != this) return NULL;
   return wtsearch_simplex(p);   
  }

  int d3_simpl_complex::remove_simplex(sc_simplex SR)
  {
    if (SR->com_of != this) return 0; 
 
    //if (SR==hull_last) cout << "Achtung! hull_last wird entfernt!\n";

    sc_simplex S1,S2,S3,S4;
    S1=SR->abc; S2=SR->abd; S3=SR->acd; S4=SR->bcd;

    if (S1 != NULL) S1->update(SR,NULL);
    if (S2 != NULL) S2->update(SR,NULL);
    if (S3 != NULL) S3->update(SR,NULL);
    if (S4 != NULL) S4->update(SR,NULL);
    
    // change vertex-links...
    if (SR->a->my == SR){ 
       if (SR->abc !=NULL) SR->a->my=SR->abc;
       else {
         if (SR->abd !=NULL) SR->a->my=SR->abd;
         else SR->a->my=SR->acd;
       }
    }
    if (SR->b->my == SR){ 
       if (SR->abc !=NULL) SR->b->my=SR->abc;
       else {
         if (SR->abd !=NULL) SR->b->my=SR->abd;
         else SR->b->my=SR->bcd;
       }
    }
    if (SR->c->my == SR){ 
       if (SR->abc !=NULL) SR->c->my=SR->abc;
       else {
         if (SR->acd !=NULL) SR->c->my=SR->acd;
         else SR->c->my=SR->bcd;
       }  
    }
    if (! SR->HULL_TR){
     if (SR->d->my == SR){ 
       if (SR->abd !=NULL) SR->d->my=SR->abd;
       else {
         if (SR->acd !=NULL) SR->d->my=SR->acd;
         else SR->d->my=SR->bcd;
       }      
     }
    }
      
    list_item i;
    i= SR->it;
    SR->com_of=NULL; delete SR;
    (Sil).del_item(i);
    
    return 1;
  }

  bool d3_simpl_complex::flippable(sc_simplex S1, sc_vertex v)
  {
    sc_vertex v2 = opposite_vertex(S1,v); 

    if (v2==NULL) return false;
    
    d3_rat_point Ap= S1->a->stor;
    d3_rat_point Bp= S1->b->stor;
    d3_rat_point Cp= S1->c->stor;
    d3_rat_point Ep= v2->stor;

    if (!S1->HULL_TR){
     d3_rat_point Dp= S1->d->stor;
     return inside_sphere(Ap,Bp,Cp,Dp,Ep);
    }
    else { // Hulltr.
     if (coplanar(Ap,Bp,Cp,Ep)){
        return test_inside(Ap,Bp,Cp,Ep);
     }
    }
    return false;
  }

  bool d3_simpl_complex::flippable(sc_simplex S1, sc_simplex S2,Simpl_Triang& Tr)
  // is common triangle flippable ?
  {
    int wert=common_triangle(S1,S2,Tr);
    if (wert==0) return false; //no common tr.

    sc_vertex v2= S2->find_other(Tr.A,Tr.B,Tr.C); 
    if (v2==NULL) return false;

    d3_rat_point Ap= S1->a->stor;
    d3_rat_point Bp= S1->b->stor;
    d3_rat_point Cp= S1->c->stor;
    d3_rat_point Ep= v2->stor;

    if (! S1->HULL_TR){
     d3_rat_point Dp= S1->d->stor;
     return inside_sphere(Ap,Bp,Cp,Dp,Ep);
    }
    else { // Hulltr.
     if (coplanar(Ap,Bp,Cp,Ep)){
        return test_inside(Ap,Bp,Cp,Ep);
     }
    }
    return false;
  }

  void d3_simpl_complex::init_dia(bool w)
  {
   sc_simplex akt;
   forall(akt,Sil){
    akt->abcdia=w;akt->abddia=w;akt->acddia=w;akt->bcddia=w;
   }
  }

  int  d3_simpl_complex::set_dia_nondia()
  // set non-diagramedge - informationsd
  {
    sc_simplex akt,other;
    d3_rat_point Ap,Bp,Cp,Dp,op;
    sc_vertex v;
    int ND_SETS=0;
    
    forall(akt,Sil){
      if (! akt->HULL_TR){
        Ap= akt->a->stor; 
        Bp= akt->b->stor; 
        Cp= akt->c->stor; 
        Dp= akt->d->stor;
        other=akt->abc;
        if (other != NULL && !other->HULL_TR){
          v=other->find_other(akt->a,akt->b,akt->c); op=v->stor;
          if (on_sphere(Ap,Bp,Cp,Dp,op)) { akt->abcdia=false; ND_SETS++;}
        }
        other=akt->abd;
        if (other != NULL && !other->HULL_TR){
          v=other->find_other(akt->a,akt->b,akt->d); op=v->stor;
          if (on_sphere(Ap,Bp,Cp,Dp,op)) { akt->abddia=false; ND_SETS++;} 
        }
        other=akt->acd;
        if (other != NULL && !other->HULL_TR){
          v=other->find_other(akt->a,akt->c,akt->d); op=v->stor;
          if (on_sphere(Ap,Bp,Cp,Dp,op)) { akt->acddia=false; ND_SETS++;}
        }
        other=akt->bcd;         
        if (other != NULL && !other->HULL_TR){
          v=other->find_other(akt->b,akt->c,akt->d); op=v->stor;
          if (on_sphere(Ap,Bp,Cp,Dp,op)) { akt->bcddia=false; ND_SETS++;}
        }   
      }
    }
    return ND_SETS;
    
  }

  bool d3_simpl_complex::local_delaunay(sc_simplex S1)
  // is  simplex S1 "local delaunay" ?
  {
    bool wert;
    wert=flippable(S1,S1->a);
    if (wert) return false;
    wert=flippable(S1,S1->b);
    if (wert) return false;
    wert=flippable(S1,S1->c);
    if (wert) return false;
    wert=flippable(S1,S1->d);
    if (wert) return false;  

    return true;  
  }

  bool d3_simpl_complex::global_delaunay(sc_simplex fst)
  {
    sc_vertex ac;
    bool flag=true;
             
    forall(ac,Vert){
     if (fst->insphere(ac->stor)) flag=false;
    }

    return flag;    
  }

  int d3_simpl_complex::get_link_index(sc_simplex S1,sc_simplex S2)
  {
    if (S1->com_of != this || S2->com_of !=this) return -1;
    if (S1 == S2) return -2;

    if (S1->abc==S2) return 1;
    if (S1->abd==S2) return 2;
    if (S1->acd==S2) return 3;
    if (S1->bcd==S2) return 4;

    return 0;
  }
  
  sc_simplex d3_simpl_complex::set_link(sc_simplex S1,int i,sc_simplex S2,int j)
  {
    if (S1->com_of != this) return NULL;
    if (S2->com_of != this) return NULL; 
    if ( i>4 || i<1 || j>4 || j<1) return NULL;
    S1->set_link(S2,i);
    S2->set_link(S1,j);

    return S1;
  }

  sc_simplex d3_simpl_complex::set_link(sc_simplex S1,sc_simplex S2, sc_vertex v1, sc_vertex v2, sc_vertex v3)
  // (*v1),(*v2),(*v3) the common vertices...
  {
    sc_vertex os1,os2;

    os1= S1->find_other(v1,v2,v3);
    os2= S2->find_other(v1,v2,v3);
    int i,j;

    if (os1 !=NULL) i= S1->index(os1); else i=4; //abc
    if (os2 !=NULL) j= S2->index(os2); else j=4; //abc

    return set_link(S1,i,S2,j);
  }

  sc_simplex d3_simpl_complex::set_link(sc_simplex S1,sc_vertex i,sc_simplex S2,sc_vertex j)
  {
    int i2,j2;
    if (i !=NULL) i2= S1->index(i); else i2=4; 
    if (j !=NULL) j2= S2->index(j); else j2=4; 
    if (i2==0 || j2==0) return NULL;
    
    return set_link(S1,i2,S2,j2);
     
  }  

  bool d3_simpl_complex::check_vert_sim_links()
  {
   sc_vertex v;
   sc_simplex akt;
   forall(v,Vert){
     if (v->my == NULL) return false;
     akt= v->my;
     if (akt->index(v) == 0 || akt->com_of != this) return false;
   }
   return true;
  }

  int d3_simpl_complex::check_delaunay()
  {
   //  all simplices local delaunay ?
   sc_simplex akt;
   bool tf; 
   //bool haupt=true;
   int counter=0;

   forall(akt,Sil){
    tf=local_delaunay(akt);
    if (tf==false) { /*haupt=false;*/ counter++; }
   }

   return counter;
  }

  int join_or_link(GRAPH<d3_rat_sphere,int>& Gout,node n1,node n2)
  {
   d3_rat_sphere s1,s2;
   s1=Gout[n1];
   s2=Gout[n2];

   Gout.new_edge(n1,n2); return 0; 
  }

  int join(GRAPH<d3_rat_point,int>& Gout,node n1,node n2)
  {
   d3_rat_point s1,s2;
   s1=Gout[n1]; s2=Gout[n2];

   if (n1==n2) return 0;
    
   if (s1==s2){
     Gout.merge_nodes(n1,n2);
     return 1;
   }
   else return 0;
  }
  

  bool d3_simpl_complex::compute_voronoi(GRAPH<d3_rat_sphere,int>& Gout)
  {
    int bz= check_delaunay();
    if (bz>0) return false;

    Gout.clear();
    sc_simplex akt;
    d3_rat_sphere *neu;
    d3_rat_point ap,bp,cp,dp;
    node nn;
    int w;

    forall(akt,Sil){
      ap= akt->a->stor; 
      bp= akt->b->stor;
      cp= akt->c->stor;

      if (akt->HULL_TR){ 
       neu= new d3_rat_sphere(ap,bp,cp,cp);
      }
      else {
       dp= akt->d->stor;
       neu= new d3_rat_sphere(ap,bp,cp,dp);
      }

      nn=Gout.new_node(*neu); 
      akt->helper= (void*)nn;
    }

    node n,n2;
    sc_simplex s1;

    forall(akt,Sil){
      n= (node)(akt->helper);
      s1= akt->abc;
      if (s1 != NULL) { n2=(node)(s1->helper);
                        w=join_or_link(Gout,n,n2);
                        if (w==1) { s1->helper= (void*)(n); } // merge...
                       }
      s1= akt->abd;
      if (s1 != NULL) { n2=(node)(s1->helper);
                        w=join_or_link(Gout,n,n2);
                        if (w==1) { s1->helper= (void*)(n); } // merge...
                       }
      s1= akt->acd;
      if (s1 != NULL) { n2=(node)(s1->helper);
                        w=join_or_link(Gout,n,n2);
                        if (w==1) { s1->helper= (void*)(n); } // merge...
                       }
      s1= akt->bcd;
      if (s1 != NULL) { n2=(node)(s1->helper); 
                        w=join_or_link(Gout,n,n2); 
                        if (w==1) { s1->helper= (void*)(n); } // merge...
                       }
    }

    return true;
  }

  bool d3_simpl_complex::get_incident_simplices(sc_vertex v,list<sc_simplex>& ret)
  {
   if (v->com_of != this) { return false; }
   if (v->my == NULL) { return false; } 

   sc_simplex start= v->my;
   sc_simplex akt;
   sc_simplex l1,l2,l3,l4;
   reset_markers();
   start->Marker=100;
   stack<sc_simplex> CAND;
   CAND.push(start);

   while (! CAND.empty()){
     akt=CAND.pop();
     ret.append(akt);
     l1=akt->abc; l2=akt->abd; l3=akt->acd; l4=akt->bcd;
     if (l1 != NULL && (l1->Marker ==-1) && (l1->index(v)!=0)) { CAND.push(l1); l1->Marker=100; }
     if (l2 != NULL && (l2->Marker ==-1) && (l2->index(v)!=0)) { CAND.push(l2); l2->Marker=100; }
     if (l3 != NULL && (l3->Marker ==-1) && (l3->index(v)!=0)) { CAND.push(l3); l3->Marker=100; }
     if (l4 != NULL && (l4->Marker ==-1) && (l4->index(v)!=0)) { CAND.push(l4); l4->Marker=100; }
   }   

   return true;
  }

  bool d3_simpl_complex::get_incident_points(sc_vertex v,list<d3_rat_point>& dl)
  {
   list<sc_simplex> si;
   sc_simplex akt;
   d3_rat_point pneu;

   bool rw=get_incident_simplices(v,si);
   if (! rw) return false;

   forall(akt,si){
      if (akt->HULL_TR) pneu= akt->circle_midpoint();
      else pneu= akt->sphere_midpoint();
      
      dl.append(pneu);
   }
   return true;
  }

  void d3_simpl_complex::kill_vlists()
  {
    sc_vertex v;
    void* zeig;
    forall(v,Vert){
        zeig=v->helper; if (zeig!=NULL) delete ((list<d3_rat_point>*)(zeig));
    }
  }

  bool d3_simpl_complex::make_vlists()
  {
    int bz= check_delaunay();

    assert(bz == 0);

    list<d3_rat_point>* aktli;
    sc_vertex v;
    forall(v,Vert){
      aktli= new list<d3_rat_point>;
      v->helper= (void*) aktli;
    }

    sc_simplex akt;

    d3_rat_point pneu;
    d3_rat_point phelp1,phelp2;
    rat_vector rv;

    void * zeig;

    forall(akt,Sil){
      if (akt->HULL_TR){ 
       pneu= akt->circle_midpoint();
       /*
       //compute here some kind of "ray"
       sc_simplex nb=akt->abc;
       if (nb==NULL) pneu= akt->circle_midpoint();
       else {
        phelp1= nb->sphere_midpoint();
        phelp2= akt->circle_midpoint();
        rv=(phelp2-phelp1);
        rv=rational(10.0)*rv;
        pneu=phelp1+rv;
       }
       */
      }
      else {
       pneu= akt->sphere_midpoint();
      }
      if (akt->HULL_TR){
        zeig=akt->a->helper; ((list<d3_rat_point>*)zeig)->append(pneu);
        zeig=akt->b->helper; ((list<d3_rat_point>*)zeig)->append(pneu);
        zeig=akt->c->helper; ((list<d3_rat_point>*)zeig)->append(pneu);
      }
      else {
        zeig=akt->a->helper; ((list<d3_rat_point>*)zeig)->append(pneu);
        zeig=akt->b->helper; ((list<d3_rat_point>*)zeig)->append(pneu);
        zeig=akt->c->helper; ((list<d3_rat_point>*)zeig)->append(pneu);
        zeig=akt->d->helper; ((list<d3_rat_point>*)zeig)->append(pneu);
      }
      
    }  
    // show only closed voronoi cells...
    forall(akt,Sil){
      if (akt->HULL_TR){
        zeig=akt->a->helper; ((list<d3_rat_point>*)zeig)->clear();
        zeig=akt->b->helper; ((list<d3_rat_point>*)zeig)->clear();
        zeig=akt->c->helper; ((list<d3_rat_point>*)zeig)->clear();
      }
    }
    
    return true;
  }

  bool d3_simpl_complex::compute_voronoi(GRAPH<d3_rat_point,int>& Gout,bool hflag) 
  {
    int bz= check_delaunay();
    if (bz>0) return false; 

    // compute VD ...
    Gout.clear();
    sc_simplex akt;

    d3_rat_point pneu;
    node neu;

    forall(akt,Sil){
     if (! akt->HULL_TR || hflag) {
      if (akt->HULL_TR){ // no voronoi nodes...
       pneu= akt->circle_midpoint();
       assert(coplanar(pneu,akt->a->stor,akt->b->stor,akt->c->stor));
      }
      else { // voronoi nodes ...
       pneu= akt->sphere_midpoint();
      }

      neu=Gout.new_node(pneu);
      akt->helper= (void*)neu;
     }
    }

    node n,n2;
    sc_simplex s1;
    int w;
    edge e1,e2;

    forall(akt,Sil){
     if (! akt->HULL_TR || hflag) {
       n= (node)(akt->helper);
       s1= akt->abc;
       if ((s1 != NULL ) && (! s1->HULL_TR || hflag))
       { n2= (node)(s1->helper); e1=Gout.new_edge(n,n2); e2=Gout.new_edge(n2,n); Gout.set_reversal(e1,e2); }
       s1= akt->abd;
       if ((s1 != NULL ) && (! s1->HULL_TR || hflag)) 
       { n2= (node)(s1->helper); e1=Gout.new_edge(n,n2); e2=Gout.new_edge(n2,n); Gout.set_reversal(e1,e2); }
       s1= akt->acd;
       if ((s1 != NULL ) && (! s1->HULL_TR || hflag)) 
       { n2= (node)(s1->helper); e1=Gout.new_edge(n,n2); e2=Gout.new_edge(n2,n); Gout.set_reversal(e1,e2); }
       s1= akt->bcd;
       if ((s1 != NULL ) && (! s1->HULL_TR || hflag)) 
       { n2= (node)(s1->helper); e1=Gout.new_edge(n,n2); e2=Gout.new_edge(n2,n); Gout.set_reversal(e1,e2); }
     }
    }
   
    // try to merge nodes...
    sc_simplex akt2;
    forall(akt,Sil){
     if (! akt->HULL_TR || hflag) {
      n= (node)(akt->helper);
      s1= akt->abc;
      if ((s1 != NULL) && (! s1->HULL_TR || hflag)) 
                      { n2= (node)(s1->helper); 
                        w=join(Gout,n,n2);
                        if (w==1) { s1->helper= (void*)(n);
			forall(akt2,Sil) { 
                          if ((node)akt2->helper==n2) 
                              akt2->helper=(void*)n; 
                         }
                        } // merge...
                      }
      s1= akt->abd;
      if ((s1 != NULL) && (! s1->HULL_TR || hflag)) 
                      { n2= (node)(s1->helper);
                        w=join(Gout,n,n2);
                        if (w==1) { s1->helper= (void*)(n);
                        forall(akt2,Sil) { 
                          if ((node)akt2->helper==n2) 
                             akt2->helper=(void*)n; 
                         }
                        } // merge...
                      }
      s1= akt->acd;
      if ((s1 != NULL) && (! s1->HULL_TR || hflag)) 
                      { n2= (node)(s1->helper);
                        w=join(Gout,n,n2);
                        if (w==1) { s1->helper= (void*)(n); 
                        forall(akt2,Sil) { 
                          if ((node)akt2->helper==n2) 
                             akt2->helper=(void*)n; 
                         }
                        } // merge...
                       }
      s1= akt->bcd;
      if ((s1 != NULL) && (! s1->HULL_TR || hflag)) 
                      { n2= (node)(s1->helper); 
                        w=join(Gout,n,n2);
                        if (w==1) { s1->helper= (void*)(n);
                        forall(akt2,Sil) { 
                           if ((node)akt2->helper==n2) 
                              akt2->helper=(void*)n; 
                         }
                        } // merge...
                       }
     }
    }
 
    return true;
  }

  void d3_simpl_complex::compute_graph(sc_simplex sakt,
                                       GRAPH<d3_rat_point,int>& Gout)
  {
   // computes a GRAPH Gout  containing (*sakt) and its neighbours

   d3_rat_point a,b,c,d;

   Gout.clear();

   list<sc_simplex> me_and_nb;
   me_and_nb.push(sakt);
   if (sakt->abc != NULL) me_and_nb.push(sakt->abc);
   if (sakt->abd != NULL) me_and_nb.push(sakt->abd);
   if (sakt->acd != NULL) me_and_nb.push(sakt->acd);
   if (sakt->bcd != NULL) me_and_nb.push(sakt->bcd);

   sc_simplex S;
   forall(S,me_and_nb){
    a=S->a->stor; 
    b=S->b->stor; 
    c=S->c->stor; 
    if (!S->HULL_TR) d=S->d->stor;

    node o1=Gout.new_node(a); 
    node o2=Gout.new_node(b); 
    node o3=Gout.new_node(c);
    node o4 = 0;
    if (!S->HULL_TR) o4=Gout.new_node(d);

    edge e1=Gout.new_edge(o1,o2); 
    edge e2=Gout.new_edge(o2,o1); 
    Gout.set_reversal(e1,e2);

    e1=Gout.new_edge(o1,o3); 
    e2=Gout.new_edge(o3,o1); 
    Gout.set_reversal(e1,e2);

    if (!S->HULL_TR){
     e1=Gout.new_edge(o1,o4); 
     e2=Gout.new_edge(o4,o1); 
     Gout.set_reversal(e1,e2);
    }

    e1=Gout.new_edge(o2,o3); 
    e2=Gout.new_edge(o3,o2); 
    Gout.set_reversal(e1,e2);

    if (!S->HULL_TR){
     e1=Gout.new_edge(o2,o4); 
     e2=Gout.new_edge(o4,o2); 
     Gout.set_reversal(e1,e2);
     e1=Gout.new_edge(o3,o4); 
     e2=Gout.new_edge(o4,o3); 
     Gout.set_reversal(e1,e2);
    }
   }   
  }

  void d3_simpl_complex::compute_surface_graph(GRAPH<d3_rat_point,int>& Gout)
  //  computes a GRAPH Gout only containing the HullTriangles of the complex
  {
   Gout.clear();

   sc_simplex S;
   forall(S,Sil){

     if (!S->HULL_TR) continue;

     d3_rat_point a=S->a->stor;
     d3_rat_point b=S->b->stor;
     d3_rat_point c=S->c->stor;

     node o1=Gout.new_node(a); 
     node o2=Gout.new_node(b); 
     node o3=Gout.new_node(c);

     edge e1=Gout.new_edge(o1,o2); 
     edge e2=Gout.new_edge(o2,o1); 
     Gout.set_reversal(e1,e2);

     e1=Gout.new_edge(o1,o3); 
     e2=Gout.new_edge(o3,o1); 
     Gout.set_reversal(e1,e2);

     e1=Gout.new_edge(o2,o3); 
     e2=Gout.new_edge(o3,o2); 
     Gout.set_reversal(e1,e2);
   } 

  }


  void d3_simpl_complex::compute_graph(GRAPH<d3_rat_point,int>& Gout)
  {
   node o1,o2,o3,o4=0;
   edge e1,e2;
   sc_simplex S;
   d3_rat_point a,b,c,d;
   Gout.clear();

   forall(S,Sil){
    a=S->a->stor; 
    b=S->b->stor; 
    c=S->c->stor;
    if (! S->HULL_TR) d=S->d->stor;

    o1=Gout.new_node(a); 
    o2=Gout.new_node(b); 
    o3=Gout.new_node(c);
    if (! S->HULL_TR) o4=Gout.new_node(d);

    e1=Gout.new_edge(o1,o2); 
    e2=Gout.new_edge(o2,o1); 
    Gout.set_reversal(e1,e2);
    e1=Gout.new_edge(o1,o3); 
    e2=Gout.new_edge(o3,o1); 
    Gout.set_reversal(e1,e2);
    if (! S->HULL_TR){
     e1=Gout.new_edge(o1,o4); 
     e2=Gout.new_edge(o4,o1); 
     Gout.set_reversal(e1,e2);
    }
    e1=Gout.new_edge(o2,o3); 
    e2=Gout.new_edge(o3,o2); 
    Gout.set_reversal(e1,e2);

    if (! S->HULL_TR){
     e1=Gout.new_edge(o2,o4); 
     e2=Gout.new_edge(o4,o2); 
     Gout.set_reversal(e1,e2);

     e1=Gout.new_edge(o3,o4); 
     e2=Gout.new_edge(o4,o3); 
     Gout.set_reversal(e1,e2);
    }
   } 
  }

  void d3_simpl_complex::compute_graph(GRAPH<d3_rat_point,int>& Gout,
                                       set<sc_vertex>& DS,list<edge>& erg)
  {
    // fuer d3-window einen ausgabefaehigen Graphen erstellen...
    // Verbindungen zwischen vertices im set als edge-liste zurück, 
    // um Farbmark. zu ermöglichen
   node o1,o2,o3,o4=0;
   edge e1,e2;
   sc_simplex S;
   d3_rat_point a,b,c,d;
   bool aw,bw,cw,dw=false;
   Gout.clear();

   forall(S,Sil){
    a=S->a->stor; 
    b=S->b->stor; 
    c=S->c->stor;
    aw= DS.member(S->a); 
    bw= DS.member(S->b); 
    cw= DS.member(S->c);

    if (! S->HULL_TR) { d=S->d->stor; dw= DS.member(S->d); }

    o1=Gout.new_node(a); 
    o2=Gout.new_node(b); 
    o3=Gout.new_node(c);
    if (! S->HULL_TR) o4=Gout.new_node(d);

    e1=Gout.new_edge(o1,o2); 
    e2=Gout.new_edge(o2,o1); 
    Gout.set_reversal(e1,e2);
    if (aw && bw) { erg.append(e1); erg.append(e2); }

    e1=Gout.new_edge(o1,o3); 
    e2=Gout.new_edge(o3,o1); 
    Gout.set_reversal(e1,e2);
    if (aw && cw) { erg.append(e1); erg.append(e2); }

    if (! S->HULL_TR){
     e1=Gout.new_edge(o1,o4); 
     e2=Gout.new_edge(o4,o1); 
     Gout.set_reversal(e1,e2);
     if (aw && dw) { erg.append(e1); erg.append(e2); }
    }
    e1=Gout.new_edge(o2,o3); 
    e2=Gout.new_edge(o3,o2); 
    Gout.set_reversal(e1,e2);
    if (bw && cw) { erg.append(e1); erg.append(e2); }
    if (! S->HULL_TR){
     e1=Gout.new_edge(o2,o4); 
     e2=Gout.new_edge(o4,o2); 
     Gout.set_reversal(e1,e2);
     if (bw && dw) { erg.append(e1); erg.append(e2); }
     e1=Gout.new_edge(o3,o4); 
     e2=Gout.new_edge(o4,o3); 
     Gout.set_reversal(e1,e2);
     if (cw && dw) { erg.append(e1); erg.append(e2); }
    }
   }
  }


bool in_sim(const d3_rat_point& p1,const d3_rat_point& p2,
            const d3_rat_point& p3,const d3_rat_point& cand)
{
 array<d3_rat_point> AT(3);
 AT[0]=p1; AT[1]=p2; AT[2]=p3;
 return contained_in_simplex(AT,cand);
}

int d3_simpl_complex::common_triangle(sc_simplex S1, sc_simplex S2, Simpl_Triang& T)
// attention! neighbour settings have to be correct for this function!
{
 int wert=get_link_index(S1,S2);
 if (wert==0) return 0;
 T.S1=S1;
 T.S2=S2;

 switch(wert){
 case 1:
  T.A=S1->a; T.B=S1->b; T.C=S1->c;
  break;
 case 2:
  if (S1->HULL_TR && S2->HULL_TR){
    T.A=S1->a; T.B=S1->b; T.C=S1->b;
  }
  else {
    T.A=S1->a; T.B=S1->b; T.C=S1->d;
  }
  break;
 case 3:
  if (S1->HULL_TR && S2->HULL_TR){
    T.A=S1->a; T.B=S1->c; T.C=S1->c;
  }
  else {
    T.A=S1->a; T.B=S1->c; T.C=S1->d;
  }
  break;
 case 4:
  if (S1->HULL_TR && S2->HULL_TR){
    T.A=S1->b; T.B=S1->c; T.C=S1->c;
  }
  else {
    T.A=S1->b; T.B=S1->c; T.C=S1->d;
  }
  break;
 }
 
 return wert;
}

int d3_simpl_complex::configuration(sc_simplex S1, sc_simplex S2, Simpl_Triang& T)
// see B. Joe (construction of 3d Delaunay triangulations using local transformations)
// for desription of configurations
{
 sc_vertex v1_other,v2_other;
 d3_rat_point ap,bp,cp,dp,ep;

 ap = T.A->stor; 
 bp = T.B->stor; 
 cp = T.C->stor;

 v1_other= S1->find_other(T.A,T.B,T.C);
 if (v1_other==NULL) return 0;
 dp= v1_other->stor;
 v2_other= S2->find_other(T.A,T.B,T.C);
 if (v2_other==NULL) return 0;
 ep= v2_other->stor;

 int o1=orientation(ap,bp,dp,ep);
 int o2=orientation(cp,ap,dp,ep);
 int o3=orientation(bp,cp,dp,ep);

 sc_vertex f1,f2;
 sc_simplex sim1,sim2;

 if (o1==0 || o2==0 || o3==0){ // configuration 3 or 4 or 5
   if (o1==0){
     if (collinear(dp,ap,ep) || collinear(dp,bp,ep)) return 4; //  conf. 4
     if (in_sim(dp,ep,bp,ap) || in_sim(dp,ep,ap,bp)) return 5; //  conf. 5
     
     f1=opposite_vertex(S1,T.C);
     f2=opposite_vertex(S2,T.C);

     // configuration 3
     if (f1==NULL && f2==NULL) return 30;
     if (f1==f2) return 31;
   }
   if (o2==0){
     if (collinear(dp,ap,ep) || collinear(dp,cp,ep)) return 4; // conf. 4
     if (in_sim(cp,dp,ep,ap) || in_sim(ap,dp,ep,cp)) return 5; // conf. 5

     f1=opposite_vertex(S1,T.B);
     f2=opposite_vertex(S2,T.B);

     // configuration 3
     if (f1==NULL && f2==NULL) return 32;
     if (f1==f2) return 33;
   }
   if (o3==0){
     if (collinear(dp,bp,ep) || collinear(dp,cp,ep)) return 4; // conf. 4
     if (in_sim(bp,dp,ep,cp) || in_sim(dp,ep,cp,bp)) return 5; // conf. 5

     f1=opposite_vertex(S1,T.A);
     f2=opposite_vertex(S2,T.A);

     // configuration 3
     if (f1==NULL && f2==NULL) return 34;
     if (f1==f2) return 35;
   }   
   return 0;
   
 }
 else { // configuration 1 or 2
  bool cs1=false,cs2=false,cs3=false;
  contained_in_simplex(bp,cp,dp,ep,ap);  
  if (!cs1) cs2=contained_in_simplex(ap,cp,dp,ep,bp);
  if (!cs1 && !cs2) cs3=contained_in_simplex(ap,bp,dp,ep,cp);   

  if (cs1 || cs2 || cs3) return 2; // configuration 2
  // configuration 1

  d3_rat_point mi= midpoint(midpoint(ap,bp),cp);
  int omi=orientation(ap,bp,dp,mi);

  if (o1==o2 && o2==o3) return 1; //abcde convex...
 
  if (o1!=omi){
   sim1= opposite_simplex(S1,T.C);
   sim2= opposite_simplex(S2,T.C);
   if ((sim1==sim2) && (sim1 !=NULL)) return 10; 
  }
  if (o2!=omi){
   sim1= opposite_simplex(S1,T.B);
   sim2= opposite_simplex(S2,T.B);
   if ((sim1==sim2) && (sim1 !=NULL)) return 11; 
  }
  if (o3!=omi){
   sim1= opposite_simplex(S1,T.A);
   sim2= opposite_simplex(S2,T.A);
   if ((sim1==sim2) && (sim1 !=NULL)) return 12; 
  }

  return 0;                   // configuration 1, but not transformable...
 }

}

void d3_simpl_complex::link_save(sc_simplex SI, sc_simplex pt1, sc_simplex pt2, list<sc_simplex>& L)
{
 sc_simplex akt;
 list<sc_simplex> nb= SI->all_neighbours();
 forall(akt,nb){
  if (akt!=pt1 && akt!=pt2) L.append(akt);
  akt->update(SI,NULL);
 }
}

void d3_simpl_complex::link_korr(sc_simplex SI, list<sc_simplex>& L,list<Simpl_Triang>& TRL)
{
  sc_simplex akt;
  Simpl_Triang atl;

  int fl;
  if (SI->HULL_TR){
    forall(akt,L) if (akt->HULL_TR) SI->link_new(akt);
  }
  else {
    forall(akt,L) {
      fl=SI->link_new(akt);
      if (fl!=0) {
        atl.S1=SI;
        atl.S2=akt;
        switch(fl){ 
	case 1: atl.A=SI->a; atl.B=SI->b; atl.C=SI->c; break; //abc
	case 2: atl.A=SI->a; atl.B=SI->b; atl.C=SI->d; break; //abd
	case 3: atl.A=SI->a; atl.B=SI->c; atl.C=SI->d; break; //acd
	case 4: atl.A=SI->b; atl.B=SI->c; atl.C=SI->d; break; //bcd
        }
        TRL.append(atl);
      }
    }
  }
}

void d3_simpl_complex::link_korr(sc_simplex SI, list<sc_simplex>& L,queue<Simpl_Triang>& TQ,sc_vertex PV)
// correct links after a flip of SI
{
  sc_simplex akt;
  Simpl_Triang atl;

  int fl;
  if (SI->HULL_TR){
    forall(akt,L) if (akt->HULL_TR) SI->link_new(akt);
  }
  else {
    forall(akt,L) {
      fl=SI->link_new(akt);
      if (fl!=0) {
        atl.S1=SI;
        atl.S2=akt;
        switch(fl){
	case 1: atl.A=SI->a; atl.B=SI->b; atl.C=SI->c; break; //abc
	case 2: atl.A=SI->a; atl.B=SI->b; atl.C=SI->d; break; //abd
	case 3: atl.A=SI->a; atl.B=SI->c; atl.C=SI->d; break; //acd
	case 4: atl.A=SI->b; atl.B=SI->c; atl.C=SI->d; break; //bcd
        }
        if (atl.A !=PV && atl.B !=PV && atl.C !=PV) TQ.append(atl);
      }
    }
  }
}

void d3_simpl_complex::flip_konf3(sc_simplex S1, sc_simplex S2,
                                  d3_simpl_complex* Cl,int konf,
                                  Simpl_Triang& T,queue<Simpl_Triang>& TQ,
                                  sc_vertex PV)
{ 
  list<sc_simplex> SN;
  list<sc_simplex> PSN; 

  sc_simplex Ps1=0, Ps2=0; 

  sc_vertex av,bv,cv,dv,ev; 

  sc_vertex fv; //for configs 31/33/35
  av=T.A; bv=T.B; cv=T.C;
  dv= S1->find_other(T.A,T.B,T.C); ev= S2->find_other(T.A,T.B,T.C);

  switch (konf) {
    case 30:
     Ps1=Cl->opposite_simplex(S1,T.C); Ps2=Cl->opposite_simplex(S2,T.C); break;
    case 31:
     Ps1=Cl->opposite_simplex(S1,T.C); Ps2=Cl->opposite_simplex(S2,T.C); break;
    case 32:
     Ps1=Cl->opposite_simplex(S1,T.B); Ps2=Cl->opposite_simplex(S2,T.B); break;
    case 33:
     Ps1=Cl->opposite_simplex(S1,T.B); Ps2=Cl->opposite_simplex(S2,T.B); break;
    case 34:
     Ps1=Cl->opposite_simplex(S1,T.A); Ps2=Cl->opposite_simplex(S2,T.A); break;
    case 35:
     Ps1=Cl->opposite_simplex(S1,T.A); Ps2=Cl->opposite_simplex(S2,T.A); break;
  }

  // save old links
  link_save(S1,S2,Ps1,SN); link_save(S2,S1,Ps2,SN);
  if (Ps1 != NULL) link_save(Ps1,Ps2,S1,PSN);
  if (Ps2 != NULL) link_save(Ps2,Ps1,S2,PSN);
  
  if (konf==30 || konf==32 || konf==34){

    S1->clear_links(); S2->clear_links();
    if (Ps1 !=NULL) Ps1->clear_links(); 
    if (Ps2 !=NULL) Ps2->clear_links();

    switch (konf){
    case 30:
     Cl->flk30++;
     S1->change(av,cv,dv,ev);
     S2->change(bv,cv,dv,ev);
     Cl->set_link(S1,S2,cv,dv,ev);
     if (Ps1 !=NULL) Ps1->change(av,dv,ev);
     if (Ps2 !=NULL) Ps2->change(bv,dv,ev);
     if (Ps1 !=NULL && Ps2!=NULL)  Cl->set_link(Ps1,Ps2,dv,dv,ev); 

     if (Ps1 !=NULL) Cl->set_link(S1,Ps1,av,dv,ev); 
     if (Ps2 !=NULL) Cl->set_link(S2,Ps2,bv,dv,ev); 
     break;
    case 32: 
     Cl->flk32++;
     S1->change(av,bv,dv,ev);
     S2->change(cv,bv,dv,ev);
     Cl->set_link(S1,S2,bv,dv,ev);
     if (Ps1 !=NULL) Ps1->change(av,dv,ev);
     if (Ps2 !=NULL) Ps2->change(cv,dv,ev);
     if (Ps1 !=NULL && Ps2!=NULL) Cl->set_link(Ps1,Ps2,dv,dv,ev);

     if (Ps1 !=NULL) Cl->set_link(S1,Ps1,av,dv,ev);
     if (Ps2 !=NULL) Cl->set_link(S2,Ps2,cv,dv,ev);
     break;
    case 34: 
     Cl->flk34++;
     S1->change(bv,av,dv,ev);
     S2->change(cv,av,dv,ev);
     Cl->set_link(S1,S2,av,dv,ev);
     if (Ps1 !=NULL) Ps1->change(bv,dv,ev);
     if (Ps2 !=NULL) Ps2->change(cv,dv,ev);
     if (Ps1 !=NULL && Ps2 !=NULL) Cl->set_link(Ps1,Ps2,dv,dv,ev); 

     if (Ps1 !=NULL) Cl->set_link(S1,Ps1,bv,dv,ev);
     if (Ps2 !=NULL) Cl->set_link(S2,Ps2,cv,dv,ev);
     break;
    }
  }
  else { // konf==31/33/35

    switch (konf){
    case 31: 
     Cl->flk31++;
     fv=Cl->opposite_vertex(S1,T.C);
     S1->clear_links(); S2->clear_links(); 
     if (Ps1 !=NULL) Ps1->clear_links(); 
     if (Ps2 !=NULL) Ps2->clear_links();
     S1->change(av,cv,dv,ev);
     S2->change(bv,cv,dv,ev);
     Cl->set_link(S1,S2,cv,dv,ev);
     if (Ps1 !=NULL) Ps1->change(av,fv,dv,ev);
     if (Ps2 !=NULL) Ps2->change(bv,fv,dv,ev);
     if (Ps1 !=NULL && Ps2!=NULL) Cl->set_link(Ps1,Ps2,fv,dv,ev);

     if (Ps1 !=NULL) Cl->set_link(S1,Ps1,av,dv,ev);
     if (Ps2 !=NULL) Cl->set_link(S2,Ps2,bv,dv,ev);
     break;
    case 33:
     Cl->flk33++;
     fv=Cl->opposite_vertex(S1,T.B);
     S1->clear_links(); S2->clear_links(); 
     if (Ps1 !=NULL) Ps1->clear_links();
     if (Ps2 !=NULL) Ps2->clear_links();
     S1->change(av,bv,dv,ev);
     S2->change(cv,bv,dv,ev);
     Cl->set_link(S1,S2,bv,dv,ev);
     if (Ps1 !=NULL) Ps1->change(av,fv,dv,ev);
     if (Ps2 !=NULL) Ps2->change(cv,fv,dv,ev);
     if (Ps1 !=NULL && Ps2!=NULL) Cl->set_link(Ps1,Ps2,fv,dv,ev);
     if (Ps1 !=NULL) Cl->set_link(S1,Ps1,av,dv,ev);
     if (Ps2 !=NULL) Cl->set_link(S2,Ps2,cv,dv,ev);
     break;
    case 35: 
     Cl->flk35++;
     fv=Cl->opposite_vertex(S1,T.A);
     S1->clear_links(); S2->clear_links(); 
     if (Ps1 !=NULL) Ps1->clear_links();
     if (Ps2 !=NULL) Ps2->clear_links();
     S1->change(bv,av,dv,ev);
     S2->change(cv,av,dv,ev);
     Cl->set_link(S1,S2,av,dv,ev);
     if (Ps1 !=NULL) Ps1->change(bv,fv,dv,ev);
     if (Ps2 !=NULL) Ps2->change(cv,fv,dv,ev);
     if (Ps1 !=NULL && Ps2 !=NULL) Cl->set_link(Ps1,Ps2,fv,dv,ev); 
     if (Ps1 !=NULL) Cl->set_link(S1,Ps1,bv,dv,ev);
     if (Ps2 !=NULL) Cl->set_link(S2,Ps2,cv,dv,ev);
     break;
    }
  }

  // correction of links
  link_korr(S1,SN,TQ,PV); link_korr(S2,SN,TQ,PV);
  if (Ps1 !=NULL) link_korr(Ps1,PSN,TQ,PV);
  if (Ps2 !=NULL) link_korr(Ps2,PSN,TQ,PV);
}


void d3_simpl_complex::flip_konf1(sc_simplex S1, sc_simplex S2,d3_simpl_complex* Cl,int konf,Simpl_Triang& T,queue<Simpl_Triang>& TQ,sc_vertex PV)
// put boundaries into TL
{
  list<sc_simplex> SN;

  sc_simplex S3; 

  sc_vertex av,bv,cv,dv,ev;
  av=T.A; bv=T.B; cv=T.C; // 3 common D3_vertices...
  dv= S1->find_other(T.A,T.B,T.C); ev= S2->find_other(T.A,T.B,T.C);

  if (konf==1){ // 1 new simplex!!
   // save old links
   link_save(S1,S2,S2,SN); link_save(S2,S1,S1,SN);
   Cl->flk1++;
   S1->change(bv,av,dv,ev); S2->change(cv,av,dv,ev);
   S1->clear_links(); S2->clear_links();
   S3=Cl->add_simplex(bv,cv,dv,ev);
   S1->bcd=S2; S2->bcd=S1; 
   S1->acd=S3; S3->acd=S1; 
   S2->acd=S3; S3->bcd=S2; 
   
   link_korr(S1,SN,TQ,PV); link_korr(S2,SN,TQ,PV); link_korr(S3,SN,TQ,PV);
  }
  else { // remove 1 simplex
    switch(konf){
    case 10:
     Cl->flk10++;
     S3=Cl->opposite_simplex(S1,T.C);
     link_save(S1,S2,S3,SN); link_save(S2,S1,S3,SN); link_save(S3,S1,S2,SN);
     Cl->remove_simplex(S3);
     S1->clear_links(); S2->clear_links();
     S1->change(cv,bv,dv,ev); S2->change(cv,av,dv,ev);  
     S1->acd=S2; S2->acd=S1; 
     break;
    case 11:
     Cl->flk11++;
     S3=Cl->opposite_simplex(S1,T.B);
     link_save(S1,S2,S3,SN); link_save(S2,S1,S3,SN); link_save(S3,S1,S2,SN); 
     Cl->remove_simplex(S3);
     S1->clear_links(); S2->clear_links();
     S1->change(bv,av,dv,ev); S2->change(bv,cv,dv,ev);
     S1->acd=S2; S2->acd=S1; 
     break;
    case 12:
     Cl->flk12++;
     S3=Cl->opposite_simplex(S1,T.A);
     link_save(S1,S2,S3,SN); link_save(S2,S1,S3,SN); link_save(S3,S1,S2,SN);  
     Cl->remove_simplex(S3);
     S1->clear_links(); S2->clear_links();
     S1->change(av,bv,dv,ev); S2->change(av,cv,dv,ev);
     S1->acd=S2; S2->acd=S1; 
     break;
    }
    link_korr(S1,SN,TQ,PV); link_korr(S2,SN,TQ,PV);
  }
}

int d3_simpl_complex::d2_test_convex(sc_vertex a,sc_vertex b,sc_vertex c,sc_vertex d)
//  returns 1, if the 4 points stored by 4 D3-vertices, that lie in a plane (!), form a convex quadrangle.

{
 d3_rat_point ap,bp,cp,dp;
 int o1,o2,o3,o4;
 ap=a->stor; bp=b->stor;cp=c->stor; dp=d->stor;

 o1=orientation_xy(ap,bp,cp);o2=orientation_xy(bp,cp,dp);
 o3=orientation_xy(cp,dp,ap);o4=orientation_xy(dp,ap,bp);

 if (o1==0 && o2==0 && o3==0 && o4==0){ 
  o1=orientation_xz(ap,bp,cp);o2=orientation_xz(bp,cp,dp);
  o3=orientation_xz(cp,dp,ap);o4=orientation_xz(dp,ap,bp);
  if (o1==0 && o2==0 && o3==0 && o4==0){
    o1=orientation_yz(ap,bp,cp);o2=orientation_yz(bp,cp,dp);
    o3=orientation_yz(cp,dp,ap);o4=orientation_yz(dp,ap,bp);
  }
 }

 if (o1==o2 && o3==o4 && o2==o3) {
  if (o1 !=0) return 1;
  else {
    o1=orientation_xz(ap,bp,cp);o2=orientation_xz(bp,cp,dp);
    o3=orientation_xz(cp,dp,ap);o4=orientation_xz(dp,ap,bp);    
    if (o1==o2 && o3==o4 && o2==o3) {
     if (o1 !=0) return 1;    
    }
    else {
     o1=orientation_yz(ap,bp,cp);o2=orientation_yz(bp,cp,dp);
     o3=orientation_yz(cp,dp,ap);o4=orientation_yz(dp,ap,bp);
     if (o1==o2 && o3==o4 && o2==o3 && o1!=0) return 1;         
    }
  }
 }

 return 0;
}

int d3_simpl_complex::flip(sc_simplex S1, sc_simplex S2,Simpl_Triang& T)
{
 int wert=1;

 if (S1->com_of != this || S2->com_of != this) return -1; 

 if (S1->HULL_TR && S2->HULL_TR){ // 2 Hulltriangles...
  list<Simpl_Triang> TRL;

  list<sc_simplex> LS;

  sc_vertex av,bv,dv,ev;
  av=T.A; bv=T.B; 
  dv= S1->find_other(T.A,T.B,T.B); ev= S2->find_other(T.A,T.B,T.B);

  int cv=d2_test_convex(dv,av,ev,bv); // d2-flip possible ?
  if (cv==0) return 0; 

  link_save(S1,S2,S2,LS);link_save(S2,S1,S1,LS);
  S1->clear_links(); 
  S2->clear_links();
  S1->change(av,dv,ev); 
  S2->change(bv,dv,ev);
  
  set_link(S1,av,S2,bv);
  link_korr(S1,LS,TRL); link_korr(S2,LS,TRL);

  return wert;
    
 }

 else {
  queue<Simpl_Triang> TQ;
  sc_vertex PV=NULL;

  int konf= configuration(S1,S2,T);

  if ( (konf==1) || (konf>9 && konf<13) || (konf>29 && konf<36) ){
   if ( (konf==1)|| (konf>9 && konf<13) ) flip_konf1(S1,S2,this,konf,T,TQ,PV);
   else flip_konf3(S1,S2,this,konf,T,TQ,PV);
  }
  return konf;
 }

}

int d3_simpl_complex::flip(sc_simplex S1, sc_simplex S2,
                           queue<Simpl_Triang>& TQ, Simpl_Triang& T,
                                                    sc_vertex PV)
{
  if (S1->HULL_TR && S2->HULL_TR) return flip(S1,S2,T);    

  int conf = configuration(S1,S2,T);

  if (conf==1 || (conf>9 && conf<13)) 
     flip_konf1(S1,S2,this,conf,T,TQ,PV);

  if (conf>29 && conf<36) 
     flip_konf3(S1,S2,this,conf,T,TQ,PV);

  return conf;

}

void d3_simpl_complex::input_complex()
{
 int NV,NSI,NN;
 int i;
 rational xw,yw,zw;
 int nb1,nb2,nb3,nb4;

 clear(); 

 cout << "Number of Vertices :"; cin >> NV;
 cout << "Number of Simplices:"; cin >> NSI;
 cout << "Number of Neighboursettings :"; cin >> NN;

 d3_rat_point* P = new d3_rat_point[NV];
 sc_vertex*    V = new sc_vertex[NV];
 sc_simplex*   S = new sc_simplex[NSI];

 for (i=0;i<NV;i++) {
  cout << i << ". point:\n";
  cout << " "; cin >> xw;
  cout << " "; cin >> yw;
  cout << " "; cin >> zw;
   
  P[i]=d3_rat_point(xw,yw,zw);
  V[i]=add_vertex(P[i]); 
 } 

 for (i=0;i<NSI;i++) { 
  cout << i << ". simplex:\n";
  cout << " 1. vertex:"; cin >> nb1;
  if (nb1 >= NV) { cout << "false input!\n"; nb1=0; }
  cout << " 2. vertex:"; cin >> nb2;
  if (nb2 >= NV) { cout << "false input!\n"; nb2=0; }
  cout << " 3. vertex:"; cin >> nb3;
  if (nb3 >= NV) { cout << "false input!\n"; nb3=0; }
  cout << " 4. vertex:"; cin >> nb4; 
  if (nb4 >= NV) { cout << "false input!\n"; nb4=0; }

  if (nb4 != -1) S[i]=add_simplex(V[nb1],V[nb2],V[nb3],V[nb4]);
  else S[i]=add_simplex(V[nb1],V[nb2],V[nb3]);
 }
 
 sc_vertex u1,u2;

 for (i=0;i<NN;i++) {
  cout << i << ". link:\n";
  cout << " 1. simplex:"; cin >> nb1;
  cout << " 1. vertex :"; cin >> nb2;
  cout << " 2. simplex:"; cin >> nb3;
  cout << " 2. vertex :"; cin >> nb4;  
  if (nb2 !=-1) u1=V[nb2]; else u1=NULL;
  if (nb4 !=-1) u2=V[nb4]; else u2=NULL; 
  set_link(S[nb1],u1,S[nb3],u2);
 }

 delete P; delete V; delete S;
}

sc_simplex d3_simpl_complex::insert_vertex(sc_simplex S,sc_vertex v)
{
 return triang_simplex(S,v);
}

sc_simplex d3_simpl_complex::triang_simplex(sc_simplex,sc_vertex, int)
{
 return 0;
}

sc_simplex d3_simpl_complex::triang_simplex(sc_simplex S,sc_vertex v)
// v inside S; triangulate new...
{
 if (v->com_of != this || S->com_of != this) return NULL;

 d3_rat_point p= v->stor;
 sc_simplex sn1,sn2,sn3;
 d3_rat_point A,B,C,D;
 sc_vertex va,vb,vc,vd;
 list<sc_simplex> Sn;

 if ( ! S->in_simplex(p)) return NULL; 

 if (S->HULL_TR){ 
  if (S->abc==NULL){ 
    va= S->a; 
    vb=S->b; 
    vc=S->c; 
    A= va->stor; 
    B= vb->stor; 
    C= vc->stor; 

    if (p==A || p==B || p==C) return NULL;

    link_save(S,NULL,NULL,Sn);

    S->clear_links();
    sn1=add_simplex(va,vb,v); 
    sn2=add_simplex(va,vc,v); 
    S->change(vb,vc,v);  
    set_link(sn1,vb,sn2,vc); 
    set_link(sn1,va,S,vc); 
    set_link(sn2,va,S,vb); 
    list<Simpl_Triang> TRL;
    link_korr(sn1,Sn,TRL); 
    link_korr(sn2,Sn,TRL); 
    link_korr(S,Sn,TRL);  

    return S;  
  }
  else {
   sc_simplex S_other=S->abc;
   
   return triang_simplex(S_other,v); 
  }
 }
 else {
  va=S->a; 
  vb=S->b; 
  vc=S->c; 
  vd=S->d;
  A = va->stor; 
  B = vb->stor; 
  C = vc->stor; 
  D = vd->stor; 

  if (p==A || p==B || p==C || p==D) return NULL;


  link_save(S,NULL,NULL,Sn);

  //new simplex
  S->clear_links();
  sn1 = add_simplex(va,vb,vc,v); 
  sn2 = add_simplex(va,vb,vd,v);
  sn3 = add_simplex(va,vc,vd,v);
  S->change(vb,vc,vd,v);

  //set new links...
  set_link(sn1,vc,sn2,vd); 
  set_link(sn1,vb,sn3,vd);
  set_link(sn1,va,S,vd);
  set_link(sn2,vb,sn3,vc); 
  set_link(sn2,va,S,vc);
  set_link(sn3,va,S,vb); 
  list<Simpl_Triang> Trl;
  link_korr(sn1,Sn,Trl); 
  link_korr(sn2,Sn,Trl); 
  link_korr(sn3,Sn,Trl); 
  link_korr(S,Sn,Trl);  

  return sn1;
 }

}

sc_simplex d3_simpl_complex::triang_simplex(sc_simplex S,d3_rat_point p)
{
 sc_vertex v= add_vertex(p);
 return triang_simplex(S,v);
}

bool d3_simpl_complex::all_delaunay_check()
{
 sc_simplex  fst;
 sc_vertex ac;
 bool flag=true;
             
 forall(fst,Sil) {
  forall(ac,Vert){
    if (fst->insphere(ac->stor))  flag=false;
  }
 }

 return flag;
}

bool d3_simpl_complex::delaunay_check(int w)
{
 int st;
 if (w==1) { st=check_delaunay(); if (st==0) return true; else return false; }
 else return all_delaunay_check();
}

int d3_simpl_complex::check(int output,ostream& ost)
// output information about the simplex complex, perform some tests...
// output==0 ... no output
// output==1 ... only errors and number of vertices/simplices
// output >1 ... like 1 but output all vertices/simplices too
{
 if (output>0) ost << "check:" << Sil.size() << " simplices; " << Vert.size() << " vertices!\n";
 sc_vertex aktual;
 sc_simplex S,S2;

 // Simplices und Vertices ausgeben...
 if (output>1){

  ost << "vertices:\n";
  ost << "---------\n";
  forall(aktual,Vert){
   ost << *aktual << "\n";
  }
  ost << "simplices:\n";
  ost << "----------\n";
  forall(S,Sil){
   ost << *S;
  }
 }

 // check links ...

 list<sc_simplex> an;
 int wert;
 int rueck=0;
 Simpl_Triang Tr;
 //int tw;
 int nbsets=0;
 sc_simplex s1,s2,s3,s4;
 int sizahl=0;
 int htrzahl=0;

 forall(S,Sil){
   sizahl++;
   if ( S->HULL_TR){
     htrzahl++;
     s1= S->abd; s2= S->acd; s3= S->bcd; s4= S->abc;
     if (s1 !=NULL) {
       if (! s1->HULL_TR) { rueck=1; if (output>0) ost << "CHECKER --- error abd ---\n"; }
     }
     if (s2 !=NULL) {
       if (! s2->HULL_TR) { rueck=1; if (output>0) ost << "CHECKER --- error acd ---\n"; } 
     }
     if (s3 !=NULL) {
       if (! s3->HULL_TR) { rueck=1; if (output>0) ost << "CHECKER --- error bcd ---\n"; }
     }
     if (s4 !=NULL) {
       if ( s4->HULL_TR)  { rueck=1; if (output>0) ost << "CHECKER --- error abc ---\n"; }
     }
   }
   // checks for non-hulltrs. ("real" simplices)
   else {
     if (coplanar(S->a->stor,S->b->stor,S->c->stor,S->d->stor)) {
       rueck=1;
       if (output>0) ost << "Problem - simplex flat!\n";
     }
     if ( S->d == NULL) {
       rueck=1;
       if (output>0) ost << "Problem - d-pointer is NULL for a non-hulltr.!\n";
     }
   }

   an=S->all_neighbours();
   nbsets=nbsets+an.size();

   forall(S2,an){
     if (S2==S) { 
      rueck=1;
      if (output>0) ost << "The neighbour is the simplex himself!\n";
     }
     wert=get_link_index(S2,S);
     if (wert < 1) { 
       if (output>0) ost << "CHECKER --- a neighbour link is not reversal!\n";
       rueck=1;
     }
     else {
       //tw=common_triangle(S, S2, Tr); 
       wert=S2->control_vert(Tr.A,Tr.B,Tr.C);    
       if (wert==0){
          if (output>0) 
          ost << "CHECKER --- false neighbourhood between simplices " 
               <<  S->name << "/" << S2->name << " " << Tr <<  " !\n";
          rueck=1; 
       }
     }
   }   
 }

 if (output>0) 
  cout << nbsets << " neighbour-links ( " << (int)(nbsets/2) << " pairs).\n";

 if (Sil.size() != sizahl) { 
   if (output>0) 
       cout << "error - number of simplices. Sil.size:" 
            << Sil.size() << " sizahl:" << sizahl << "\n";
   rueck=1;
 }
 
 if (output>0) cout << htrzahl << " hulltriangles!\n";

 return rueck;
}

bool test_inside(d3_rat_point a,d3_rat_point b,d3_rat_point c,d3_rat_point other)
{
 d3_rat_point d=point_on_positive_side(a,b,c);
 bool w=inside_sphere(a,b,c,d,other);
 return w;
}

LEDA_END_NAMESPACE
