Index: /issm/trunk/src/c/Bamgx/Mesh2.cpp
===================================================================
--- /issm/trunk/src/c/Bamgx/Mesh2.cpp	(revision 2810)
+++ /issm/trunk/src/c/Bamgx/Mesh2.cpp	(revision 2811)
@@ -49,6 +49,4 @@
 	int hinterpole=1;
 
-
-	long NbUnSwap =0;
 	int  ForDebugging = 0;
 	const Direction NoDirOfSearch = Direction();
@@ -428,25 +426,4 @@
 			return er;
 		} 
-
-
-
-		Metric Triangles::MetricAt  (const R2 & A) const
-		{ //if ((vertices <= &v) && (vertices < v+nbv)) return v.m;
-			I2 a = toI2(A);
-			Icoor2 deta[3];
-			Triangle * t =FindTriangleContening(a,deta);
-			if (t->det <0) { // outside
-				double ba,bb;
-				TriangleAdjacent edge= CloseBoundaryEdge(a,t,ba,bb) ;
-				return Metric(ba,*edge.EdgeVertex(0),bb,*edge.EdgeVertex(1));}
-			else { // inside
-				Real8   aa[3];
-				Real8 s = deta[0]+deta[1]+deta[2];
-				aa[0]=deta[0]/s;
-				aa[1]=deta[1]/s;
-				aa[2]=deta[2]/s;
-				return Metric(aa,(*t)[0],(*t)[1],(*t)[2]);
-			}
-		}
 
 
@@ -988,121 +965,5 @@
 
 
-		int Triangle::swap(Int2 a,int koption){
-			if(a/4 !=0) return 0;// arete lock or MarkUnSwap
-
-			register Triangle *t1=this,*t2=at[a];// les 2 triangles adjacent
-			register Int1 a1=a,a2=aa[a];// les 2 numero de l arete dans les 2 triangles
-			if(a2/4 !=0) return 0; // arete lock or MarkUnSwap
-
-			register Vertex  *sa=t1->ns[VerticesOfTriangularEdge[a1][0]];
-			register Vertex  *sb=t1->ns[VerticesOfTriangularEdge[a1][1]];
-			register Vertex  *s1=t1->ns[OppositeVertex[a1]];
-			register Vertex  *s2=t2->ns[OppositeVertex[a2]];
-
-			Icoor2 det1=t1->det , det2=t2->det ;
-			Icoor2 detT = det1+det2;
-			Icoor2 detA = Abs(det1) + Abs(det2);
-			Icoor2 detMin = Min(det1,det2);
-
-			int OnSwap = 0;       
-			// si 2 triangle infini (bord) => detT = -2;
-			if (sa == 0) {// les deux triangles sont frontieres
-				det2=bamg::det(s2->i,sb->i,s1->i);
-				OnSwap = det2 >0;}
-			else if (sb == 0) { // les deux triangles sont frontieres
-				det1=bamg::det(s1->i,sa->i,s2->i);
-				OnSwap = det1 >0;}
-			else if(( s1 != 0) && (s2 != 0) ) {
-				det1 = bamg::det(s1->i,sa->i,s2->i);
-				det2 = detT - det1;
-				OnSwap = (Abs(det1) + Abs(det2)) < detA;
-
-				Icoor2 detMinNew=Min(det1,det2);
-				//     if (detMin<0 && (Abs(det1) + Abs(det2) == detA)) OnSwap=BinaryRand();// just for test   
-				if (! OnSwap &&(detMinNew>0)) {
-					OnSwap = detMin ==0;
-					if (! OnSwap) {
-						int  kopt = koption;
-						while (1)
-							if(kopt) {
-								// critere de Delaunay pure isotrope
-								register Icoor2 xb1 = sb->i.x - s1->i.x,
-										 x21 = s2->i.x - s1->i.x,
-										 yb1 = sb->i.y - s1->i.y,
-										 y21 = s2->i.y - s1->i.y,
-										 xba = sb->i.x - sa->i.x, 
-										 x2a = s2->i.x - sa->i.x,
-										 yba = sb->i.y - sa->i.y,
-										 y2a = s2->i.y - sa->i.y;
-								register double
-									cosb12 =  double(xb1*x21 + yb1*y21),
-										   cosba2 =  double(xba*x2a + yba*y2a) ,
-										   sinb12 = double(det2),
-										   sinba2 = double(t2->det);
-
-
-								// angle b12 > angle ba2 => cotg(angle b12) < cotg(angle ba2)
-								OnSwap =  ((double) cosb12 * (double)  sinba2) <  ((double) cosba2 * (double) sinb12);
-								//  	 if(CurrentTh) 
-								//  	   cout << "swap " << CurrentTh->Number(sa) << " " << CurrentTh->Number(sb) << " " ;
-								//  	 cout <<  cosb12 << " " <<  sinba2 << " "  <<  cosba2 << " " << sinb12 
-								//  	      << " Onswap = " <<  OnSwap << endl;
-								break;
-							}
-							else 
-							{	
-								// critere de Delaunay anisotrope 
-								Real8 som;
-								I2 AB=(I2) *sb - (I2) *sa;
-								I2 MAB2=((I2) *sb + (I2) *sa);
-								R2 MAB(MAB2.x*0.5,MAB2.y*0.5);
-								I2 A1=(I2) *s1 - (I2) *sa;
-								I2 D = (I2) * s1 - (I2) * sb ;
-								R2 S2(s2->i.x,s2->i.y);
-								R2 S1(s1->i.x,s1->i.y);
-								{
-									Metric M=s1->m;
-									R2 ABo = M.Orthogonal(AB);
-									R2 A1o = M.Orthogonal(A1);
-									// (A+B)+ x ABo = (S1+B)/2+ y A1 
-									// ABo x - A1o y =  (S1+B)/2-(A+B)/2 = (S1-B)/2 = D/2
-									double dd = Abs(ABo.x*A1o.y)+Abs(ABo.y*A1o.x);
-									double d = (ABo.x*A1o.y - ABo.y*A1o.x)*2; // because D/2
-									if (Abs(d) > dd*1.e-3) {
-										R2 C(MAB+ABo*((D.x*A1o.y - D.y*A1o.x)/d));
-										som  = M(C - S2)/M(C - S1);
-									} else 
-									{kopt=1;continue;}
-
-								}
-								{
-									Metric M=s2->m;
-									R2 ABo = M.Orthogonal(AB);
-									R2 A1o = M.Orthogonal(A1);
-									// (A+B)+ x ABo = (S1+B)/2+ y A1 
-									// ABo x - A1o y =  (S1+B)/2-(A+B)/2 = (S1-B)/2 = D/2 
-									double dd = Abs(ABo.x*A1o.y)+Abs(ABo.y*A1o.x);
-									double d = (ABo.x*A1o.y - ABo.y*A1o.x)*2; // because D/2
-									if(Abs(d) > dd*1.e-3) {
-										R2 C(MAB+ABo*((D.x*A1o.y - D.y*A1o.x)/d));
-										som  += M(C - S2)/M(C -  S1);
-									} else 
-									{kopt=1;continue;}
-								}
-								OnSwap = som < 2;
-								break;
-							}
-
-					} // OnSwap 
-				} // (! OnSwap &&(det1 > 0) && (det2 > 0) )
-			}
-			if( OnSwap ) 
-				bamg::swap(t1,a1,t2,a2,s1,s2,det1,det2);
-			else {
-				NbUnSwap ++;
-				t1->SetMarkUnSwap(a1);     
-			}
-			return OnSwap;
-		}
+
 
 		Real8  Vertex::Smoothing(Triangles & Th,const Triangles & BTh,Triangle  * & tstart ,Real8 omega)
@@ -1213,1509 +1074,4 @@
 		}
 
-
-
-
-		void Triangles::Add( Vertex & s,Triangle * t, Icoor2 * det3) 
-		{
-			// -------------------------------------------
-			//             s2
-			//                                            !
-			//             /|\                            !
-			//            / | \                           !
-			//           /  |  \                          !
-			//    tt1   /   |   \ tt0                     !
-			//         /    |s   \                        !
-			//        /     .     \                       !
-			//       /  .      `   \                      !
-			//      / .           ` \                     !
-			//      ----------------                      !
-			//   s0       tt2       s1
-			//-------------------------------------------- 
-
-			Triangle * tt[3]; // the 3 new Triangles
-			Vertex &s0 = (* t)[0], &s1=(* t)[1], &s2=(* t)[2];
-			Icoor2  det3local[3];
-			int infv = &s0 ?  ((  &s1 ? ( &s2  ? -1 : 2) : 1  )) : 0;
-			// infv = ordre of the infini vertex (null)
-			register int nbd0 =0; // number of zero det3
-			register int izerodet=-1,iedge; // izerodet = egde contening the vertex s
-			Icoor2 detOld = t->det;
-
-			if ( ( infv <0 ) && (detOld <0) ||  ( infv >=0  ) && (detOld >0) ) 
-			{
-				cerr << "  infv " << infv << " det = " << detOld << endl;
-				cerr << Number(s) << " "<< Number(s0) << " "  
-					<< Number(s1) << " "  << Number(s2) << endl;
-				MeshError(3);
-			}
-
-			// if det3 do not exist then constuct det3
-			if (!det3) { 
-				det3 = det3local; // alloc 
-				if ( infv<0 ) {
-					det3[0]=bamg::det(s ,s1,s2);
-					det3[1]=bamg::det(s0,s ,s2);
-					det3[2]=bamg::det(s0,s1,s );}
-				else { 
-					// one of &s1  &s2  &s0 is NULL so (&si || &sj) <=> !&sk
-					det3[0]=  &s0 ? -1  : bamg::det(s ,s1,s2) ;
-					det3[1]=  &s1 ? -1 : bamg::det(s0,s ,s2) ;
-					det3[2]=  &s2 ? -1 : bamg::det(s0,s1,s ) ;}}
-
-
-					if (!det3[0]) izerodet=0,nbd0++;
-					if (!det3[1]) izerodet=1,nbd0++;
-					if (!det3[2]) izerodet=2,nbd0++;
-
-					if  (nbd0 >0 ) // point s on a egde or on a vertex 
-						if (nbd0 == 1) {
-							iedge = OppositeEdge[izerodet];
-							TriangleAdjacent ta = t->Adj(iedge);
-
-							// the point is on the edge 
-							// if the point is one the boundary 
-							// add the point in outside part 
-							if ( t->det >=0) { // inside triangle
-								if ((( Triangle *) ta)->det < 0 ) {
-									// add in outside triangle 
-									Add(s,( Triangle *) ta);
-									return;}
-							}}
-						else {
-							cerr << " bug  " << nbd0 <<endl;
-							cerr << " Bug double points in " << endl ;
-							cerr << " s = " << Number(s) << " " <<  s << endl;
-							cerr << " s0 = "<< Number(s0) << " "  << s0 << endl;
-							cerr << " s1 = "<< Number(s1) << " "  << s1 << endl;
-							cerr << " s2 = "<< Number(s2) << " "  << s2 << endl;
-							MeshError(5,this);}
-
-							// remove de MarkUnSwap edge
-							t->SetUnMarkUnSwap(0);     
-							t->SetUnMarkUnSwap(1);     
-							t->SetUnMarkUnSwap(2);
-
-							tt[0]= t;
-							tt[1]= &triangles[nbt++];
-							tt[2]= &triangles[nbt++];
-
-							if (nbt>nbtx) {
-								cerr << " No enougth triangles " << endl;
-								MeshError(999,this);
-							}
-
-							*tt[1]=   *tt[2]= *t;
-							// gestion of the link
-							tt[0]->link=tt[1];
-							tt[1]->link=tt[2]; 
-
-							(* tt[0])(OppositeVertex[0])=&s;
-							(* tt[1])(OppositeVertex[1])=&s;
-							(* tt[2])(OppositeVertex[2])=&s;
-
-							tt[0]->det=det3[0];
-							tt[1]->det=det3[1];
-							tt[2]->det=det3[2];         
-
-							//  update adj des triangles externe 
-							tt[0]->SetAdjAdj(0);
-							tt[1]->SetAdjAdj(1);
-							tt[2]->SetAdjAdj(2);
-							//  update des adj des 3 triangle interne
-							const int i0 = 0;
-							const int i1= NextEdge[i0];
-							const int i2 = PreviousEdge[i0];
-
-							tt[i0]->SetAdj2(i2,tt[i2],i0);
-							tt[i1]->SetAdj2(i0,tt[i0],i1);
-							tt[i2]->SetAdj2(i1,tt[i1],i2);
-
-							tt[0]->SetTriangleContainingTheVertex();
-							tt[1]->SetTriangleContainingTheVertex();
-							tt[2]->SetTriangleContainingTheVertex();
-
-
-							// swap if the point s is on a edge
-							if(izerodet>=0) {
-								//  cout << " the point s is on a edge =>swap " << iedge << " "  << *tt[izerodet] << endl;
-								int rswap =tt[izerodet]->swap(iedge);
-
-								if (!rswap) 
-								{
-									cout << " Pb swap the point s is on a edge =>swap " << iedge << " "  << *tt[izerodet] << endl;
-								}
-								assert(rswap);
-							}
-		}
-
-
-		Int4  Triangles::SplitInternalEdgeWithBorderVertices()
-		{
-			Int4 NbSplitEdge=0;
-			SetVertexFieldOn();  
-			Int4 it;
-			Int4 nbvold=nbv;
-			long int verbosity=2;
-			for (it=0;it<nbt;it++)
-			{
-				Triangle &t=triangles[it];
-				if (t.link)
-					for (int j=0;j<3;j++)
-						if(!t.Locked(j) && !t.Hidden(j)){
-							Triangle &tt = *t.TriangleAdj(j);
-							if ( &tt && tt.link && it < Number(tt)) 
-							{ // an internal edge 
-								Vertex &v0 = t[VerticesOfTriangularEdge[j][0]];
-								Vertex &v1 = t[VerticesOfTriangularEdge[j][1]];
-								if (v0.on && v1.on)
-								{
-									R2 P= ((R2) v0 + (R2) v1)*0.5;
-									if ( nbv<nbvx) {
-										vertices[nbv].r = P;
-										vertices[nbv++].m = Metric(0.5,v0.m,0.5,v1.m);
-										vertices[nbv].ReferenceNumber=0;
-										vertices[nbv].DirOfSearch = NoDirOfSearch ;
-									}
-									NbSplitEdge++;
-									if (verbosity>7)
-										cout <<" Internal edge with two vertices on boundary" 
-											<< Number(v0) << " " << Number(v1) << " by " <<  endl;
-								}
-							}
-						}
-			}
-			ReMakeTriangleContainingTheVertex();    
-			if (nbvold!=nbv) 
-			{
-				Int4  iv = nbvold;
-				Int4 NbSwap = 0;
-				Icoor2 dete[3];  
-				for (Int4 i=nbvold;i<nbv;i++) 
-				{// for all the new point
-					Vertex & vi = vertices[i];
-					vi.i = toI2(vi.r);
-					vi.r = toR2(vi.i);
-					//      if (!quadtree->ToClose(vi,seuil,hi,hj)) {
-					// a good new point 
-					vi.ReferenceNumber=0; 
-					vi.DirOfSearch =NoDirOfSearch;
-					//	cout << " Add " << Number(vi) << " " << vi 
-					// << "   " <<  Number(vi) << " <--> " << Number(vi) <<endl;
-					Triangle *tcvi = FindTriangleContening(vi.i,dete);
-					if (tcvi && !tcvi->link) {
-						cout << i <<  " PB insert point " << Number(vi) << vi << Number(vi) 
-							<< " tcvi = " << tcvi << " " << tcvi->link << endl;
-						cout << (*tcvi)[1] <<  (*tcvi)[2] << endl;
-						tcvi = FindTriangleContening(vi.i,dete);
-						cout << (*tcvi)[1] <<  (*tcvi)[2] << endl;
-						MeshError(1001,this);
-					}
-
-
-					quadtree->Add(vi);
-					assert (tcvi && tcvi->det >= 0) ;// internal 
-					Add(vi,tcvi,dete);
-					NbSwap += vi.Optim(1);          
-					iv++;
-					//      }
-				}
-				if (verbosity>3) 
-				{
-					cout << "    Nb Of New Point " << iv ;
-					cout << " Nb swap = " << NbSwap << " to  split internal edges with border vertices" ;}
-
-					nbv = iv;
-			}
-			if (NbSplitEdge >  nbv-nbvold)
-				cout << " Warning not enough vertices  to split all internal edges "  << endl
-					<< "    we lost " << NbSplitEdge - ( nbv-nbvold) << " Edges Sorry " << endl;
-			if (verbosity>2)
-				cout << "SplitInternalEdgeWithBorderVertices: Number of splited edge " << NbSplitEdge << endl;
-			return  NbSplitEdge;
-		}
-		Int4 Triangles::InsertNewPoints(Int4 nbvold,Int4 & NbTSwap)
-		{
-			long int verbosity=2;
-			Real8 seuil= 1.414/2 ;// for two close point 
-			Int4 i;
-			// insertion part --- 
-
-			const Int4 nbvnew = nbv-nbvold;
-			if (verbosity>5) 
-				cout << "    Try to Insert the " <<nbvnew<< " new points " << endl;  
-			Int4 NbSwap=0;
-			Icoor2 dete[3];
-
-			// construction d'un ordre aleatoire 
-			if (! nbvnew) 
-				return 0; 
-			if (nbvnew) {
-				const Int4 PrimeNumber= AGoodNumberPrimeWith(nbv)  ;
-				Int4 k3 = rand()%nbvnew ; 
-				for (Int4 is3=0; is3<nbvnew; is3++) {
-					register Int4 j = nbvold +(k3 = (k3 + PrimeNumber)% nbvnew);
-					register Int4 i = nbvold+is3; 
-					ordre[i]= vertices + j;
-					ordre[i]->ReferenceNumber=i;
-				}
-				// be carefull 
-				Int4  iv = nbvold;
-				for (i=nbvold;i<nbv;i++) 
-				{// for all the new point
-					Vertex & vi = *ordre[i];
-					vi.i = toI2(vi.r);
-					vi.r = toR2(vi.i);
-					Real4 hx,hy;
-					vi.m.Box(hx,hy);
-					Icoor1 hi=(Icoor1) (hx*coefIcoor),hj=(Icoor1) (hy*coefIcoor);
-					if (!quadtree->ToClose(vi,seuil,hi,hj)) 
-					{
-						// a good new point 
-						Vertex & vj = vertices[iv];
-						Int4 j = vj.ReferenceNumber; 
-						assert( &vj== ordre[j]);
-						if(i!=j)
-						{ //  for valgring 
-							Exchange(vi,vj);
-							Exchange(ordre[j],ordre[i]);
-						}
-						vj.ReferenceNumber=0; 
-						//	cout << " Add " << Number(vj) << " " << vj 
-						// << "   " <<  Number(vi) << " <--> " << Number(vj) <<endl;
-						Triangle *tcvj = FindTriangleContening(vj.i,dete);
-						if (tcvj && !tcvj->link) 
-						{
-							cerr << i <<  " PB insert point " << Number(vj) << vj << Number(vi) 
-								<< " tcvj = " << tcvj << " " << tcvj->link << endl;
-							cerr << (*tcvj)[1] <<  (*tcvj)[2] << endl;
-							tcvj = FindTriangleContening(vj.i,dete);
-							cout << (*tcvj)[1] <<  (*tcvj)[2] << endl;
-							MeshError(1001,this);
-						}
-
-
-						quadtree->Add(vj);
-						assert (tcvj && tcvj->det >= 0) ;// internal 
-						Add(vj,tcvj,dete);
-						NbSwap += vj.Optim(1);          
-						iv++;
-					}
-				} 
-				if (verbosity>3) {
-					cout << "    Nb Of New Point " << iv << " Nb Of To close Points " << nbv-iv ;
-					cout << " Nb swap = " << NbSwap << " after " ;}
-
-					nbv = iv;
-			}
-
-			for (i=nbvold;i<nbv;i++) 
-				NbSwap += vertices[i].Optim(1);  
-			if (verbosity>3) 
-				cout << " NbSwap = " <<  NbSwap << endl;
-
-
-			NbTSwap +=  NbSwap ;
-			return nbv-nbvold;
-
-		}
-		void  Triangles::NewPoints(Triangles & Bh,int KeepBackVertex)
-		{ // Triangles::NewPoints
-			long int verbosity=2;
-			Int4 nbtold(nbt),nbvold(nbv);
-			if (verbosity>2) 
-				cout << "  -- Triangles::NewPoints ";
-			if (verbosity>3)cout <<  " nbv (in)  on Boundary  = " << nbv  <<endl;
-			Int4 i,k;
-			int j;
-			Int4 *first_np_or_next_t = new Int4[nbtx];
-			Int4 NbTSwap =0;
-			//    insert old point
-			nbtold = nbt;
-
-			if (KeepBackVertex && (&Bh != this) && (nbv+Bh.nbv< nbvx)) 
-			{
-				//   Bh.SetVertexFieldOn();
-				for (i=0;i<Bh.nbv;i++)
-				{ 
-					Vertex & bv = Bh[i];
-					if (!bv.on) {
-						vertices[nbv].r = bv.r;
-						vertices[nbv++].m = bv.m;}
-				}
-				int nbv1=nbv;
-				Bh.ReMakeTriangleContainingTheVertex();     
-				InsertNewPoints(nbvold,NbTSwap)   ;            
-				if (verbosity>2)
-					cout <<  "      (Nb of Points from background mesh  = " 
-						<< nbv-nbvold  << " / " << nbv1-nbvold << ")" << endl;
-			}  
-			else 
-				Bh.ReMakeTriangleContainingTheVertex();     
-
-			Triangle *t;
-			// generation of the list of next Triangle 
-			// at 1 time we test all the triangles
-			Int4 Headt =0,next_t;
-			for(i=0;i<nbt;i++)
-				first_np_or_next_t[i]=-(i+1);
-			// end list i >= nbt 
-			// the list of test triangle is 
-			// the next traingle on i is  -first_np_or_next_t[i]
-			int iter=0;
-			// Big loop 
-			do {
-				iter++;
-				nbtold = nbt;
-				nbvold = nbv;
-
-				// default size of  IntersectionTriangle
-
-				i=Headt;
-				next_t=-first_np_or_next_t[i];
-				for(t=&triangles[i];i<nbt;t=&triangles[i=next_t],next_t=-first_np_or_next_t[i]) 
-				{ // for each triangle  t
-					// we can change first_np_or_next_t[i]
-					//      cout << " Do the triangle " << i << " Next_t=" << next_t << endl;
-					assert(i>=0 && i < nbt );
-					first_np_or_next_t[i] = iter; 
-					for(j=0;j<3;j++)
-					{ // for each edge 
-						TriangleAdjacent tj(t,j);
-						Vertex & vA = * tj.EdgeVertex(0);
-						Vertex & vB = * tj.EdgeVertex(1);
-
-						if (!t->link) continue;// boundary
-						if (t->det <0) continue;
-						if (t->Locked(j)) continue;
-
-						TriangleAdjacent tadjj = t->Adj(j);	  
-						Triangle * ta= tadjj;
-
-						if (ta->det <0) continue;	  
-
-						R2 A = vA;
-						R2 B = vB;
-
-						k=Number(ta);
-
-						if(first_np_or_next_t[k]==iter)  // this edge is done before 
-							continue; // next edge of the triangle 
-
-						//const Int4 NbvOld = nbv;
-						lIntTria.SplitEdge(Bh,A,B);
-						lIntTria.NewPoints(vertices,nbv,nbvx);
-					} // end loop for each edge 
-
-				}// for triangle   
-
-				if (!InsertNewPoints(nbvold,NbTSwap)) 
-					break;
-
-				for (i=nbtold;i<nbt;i++)
-					first_np_or_next_t[i]=iter;
-
-				Headt = nbt; // empty list 
-				for (i=nbvold;i<nbv;i++) 
-				{ // for all the triangle contening the vertex i
-					Vertex * s  = vertices + i;
-					TriangleAdjacent ta(s->t, EdgesVertexTriangle[s->vint][1]);
-					Triangle * tbegin= (Triangle*) ta;
-					Int4 kt;
-					do { 
-						kt = Number((Triangle*) ta);
-						if (first_np_or_next_t[kt]>0) 
-							first_np_or_next_t[kt]=-Headt,Headt=kt;
-						assert( ta.EdgeVertex(0) == s);
-						ta = Next(Adj(ta));
-					} while ( (tbegin != (Triangle*) ta)); 
-				}   
-
-			} while (nbv!=nbvold);
-
-			delete []  first_np_or_next_t;
-
-			Int4 NbSwapf =0,NbSwp;
-
-			// bofbof 
-
-
-			NbSwp = NbSwapf;
-			for (i=0;i<nbv;i++)
-				NbSwapf += vertices[i].Optim(0);
-			/*
-			   for (i=0;i<nbv;i++)
-			   NbSwapf += vertices[i].Optim(0);
-			   for (i=0;i<nbv;i++)
-			   NbSwapf += vertices[i].Optim(0);
-			   for (i=0;i<nbv;i++)
-			   NbSwapf += vertices[i].Optim(0);
-			   for (i=0;i<nbv;i++)
-			   NbSwapf += vertices[i].Optim(0);
-			   */
-			NbTSwap +=  NbSwapf ;
-			if (verbosity>3) cout << "   " ;
-			if (verbosity>2) 
-				cout << " Nb Of Vertices =" << nbv << " Nb of triangles = " << nbt-NbOutT 
-					<< " NbSwap final = " << NbSwapf << " Nb Total Of Swap = " << NbTSwap << endl;
-
-
-		}
-
-		void  Triangles::NewPointsOld(Triangles & Bh)
-		{ // Triangles::NewPointsOld
-			long int verbosity=2;
-			Real8 seuil= 0.7 ;// for two neart point 
-			if (verbosity>1) 
-				cout << " begin :  Triangles::NewPointsOld " << endl;
-			Int4 i,k;
-			int j;
-			Int4 BeginNewPoint[3];
-			Int4 EndNewPoint[3];
-#ifdef TRACETRIANGLE
-			Int4 trace=0;
-#endif
-			int step[3];
-			Int4 *first_np_or_next_t = new Int4[nbtx];
-			Int4 ColorEdge[3];
-			Int4 color=-1;
-			Triangle *t;
-			// generation of the list of next Triangle 
-			// at 1 time we test all the triangles
-			Int4 Headt =0,next_t;
-			for(i=0;i<nbt;i++)
-				first_np_or_next_t[i]=-(i+1);
-			// end list i >= nbt 
-			// the list of test triangle is 
-			// the next Triangle on i is  -first_np_or_next_t[i]
-			Int4 nbtold,nbvold;
-
-			// Big loop 
-			do {
-				nbtold = nbt;
-				nbvold = nbv;
-				// default size of  IntersectionTriangle
-
-				i=Headt;
-				next_t=-first_np_or_next_t[i];
-				for(t=&triangles[i];i<nbt;t=&triangles[i=next_t],next_t=-first_np_or_next_t[i]) 
-				{ // for each triangle  t
-					// we can change first_np_or_next_t[i]
-#ifdef TRACETRIANGLE
-					trace =  TRACETRIANGLE <0 ? 1 : i == TRACETRIANGLE;
-#endif
-					//      cout << " Do the triangle " << i << " Next_t=" << next_t << endl;
-					assert(i>=0 && i < nbt );
-					first_np_or_next_t[i] = nbv; // to save the fist new point of triangle
-					for(j=0;j<3;j++)
-					{ // for each edge 
-						TriangleAdjacent tj(t,j);
-						// color++;// the color is 3i+j
-						color = 3*i + j ;;
-						ColorEdge[j]=color;
-						BeginNewPoint[j]=nbv;
-						EndNewPoint[j]=nbv-1;
-						step[j]=1;// right sens 
-						Vertex & vA = * tj.EdgeVertex(0);
-						Vertex & vB = * tj.EdgeVertex(1);
-
-#ifdef TRACETRIANGLE
-						if(trace) {
-							cout << " i " << Number(vA) <<" j "<<  Number(vB) 
-								<< " "  << t->Locked(j) ;
-						}
-#endif
-						if (!t->link) continue;// boundary
-						if (t->det <0) continue;
-						if (t->Locked(j)) continue;
-
-						TriangleAdjacent tadjj = t->Adj(j);	  
-						Triangle * ta= tadjj;
-
-						if (ta->det <0) continue;	  
-
-						R2 A = vA;
-						R2 B = vB;
-
-						k=Number(ta);
-						// the 2 opposite vertices 
-						const Vertex & vC1  =  *tj.OppositeVertex();
-						const Vertex & vC2 = *tadjj.OppositeVertex();
-
-#ifdef TRACETRIANGLE
-						trace = trace || k == TRACETRIANGLE;
-						if(trace) {
-							cout << "Test Arete " << i << " AB = " << A << B 
-								<< "i "  <<Number(vA)<< "j" <<Number(vB); 
-							cout << " link" <<(int)t->link << " ta=" << Number( ta) 
-								<< " det " <<ta->det ;
-							cout << " hA = " <<vA.m.h << " hB = " <<vB.m.h ;
-							cout << " loc " << ta->Locked(j) << endl;
-						}
-#endif
-
-						if(first_np_or_next_t[k]>0) { // this edge is done before 
-							// find the color of the edge and begin , end of newpoint
-							register int kk = t->NuEdgeTriangleAdj(j);
-							assert ((*t)(VerticesOfTriangularEdge[j][0]) == (*ta)(VerticesOfTriangularEdge[kk][1]));
-							assert ((*t)(VerticesOfTriangularEdge[j][1]) == (*ta)(VerticesOfTriangularEdge[kk][0]));
-							register Int4 kolor =3*k + kk;
-							ColorEdge[j]=kolor;
-							register Int4 kkk= 1;
-							step[j]=-1;// other sens 
-							BeginNewPoint[j]=0;
-							EndNewPoint[j]=-1; // empty list          
-							for (Int4 iv=first_np_or_next_t[k];iv<nbv;iv++) 
-								if (vertices[iv].color > kolor) 
-									break; // the color is passed            
-								else if (vertices[iv].color == kolor) {
-									EndNewPoint[j]=iv; 
-									if (kkk) // one time test
-										kkk=0,BeginNewPoint[j]=iv;}
-									continue; // next edge of the triangle 
-						} // end  if( k < i) 
-
-
-						const Int4 NbvOld = nbv;
-						lIntTria.SplitEdge(Bh,A,B);
-						// Int4 NbvNp =
-						lIntTria.NewPoints(vertices,nbv,nbvx);
-						Int4 nbvNew=nbv;
-						nbv = NbvOld;
-						for (Int4 iv=NbvOld;iv<nbvNew;iv++) {
-							vertices[nbv].color = color;
-							vertices[nbv].ReferenceNumber=nbv;// circular link
-							R2 C =  vertices[iv].r;
-							vertices[nbv].r =  C;
-							vertices[nbv].m =  vertices[iv].m ;
-							// test if the new point is not to close to the 2 opposite vertex
-							R2 CC1 = C-vC1 , CC2 = C-vC2;
-							if (   (  (vC1.m(CC1) + vertices[nbv].m(CC1)) >  seuil)
-									&& (  (vC2.m(CC2) + vertices[nbv].m(CC2)) >  seuil) )
-								nbv++;
-						}
-
-						EndNewPoint[j] = nbv-1;
-					} // end loop for each edge 
-
-#ifdef TRACETRIANGLE
-					if(trace) {
-						// verification des point cree 
-						cout << "\n ------------ " << t->link << " " << t->det 
-							<< " b " << BeginNewPoint[0] << " " << BeginNewPoint[1]
-							<< " " << BeginNewPoint[2] << " " 
-							<< " e " << EndNewPoint[0] << " " << EndNewPoint[1] 
-							<< " " << EndNewPoint[2] << " " 
-							<< " s " << step[0] << " " << step[1] << " " << step[2] << " " 
-							<<  endl;
-					}
-#endif
-
-					if (!t->link) continue;// boundary
-					if (t->det<=0) continue;// outside 
-					//      continue;
-					for(int j0=0;j0<3;j0++)
-						for (Int4 i0= BeginNewPoint[j0]; i0 <= EndNewPoint[j0];i0++)
-						{
-							// find the neart  point one the opposite edge 
-							// to compute i1
-							Vertex & vi0 = vertices[i0];
-							int kstack = 0;
-							Int4 stack[10];
-							//   Int4 savRef[10];
-							int j1 = j0; 
-							while (j0 != (j1 = NextEdge[j1])) {//loop on the 2 other edge
-								// computation of the intersection of edge j1 and DOrto
-								// take the good sens 
-
-								if (BeginNewPoint[j1]> EndNewPoint[j1])
-									continue; // 
-								else if (EndNewPoint[j1] - BeginNewPoint[j1] <1) {
-									for (Int4 ii1= BeginNewPoint[j1];ii1<=EndNewPoint[j1];ii1++)
-										stack[kstack++] = ii1;
-									continue;}
-
-
-									int k0,k1;
-									if (step[j1]<0) k0=1,k1=0; // reverse
-									else k0=0,k1=1; 
-									R2 V10 = (R2)(*t)[VerticesOfTriangularEdge[j1][k0]];
-									R2 V11 = (R2)(*t)[VerticesOfTriangularEdge[j1][k1]];
-									R2 D = V11-V10;
-									Real8 c0 =  vi0.m(D,(R2) vi0);
-
-									Real8 c10 =  vi0.m(D,V10);
-									Real8 c11 =  vi0.m(D,V11);
-
-									Real8 s;
-									//cout << " --i0 = " << i0  << D  << V10 << V11 << endl ;
-									//cout << "   c10 " <<  c10 << " c0 " << c0 << " c11 " << c11 << endl;
-									if (( c10 < c0 ) && (c0 < c11)) 
-										s = (c11-c0)/(c11-c10);
-									else if  (( c11 < c0 ) && (c0 < c10)) 
-										s = (c11-c0) /(c11-c10);
-									else break;
-									R2 VP = V10*s + V11*(1-s);
-									int sss = (c11-c10) >0 ? 1 : -1;
-									// find the 2 point by dichotomie
-									//cout << "   t =" << Number(t) << " c0 " << c0  ;
-									Int4 ii0 =  BeginNewPoint[j1];
-									Int4 ii1 =  EndNewPoint[j1];	     
-									Real8 ciii=-1,cii0=-1,cii1=-1  ;
-									if ( sss * ((cii0=vi0.m(D,(R2) vertices[ii0]))- c0) >0 )  
-										stack[kstack++] = ii0;//cout << " add+0 " << ii0;
-									else if ( sss * ((cii1=  vi0.m(D ,(R2) vertices[ii1]))- c0) < 0 )  
-										stack[kstack++] = ii1;//cout << " add+1 " << ii1;
-									else {
-										while ((ii1-ii0)> 1) {
-											Int4 iii = (ii0+ii1)/2;
-											ciii = vi0.m( D ,(R2) vertices[iii]);
-											//cout << " (iii = " << iii << " " <<  ciii << ") ";
-											if ( sss * (ciii - c0) <0 )  ii0 = iii;
-											else ii1 = iii;}	        	      
-											stack[kstack++] = ii0;// cout << " add0 " << ii0;
-											if (ii1 != ii0)  stack[kstack++] = ii1;//cout << " add1 " << ii1;
-									}
-									if (kstack >5) // bug ?
-										cout << "NewPoints: bug????? " << kstack << " stack  " << stack[kstack]<< endl;
-							}
-
-							stack[kstack++] = -1; // to stop
-							Int4 i1;
-							kstack =0; 
-							while( (i1=stack[kstack++]) >= 0) 
-							{ // the two parameter is i0 and i1 
-								assert(i1 < nbv && i1 >= 0);
-								assert(i0 < nbv && i0 >= 0);
-								assert(i1 != i0);
-								R2 v01 = (R2) vertices[i1]- (R2) vertices[i0];
-								Real8 d01 = (vertices[i0].m(v01) + vertices[i1].m(v01));
-
-
-#ifdef TRACETRIANGLE
-								if(trace) {
-									cout << "\n test j" << j <<" "  << i0 
-										<< " " << i1 << " d01=" << d01 <<endl;}
-#endif
-								assert (i0 >= nbvold);
-								assert (i1 >= nbvold);
-								assert(i0 != i1);
-								if (d01 == 0) 
-									break; 
-								if ( d01 < seuil) 
-									if (i1<nbvold) {
-										// remove all the points i0;
-										register Int4 ip,ipp;
-										for  (ip=i0;i0 != (ipp = vertices[ip].ReferenceNumber);ip=ipp)
-											vertices[ip].ReferenceNumber = -1;// mark remove
-										vertices[ip].ReferenceNumber = -1;// mark remove
-									}
-									else {
-										// remove on of two points
-										register Int4 ip0, ip1, ipp0,ipp1;
-										register int kk0=1,kk1=1;
-										// count the number of common points to compute weight w0,w1
-										for  (ip0=i0;i0 != (ipp0 = vertices[ip0].ReferenceNumber);ip0=ipp0) kk0++;
-										for  (ip1=i1;i1 != (ipp1 = vertices[ip1].ReferenceNumber);ip1=ipp1) kk1++;
-
-										register Real8 w0 = ((Real8) kk0)/(kk0+kk1);
-										register Real8 w1 = ((Real8) kk1)/(kk0+kk1);
-
-										// make a circular link
-										Exchange(vertices[i0].ReferenceNumber,vertices[i1].ReferenceNumber);
-										// the new coordinate 
-										R2 C //= vertices[i0] ;
-										=  vertices[i0].r *w0 + vertices[i1].r* w1;
-
-#ifdef TRACETRIANGLE
-										if(trace) {
-											cout << "\n ref = "<< vertices[i0].ref << " " <<vertices[i1].ref <<endl;
-										}
-#endif    
-										// update the new point points of the list 
-										for  (ip0=i0;i0 != (ipp0 = vertices[ip0].ReferenceNumber);ip0=ipp0)
-											vertices[ip0].r = C;	      
-										vertices[ip0].r = C;
-									}
-							}
-						} // for (i0= ....
-				}// for triangle   
-
-				// remove of all the double points
-
-				Int4 ip,ipp,kkk=nbvold;
-				for (i=nbvold;i<nbv;i++) 
-					if (vertices[i].ReferenceNumber>=0) {// good points
-						//  cout <<" i = " << i ;
-						for  (ip=i;i != (ipp = vertices[ip].ReferenceNumber);ip=ipp)
-							vertices[ip].ReferenceNumber = -1;// mark remove
-						vertices[ip].ReferenceNumber = -1;// mark remove
-						// cout << i << " ---> " << kkk << endl;        
-						vertices[kkk] = vertices[i];
-						vertices[kkk].i = toI2(vertices[kkk].r);
-						vertices[kkk++].ReferenceNumber = 0;
-
-					} 
-
-				// insertion part --- 
-
-				const Int4 nbvnew = kkk-nbvold;
-
-				cout << "    Remove " << nbv - kkk  << " to close  vertex " ;
-				cout << " and   Insert the " <<nbvnew<< " new points " << endl;  
-				nbv = kkk;
-				Int4 NbSwap=0;
-				Icoor2 dete[3];
-
-				// construction d'un ordre aleatoire 
-				if (! nbvnew) 
-					break; 
-				if (nbvnew) {
-					const Int4 PrimeNumber= AGoodNumberPrimeWith(nbv)  ;
-					Int4 k3 = rand()%nbvnew ; 
-					for (Int4 is3=0; is3<nbvnew; is3++) 
-						ordre[nbvold+is3]= &vertices[nbvold +(k3 = (k3 + PrimeNumber)% nbvnew)];
-
-					for (i=nbvold;i<nbv;i++) 
-					{ Vertex * vi = ordre[i];
-						Triangle *tcvi = FindTriangleContening(vi->i,dete);
-						//     Vertex * nv =  quadtree->NearestVertex(vi->i.x,vi->i.y);
-						//      cout << " Neart Vertex of "  << Number(vi)<< vi->i << " is " 
-						//   << Number(nv) << nv->i  << endl;
-						// Int4  kt = Number(tcvi);
-						// 
-
-						quadtree->Add(*vi); //
-						assert (tcvi->det >= 0) ;// internal 
-						Add(*vi,tcvi,dete),NbSwap += vi->Optim(1);          
-					}  
-				}
-				cout << " Nb swap = " << NbSwap << " after " ;
-
-				for (i=nbvold;i<nbv;i++) 
-					NbSwap += vertices[i].Optim(1);  
-				cout << NbSwap << endl;
-
-				for (i=nbtold;i<nbt;i++)
-					first_np_or_next_t[i]=1;
-
-				Headt = nbt; // empty list 
-				for (i=nbvold;i<nbv;i++) 
-				{ // for all the triangle contening the vertex i
-					Vertex * s  = vertices + i;
-					TriangleAdjacent ta(s->t, EdgesVertexTriangle[s->vint][1]);
-					Triangle * tbegin= (Triangle*) ta;
-					Int4 kt;
-					do { 
-						kt = Number((Triangle*) ta);
-						if (first_np_or_next_t[kt]>0) 
-							first_np_or_next_t[kt]=-Headt,Headt=kt;
-						assert( ta.EdgeVertex(0) == s);
-						ta = Next(Adj(ta));
-					} while ( (tbegin != (Triangle*) ta)); 
-				}
-
-
-			} while (nbv!=nbvold);
-			delete []  first_np_or_next_t;
-			cout << " end :  Triangles::NewPoints old  nbv=" << nbv << endl;
-
-		}
-
-		void Triangles::Insert() 
-		{
-			long int verbosity=2;
-			if (verbosity>2) cout << "  -- Insert initial " << nbv << " vertices " << endl ;
-			Triangles * OldCurrentTh =CurrentTh;
-
-			CurrentTh=this;
-			double time0=CPUtime(),time1,time2,time3;
-			SetIntCoor();
-			Int4 i;
-			for (i=0;i<nbv;i++) 
-				ordre[i]= &vertices[i] ;
-
-			// construction d'un ordre aleatoire 
-			const Int4 PrimeNumber= AGoodNumberPrimeWith(nbv) ;
-			Int4 k3 = rand()%nbv ; 
-			for (int is3=0; is3<nbv; is3++) 
-				ordre[is3]= &vertices[k3 = (k3 + PrimeNumber)% nbv];
-
-
-
-
-			for (i=2 ; det( ordre[0]->i, ordre[1]->i, ordre[i]->i ) == 0;) 
-				if  ( ++i >= nbv) {
-					cerr << " All the vertices are aline " << endl;
-					MeshError(998,this); }
-
-					// echange i et 2 dans ordre afin 
-					// que les 3 premiers ne soit pas aligne
-					Exchange( ordre[2], ordre[i]);
-
-					// on ajoute un point a l'infini pour construire le maillage
-					// afin d'avoir une definition simple des aretes frontieres
-					nbt = 2;
-
-
-					// on construit un maillage trivale forme
-					// d'une arete et de 2 triangles
-					// construit avec le 2 aretes orientes et 
-					Vertex *  v0=ordre[0], *v1=ordre[1];
-
-					triangles[0](0) = 0; // sommet pour infini 
-					triangles[0](1) = v0;
-					triangles[0](2) = v1;
-
-					triangles[1](0) = 0;// sommet pour infini 
-					triangles[1](2) = v0;
-					triangles[1](1) = v1;
-					const int e0 = OppositeEdge[0];
-					const int e1 = NextEdge[e0];
-					const int e2 = PreviousEdge[e0];
-					triangles[0].SetAdj2(e0, &triangles[1] ,e0);
-					triangles[0].SetAdj2(e1, &triangles[1] ,e2);
-					triangles[0].SetAdj2(e2, &triangles[1] ,e1);
-
-					triangles[0].det = -1;  // faux triangles
-					triangles[1].det = -1;  // faux triangles
-
-					triangles[0].SetTriangleContainingTheVertex();
-					triangles[1].SetTriangleContainingTheVertex();
-
-					triangles[0].link=&triangles[1];
-					triangles[1].link=&triangles[0];
-
-					//  nbtf = 2;
-					if (  !quadtree )  quadtree = new QuadTree(this,0);
-					quadtree->Add(*v0);
-					quadtree->Add(*v1);
-
-					// on ajoute les sommets un Ò un 
-					Int4 NbSwap=0;
-
-					time1=CPUtime();
-
-					if (verbosity>3) cout << "  -- Begin of insertion process " << endl;
-
-					for (Int4 icount=2; icount<nbv; icount++) {
-						Vertex *vi  = ordre[icount];
-						//    cout << " Insert " << Number(vi) << endl;
-						Icoor2 dete[3];
-						Triangle *tcvi = FindTriangleContening(vi->i,dete);
-						quadtree->Add(*vi); 
-						Add(*vi,tcvi,dete);
-						NbSwap += vi->Optim(1,0);
-
-					}// fin de boucle en icount
-					time2=CPUtime();
-					if (verbosity>3) 
-						cout << "    NbSwap of insertion " <<    NbSwap 
-							<< " NbSwap/Nbv " <<  (float) NbSwap / (float) nbv 
-							<< " NbUnSwap " << NbUnSwap << " Nb UnSwap/Nbv " 
-							<< (float)NbUnSwap /(float) nbv 
-							<<endl;
-					NbUnSwap = 0;
-					// construction d'un ordre aleatoire 
-					//  const int PrimeNumber= (nbv % 999983) ? 1000003: 999983 ;
-#ifdef NBLOOPOPTIM
-
-					k3 = rand()%nbv ; 
-					for (int is4=0; is4<nbv; is4++) 
-						ordre[is4]= &vertices[k3 = (k3 + PrimeNumber)% nbv];
-
-					double timeloop = time2 ;
-					for(int Nbloop=0;Nbloop<NBLOOPOPTIM;Nbloop++) 
-					{
-						double time000 = timeloop;
-						Int4  NbSwap = 0;
-						for (int is1=0; is1<nbv; is1++) 
-							NbSwap += ordre[is1]->Optim(0,0);
-						timeloop = CPUtime();
-						if (verbosity>3) 
-							cout << "    Optim Loop "<<Nbloop<<" NbSwap: " <<  NbSwap 
-								<< " NbSwap/Nbv " 	   <<  (float) NbSwap / (float) nbv 
-								<< " CPU=" << timeloop - time000 << "  s, " 
-								<< " NbUnSwap/Nbv " << (float)NbUnSwap /(float) nbv  
-								<<  endl;
-						NbUnSwap = 0;
-						if(!NbSwap) break;
-					}
-					ReMakeTriangleContainingTheVertex(); 
-					// because we break the TriangleContainingTheVertex
-#endif
-					time3=CPUtime();
-					if (verbosity>4) 
-						cout << "    init " << time1 - time0 << " initialisation,  " 
-							<< time2 - time1 << "s, insert point  " 
-							<< time3 -time2 << "s, optim " << endl
-							<< "     Init Total Cpu Time = " << time3 - time0 << "s " << endl;
-
-					CurrentTh=OldCurrentTh;
-		}
-
-
-		void Triangles::ForceBoundary()
-		{
-			long int verbosity=2;
-			if (verbosity > 2)
-				cout << "  -- ForceBoundary  nb of edge " << nbe << endl;
-			int k=0;
-			Int4  nbfe=0,nbswp=0,Nbswap=0;
-			for (Int4 t = 0; t < nbt; t++)  
-				if (!triangles[t].det)
-					k++,cerr << " det T" << t << " = " << 0 << endl;
-			if (k!=0) {
-				cerr << " ther is  " << k << "  triangles of mes = 0 " << endl;
-				MeshError(11,this);}
-
-				TriangleAdjacent ta(0,0);
-				for (Int4 i = 0; i < nbe; i++) 
-				{
-					nbswp =  ForceEdge(edges[i][0],edges[i][1],ta);
-
-					if ( nbswp < 0) 	k++;
-					else Nbswap += nbswp;
-					if (nbswp) nbfe++;
-					if ( nbswp < 0 && k < 5)
-					{
-						cerr << " Missing  Edge " << i << " v0 =  " << Number(edges[i][0]) << edges[i][0].r
-							<<" v1= " << Number(edges[i][1]) << edges[i][1].r << " " << edges[i].on->Cracked() << "  " << (Triangle *) ta ;
-						if(ta.t)
-						{
-							Vertex *aa = ta.EdgeVertex(0), *bb = ta.EdgeVertex(1);  
-							cerr << " crossing with  [" << Number(aa) << ", " << Number(bb) << "]\n";
-						}
-						else cerr << endl;
-
-					}
-					if ( nbswp >=0 && edges[i].on->Cracked())
-						ta.SetCracked();
-				}
-
-
-				if (k!=0) {
-					cerr << " they is " << k << " lost edges " << endl;
-					cerr << " The boundary is crossing may be!" << endl;
-					MeshError(10,this);
-				}
-				for (Int4 j=0;j<nbv;j++)
-					Nbswap +=  vertices[j].Optim(1,0);
-				if (verbosity > 3)
-					cout << "     Nb of inforced edge = " << nbfe << " Nb of Swap " << Nbswap << endl;
-
-		}
-
-		void Triangles::FindSubDomain(int OutSide=0)
-		{
-			long int verbosity=0;
-
-			if (verbosity >2)
-			{
-				if (OutSide)
-					cout << "  -- Find all external sub-domain ";	
-				else
-					cout << "  -- Find all internal sub-domain ";
-				if(verbosity>99)
-				{
-
-					for(int i=0;i<nbt;++i)
-						cout << i<< " " << triangles[i] << endl;
-				}
-
-			}
-			// if (verbosity > 4) cout << " OutSide=" << OutSide << endl;
-			short * HeapArete = new short[nbt];
-			Triangle  **  HeapTriangle = new Triangle*  [nbt];
-			Triangle *t,*t1;
-			Int4 k,it;
-
-			for (Int4 itt=0;itt<nbt;itt++) 
-				triangles[itt].link=0; // par defaut pas de couleur
-
-			Int4  NbSubDomTot =0;
-			for ( it=0;it<nbt;it++)  { 
-				if ( ! triangles[it].link  ) {
-					t = triangles + it;
-					NbSubDomTot++;; // new composante connexe
-					Int4 i = 0; // niveau de la pile 
-					t->link = t ; // sd forme d'un triangle cicular link
-
-					HeapTriangle[i] =t ; 
-					HeapArete[i] = 3;
-
-					while (i >= 0) // boucle sur la pile
-					{ while ( HeapArete[i]--) // boucle sur les 3 aretes 
-						{ 
-							int na =  HeapArete[i];
-							Triangle * tc =  HeapTriangle[i]; // triangle courant
-							if( ! tc->Locked(na)) // arete non frontiere
-							{
-								Triangle * ta = tc->TriangleAdj(na) ; // næ triangle adjacent
-								if (ta->link == 0 ) // non deja chainer => on enpile
-								{ 
-									i++;
-									ta->link = t->link ;  // on chaine les triangles
-									t->link = ta ;  // d'un meme sous domaine          
-									HeapArete[i] = 3; // pour les 3 triangles adjacents
-									HeapTriangle[i] = ta;
-								}}
-						} // deplie fin de boucle sur les 3 adjacences
-						i--;
-					}          
-				}      
-			}
-
-			// supression de tous les sous domaine infini <=>  contient le sommet NULL
-			it =0;
-			NbOutT = 0;
-			while (it<nbt) {
-				if (triangles[it].link) 
-				{ 
-					if (!( triangles[it](0) &&  triangles[it](1) &&  triangles[it](2) )) 
-					{
-						// infini triangle 
-						NbSubDomTot --;
-						//  cout << " triangle infini " << it << triangles[it] << endl;
-						t=&triangles[it];
-						NbOutT--;  // on fait un coup de trop. 
-						while  (t){ // cout << Number(t) << " " << endl;
-							NbOutT++;
-							t1=t;
-							t=t->link;
-							t1->link=0;}//while (t)
-					}
-				}   
-				it++;} // end while (it<nbt)
-				if (nbt == NbOutT ||  !NbSubDomTot) 
-				{
-					cout << "\n error : " <<  NbOutT << " " << NbSubDomTot <<" " << nbt << endl;
-					cerr << "Error: The boundary is not close => All triangles are outside " << endl;
-					MeshError(888,this);
-				}
-
-				delete [] HeapArete;
-				delete [] HeapTriangle;
-
-
-				if (OutSide|| !Gh.subdomains || !Gh.NbSubDomains ) 
-				{ // No geom sub domain
-					Int4 i;
-					if (subdomains) delete [] subdomains;
-					subdomains = new SubDomain[ NbSubDomTot];
-					NbSubDomains=  NbSubDomTot;
-					for ( i=0;i<NbSubDomains;i++) {
-						subdomains[i].head=NULL;
-						subdomains[i].ref=i+1;
-					}
-					Int4 * mark = new Int4[nbt];
-					for (it=0;it<nbt;it++)
-						mark[it]=triangles[it].link ? -1 : -2;
-
-					it =0;
-					k = 0;
-					while (it<nbt) {
-						if (mark[it] == -1) {
-							t1 = & triangles[it];
-							t = t1->link;
-							mark[it]=k;
-							subdomains[k].head = t1;
-							// cout << " New -- " << Number(t1) << " " << it << endl;
-							do {// cout << " k " << k << " " << Number(t) << endl;
-								mark[Number(t)]=k;
-								t=t->link;
-							} while (t!=t1);
-							mark[it]=k++;}
-							//    else if(mark[it] == -2 ) triangles[it].Draw(999);
-							it++;} // end white (it<nbt)
-							assert(k== NbSubDomains);
-							if(OutSide) 
-							{
-								//  to remove all the sub domain by parity adjacents
-								//  because in this case we have only the true boundary edge
-								// so teh boundary is manifold
-								Int4 nbk = NbSubDomains;
-								while (nbk)
-									for (it=0;it<nbt && nbk ;it++)
-										for (int na=0;na<3 && nbk ;na++)
-										{
-											Triangle *ta = triangles[it].TriangleAdj(na);
-											Int4 kl = ta ? mark[Number(ta)] : -2;
-											Int4 kr = mark[it];
-											if(kr !=kl) {
-												//cout << kl << " " << kr << " rl "  << subdomains[kl].ref
-												// << " rr " << subdomains[kr].ref ;
-												if (kl >=0 && subdomains[kl].ref <0 && kr >=0 && subdomains[kr].ref>=0)
-													nbk--,subdomains[kr].ref=subdomains[kl].ref-1;
-												if (kr >=0 && subdomains[kr].ref <0 && kl >=0 && subdomains[kl].ref>=0)
-													nbk--,subdomains[kl].ref=subdomains[kr].ref-1;
-												if(kr<0 && kl >=0 && subdomains[kl].ref>=0)
-													nbk--,subdomains[kl].ref=-1;
-												if(kl<0 && kr >=0 && subdomains[kr].ref>=0)
-													nbk--,subdomains[kr].ref=-1;
-												//   cout << " after \t "   
-												//	 << kl << subdomains[kl].ref << " rr " << kr 
-												// << subdomains[kr].ref << endl;
-											}
-										}
-								//  cout << subdomains[0].ref << subdomains[1].ref << endl;
-								Int4  j=0;
-								for ( i=0;i<NbSubDomains;i++)
-									if((-subdomains[i].ref) %2) { // good 
-										//cout << " sudom ok  = " << i << " " << subdomains[i].ref
-										// << " " << (-subdomains[i].ref) %2 << endl;
-										if(i != j) 
-											Exchange(subdomains[i],subdomains[j]);
-										j++;}
-									else
-									{ //cout << " remove sub domain " << i << endl;
-										t= subdomains[i].head;
-										while  (t){// cout << Number(t) << " " << endl;
-											NbOutT++;
-											t1=t;
-											t=t->link;
-											t1->link=0;}//while (t)
-									}
-
-								if(verbosity>4)
-									cout << " Number of remove sub domain (OutSideMesh) =" << NbSubDomains-j << endl;
-								NbSubDomains=j;
-							}
-
-							delete []  mark; 
-
-				}
-				else
-				{ // find the head for all sub domaine
-					if (Gh.NbSubDomains != NbSubDomains && subdomains)
-						delete [] subdomains, subdomains=0;
-					if (! subdomains  ) 
-						subdomains = new SubDomain[ Gh.NbSubDomains];
-					NbSubDomains =Gh.NbSubDomains;
-					if(verbosity>4)
-						cout << "     find the " << NbSubDomains << " sub domain " << endl;
-					Int4 err=0;
-					ReMakeTriangleContainingTheVertex();
-					Int4 * mark = new Int4[nbt];
-					Edge **GeometricalEdgetoEdge = MakeGeometricalEdgeToEdge();
-
-					for (it=0;it<nbt;it++)
-						mark[it]=triangles[it].link ? -1 : -2;
-					Int4 inew =0;
-					for (Int4 i=0;i<NbSubDomains;i++) 
-					{
-						GeometricalEdge &eg = *Gh.subdomains[i].edge;
-						subdomains[i].ref = Gh.subdomains[i].ref;
-						int ssdlab = subdomains[i].ref;
-						// by carefull is not easy to find a edge create from a GeometricalEdge 
-						// see routine MakeGeometricalEdgeToEdge
-						Edge &e = *GeometricalEdgetoEdge[Gh.Number(eg)];
-						assert(&e);
-						Vertex * v0 =  e(0),*v1 = e(1);
-						Triangle *t  = v0->t;
-						int sens = Gh.subdomains[i].sens;
-						// test if ge and e is in the same sens 
-						//	cout << " geom edge = " <<  Gh.Number(eg) <<" @" << &eg << " ref = " << subdomains[i].ref 
-						//     << " ref edge =" << eg.ref << " sens " << sens ;
-						if (((eg[0].r-eg[1].r),(e[0].r-e[1].r))<0)
-							sens = -sens ;
-						subdomains[i].sens = sens;
-						subdomains[i].edge = &e;
-						//	cout << " sens " << sens << " in geom " << eg[0].r << eg[1].r << " in mesh  " << e[0].r << e[1].r << endl;
-						//	cout << "  v0 , v1 = " << Number(v0) << " "  << Number(v1) << endl;
-						assert(t && sens);
-
-						TriangleAdjacent  ta(t,EdgesVertexTriangle[v0->vint][0]);// previous edges
-
-						while (1) 
-						{
-							assert( v0 == ta.EdgeVertex(1) );
-							//	 cout << " recherche " << Number( ta.EdgeVertex(0)) << endl;
-							if (ta.EdgeVertex(0) == v1) { // ok we find the edge
-								if (sens>0)  
-									subdomains[i].head=t=Adj(ta);
-								else 
-									subdomains[i].head=t=ta;
-								//cout << "      triangle  =" << Number(t) << " = " << (*t)[0].r <<  (*t)[1].r <<  (*t)[2].r << endl;
-								if(t<triangles || t >= triangles+nbt || t->det < 0 
-										|| t->link == 0) // Ajoute aout 200 
-								{
-									cerr << " Error in the def of sub domain "<<i
-										<< " form border " << NbSubDomains - i  << "/" << NbSubDomains
-										<< ": Bad sens  " << Gh.Number(eg) <<" "<< sens <<  endl;  
-									err++;
-									break;}
-									Int4 it = Number(t);
-									if (mark[it] >=0) {
-										if(verbosity>10)
-											cerr << "     Warning: the sub domain " << i << " ref = " << subdomains[i].ref 
-												<< " is previouly defined with "  <<mark[it] << " ref = " << subdomains[mark[it]].ref
-												<< " skip this def " << endl;
-										break;}
-										if(i != inew) 
-											Exchange(subdomains[i],subdomains[inew]);
-										inew++;
-										Triangle *tt=t;
-										Int4 kkk=0;
-										do 
-										{
-											kkk++;
-											assert(mark[Number(tt)]<0);
-											mark[Number(tt)]=i;
-											tt=tt->link;
-										} while (tt!=t);
-										if(verbosity>7)
-											cout << "     Nb de triangles dans le sous domaine " << i << " de ref " << subdomains[i].ref << " = " << kkk << endl;
-										break;}
-										ta = Previous(Adj(ta));         
-										if(t == (Triangle *) ta) {
-											err++;
-											cerr << " Error in the def of sub domain " << i 
-												<< " edge=" << Gh.Number(eg) << " " << sens << endl;
-											break;}
-											//         cout << " NB of remove subdomain " << NbSubDomTot-NbSubDomains<< endl;
-
-						}
-
-					}
-					if (err) MeshError(777,this);
-
-					if (inew < NbSubDomains) {
-						if (verbosity>5) 
-							cout << "     Warning: We remove " << NbSubDomains-inew << " SubDomains " << endl;
-						NbSubDomains=inew;}
-
-
-						for (it=0;it<nbt;it++)
-							if ( mark[it] ==-1 ) 
-								NbOutT++,triangles[it].link =0;
-						delete [] GeometricalEdgetoEdge;
-						delete [] mark;
-
-				}
-				NbOutT=0;
-				for (it=0;it<nbt;it++) 
-					if(!triangles[it].link)  NbOutT++;
-				if (verbosity> 4)
-					cout << "    " ;
-				if (verbosity> 2)
-					cout << " Nb of Sub borned Domain  = " <<  NbSubDomTot << " NbOutTriangles = " << NbOutT <<endl;
-
-
-		}
-		void Triangles::ReNumberingVertex(Int4 * renu)
-		{
-			// warning be carfull because pointeur
-			// from on mesh to over mesh 
-			//  --  so do ReNumbering a the beginning
-			Vertex * ve = vertices+nbv;
-			Int4 it,ie,i;
-
-			for ( it=0;it<nbt;it++) 
-				triangles[it].ReNumbering(vertices,ve,renu);
-
-			for ( ie=0;ie<nbe;ie++) 
-				edges[ie].ReNumbering(vertices,ve,renu);
-
-			for (i=0;i< NbVerticesOnGeomVertex;i++)
-			{
-				Vertex *v = VerticesOnGeomVertex[i].mv;
-				if (v>=vertices && v < ve)
-					VerticesOnGeomVertex[i].mv=vertices+renu[Number(v)];
-			}
-
-			for (i=0;i< NbVerticesOnGeomEdge;i++)
-			{
-				Vertex *v =VerticesOnGeomEdge[i].mv;
-				if (v>=vertices && v < ve)
-					VerticesOnGeomEdge[i].mv=vertices+renu[Number(v)];
-			}
-
-			for (i=0;i< NbVertexOnBThVertex;i++)
-			{
-				Vertex *v=VertexOnBThVertex[i].v;
-				if (v>=vertices && v < ve)
-					VertexOnBThVertex[i].v=vertices+renu[Number(v)];
-			}
-
-			for (i=0;i< NbVertexOnBThEdge;i++)
-			{
-				Vertex *v=VertexOnBThEdge[i].v;
-				if (v>=vertices && v < ve)
-					VertexOnBThEdge[i].v=vertices+renu[Number(v)];
-			}
-
-			// move the Vertices without a copy of the array 
-			// be carefull not trivial code 
-			Int4 j;
-			for ( it=0;it<nbv;it++) // for all sub cycles of the permutation renu
-				if (renu[it] >= 0) // a new sub cycle
-				{ 
-					i=it;
-					Vertex ti=vertices[i],tj;
-					while ( (j=renu[i]) >= 0) 
-					{ // i is old, and j is new 
-						renu[i] = -1-renu[i]; // mark 
-						tj = vertices[j]; // save new
-						vertices[j]= ti; // new <- old
-						i=j;     // next 
-						ti = tj;
-					}  
-				}
-			if (quadtree) 
-			{  delete quadtree;
-				quadtree = new QuadTree(this);
-			}
-			for ( it=0;it<nbv;it++)
-				renu[i]= -renu[i]-1;
-
-		}
-		void Triangles::ReNumberingTheTriangleBySubDomain(bool justcompress)
-		{
-			long int verbosity=0;
-			Int4 *renu= new Int4[nbt];
-			register Triangle *t0,*t,*te=triangles+nbt;
-			register Int4 k=0,it,i,j;
-
-			for ( it=0;it<nbt;it++) 
-				renu[it]=-1; // outside triangle 
-			for ( i=0;i<NbSubDomains;i++)
-			{ 
-				t=t0=subdomains[i].head;
-				assert(t0); // no empty sub domain
-				do { 
-					Int4 kt = Number(t);
-					assert(kt>=0 && kt < nbt );
-					assert(renu[kt]==-1);
-					renu[kt]=k++;
-				}
-				while (t0 != (t=t->link));
-			}
-			if (verbosity>9)
-				cout << " number of inside triangles " << k << " nbt = " << nbt << endl;
-			// take is same numbering if possible    
-			if(justcompress)
-				for ( k=0,it=0;it<nbt;it++) 
-					if(renu[it] >=0 ) 
-						renu[it]=k++;
-
-			// put the outside triangles at the end
-			for ( it=0;it<nbt;it++) 
-				if (renu[it]==-1) 
-					renu[it]=k++;
-
-			assert(k == nbt);
-			// do the change on all the pointeur 
-			for ( it=0;it<nbt;it++)
-				triangles[it].ReNumbering(triangles,te,renu);
-
-			for ( i=0;i<NbSubDomains;i++)
-				subdomains[i].head=triangles+renu[Number(subdomains[i].head)];
-
-			// move the Triangles  without a copy of the array 
-			// be carefull not trivial code 
-			for ( it=0;it<nbt;it++) // for all sub cycles of the permutation renu
-				if (renu[it] >= 0) // a new sub cycle
-				{ 
-					i=it;
-					Triangle ti=triangles[i],tj;
-					while ( (j=renu[i]) >= 0) 
-					{ // i is old, and j is new 
-						renu[i] = -1; // mark 
-						tj = triangles[j]; // save new
-						triangles[j]= ti; // new <- old
-						i=j;     // next 
-						ti = tj;
-					}  
-				}
-			delete [] renu;
-			nt = nbt - NbOutT;
-
-		}
-		Int4  Triangles::ConsRefTriangle(Int4 *reft) const
-		{
-			long int verbosity=0;
-			assert(reft);
-			register Triangle *t0,*t;
-			register Int4 k=0, num;   
-			for (Int4 it=0;it<nbt;it++) 
-				reft[it]=-1; // outside triangle 
-			for (Int4 i=0;i<NbSubDomains;i++)
-			{ 
-				t=t0=subdomains[i].head;
-				assert(t0); // no empty sub domain
-				// register Int4 color=i+1;// because the color 0 is outside triangle
-				do { k++;
-					num = Number(t);
-					assert(num>=0 &&num < nbt);
-					reft[num]=i;
-					//  cout << Number(t0) << " " <<Number(t)<< " "  << i << endl;
-				}
-				while (t0 != (t=t->link));
-			}
-			//  NbOutT = nbt - k;
-			if (verbosity>5) 
-				cout << " Nb of Sub Domain =" << NbSubDomains  << " Nb of In Triangles " << k 
-					<< " Nbt = " << nbt << " Out Triangles = " << nbt - k <<  endl;
-
-			return k;   
-
-		}
-
-		/*
-		   void Triangles::ConsLinkTriangle()
-		   {
-		   for (Int4 i=0;i<NbSubDomains;i++)
-		   subdomains[i].head=0;
-		   register Triangle * t=triangles,*tend = triangles+nbt,*hst;
-		   for (;t<tend;t++)
-		   {  
-		   if (t->link) 
-		   {
-		   register Int4 color = t->color-1;
-		   assert(color<NbSubDomains && color>=0);
-		   if (hst=subdomains[color].head) {
-		   t->link=hst->link;
-		   hst->link=t; }
-		   else {
-		   subdomains[color].head = t;
-		   t->link=t;}// circular link         
-		   }
-		   }
-		   {
-		   for (Int4 i=0;i<NbSubDomains;i++)
-		   assert(subdomains[i].head);
-		   }
-
-		   }
-		   */
-		/* void Triangles::RandomInit() 
-		   { 
-		//  Meshbegin = vertices;
-		//  Meshend  = vertices + nbvx;
-		nbv = nbvx;
-		for (int i = 0; i < nbv; i++)
-		{
-		vertices[i].r.x= rand();
-		vertices[i].r.y= rand();
-		vertices[i].ref = 0;
-		}
-		}
-		void Triangles::CubeInit(int n,int m) 
-		{ 
-		//  nbvx = n*m;
-		//  Meshbegin = vertices;
-		// Meshend  = vertices + nbvx;
-		nbv = n*m;
-		assert(nbv <= nbvx);
-		int k =0;
-		for (int i = 0; i < n; i++)
-		for (int j = 0; j < m; j++)
-		{
-		vertices[k].r.x= i;
-		vertices[k].r.y= j;
-		vertices[k++].ref = 0;
-		}
-		}
-		*/
 		Vertex * Triangles::NearestVertex(Icoor1 i,Icoor1 j) 
 		{ return  quadtree->NearestVertex(i,j); } 
@@ -2804,1688 +1160,6 @@
 					<< " " << vertices 
 					<< " " << ordre << " " <<  triangles <<endl;
-
 		}
 
-		void Triangles::GeomToTriangles1(Int4 inbvx,int KeepBackVertices) 
-		{ 
-			Gh.NbRef++;// add a ref to Gh
-
-
-			/************************************************************************* 
-			// methode in 2 step
-			// 1 - compute the number of new edge to allocate
-			// 2 - construct the edge
-remark: 
-in this part we suppose to have a background mesh with the same
-geometry 
-
-To construct the discretisation of the new mesh we have to 
-rediscretize the boundary of background Mesh 
-because we have only the pointeur from the background mesh to the geometry.
-We need the abcisse of the background mesh vertices on geometry
-so a vertex is 
-0 on GeometricalVertex ;
-1 on GeometricalEdge + abcisse
-2 internal 
-
-			 *************************************************************************/
-			assert(&BTh.Gh == &Gh);
-
-			long int verbosity=0;
-			BTh.NbRef++; // add a ref to BackGround Mesh
-			PreInit(inbvx);
-			BTh.SetVertexFieldOn();
-				int * bcurve = new int[Gh.NbOfCurves]; // 
-
-				// we have 2 ways to make the loop 
-				// 1) on the geometry 
-				// 2) on the background mesh
-				//  if you do the loop on geometry, we don't have the pointeur on background,
-				//  and if you do the loop in background we have the pointeur on geometry
-				// so do the walk on  background
-				//  Int4 NbVerticesOnGeomVertex;
-				//  VertexOnGeom * VerticesOnGeomVertex;  
-				//  Int4 NbVerticesOnGeomEdge;
-				//  VertexOnGeom * VerticesOnGeomEdge;
-
-
-				NbVerticesOnGeomVertex=0;
-				NbVerticesOnGeomEdge=0;
-				//1 copy of the  Required vertex
-				int i; 
-				for ( i=0;i<Gh.nbv;i++)
-					if (Gh[i].Required()) NbVerticesOnGeomVertex++;
-
-				VerticesOnGeomVertex = new VertexOnGeom[NbVerticesOnGeomVertex];
-				VertexOnBThVertex = new VertexOnVertex[NbVerticesOnGeomVertex];
-				//
-				if( NbVerticesOnGeomVertex >= nbvx) 
-				{
-					cerr << " Too much vertices on geometry " << NbVerticesOnGeomVertex << " >= " << nbvx << endl; 
-					MeshError(1,this);
-				}
-				assert(vertices);
-				for (i=0;i<Gh.nbv;i++)
-					if (Gh[i].Required()) {//Gh  vertices Required
-						vertices[nbv] =  Gh[i];
-						vertices[nbv].i = I2(0,0);
-						Gh[i].to = vertices + nbv;// save Geom -> Th
-						VerticesOnGeomVertex[nbv]= VertexOnGeom(vertices[nbv],Gh[i]);
-						// cout << "--------- "  <<Number(Gh[i].to) << " " << Gh[i].to << " " << i << endl;
-						nbv++;}
-					else Gh[i].to=0;
-				// 
-				for (i=0;i<BTh.NbVerticesOnGeomVertex;i++)
-				{ 
-					VertexOnGeom & vog = BTh.VerticesOnGeomVertex[i];
-					if (vog.IsRequiredVertex()) {
-						GeometricalVertex * gv = vog;
-						Vertex *bv = vog;
-						assert(gv->to);// use of Geom -> Th
-						VertexOnBThVertex[NbVertexOnBThVertex++] = VertexOnVertex(gv->to,bv);
-						gv->to->m = bv->m; // for taking the metrix of the background mesh
-						;}
-				}
-				assert(NbVertexOnBThVertex == NbVerticesOnGeomVertex);
-				// new stuff FH with curve
-				//  find the begin of the curve in BTh
-				{
-					Gh.UnMarkEdges();	
-					int bfind=0;
-					/*
-					   cout << " nb curves = " << Gh.NbOfCurves << endl;
-					   for(int i=0;i<Gh.NbOfCurves ;i++)
-					   {
-					   cout << " Curve " << i << " begin e=" << Gh.Number(Gh.curves[i].be) << " k=" << Gh.curves[i].kb 
-					   << "  end e= " << Gh.Number(Gh.curves[i].ee) << " k=" << Gh.curves[i].ke << endl;
-					   }*/
-					for (int i=0;i<Gh.NbOfCurves;i++)
-					{
-						bcurve[i]=-1; 
-					}
-
-					for (int iedge=0;iedge<BTh.nbe;iedge++) 
-					{      
-						Edge & ei = BTh.edges[iedge];
-						for(int je=0;je<2;je++) // for the 2 extremites
-							if (!ei.on->Mark() && ei[je].on->IsRequiredVertex() )
-							{
-								// a begin of curve 
-								int nc = ei.on->CurveNumber;
-
-								//cout << "curve " <<  nc << " v " << Gh.Number((GeometricalVertex *) *ei[je].on) << " "
-								//     << " e "  << " " << Gh.Number(ei.on) << " vc " << Gh.Number((*Gh.curves[nc].be)[Gh.curves[nc].kb]) << endl;
-								if(
-										ei.on==Gh.curves[nc].be    && 
-										(GeometricalVertex *) *ei[je].on == &(*Gh.curves[nc].be)[Gh.curves[nc].kb] //  same extremity 
-								  )     
-								{ 
-									// cout << " find " << endl;
-									bcurve[nc]=iedge*2+je;
-									bfind++;	
-								}      
-							}
-					} 
-					assert( bfind==Gh.NbOfCurves);
-				}          
-				// method in 2 + 1 step 
-				//  0.0) compute the length and the number of vertex to do allocation
-				//  1.0)  recompute the length
-				//  1.1)   compute the  vertex 
-				Int4 nbex=0,NbVerticesOnGeomEdgex=0;
-				for (int step=0; step <2;step++)
-				{
-					Int4 NbOfNewPoints=0;
-					Int4 NbOfNewEdge=0;
-					Int4 iedge;
-					Gh.UnMarkEdges();	
-					/*   add Curve loop  FH    
-					// find a starting back groud edges to walk 
-					for (iedge=0;iedge<BTh.nbe;iedge++) {      
-					Edge & ei = BTh.edges[iedge];
-					for(int jedge=0;jedge<2;jedge++) // for the 2 extremites
-					if (!ei.on->Mark() && ei[jedge].on->IsRequiredVertex() )
-					{
-					*/  
-					// new code FH 2004 
-					Real8 L=0;
-					for (int icurve=0;icurve<Gh.NbOfCurves;icurve++)
-					{ 
-						iedge=bcurve[icurve]/2;
-						int jedge=bcurve[icurve]%2;
-						if( ! Gh.curves[icurve].master) continue; // we skip all equi curve
-						Edge & ei = BTh.edges[iedge];
-						// warning: ei.on->Mark() can be change in
-						// loop for(jedge=0;jedge<2;jedge++) 
-						// new curve  
-						// good the find a starting edge 
-						Real8 Lstep=0,Lcurve=0;// step between two points   (phase==1) 
-						Int4 NbCreatePointOnCurve=0;// Nb of new points on curve     (phase==1) 
-
-
-						//    cout.precision(16);
-						for(int phase=0;phase<=step;phase++) 
-						{
-
-							for(Curve * curve= Gh.curves+icurve;curve;curve= curve->next)
-							{
-
-								int icurveequi= Gh.Number(curve);
-
-								if( phase == 0 &&  icurveequi != icurve)  continue;
-
-								int k0=jedge,k1;
-								Edge * pe=  BTh.edges+iedge;
-								//GeometricalEdge *ong = ei.on;
-								int iedgeequi=bcurve[icurveequi]/2;
-								int jedgeequi=bcurve[icurveequi]%2;
-
-								int k0equi=jedgeequi,k1equi;		  
-								Edge * peequi= BTh.edges+iedgeequi;
-								GeometricalEdge *ongequi = peequi->on;
-
-								Real8 sNew=Lstep;// abcisse of the new points (phase==1) 
-								L=0;// length of the curve
-								Int4 i=0;// index of new points on the curve
-								register GeometricalVertex * GA0 = *(*peequi)[k0equi].on;
-								Vertex *A0;
-								A0 = GA0->to;  // the vertex in new mesh
-								Vertex *A1;
-								VertexOnGeom *GA1;
-								Edge * PreviousNewEdge = 0;
-								//  cout << "  --------------New Curve phase " << phase 
-								//       << "---------- A0=" << *A0 << ei[k0]  <<endl;
-								assert (A0-vertices>=0 && A0-vertices <nbv);
-								if(ongequi->Required() ) 
-								{
-									GeometricalVertex *GA1 = *(*peequi)[1-k0equi].on;
-									A1 = GA1->to;  //
-								}       
-								else 
-									for(;;) 
-									{
-										//   assert(pe && BTh.Number(pe)>=0 && BTh.Number(pe)<=BTh.nbe);
-										Edge &ee=*pe; 
-										Edge &eeequi=*peequi; 
-										k1 = 1-k0; // next vertex of the edge 
-										k1equi= 1 - k0equi;
-
-										assert(pe  && ee.on);
-										ee.on->SetMark();
-										Vertex & v0=ee[0], & v1=ee[1];
-										R2 AB= (R2) v1 - (R2) v0;
-										Real8 L0=L,LAB;
-										LAB =  LengthInterpole(v0.m,v1.m,AB);
-										L+= LAB;    
-										if (phase) {// computation of the new points
-											while ((i!=NbCreatePointOnCurve) && sNew <= L) { 
-												//    cout  << " L0= " << L0 << " L " << L << " sN=" 
-												//         << sNew << " LAB=" << LAB << " NBPC =" <<NbCreatePointOnCurve<< " i " << i  << endl;
-												assert (sNew >= L0);
-												assert(LAB);
-
-
-												assert(vertices && nbv<nbvx);
-												assert(edges && nbe < nbex);
-												assert(VerticesOnGeomEdge && NbVerticesOnGeomEdge < NbVerticesOnGeomEdgex);
-												// new vertex on edge
-												A1=vertices+nbv++;
-												GA1=VerticesOnGeomEdge+NbVerticesOnGeomEdge;
-												Edge *e = edges + nbe++;
-												Real8 se= (sNew-L0)/LAB;
-												assert(se>=0 && se < 1.000000001);
-												se =  abscisseInterpole(v0.m,v1.m,AB,se,1);
-												assert(se>=0 && se <= 1);
-												//((k1==1) != (k1==k1equi))
-												se = k1 ? se : 1. - se;
-												se = k1==k1equi ? se : 1. - se;
-												VertexOnBThEdge[NbVerticesOnGeomEdge++] = VertexOnEdge(A1,&eeequi,se); // save 
-												ongequi = Gh.ProjectOnCurve(eeequi,se,*A1,*GA1); 
-												A1->ReferenceNumber = eeequi.ref;
-												A1->DirOfSearch =NoDirOfSearch;
-												//cout << icurveequi << " " << i << " " <<  *A1 << endl;
-												e->on = ongequi;
-												e->v[0]=  A0;
-												e->v[1]=  A1;
-												if(verbosity>99)
-													cout << i << "+ New P "<< nbv-1 << " "  <<sNew<< " L0=" << L0 
-														<< " AB=" << LAB << " s=" << (sNew-L0)/LAB << " se= "  
-														<< se <<" B edge " << BTh.Number(ee) << " signe = " << k1 <<" " << A1->r <<endl;
-
-												e->ref = eeequi.ref;
-												e->adj[0]=PreviousNewEdge;
-
-												if (PreviousNewEdge)
-													PreviousNewEdge->adj[1] =  e;
-												PreviousNewEdge = e;
-												A0=A1;
-												sNew += Lstep;
-												//   cout << " sNew = " << sNew << " L = " << L 
-												//        << "  ------" <<NbCreatePointOnCurve << " " << i <<  endl;
-												if (++i== NbCreatePointOnCurve) break;
-											}
-
-										}               
-										assert(ee.on->CurveNumber==ei.on->CurveNumber);
-										if(verbosity>98) cout <<  BTh.Number(ee) << " " << " on=" << *ee[k1].on << " "<< ee[k1].on->IsRequiredVertex() <<  endl;
-										if ( ee[k1].on->IsRequiredVertex()) {
-											assert(eeequi[k1equi].on->IsRequiredVertex());
-											register GeometricalVertex * GA1 = *eeequi[k1equi].on;
-											A1=GA1->to;// the vertex in new mesh
-											assert (A1-vertices>=0 && A1-vertices <nbv);
-											break;}
-											if (!ee.adj[k1])
-											{cerr << "Error adj edge " << BTh.Number(ee) << ", nbe = "  << nbe 
-												<< " Gh.vertices " << Gh.vertices 
-													<< " k1 = " << k1 << " on=" << *ee[k1].on << endl;
-												cerr << ee[k1].on->gv-Gh.vertices << endl;
-											}
-											pe = ee.adj[k1]; // next edge
-											k0 = pe->Intersection(ee); 
-											peequi= eeequi.adj[k1equi];  // next edge
-											k0equi=peequi->Intersection(eeequi);            
-									}// for(;;) end of the curve
-
-
-								if (phase) // construction of the last edge
-								{
-									Edge *e = edges + nbe++;
-									if (verbosity>10) 
-										cout << " Fin curve A1" << *A1 << " " << icurve << " <=> " << icurveequi <<"-----" <<
-											NbCreatePointOnCurve << " == " <<i<<endl;
-									e->on  = ongequi;
-									e->v[0]=  A0;
-									e->v[1]=	A1;
-									e->ref = peequi->ref;
-									e->adj[0]=PreviousNewEdge;
-									e->adj[1]=0;
-									if (PreviousNewEdge)
-										PreviousNewEdge->adj[1] =  e;
-									PreviousNewEdge = e;
-
-									assert(i==NbCreatePointOnCurve);
-
-								}
-							} //  end loop on equi curve 
-
-							if (!phase)  { // 
-								Int4 NbSegOnCurve = Max((Int4)(L+0.5),(Int4) 1);// nb of seg
-								Lstep = L/NbSegOnCurve; 
-								Lcurve = L;
-								NbCreatePointOnCurve = NbSegOnCurve-1;
-
-								for(Curve * curve= Gh.curves+icurve;curve;curve= curve->next)
-								{
-									NbOfNewEdge += NbSegOnCurve;
-									NbOfNewPoints += NbCreatePointOnCurve;
-								}
-								if(verbosity>5)
-									cout << icurve << " NbSegOnCurve = " <<  NbSegOnCurve << " Lstep=" 
-										<< Lstep <<" " << NbOfNewPoints<< " NBPC= " << NbCreatePointOnCurve <<endl;
-								// do'nt 
-								//  if(NbCreatePointOnCurve<1) break;
-							}
-						}//for(phase;;)
-						/*  modif FH add Curve class  		  
-							}}//for (iedge=0;iedge<BTh.nbe;iedge++) 
-							*/
-						// new code Curve class  	
-				} //  end of curve loop 
-				// end new code	    
-				// do the allocation
-				if(step==0) 
-				{
-					//if(!NbOfNewPoints) break;// nothing ????? bug 
-					if(nbv+NbOfNewPoints > nbvx) 
-					{
-						cerr << " Too much vertices on geometry " << nbv+NbOfNewPoints  << " >= " << nbvx << endl;
-						MeshError(3,this);
-					}
-					//cout << " NbOfNewEdge" << NbOfNewEdge << " NbOfNewPoints " << NbOfNewPoints << endl;
-					edges = new Edge[NbOfNewEdge];
-					nbex = NbOfNewEdge;
-					if(NbOfNewPoints) { // 
-						VerticesOnGeomEdge = new VertexOnGeom[NbOfNewPoints];
-						NbVertexOnBThEdge =NbOfNewPoints;
-						VertexOnBThEdge = new  VertexOnEdge[NbOfNewPoints];
-						NbVerticesOnGeomEdgex = NbOfNewPoints; }
-						NbOfNewPoints =0;
-						NbOfNewEdge = 0;
-				}
-				} // for(step;;)
-				assert(nbe);
-
-				delete [] bcurve;
-
-
-				Insert();
-				ForceBoundary();
-				FindSubDomain();
-
-				NewPoints(BTh,KeepBackVertices) ;
-				CurrentTh = 0;
-		}
-
-		void Triangles::GeomToTriangles0(Int4 inbvx) 
-		{
-			Gh.NbRef++;// add a ref to GH
-
-
-			Int4 i,NbOfCurves=0,NbNewPoints,NbEdgeCurve;
-			Real8 lcurve, lstep,s;
-
-				R2 AB;
-				GeometricalVertex *a,*b;
-				Vertex *va,*vb;
-				GeometricalEdge * e;
-				PreInit(inbvx);
-				int  background = &BTh != this;
-				//  int  SameGeom = background && (&BTh.Gh == &Gh);
-				nbv = 0;
-				NbVerticesOnGeomVertex=0;
-				NbVerticesOnGeomEdge=0;
-				for (i=0;i<Gh.nbv;i++)
-					if (Gh[i].Required() && Gh[i].IsThe() ) NbVerticesOnGeomVertex++;
-				VerticesOnGeomVertex = new VertexOnGeom[NbVerticesOnGeomVertex];  
-				//
-				if( NbVerticesOnGeomVertex >= nbvx) 
-				{
-					cerr << " Too much vertices on geometry " << NbVerticesOnGeomVertex << " >= " << nbvx << endl;
-					MeshError(1,this);
-				}
-				for (i=0;i<Gh.nbv;i++)
-					if (Gh[i].Required()&& Gh[i].IsThe()  ) {//Gh  vertices Required
-						if (nbv < nbvx)
-							vertices[nbv] = Gh[i];
-						Gh[i].to = vertices + nbv;// save Geom -> Th
-						VerticesOnGeomVertex[nbv]= VertexOnGeom(*Gh[i].to,Gh[i]);
-						//  cout << "--------- "  <<Number(Gh[i].to) << " " << Gh[i].to << " " << i << endl;
-						nbv++;
-					}
-				//  assert( Gh.nbv < nbvx);
-
-				// Method in 2 step:  0 and 1 
-				// 1) compute de nb of edge 
-				// 2) construct the edge    
-				// generation of the curves
-				assert(! edges);
-				// 2 step 
-				// --step=0 to compute the number of edges + alloc at end
-				// --step=1 to construct the edges
-				for (int step=0;step<2;step++) 
-				{//  for (int step=0;step<2;step++) 
-					Int4 nbex = 0;
-					nbe = 0;
-					Int4 NbVerticesOnGeomEdge0=NbVerticesOnGeomEdge;
-					//  cout <<  "  -------------- step =" << step << endl;
-					Gh.UnMarkEdges();	
-					NbOfCurves = 0;
-					for (i=0;i<Gh.nbe;i++) {
-						GeometricalEdge & ei = Gh.edges[i];   
-						if (!ei.Dup()) // a good curve (not dup )
-							for(int j=0;j<2;j++) 
-								if (!ei.Mark() && ei[j].Required()) { 
-									// warning ei.Mark() can be change in loop for(j=0;j<2;j++) 
-									//  cout << " New curve = " << NbOfCurves << endl;
-									Int4 nbvend  =0;
-
-									Edge * PreviousNewEdge=0;
-
-									lstep = -1;//to do not create points
-									if(ei.Required())
-									{
-										if (j==0)
-											if(step==0)
-												nbe++;
-											else
-											{ 
-												e = & ei;
-												a=ei(0)->The();
-												b=ei(1)->The();
-												assert(edges);
-												edges[nbe].v[0]=a->to;
-												edges[nbe].v[1]=b->to;;
-												edges[nbe].ref = e->ref;
-												edges[nbe].on = e;
-												edges[nbe].adj[0] = 0;
-												edges[nbe].adj[1] = 0;
-												nbe++;}
-									}
-									else 
-									{ // on curve ------
-										for ( int kstep=0;kstep<= step;kstep++)
-										{ // begin  for ( int kstep=0;kstep<= step;kstep++)
-											// if 2nd step where 2 step
-											// -- 1 compute le length of the curve
-											// -- create the points and edge
-											PreviousNewEdge=0;
-											NbNewPoints=0;
-											NbEdgeCurve=0;
-											assert(nbvend < nbvx); 
-											lcurve =0;
-											s = lstep;
-											int k=j;
-											e = & ei;
-											a=ei(k)->The();
-											va = a->to;
-											e->SetMark();
-											//  cout << " New curve " ;
-
-											// if SameGeo  We have go in the background geometry 
-											// to find the discretisation of the curve
-
-											for(;;) 
-											{ 
-												k = 1-k;
-												b= (*e)(k)->The();
-												AB = b->r - a->r;
-												Metric MA = background ? BTh.MetricAt(a->r) :a->m ;
-												Metric MB =  background ? BTh.MetricAt(b->r) :b->m ;
-												Real8 ledge = (MA(AB) + MB(AB))/2;
-												// 
-												const int MaxSubEdge = 10;
-												int NbSubEdge = 1;
-												Real8 lSubEdge[MaxSubEdge];
-												R2 A,B;
-												if (ledge < 1.5) 
-													lSubEdge[0] = ledge;
-												else {
-													NbSubEdge = Min( MaxSubEdge, (int) (ledge +0.5));
-													A= a->r;
-													Metric MAs =MA,MBs;
-													// cout << " lSubEdge old=" << ledge 
-													//      << " new " << A << MA << endl;
-													ledge = 0; 
-													Real8 x =0, xstep= 1. /  NbSubEdge;
-													for (int kk=0; kk < NbSubEdge; kk++,A=B,MAs=MBs ) {
-														x += xstep;
-														B =  e->F(k ? x : 1-x);
-														MBs= background ? BTh.MetricAt(B) :Metric(1-x, MA, x ,MB);
-														AB = A-B;
-														lSubEdge[kk]= (ledge += (MAs(AB)+MBs(AB))/2);
-														// cout << "     " << lSubEdge[kk] << " x " << x  
-														//      << " " << A << B << MA << MB<< endl ;
-													}
-													//  cout << endl;
-												}
-
-												Real8 lcurveb = lcurve+ ledge ;
-												while (lcurve<=s && s <= lcurveb && nbv < nbvend)
-												{
-													// New points
-
-													// Real8 aa=(lcurveb-s)/ledge;
-													// Real8 bb=(s-lcurve)/ledge;
-
-													Real8 ss = s-lcurve;
-													// 1) find the SubEdge containing ss by dichotomie
-													int kk0=-1,kk1=NbSubEdge-1,kkk;
-													Real8 ll0=0,ll1=ledge,llk;
-													while (kk1-kk0>1)
-													{
-														if (ss < (llk=lSubEdge[kkk=(kk0+kk1)/2]))
-															kk1=kkk,ll1=llk;
-														else
-															kk0=kkk,ll0=llk;}
-														assert(kk1 != kk0);
-
-														Real8 sbb = (ss-ll0  )/(ll1-ll0);
-														Real8 bb = (kk1+sbb)/NbSubEdge, aa=1-bb;
-
-														// new vertex on edge
-														vb = &vertices[nbv++];
-														vb->m = Metric(aa,a->m,bb,b->m);
-														vb->ReferenceNumber = e->ref;
-														vb->DirOfSearch =NoDirOfSearch;
-														Real8 abcisse = k ? bb : aa;
-														vb->r =  e->F( abcisse );
-														VerticesOnGeomEdge[NbVerticesOnGeomEdge++]= VertexOnGeom(*vb,*e,abcisse);        
-
-														// to take in account the sens of the edge
-
-														s += lstep;
-														edges[nbe].v[0]=va;
-														edges[nbe].v[1]=vb;
-														edges[nbe].ref = e->ref;
-														edges[nbe].on = e;
-														edges[nbe].adj[0] = PreviousNewEdge;
-														if(PreviousNewEdge)
-															PreviousNewEdge->adj[1] = &edges[nbe];
-														PreviousNewEdge = edges + nbe;
-														nbe++;
-														va = vb;
-												}
-												lcurve = lcurveb;
-												e->SetMark();
-												// cout << e-Gh.edges << ", " << k << " " 
-												//      <<(*e)[k].r <<" " <<(*e)[1-k].r <<" " 
-												//      << lcurve<< ";; " ;                          
-												a=b;
-												if (b->Required() ) break;
-												int kprev=k;
-												k = e->SensAdj[kprev];// next vertices
-												e = e->Adj[kprev];
-												assert(e);
-											}// for(;;)
-											vb = b->to;
-											//            cout << endl;
-											NbEdgeCurve = Max((Int4) (lcurve +0.5), (Int4) 1);
-											NbNewPoints = NbEdgeCurve-1;
-											if(!kstep)
-											{ NbVerticesOnGeomEdge0 += NbNewPoints;
-												NbOfCurves++;}
-
-												nbvend=nbv+NbNewPoints; 
-
-												lstep = lcurve / NbEdgeCurve;
-												//   cout <<"lstep " << lstep << " lcurve " 
-												//    << lcurve << " NbEdgeCurve " << NbEdgeCurve << " " <<NbVerticesOnGeomEdge0<<" " <<NbVerticesOnGeomEdge<<" step =" <<step<<  endl;
-										} 
-										// end of curve --
-										if (edges) { // last edges of the curves 
-											edges[nbe].v[0]=va;
-											edges[nbe].v[1]=vb;
-											edges[nbe].ref = e->ref;
-											edges[nbe].on = e;
-											edges[nbe].adj[0] = PreviousNewEdge;
-											edges[nbe].adj[1] = 0;
-											if(PreviousNewEdge)
-												PreviousNewEdge->adj[1] = & edges[nbe];
-
-											nbe++;}
-										else
-											nbe += NbEdgeCurve;
-									} // end on  curve ---
-								} // if (edges[i][j].Corner())  
-					} // for (i=0;i<nbe;i++)
-					if(!step) {
-						// cout << "edges " << edges << " VerticesOnGeomEdge " <<VerticesOnGeomEdge << endl;
-						assert(!edges);
-						assert(!VerticesOnGeomEdge);
-						edges = new Edge[nbex=nbe];
-						if(NbVerticesOnGeomEdge0)
-							VerticesOnGeomEdge = new VertexOnGeom[NbVerticesOnGeomEdge0];
-						assert(edges);
-						assert(VerticesOnGeomEdge || NbVerticesOnGeomEdge0 ==0);
-						// do the vertex on a geometrical vertex
-						NbVerticesOnGeomEdge0 = NbVerticesOnGeomEdge;       
-					}
-					else 
-						assert(NbVerticesOnGeomEdge == NbVerticesOnGeomEdge0);
-					//     cout << " Nb of Curves = " << NbOfCurves << "nbe = " << nbe 
-					//	  << "== " << nbex << "  nbv = " << nbv <<  endl;
-					assert(nbex=nbe);
-				} // for (step=0;step<2;step++)
-
-				Insert();
-				ForceBoundary();
-				FindSubDomain();
-
-				// NewPointsOld(*this) ;
-				NewPoints(*this,0) ;
-				CurrentTh = 0;
-		}
-
-		Edge** Triangles::MakeGeometricalEdgeToEdge()
-		{
-			assert(Gh.nbe);
-			Edge **e= new (Edge* [Gh.nbe]);
-
-			Int4 i;
-			for ( i=0;i<Gh.nbe ; i++)
-				e[i]=NULL;
-			for ( i=0;i<nbe ; i++) 
-			{ 
-				Edge * ei = edges+i;
-				GeometricalEdge *on = ei->on; 
-				e[Gh.Number(on)] = ei;    
-			}
-			for ( i=0;i<nbe ; i++) 
-				for (int ii=0;ii<2;ii++) { 
-					Edge * ei = edges+i;
-					GeometricalEdge *on = ei->on;
-					int j= ii;
-					while (!(*on)[j].Required()) { 
-						//	cout << i << " " << ii << " j= " << j << " curve = " 
-						//           <<  on->CurveNumber << "  " << Gh.Number(on) << " on " << j 
-						//   << " s0 " << Gh.Number( (*on)[0]) << " s1  " << Gh.Number( (*on)[1]) 
-						//   << " ->  " ;
-						Adj(on,j); // next geom edge
-						j=1-j;
-						//       cout << Gh.Number(on) << "  " << j  << " e[ON] =  " <<  e[Gh.Number(on)] 
-						//    << " s0 " << Gh.Number( (*on)[0]) << " s1  " << Gh.Number( (*on)[1]) << endl; 
-						if (e[Gh.Number(on)])  break; // optimisation     
-						e[Gh.Number(on)] = ei; 
-					}
-				}
-
-			int kk=0;
-			for ( i=0;i<Gh.nbe ; i++)
-				if (!e[i]) 
-					if(kk++<10) {
-						cerr << " Bug -- the geometrical edge " << i << " is on no edge curve = " << Gh.edges[i].CurveNumber 
-							<< " s0 " << Gh.Number( Gh.edges[i][0]) << " s1  " << Gh.Number( Gh.edges[i][1]) << endl; 
-						//	 assert( e[i]);
-					}
-			if(kk) MeshError(997,this);
-
-			return e;
-		}
-
-		Triangles::~Triangles() {
-			long int verbosity=2;
-			//assert(NbRef<=0);
-			if (CurrentTh == this) CurrentTh=0;
-			//if(vertices)  delete [] vertices; //TEST  crash if not commented
-			if(edges)     delete [] edges;
-			if(triangles) delete [] triangles;
-			if(quadtree)  delete  quadtree;
-			//if(ordre)     delete [] ordre; //TEST  crash if not commented
-			if( subdomains) delete []  subdomains;
-			if (VerticesOnGeomEdge) delete [] VerticesOnGeomEdge;
-			if (VerticesOnGeomVertex) delete [] VerticesOnGeomVertex;
-			//if (name) delete [] name; //TEST crash if not commented
-			if (identity) delete [] identity;
-			if (VertexOnBThVertex) delete [] VertexOnBThVertex;
-			if (VertexOnBThEdge) delete [] VertexOnBThEdge;
-
-			if (&Gh) {
-				if (Gh.NbRef>0) Gh.NbRef--;
-				else if (Gh.NbRef==0) delete &Gh;
-			}
-			if (&BTh && (&BTh != this)) {
-				if (BTh.NbRef>0) BTh.NbRef--;
-				else if (BTh.NbRef==0) delete &BTh;
-			}
-			PreInit(0); // set all to zero 
-		}
-
-		void Triangles::SetIntCoor(const char * strfrom)
-		{
-			pmin =  vertices[0].r;
-			pmax =  vertices[0].r;
-
-			// recherche des extrema des vertices pmin,pmax
-			Int4 i;
-			for (i=0;i<nbv;i++) {
-				pmin.x = Min(pmin.x,vertices[i].r.x);
-				pmin.y = Min(pmin.y,vertices[i].r.y);
-				pmax.x = Max(pmax.x,vertices[i].r.x);
-				pmax.y = Max(pmax.y,vertices[i].r.y);
-			}
-			R2 DD = (pmax-pmin)*0.05;
-			pmin = pmin-DD;
-			pmax = pmax+DD; 
-			coefIcoor= (MaxICoor)/(Max(pmax.x-pmin.x,pmax.y-pmin.y));
-			assert(coefIcoor >0);
-
-			// generation of integer coord  
-			for (i=0;i<nbv;i++) {
-				vertices[i].i = toI2(vertices[i].r);    
-			}
-
-			// computation of the det 
-			int Nberr=0;
-			for (i=0;i<nbt;i++)
-			{
-				Vertex & v0 = triangles[i][0];
-				Vertex & v1 = triangles[i][1];
-				Vertex & v2 = triangles[i][2];
-				if ( &v0 && &v1 &&  &v2 ) // a good triangles;
-				{
-					triangles[i].det= det(v0,v1,v2);
-					if (triangles[i].det <=0 && Nberr++ <10)
-					{
-						if(Nberr==1)
-							if (strfrom)
-								cerr << "+++ Fatal Error " << strfrom << "(SetInCoor)  Error :  area of Triangle < 0 " << endl; 
-							else 
-								cerr << "+++  Fatal Error Triangle (in SetInCoor) area of Triangle < 0" << endl;
-						cerr << " Triangle " << i << "  det  (I2) = " << triangles[i].det ;
-						cerr << " (R2) " << Det(v1.r-v0.r,v2.r-v0.r);
-						cerr << "; The 3  vertices " << endl;
-						cerr << Number(v0) << " "  << Number(v1) << " " 
-							<< Number(v2) << " : " ;
-						cerr << v0.r << v1.r << v2.r << " ; ";
-						cerr << v0.i << v1.i << v2.i << endl;
-					}
-				}
-				else
-					triangles[i].det= -1; // Null triangle; 
-			}
-			if (Nberr) MeshError(899,this);
-
-		}
-
-		void Triangles::FillHoleInMesh() {
-
-			Triangles* OldCurrentTh =CurrentTh;
-			CurrentTh=this;
-
-			int verbosity=0;
-
-			// generation of the integer coordinate
-			  {
-
-				// find extrema coordinates of vertices pmin,pmax
-				Int4 i;
-				if(verbosity>2) printf("      Filling holes in mesh of %i vertices\n",nbv); 
-
-				//initialize ordre
-				assert(ordre);
-				for (i=0;i<nbv;i++) ordre[i]=0;
-
-				NbSubDomains =0;
-
-				/* generation of the adjacence of the triangles*/
-
-				SetOfEdges4* edge4= new SetOfEdges4(nbt*3,nbv);
-
-				//initialize st
-				Int4* st = new Int4[nbt*3];
-				for (i=0;i<nbt*3;i++) st[i]=-1;
-
-				//check number of edges
-				Int4 kk =0;
-				for (i=0;i<nbe;i++){
-					kk=kk+(i == edge4->addtrie(Number(edges[i][0]),Number(edges[i][1])));
-				}
-				if (kk != nbe) { 
-					throw ErrorException(__FUNCT__,exprintf("Some Double edge in the mesh, the number is %i",kk-nbe));
-				}
-
-				//
-				for (i=0;i<nbt;i++){
-					for (int j=0;j<3;j++) {
-						Int4 k =edge4->addtrie(Number(triangles[i][VerticesOfTriangularEdge[j][0]]),
-									Number(triangles[i][VerticesOfTriangularEdge[j][1]]));
-						Int4 invisible = triangles[i].Hidden(j);
-						if(st[k]==-1){
-							st[k]=3*i+j;
-						}
-						else if(st[k]>=0) {
-							assert( ! triangles[i].TriangleAdj(j) && !triangles[st[k] / 3].TriangleAdj((int) (st[k]%3)));
-
-							triangles[i].SetAdj2(j,triangles + st[k] / 3,(int) (st[k]%3));
-							if (invisible)  triangles[i].SetHidden(j);
-							if (k<nbe) {
-								triangles[i].SetLocked(j);
-							}
-							st[k]=-2-st[k]; 
-						}
-						else {
-							throw ErrorException(__FUNCT__,exprintf("The edge (%i , %i) belongs to more than 2 triangles",
-											Number(triangles[i][VerticesOfTriangularEdge[j][0]]),Number(triangles[i][VerticesOfTriangularEdge[j][1]])));
-						}
-					}
-				}
-				if(verbosity>5) {
-					printf("         info on Mesh %s:\n",name);
-					printf("            - number of vertices    = %i \n",nbv); 
-					printf("            - number of triangles   = %i \n",nbt); 
-					printf("            - number of given edges = %i \n",nbe); 
-					printf("            - number of all edges   = %i \n"  ,edge4->nb()); 
-					printf("            - Euler number 1 - nb of holes = %i \n"  ,nbt-edge4->nb()+nbv); 
-				}
-
-				// check the consistant of edge[].adj and the geometrical required  vertex
-				Int4 k=0;
-				for (i=0;i<edge4->nb();i++){
-					if (st[i] >=0){ // edge alone 
-						if (i < nbe) {
-							Int4 i0=edge4->i(i);
-							ordre[i0] = vertices+i0;
-							Int4 i1=edge4->j(i);
-							ordre[i1] = vertices+i1;
-						}
-						else {
-							k=k+1;
-							if (k <20) {
-								throw ErrorException(__FUNCT__,exprintf("Lost boundary edges %i : %i %i",i,edge4->i(i),edge4->j(i)));
-							}
-						}
-					}
-				}
-				if(k != 0) {
-					throw ErrorException(__FUNCT__,exprintf("%i boundary edges  are not defined as edges",k));
-				}
-
-				/* mesh generation with boundary points*/
-				Int4 nbvb = 0;
-				for (i=0;i<nbv;i++){ 
-					vertices[i].t=0;
-					vertices[i].vint=0;
-					if (ordre[i]){ 
-						ordre[nbvb++] = ordre[i];
-					}
-				}
-
-				Triangle* savetriangles= triangles;
-				Int4 savenbt=nbt;
-				Int4 savenbtx=nbtx;
-				SubDomain * savesubdomains = subdomains;
-				subdomains = 0;
-
-				Int4  Nbtriafillhole = 2*nbvb;
-				Triangle* triafillhole =new Triangle[Nbtriafillhole];
-				triangles =  triafillhole;
-
-				nbt=2;
-				nbtx= Nbtriafillhole;
-
-				for (i=2 ; det( ordre[0]->i, ordre[1]->i, ordre[i]->i ) == 0;) 
-				 if  ( ++i >= nbvb) {
-					 cerr << "FillHoleInMesh: All the vertices are aline " << nbvb << endl;
-					 MeshError(998,this); }
-					 Exchange( ordre[2], ordre[i]);
-
-					 Vertex *  v0=ordre[0], *v1=ordre[1];
-
-
-					 triangles[0](0) = 0; // sommet pour infini 
-					 triangles[0](1) = v0;
-					 triangles[0](2) = v1;
-
-					 triangles[1](0) = 0;// sommet pour infini 
-					 triangles[1](2) = v0;
-					 triangles[1](1) = v1;
-					 const int e0 = OppositeEdge[0];
-					 const int e1 = NextEdge[e0];
-					 const int e2 = PreviousEdge[e0];
-					 triangles[0].SetAdj2(e0, &triangles[1] ,e0);
-					 triangles[0].SetAdj2(e1, &triangles[1] ,e2);
-					 triangles[0].SetAdj2(e2, &triangles[1] ,e1);
-
-					 triangles[0].det = -1;  // faux triangles
-					 triangles[1].det = -1;  // faux triangles
-
-					 triangles[0].SetTriangleContainingTheVertex();
-					 triangles[1].SetTriangleContainingTheVertex();
-
-					 triangles[0].link=&triangles[1];
-					 triangles[1].link=&triangles[0];
-
-					 if (!quadtree ) 
-					  delete  quadtree; // ->ReInitialise();
-
-					 quadtree = new QuadTree(this,0);
-					 quadtree->Add(*v0);
-					 quadtree->Add(*v1);
-
-					 // We add the vertices one by one
-					 Int4 NbSwap=0;
-					 for (Int4 icount=2; icount<nbvb; icount++) {
-						 Vertex *vi  = ordre[icount];
-						 //	  cout << " Add vertex " <<  Number(vi) << endl;
-						 Icoor2 dete[3];
-						 Triangle *tcvi = FindTriangleContening(vi->i,dete);
-						 quadtree->Add(*vi); 
-						 Add(*vi,tcvi,dete);
-						 NbSwap += vi->Optim(1,1);
-					 }
-
-					 // inforce the boundary 
-					 TriangleAdjacent ta(0,0);
-					 Int4 nbloss = 0,knbe=0;
-					 for ( i = 0; i < nbe; i++){
-						 if (st[i] >=0){  // edge alone => on border ...  FH oct 2009
-							 Vertex & a=edges[i][0], & b =    edges[i][1];
-							 if (a.t && b.t) // le bug est la si maillage avec des bod non raffine 1.
-								{
-								 knbe++;
-								 if (ForceEdge(a,b,ta)<0)
-								  nbloss++;
-								}
-						 }
-					 }
-					 if(nbloss) {
-						 cerr << " we loss some  " << nbloss << " "  << " edges other " << knbe << endl;
-						 MeshError(1100,this);
-					 }
-
-					 FindSubDomain(1);
-					 // remove all the hole 
-					 // remove all the good sub domain
-					 Int4 krm =0;
-					 for (i=0;i<nbt;i++){
-						 if (triangles[i].link){ // remove triangles
-							 krm++;
-							 for (int j=0;j<3;j++)
-								{
-								 TriangleAdjacent ta =  triangles[i].Adj(j);
-								 Triangle & tta = * (Triangle *) ta;
-								 if(! tta.link) // edge between remove and not remove 
-									{ // change the link of ta;
-									 int ja = ta;
-									 Vertex *v0= ta.EdgeVertex(0);
-									 Vertex *v1= ta.EdgeVertex(1);
-									 Int4 k =edge4->addtrie(v0?Number(v0):nbv,v1? Number(v1):nbv);
-									 assert(st[k] >=0); 
-									 tta.SetAdj2(ja,savetriangles + st[k] / 3,(int) (st[k]%3));
-									 ta.SetLock();
-									 st[k]=-2-st[k]; 
-									}
-								}
-						 }
-					 }
-						 Int4 NbTfillHoll =0;
-						 for (i=0;i<nbt;i++){
-							 if (triangles[i].link) {
-								 triangles[i]=Triangle((Vertex *) NULL,(Vertex *) NULL,(Vertex *) NULL);
-								 triangles[i].color=-1;
-							 }
-							 else
-								{
-								 triangles[i].color= savenbt+ NbTfillHoll++;
-								}
-						 }
-						 // cout <<      savenbt+NbTfillHoll << " " <<  savenbtx  << endl;
-						 assert(savenbt+NbTfillHoll <= savenbtx );
-						 // copy of the outside triangles in saveTriangles 
-						 for (i=0;i<nbt;i++){
-							 if(triangles[i].color>=0) {
-								 savetriangles[savenbt]=triangles[i];
-								 savetriangles[savenbt].link=0;
-								 savenbt++;
-							 }
-						 }
-						 // gestion of the adj
-						 k =0;
-						 Triangle * tmax = triangles + nbt;
-						 for (i=0;i<savenbt;i++)  
-							{ 
-							 Triangle & ti = savetriangles[i];
-							 for (int j=0;j<3;j++)
-								{
-								 Triangle * ta = ti.TriangleAdj(j);
-								 int aa = ti.NuEdgeTriangleAdj(j);
-								 int lck = ti.Locked(j);
-								 if (!ta) k++; // bug 
-								 else if ( ta >= triangles && ta < tmax) 
-									{
-									 ta= savetriangles + ta->color;
-									 ti.SetAdj2(j,ta,aa);
-									 if(lck) ti.SetLocked(j);
-									}
-								}
-							}
-						 //	 OutSidesTriangles = triangles;
-						 //	Int4 NbOutSidesTriangles = nbt;
-
-						 // restore triangles;
-						 nbt=savenbt;
-						 nbtx=savenbtx;
-						 delete [] triangles;
-						 delete [] subdomains;
-						 triangles = savetriangles;
-						 subdomains = savesubdomains;
-						 //	 cout <<  triangles << " <> " << OutSidesTriangles << endl; 
-						 /*	 k=0;
-								 for (i=0;i<nbt;i++)
-								 for (int j=0;j<3;j++)
-								 if (!triangles[i].TriangleAdj(j))
-								 k++;
-								 */
-						 if (k) {
-							 cerr << "Error Nb of triangles edge alone = " << k << endl;
-							 MeshError(9997,this);
-						 }
-						 FindSubDomain();
-						 // cout << " NbTOld = " << NbTold << " ==  " << nbt - NbOutT << " " << nbt << endl;
-
-						 delete edge4;
-						 delete [] st;
-						 for (i=0;i<nbv;i++)
-						  quadtree->Add(vertices[i]);
-
-						 SetVertexFieldOn();
-
-						 for (i=0;i<nbe;i++)
-						  if(edges[i].on) 
-							for(int j=0;j<2;j++)
-							 if (!edges[i].adj[j])
-							  if(!edges[i][j].on->IsRequiredVertex()) {
-								  cerr << " Erreur adj et sommet requis edges [" << i <<  "][ " << j << "]= "
-									 <<  Number(edges[i][j]) << " : "  << " on = " << Gh.Number(edges[i].on) ;
-								  if (edges[i][j].on->OnGeomVertex())
-									cerr << " vertex " << Gh.Number(edges[i][j].on->gv);
-								  else if (edges[i][j].on->OnGeomEdge())
-									cerr << "Edges " << Gh.Number(edges[i][j].on->ge);
-								  else
-									cerr << " = " << edges[i][j].on ;
-								  cerr << endl;
-							  }
-			  }
-			CurrentTh=OldCurrentTh;
-		}
-
-		Triangles::Triangles(Triangles & Th,Geometry * pGh,Triangles * pBth,Int4 nbvxx) // COPY OPERATOR
-			: Gh(*(pGh?pGh:&Th.Gh)), BTh(*(pBth?pBth:this))
-			{
-				Gh.NbRef++;
-				nbvxx = Max(nbvxx,Th.nbv); 
-				Int4 i;
-				// do all the allocation to be sure all the pointer existe
-
-				char * cname = 0;
-				if (Th.name) 
-				{
-					cname = new char[strlen(Th.name)+1];
-					strcpy(cname,Th.name);
-				}
-				PreInit(nbvxx,cname);// to make the allocation 
-				// copy of triangles
-				nt=Th.nt;
-				nbv = Th.nbv;
-				nbt = Th.nbt;
-				nbiv = Th.nbiv;
-				nbe = Th.nbe;
-				NbSubDomains = Th.NbSubDomains;
-				NbOutT = Th.NbOutT;
-				NbOfQuad =  Th.NbOfQuad ;
-				NbOfSwapTriangle =0;
-				NbVerticesOnGeomVertex = Th.NbVerticesOnGeomVertex;
-				if(NbVerticesOnGeomVertex)
-					VerticesOnGeomVertex = new VertexOnGeom[NbVerticesOnGeomVertex];
-				NbVerticesOnGeomEdge = Th.NbVerticesOnGeomEdge;
-				if (NbVerticesOnGeomEdge)
-					VerticesOnGeomEdge = new VertexOnGeom[NbVerticesOnGeomEdge] ;
-				if (& BTh == & Th.BTh) // same back ground 
-				{
-					BTh.NbRef++;
-					NbVertexOnBThVertex = Th.NbVertexOnBThVertex;
-					if(NbVertexOnBThVertex)
-						VertexOnBThVertex = new VertexOnVertex[NbVertexOnBThVertex];
-					NbVertexOnBThEdge = Th.NbVertexOnBThEdge;
-					if(NbVertexOnBThEdge)
-						VertexOnBThEdge = new VertexOnEdge[NbVertexOnBThEdge];
-				}
-				else 
-				{ // no add on back ground mesh 
-					BTh.NbRef++;
-					NbVertexOnBThVertex=0;
-					VertexOnBThVertex=0;
-					NbVertexOnBThEdge=0;
-					VertexOnBThEdge=0;
-					//       assert (& BTh == this); // --- a voir 
-
-				}
-
-
-				if(nbe)
-					edges = new Edge[nbe];
-				if(NbSubDomains)
-					subdomains = new SubDomain[NbSubDomains];
-				pmin = Th.pmin;
-				pmax = Th.pmax;
-				coefIcoor = Th.coefIcoor;
-				for(i=0;i<nbt;i++)
-					triangles[i].Set(Th.triangles[i],Th,*this);
-				for(i=0;i<nbe;i++)
-					edges[i].Set(Th,i,*this);
-				for(i=0;i<nbv;i++)
-					vertices[i].Set(Th.vertices[i],Th,*this);
-				for(i=0;i<NbSubDomains;i++)  
-					subdomains[i].Set(Th,i,*this);
-				for (i=0;i<NbVerticesOnGeomVertex;i++)
-					VerticesOnGeomVertex[i].Set(Th.VerticesOnGeomVertex[i],Th,*this);
-				for (i=0;i<NbVerticesOnGeomEdge;i++)
-					VerticesOnGeomEdge[i].Set(Th.VerticesOnGeomEdge[i],Th,*this);
-				quadtree=0;
-
-
-				//  assert(!OutSidesTriangles);
-			}
-
-Int4  Triangle::Optim(Int2 i,int koption)
-{
-	// turne around in positif sens
-	Int4 NbSwap =0;
-	Triangle  *t = this;
-	int k=0,j =OppositeEdge[i];
-	int jp = PreviousEdge[j];
-	// initialise   tp, jp the previous triangle & edge
-	Triangle *tp= at[jp];
-	jp = aa[jp]&3;
-	do {
-		//    cout << *t << " " <<  j  << "\n\t try swap " ;
-		while (t->swap(j,koption))
-		{
-			NbSwap++;
-			assert(k++<20000);
-			t=  tp->at[jp];      // set unchange t qnd j for previous triangles
-			j=  NextEdge[tp->aa[jp]&3];
-			//   cout << "\n\t s  " <<  *t << " " << j << endl;
-		}
-		// end on this  Triangle 
-		tp = t;
-		jp = NextEdge[j];
-
-		t=  tp->at[jp];      // set unchange t qnd j for previous triangles
-		j=  NextEdge[tp->aa[jp]&3];
-
-	} while( t != this);
-	return NbSwap;
-}
-
-void Triangles::SmoothingVertex(int nbiter,Real8 omega )
-{ 
-	long int verbosity=0;
-	//  if quatree exist remove it end reconstruct
-	if (quadtree) delete quadtree;
-	quadtree=0;
-	ReMakeTriangleContainingTheVertex();
-	Triangle vide; // a triangle to mark the boundary vertex
-	Triangle   ** tstart= new Triangle* [nbv];
-	Int4 i,j,k;
-	//   attention si Background == Triangle alors on ne peut pas utiliser la rechech rapide 
-	if ( this == & BTh)
-		for ( i=0;i<nbv;i++)
-			tstart[i]=vertices[i].t;     
-	else 
-		for ( i=0;i<nbv;i++)
-			tstart[i]=0;
-	for ( j=0;j<NbVerticesOnGeomVertex;j++ ) 
-		tstart[ Number(VerticesOnGeomVertex[j].mv)]=&vide;
-	for ( k=0;k<NbVerticesOnGeomEdge;k++ ) 
-		tstart[ Number(VerticesOnGeomEdge[k].mv)]=&vide;
-	if(verbosity>2) 
-		cout << "  -- SmoothingVertex: nb Iteration = " << nbiter << " Omega = " << omega << endl;
-	for (k=0;k<nbiter;k++)
-	{
-		Int4 i,NbSwap =0;
-		Real8 delta =0;
-		for ( i=0;i<nbv;i++)
-			if (tstart[i] != &vide) // not a boundary vertex 
-				delta=Max(delta,vertices[i].Smoothing(*this,BTh,tstart[i],omega));
-		if (!NbOfQuad)
-			for ( i=0;i<nbv;i++)
-				if (tstart[i] != &vide) // not a boundary vertex 
-					NbSwap += vertices[i].Optim(1);
-		if (verbosity>3)
-			cout << "    Move max = " <<  sqrt(delta) << " iteration = " 
-				<< k << " Nb of Swap = " << NbSwap << endl;
-	}
-
-	delete [] tstart;
-	if (quadtree) quadtree= new QuadTree(this);
-}
-void Triangles::MakeQuadTree()
-{  
-	long int verbosity=0;
-	if(verbosity>8)
-		cout << "      MakeQuadTree" << endl;
-	if (  !quadtree )  quadtree = new QuadTree(this);
-
-}
-void  Triangles::ShowRegulaty() const// Add FH avril 2007 
-{
-	const  Real8  sqrt32=sqrt(3.)*0.5; 
-	const Real8  aireKh=sqrt32*0.5;
-	D2  Beq(1,0),Heq(0.5,sqrt32);
-	D2xD2 Br(D2xD2(Beq,Heq).t());
-	D2xD2 B1r(Br.inv());
-	/*   D2xD2 BB = Br.t()*Br;
-		 cout << " BB = " << BB << " " << Br*B1r <<  endl; 
-		 MetricAnIso MMM(BB.x.x,BB.x.y,BB.y.y);
-		 MatVVP2x2 VMM(MMM);
-		 cout << " " << VMM.lambda1 << " " << VMM.lambda2 <<  endl; 
-		 */
-	double gammamn=1e100,hmin=1e100;
-	double gammamx=0,hmax=0;
-	double beta=1e100;
-	double beta0=0;
-	double  alpha2=0;
-	double area=0,Marea=0;
-	// Real8 cf= Real8(coefIcoor);
-	// Real8 cf2= 6.*cf*cf;
-	int nt=0;
-	for (int it=0;it<nbt;it++)
-		if ( triangles[it].link) 
-		{
-			nt++;
-			Triangle &K=triangles[it];
-			Real8  area3= Area2((R2) K[0],(R2) K[1],(R2) K[2])/6.;
-			area+= area3;
-			D2xD2 B_Kt(K[0],K[1],K[2]);
-			D2xD2 B_K(B_Kt.t());
-			D2xD2 B1K = Br*B_K.inv();
-			D2xD2 BK =  B_K*B1r;
-			D2xD2 B1B1 = B1K.t()*B1K;
-			MetricAnIso MK(B1B1.x.x,B1B1.x.y,B1B1.y.y);
-			MatVVP2x2 VMK(MK);
-			alpha2 = Max(alpha2,Max(VMK.lambda1/VMK.lambda2,VMK.lambda2/VMK.lambda1));
-			// cout << B_K << " * " << B1r << " == " << BK << " " << B_K*B_K.inv() << endl;
-			Real8 betaK=0;
-
-			for (int j=0;j<3;j++)
-			{
-				Real8 he= Norme2(R2(K[j],K[(j+1)%3]));
-				hmin=Min(hmin,he);
-				hmax=Max(hmax,he);
-				Vertex & v=K[j];
-				D2xD2 M((MetricAnIso)v);
-				betaK += sqrt(M.det());
-
-				D2xD2 BMB = BK.t()*M*BK;
-				MetricAnIso M1(BMB.x.x,BMB.x.y,BMB.y.y);
-				MatVVP2x2 VM1(M1);
-				//cout << B_K <<" " <<  M << " " <<  he << " " << BMB << " " << VM1.lambda1 << " " << VM1.lambda2<<   endl; 
-				gammamn=Min3(gammamn,VM1.lambda1,VM1.lambda2);
-				gammamx=Max3(gammamx,VM1.lambda1,VM1.lambda2);		
-			}
-			betaK *= area3;//  1/2 (somme sqrt(det))* area(K)
-			Marea+= betaK;
-			// cout << betaK << " " << area3 << " " << beta << " " << beta0 << " " << area3*3*3*3 <<endl;
-			beta=min(beta,betaK);
-			beta0=max(beta0,betaK);
-		}   
-	area*=3; 
-	gammamn=sqrt(gammamn);
-	gammamx=sqrt(gammamx);    
-	cout << "  -- adaptmesh Regulary:  Nb triangles " << nt <<  " , h  min " << hmin  << " , h max " << hmax << endl;  
-	cout << "     area =  " << area << " , M area = " << Marea << " , M area/( |Khat| nt) " << Marea/(aireKh*nt) << endl; 
-	cout << "     infiny-regulaty:  min " << gammamn << "  max " << gammamx << endl;  
-	cout << "     anisomax  "<< sqrt(alpha2) << ", beta max = " << 1./sqrt(beta/aireKh) 
-		<< " min  "<<  1./sqrt(beta0/aireKh)  << endl;
-}
-void  Triangles::ShowHistogram() const
-{
-
-	const Int4 kmax=10;
-	const Real8 llmin = 0.5,llmax=2;
-	const Real8 lmin=log(llmin),lmax=log(llmax),delta= kmax/(lmax-lmin);
-	Int4 histo[kmax+1];
-	Int4 i,it,k, nbedges =0;
-	for (i=0;i<=kmax;i++) histo[i]=0;
-	for (it=0;it<nbt;it++)
-		if ( triangles[it].link) 
-		{
-
-			for (int j=0;j<3;j++)
-			{
-				Triangle *ta = triangles[it].TriangleAdj(j);
-				if ( !ta || !ta->link || Number(ta) >= it) 
-				{ 
-					Vertex & vP = triangles[it][VerticesOfTriangularEdge[j][0]];
-					Vertex & vQ = triangles[it][VerticesOfTriangularEdge[j][1]];
-					if ( !& vP || !&vQ) continue;
-					R2 PQ = vQ.r - vP.r;
-					Real8 l = log(LengthInterpole(vP,vQ,PQ));
-					nbedges++;
-					k = (int) ((l - lmin)*delta);
-					k = Min(Max(k,0L),kmax);
-					histo[k]++;
-				}
-			}
-		}  
-	cout << "  -- Histogram of the unit mesh,  nb of edges" << nbedges << endl <<endl;
-
-	cout << "        length of edge in   | % of edge  | Nb of edges " << endl;
-	cout << "        ------------------- | ---------- | ----------- " << endl;
-	for   (i=0;i<=kmax;i++)
-	{ 
-		cout << "    " ;
-		cout.width(10);
-		if (i==0) cout  << " 0 " ;
-		else cout  << exp(lmin+i/delta) ;
-		cout.width(); cout << "," ;
-		cout.width(10);
-		if (i==kmax) cout << " +infty " ;
-		else cout  << exp(lmin+(i+1)/delta) ;
-		cout.width();cout << "   |   " ;
-
-		cout.precision(4);
-		cout.width(6);
-		cout <<  ((long)  ((10000.0 * histo[i])/ nbedges))/100.0 ;
-		cout.width();
-		cout.precision();
-		cout <<  "   |   " << histo[i] <<endl;
-	}
-	cout << "        ------------------- | ---------- | ----------- " << endl <<endl;
-
-}
-
-int  Triangles::Crack()
-{ 
-	assert(NbCrackedEdges ==0 || NbCrackedVertices >0); 
-	for (int i=0;i<NbCrackedEdges;i++)
-		CrackedEdges[i].Crack();
-	return NbCrackedEdges;
-}
-
-int Triangles::UnCrack() 
-{ 
-	assert(NbCrackedEdges ==0 || NbCrackedVertices >0); 
-	for (int i=0;i<NbCrackedEdges;i++)
-		CrackedEdges[i].UnCrack();
-	return NbCrackedEdges;
-}
-
-int Triangles::CrackMesh()
-{
-	long int verbosity=0;
-	Triangles *CurrentThOld = CurrentTh;
-	//  computed the number of cracked edge
-	int i,k;
-	for (k=i=0;i<nbe;i++)
-		if(edges[i].on->Cracked()) k++;
-	if( k==0) return 0;
-	CurrentTh = this;
-	cout << " Nb of Cracked Edges = " << k << endl;
-	NbCrackedEdges =k;
-	CrackedEdges = new  CrackedEdge[k];
-	//  new edge
-	Edge * e = new Edge[ nbe + k];
-
-	// copy
-	for (i=0;i<nbe;i++) 
-		e[i] = edges[i];
-	delete edges;
-	edges = e;
-
-	const int  nbe0  = nbe;
-	for (k=i=0;i<nbe0;i++) // on double les arete cracked 
-		if(edges[i].on->Cracked())
-		{
-			e[nbe] = e[i];
-			//  return the edge 
-			e[nbe].v[0] =  e[i].v[1];
-			e[nbe].v[1] =  e[i].v[0];
-			e[nbe].on = e[i].on->link ; // fqux 
-			CrackedEdges[k++]=CrackedEdge(edges,i,nbe);
-			nbe++;
-		}
-	ReMakeTriangleContainingTheVertex() ; 
-	//  
-	int nbcrakev  =0;
-	Vertex *vlast = vertices + nbv;
-	Vertex *vend = vertices + nbvx; // end of array
-	for (int iv=0;iv<nbv;iv++) // vertex 
-	{
-		Vertex & v= vertices[iv];
-		Vertex * vv = & v;  
-		int kk=0; // nb cracked
-		int kc=0; 
-		int kkk =0; // nb triangle  with same number 
-		Triangle * tbegin = v.t;
-		int i  = v.vint;       
-		assert(tbegin && (i >= 0 ) && (i <3));
-		// turn around the vertex v
-		TriangleAdjacent ta(tbegin,EdgesVertexTriangle[i][0]);// previous edge
-		int k=0;
-		do {
-			int kv = VerticesOfTriangularEdge[ta][1];
-			k++; 
-			Triangle * tt (ta);
-			if ( ta.Cracked() ) 
-			{   
-				TriangleAdjacent tta=(ta.Adj());
-				assert(tta.Cracked());
-				if ( kk == 0) tbegin=ta,kkk=0;  //  begin by a cracked edge  => restart                
-				if (  kkk ) { kc =1;vv = vlast++;  kkk = 0; } // new vertex if use 
-				kk++;// number of cracked edge view                 
-			}
-			if ( tt->link ) { // if good triangles store the value 
-				int it = Number(tt);
-				assert(it < nt);
-				(*tt)(kv)= vv; //   Change the vertex of triangle 
-				if(vv<vend) {*vv= v;vv->ReferenceNumber=iv;} // copy the vertex value + store the old vertex number in ref 
-				//	  tt->SetTriangleContainingTheVertex();
-				kkk++;
-			} else if (kk) { // crack + boundary 
-				if (  kkk ) { kc =1;vv = vlast++;  kkk = 0; } // new vertex if use 
-			}
-
-			ta = Next(ta).Adj(); 
-		} while ( (tbegin != ta)); 
-		assert(k);
-		if (kc)  nbcrakev++;
-	}
-
-	if ( nbcrakev ) 
-		for (int iec =0;iec < NbCrackedEdges; iec ++)
-			CrackedEdges[iec].Set();
-
-	//  set the ref 
-	cout << " set the ref " <<  endl ;
-	NbCrackedVertices =   nbcrakev;
-	// int nbvo = nbv;
-	nbv = vlast - vertices;
-	int nbnewv =  nbv - nbv; // nb of new vrtices 
-	if (nbcrakev && verbosity > 1 )
-		cout << " Nb of craked vertices = " << nbcrakev << " Nb of created vertices " <<   nbnewv<< endl;
-	// all the new vertices are on geometry 
-	//  BOFBO--  A VOIR
-	if (nbnewv)
-	{ // 
-		Int4 n = nbnewv+NbVerticesOnGeomVertex;
-		Int4 i,j,k;
-		VertexOnGeom * vog = new VertexOnGeom[n];
-		for ( i =0; i<NbVerticesOnGeomVertex;i++) 
-			vog[i]=VerticesOnGeomVertex[i];
-		delete [] VerticesOnGeomVertex;
-		VerticesOnGeomVertex = vog;
-		// loop on cracked edge 
-		Vertex * LastOld = vertices + nbv - nbnewv;
-		for (int iec =0;iec < NbCrackedEdges; iec ++)
-			for (k=0;k<2;k++)
-			{
-				Edge & e = *( k ? CrackedEdges[iec].a.edge : CrackedEdges[iec].b.edge);
-				for (j=0;j<2;j++) 
-				{
-					Vertex * v = e(j);
-					if ( v >=  LastOld)
-					{ // a new vertex 
-						Int4 old = v->ReferenceNumber ; // the old same vertex 
-						Int4 i  = ( v - LastOld);
-						//  if the old is on vertex => warning
-						// else the old is on edge => ok 
-						vog[i] = vog[old];
-						//  		    vog[i].mv = v;
-						//g[i].ge = ;
-						//og[i].abcisse = ;
-					}
-
-				}
-			}
-
-		NbVerticesOnGeomVertex = n;
-	}
-	SetVertexFieldOn();
-
-
-	if (vlast >= vend)
-	{  
-		cerr << " Not enougth vertices to crack the mesh we need " << nbv << " vertices " << endl;
-		MeshError(555,this);
-	}
-	cout << "  NbCrackedVertices " <<  NbCrackedVertices << endl;
-	CurrentTh = CurrentThOld;
-	return  NbCrackedVertices;
-}
-
-	Triangles::Triangles(const Triangles & Tho,const int *flag ,const int *bb)
-: Gh(*(new Geometry())), BTh(*this)
-{ // truncature
-	// 
-
-	char cname[] = "trunc";
-
-	int i,k,itadj;
-	int kt=0;
-	int * kk    = new int [Tho.nbv];
-	Int4 * reft = new Int4[Tho.nbt];
-	Int4 nbInT =    Tho.ConsRefTriangle(reft);
-	Int4 * refv = new Int4[Tho.nbv];
-
-	for (i=0;i<Tho.nbv;i++)
-		kk[i]=-1;
-	for (i=0;i<Tho.nbv;i++)
-		refv[i]=0;
-	int nbNewBedge =0;
-	//  int nbOldBedge =0;  
-	for (i=0;i<Tho.nbt;i++)
-		if(  reft[i] >=0 && flag[i]) 
-		{
-			const Triangle & t = Tho.triangles[i];
-			kt++;
-			kk[Tho.Number(t[0])]=1;
-			kk[Tho.Number(t[1])]=1;
-			kk[Tho.Number(t[2])]=1;
-			itadj=Tho.Number(t.TriangleAdj(0));
-			if (  reft[itadj] >=0 && !flag[itadj])
-			{ nbNewBedge++;
-				refv[Tho.Number(t[VerticesOfTriangularEdge[0][0]])]=bb[i];
-				refv[Tho.Number(t[VerticesOfTriangularEdge[0][1]])]=bb[i];
-			}
-			itadj=Tho.Number(t.TriangleAdj(1));
-			if (  reft[itadj] >=0 && !flag[itadj])
-			{ nbNewBedge++;
-				refv[Tho.Number(t[VerticesOfTriangularEdge[1][0]])]=bb[i];
-				refv[Tho.Number(t[VerticesOfTriangularEdge[1][1]])]=bb[i];}
-				itadj=Tho.Number(t.TriangleAdj(2));
-				if (  reft[itadj] >=0 && !flag[itadj])
-				{ nbNewBedge++;
-					refv[Tho.Number(t[VerticesOfTriangularEdge[2][0]])]=bb[i];
-					refv[Tho.Number(t[VerticesOfTriangularEdge[2][1]])]=bb[i];}
-		}
-	k=0;
-	for (i=0;i<Tho.nbv;i++)
-		if (kk[i]>=0) 
-			kk[i]=k++;
-	cout << " number of vertices " << k << " remove = " << Tho.nbv - k << endl;
-	cout << " number of triangles " << kt << " remove = " << nbInT-kt << endl;
-	cout << " number of New boundary edge " << nbNewBedge << endl;
-	Int4 inbvx =k;
-	PreInit(inbvx,cname);
-	for (i=0;i<Tho.nbv;i++)
-		if (kk[i]>=0) 
-		{
-			vertices[nbv] = Tho.vertices[i];
-			if (!vertices[nbv].ref())
-				vertices[nbv].ReferenceNumber = refv[i];
-			nbv++;
-		}
-	assert(inbvx == nbv);
-	for (i=0;i<Tho.nbt;i++)
-		if(  reft[i] >=0 && flag[i]) 
-		{
-			const Triangle & t = Tho.triangles[i];
-			int i0 = Tho.Number(t[0]);
-			int i1 = Tho.Number(t[1]);
-			int i2 = Tho.Number(t[2]);
-			assert(i0>=0 && i1 >= 0 && i2  >= 0);
-			assert(i0<Tho.nbv && i1 <Tho.nbv && i2  <Tho.nbv);
-			// cout <<i<< " F" <<  flag[i] << " T " << nbt << "   = " <<  kk[i0] << " " << kk[i1] << " " << kk[i2] ;
-			// cout << " OT  " <<  i0 << " "  << i1 << " " << i2  << " " << reft[i] << endl;
-			triangles[nbt] = Triangle(this,kk[i0],kk[i1],kk[i2]);
-			triangles[nbt].color = Tho.subdomains[reft[i]].ref; 
-			nbt++;           
-		}
-	assert(kt==nbt);
-	if (nbt ==0 && nbv ==0) {
-		cout << "Error all triangles was remove " << endl;
-		MeshError(999,this);
-	}
-	delete [] kk;
-	delete [] reft;
-	delete [] refv;
-	double cutoffradian = 10.0/180.0*Pi;
-	ConsGeometry(cutoffradian);
-	Gh.AfterRead(); 
-	SetIntCoor();
-	FillHoleInMesh();
-
-	assert(NbSubDomains);
-	assert(subdomains[0].head && subdomains[0].head->link);
-
-}
-
-Triangle * Triangles::FindTriangleContening(const I2 & B,Icoor2 dete[3], Triangle *tstart) const { // in: B 
-	// out: t
-	// out : dete[3]
-	// t the triangle and s0,s1,s2 the 3 vertices of t
-	// in dete[3] = { det(B,s1,s2) , det(s0,B,s2), det(s0,s1,B)}
-	// with det(a,b,c ) = -1 if one of 3 vertices a,b,c is NULL 
-	Triangle * t=0;	
-	int j,jp,jn,jj;
-	if (tstart) 
-		t=tstart;
-	else 
-	{
-		assert(quadtree);
-		Vertex *a = quadtree->NearestVertex(B.x,B.y) ;
-
-		if (! a || !a->t ) {
-			if (a) 
-			{cerr << " Attention PB TriangleConteningTheVertex  vertex number=" << Number(a) << endl;
-				cerr  << "We forget a call to ReMakeTriangleContainingTheVertex" << endl;}
-				cerr << " Pb with " << B << toR2(B) << endl;
-				MeshError(7777);
-		}
-		assert(a>= vertices && a < vertices+nbv);
-		//  int k=0;
-		t = a->t;
-		assert(t>= triangles && t < triangles+nbt);
-
-	}
-	Icoor2  detop ;
-	int kkkk =0; // number of test triangle 
-
-	while ( t->det < 0) 
-	{ // the initial triangles is outside  
-		int k0=(*t)(0) ?  ((  (*t)(1) ? ( (*t)(2) ? -1 : 2) : 1  )) : 0;
-		assert(k0>=0); // k0 the NULL  vertex 
-		int k1=NextVertex[k0],k2=PreviousVertex[k0];
-		dete[k0]=det(B,(*t)[k1],(*t)[k2]);
-		dete[k1]=dete[k2]=-1;     
-		if (dete[k0] > 0) // outside B 
-			return t; 
-		t = t->TriangleAdj(OppositeEdge[k0]);
-		assert(kkkk++ < 2);
-	}
-
-	jj=0;
-	detop = det(*(*t)(VerticesOfTriangularEdge[jj][0]),*(*t)(VerticesOfTriangularEdge[jj][1]),B);
-
-	while(t->det  > 0 ) 
-	{ 
-		assert( kkkk++ < 2000 ); 
-		j= OppositeVertex[jj];
-		dete[j] = detop;  //det(*b,*s1,*s2);
-		jn = NextVertex[j];
-		jp = PreviousVertex[j];
-		dete[jp]= det(*(*t)(j),*(*t)(jn),B);
-		dete[jn] = t->det-dete[j] -dete[jp];
-
-		// count the number k of  dete <0
-		int k=0,ii[3];
-		if (dete[0] < 0 ) ii[k++]=0; 
-		if (dete[1] < 0 ) ii[k++]=1;
-		if (dete[2] < 0 ) ii[k++]=2;
-		// 0 => ok
-		// 1 => go in way 1
-		// 2 => two way go in way 1 or 2 randomly
-
-		if (k==0) 
-			break;
-		if (k == 2 && BinaryRand())
-			Exchange(ii[0],ii[1]);
-		assert ( k  < 3);
-		TriangleAdjacent t1 = t->Adj(jj=ii[0]);
-		if ((t1.det() < 0 ) && (k == 2))
-			t1 = t->Adj(jj=ii[1]);
-		t=t1;
-		j=t1;// for optimisation we now the -det[OppositeVertex[j]];
-		detop = -dete[OppositeVertex[jj]];
-		jj = j;
-	}
-
-	if (t->det<0) // outside triangle 
-		dete[0]=dete[1]=dete[2]=-1,dete[OppositeVertex[jj]]=detop;
-	//  NbOfTriangleSearchFind += kkkk;  
-	return t;
-}
 
 double QuadQuality(const Vertex & a,const Vertex &b,const Vertex &c,const Vertex &d) {
Index: /issm/trunk/src/c/Bamgx/Triangles.cpp
===================================================================
--- /issm/trunk/src/c/Bamgx/Triangles.cpp	(revision 2810)
+++ /issm/trunk/src/c/Bamgx/Triangles.cpp	(revision 2811)
@@ -14,4 +14,5 @@
 
 	static const  Direction NoDirOfSearch=Direction();
+	long NbUnSwap =0;
 
 	/*Constructors/Destructors*/
@@ -26,4 +27,207 @@
 		FillHoleInMesh();
 	}
+	/*}}}1*/
+	/*FUNCTION Triangles::Triangles(const Triangles & Tho,const int *flag ,const int *bb){{{1*/
+	Triangles::Triangles(const Triangles & Tho,const int *flag ,const int *bb)
+	  : Gh(*(new Geometry())), BTh(*this) {
+
+		  char cname[] = "trunc";
+
+		  int i,k,itadj;
+		  int kt=0;
+		  int * kk    = new int [Tho.nbv];
+		  Int4 * reft = new Int4[Tho.nbt];
+		  Int4 nbInT =    Tho.ConsRefTriangle(reft);
+		  Int4 * refv = new Int4[Tho.nbv];
+
+		  for (i=0;i<Tho.nbv;i++)
+			kk[i]=-1;
+		  for (i=0;i<Tho.nbv;i++)
+			refv[i]=0;
+		  int nbNewBedge =0;
+		  //  int nbOldBedge =0;  
+		  for (i=0;i<Tho.nbt;i++)
+			if(  reft[i] >=0 && flag[i]) 
+			  {
+				const Triangle & t = Tho.triangles[i];
+				kt++;
+				kk[Tho.Number(t[0])]=1;
+				kk[Tho.Number(t[1])]=1;
+				kk[Tho.Number(t[2])]=1;
+				itadj=Tho.Number(t.TriangleAdj(0));
+				if (  reft[itadj] >=0 && !flag[itadj])
+				  { nbNewBedge++;
+					refv[Tho.Number(t[VerticesOfTriangularEdge[0][0]])]=bb[i];
+					refv[Tho.Number(t[VerticesOfTriangularEdge[0][1]])]=bb[i];
+				  }
+				itadj=Tho.Number(t.TriangleAdj(1));
+				if (  reft[itadj] >=0 && !flag[itadj])
+				  { nbNewBedge++;
+					refv[Tho.Number(t[VerticesOfTriangularEdge[1][0]])]=bb[i];
+					refv[Tho.Number(t[VerticesOfTriangularEdge[1][1]])]=bb[i];}
+					itadj=Tho.Number(t.TriangleAdj(2));
+					if (  reft[itadj] >=0 && !flag[itadj])
+					  { nbNewBedge++;
+						refv[Tho.Number(t[VerticesOfTriangularEdge[2][0]])]=bb[i];
+						refv[Tho.Number(t[VerticesOfTriangularEdge[2][1]])]=bb[i];}
+			  }
+		  k=0;
+		  for (i=0;i<Tho.nbv;i++)
+			if (kk[i]>=0) 
+			 kk[i]=k++;
+		  cout << " number of vertices " << k << " remove = " << Tho.nbv - k << endl;
+		  cout << " number of triangles " << kt << " remove = " << nbInT-kt << endl;
+		  cout << " number of New boundary edge " << nbNewBedge << endl;
+		  Int4 inbvx =k;
+		  PreInit(inbvx,cname);
+		  for (i=0;i<Tho.nbv;i++)
+			if (kk[i]>=0) 
+			  {
+				vertices[nbv] = Tho.vertices[i];
+				if (!vertices[nbv].ref())
+				 vertices[nbv].ReferenceNumber = refv[i];
+				nbv++;
+			  }
+		  assert(inbvx == nbv);
+		  for (i=0;i<Tho.nbt;i++)
+			if(  reft[i] >=0 && flag[i]) 
+			  {
+				const Triangle & t = Tho.triangles[i];
+				int i0 = Tho.Number(t[0]);
+				int i1 = Tho.Number(t[1]);
+				int i2 = Tho.Number(t[2]);
+				assert(i0>=0 && i1 >= 0 && i2  >= 0);
+				assert(i0<Tho.nbv && i1 <Tho.nbv && i2  <Tho.nbv);
+				// cout <<i<< " F" <<  flag[i] << " T " << nbt << "   = " <<  kk[i0] << " " << kk[i1] << " " << kk[i2] ;
+				// cout << " OT  " <<  i0 << " "  << i1 << " " << i2  << " " << reft[i] << endl;
+				triangles[nbt] = Triangle(this,kk[i0],kk[i1],kk[i2]);
+				triangles[nbt].color = Tho.subdomains[reft[i]].ref; 
+				nbt++;           
+			  }
+		  assert(kt==nbt);
+		  if (nbt ==0 && nbv ==0) {
+			  cout << "Error all triangles was remove " << endl;
+			  MeshError(999,this);
+		  }
+		  delete [] kk;
+		  delete [] reft;
+		  delete [] refv;
+		  double cutoffradian = 10.0/180.0*Pi;
+		  ConsGeometry(cutoffradian);
+		  Gh.AfterRead(); 
+		  SetIntCoor();
+		  FillHoleInMesh();
+
+		  assert(NbSubDomains);
+		  assert(subdomains[0].head && subdomains[0].head->link);
+
+	  }
+	/*}}}1*/
+	/*FUNCTION Triangles::~Triangles(){{{1*/
+	Triangles::~Triangles() {
+		long int verbosity=2;
+		//assert(NbRef<=0);
+		if (CurrentTh == this) CurrentTh=0;
+		//if(vertices)  delete [] vertices; //TEST  crash if not commented
+		if(edges)     delete [] edges;
+		if(triangles) delete [] triangles;
+		if(quadtree)  delete  quadtree;
+		//if(ordre)     delete [] ordre; //TEST  crash if not commented
+		if( subdomains) delete []  subdomains;
+		if (VerticesOnGeomEdge) delete [] VerticesOnGeomEdge;
+		if (VerticesOnGeomVertex) delete [] VerticesOnGeomVertex;
+		//if (name) delete [] name; //TEST crash if not commented
+		if (identity) delete [] identity;
+		if (VertexOnBThVertex) delete [] VertexOnBThVertex;
+		if (VertexOnBThEdge) delete [] VertexOnBThEdge;
+
+		if (&Gh) {
+			if (Gh.NbRef>0) Gh.NbRef--;
+			else if (Gh.NbRef==0) delete &Gh;
+		}
+		if (&BTh && (&BTh != this)) {
+			if (BTh.NbRef>0) BTh.NbRef--;
+			else if (BTh.NbRef==0) delete &BTh;
+		}
+		PreInit(0); // set all to zero 
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::Triangles(Triangles & Th,Geometry * pGh,Triangles * pBth,Int4 nbvxx) COPY{{{1*/
+	Triangles::Triangles(Triangles & Th,Geometry * pGh,Triangles * pBth,Int4 nbvxx)
+	  : Gh(*(pGh?pGh:&Th.Gh)), BTh(*(pBth?pBth:this)) {
+		  Gh.NbRef++;
+		  nbvxx = Max(nbvxx,Th.nbv); 
+		  Int4 i;
+		  // do all the allocation to be sure all the pointer existe
+
+		  char * cname = 0;
+		  if (Th.name) 
+			 {
+			  cname = new char[strlen(Th.name)+1];
+			  strcpy(cname,Th.name);
+			 }
+		  PreInit(nbvxx,cname);// to make the allocation 
+		  // copy of triangles
+		  nt=Th.nt;
+		  nbv = Th.nbv;
+		  nbt = Th.nbt;
+		  nbiv = Th.nbiv;
+		  nbe = Th.nbe;
+		  NbSubDomains = Th.NbSubDomains;
+		  NbOutT = Th.NbOutT;
+		  NbOfQuad =  Th.NbOfQuad ;
+		  NbOfSwapTriangle =0;
+		  NbVerticesOnGeomVertex = Th.NbVerticesOnGeomVertex;
+		  if(NbVerticesOnGeomVertex)
+			VerticesOnGeomVertex = new VertexOnGeom[NbVerticesOnGeomVertex];
+		  NbVerticesOnGeomEdge = Th.NbVerticesOnGeomEdge;
+		  if (NbVerticesOnGeomEdge)
+			VerticesOnGeomEdge = new VertexOnGeom[NbVerticesOnGeomEdge] ;
+		  if (& BTh == & Th.BTh) // same back ground 
+			 {
+			  BTh.NbRef++;
+			  NbVertexOnBThVertex = Th.NbVertexOnBThVertex;
+			  if(NbVertexOnBThVertex)
+				VertexOnBThVertex = new VertexOnVertex[NbVertexOnBThVertex];
+			  NbVertexOnBThEdge = Th.NbVertexOnBThEdge;
+			  if(NbVertexOnBThEdge)
+				VertexOnBThEdge = new VertexOnEdge[NbVertexOnBThEdge];
+			 }
+		  else 
+			 { // no add on back ground mesh 
+			  BTh.NbRef++;
+			  NbVertexOnBThVertex=0;
+			  VertexOnBThVertex=0;
+			  NbVertexOnBThEdge=0;
+			  VertexOnBThEdge=0;
+			  //       assert (& BTh == this); // --- a voir 
+
+			 }
+
+
+		  if(nbe)
+			edges = new Edge[nbe];
+		  if(NbSubDomains)
+			subdomains = new SubDomain[NbSubDomains];
+		  pmin = Th.pmin;
+		  pmax = Th.pmax;
+		  coefIcoor = Th.coefIcoor;
+		  for(i=0;i<nbt;i++)
+			triangles[i].Set(Th.triangles[i],Th,*this);
+		  for(i=0;i<nbe;i++)
+			edges[i].Set(Th,i,*this);
+		  for(i=0;i<nbv;i++)
+			vertices[i].Set(Th.vertices[i],Th,*this);
+		  for(i=0;i<NbSubDomains;i++)  
+			subdomains[i].Set(Th,i,*this);
+		  for (i=0;i<NbVerticesOnGeomVertex;i++)
+			VerticesOnGeomVertex[i].Set(Th.VerticesOnGeomVertex[i],Th,*this);
+		  for (i=0;i<NbVerticesOnGeomEdge;i++)
+			VerticesOnGeomEdge[i].Set(Th.VerticesOnGeomEdge[i],Th,*this);
+		  quadtree=0;
+
+
+		  //  assert(!OutSidesTriangles);
+	  }
 	/*}}}1*/
 
@@ -1648,4 +1852,3070 @@
 	}
 	/*}}}1*/
+	/*FUNCTION Triangles::swap{{{1*/
+	int Triangle::swap(Int2 a,int koption){
+		if(a/4 !=0) return 0;// arete lock or MarkUnSwap
+
+		register Triangle *t1=this,*t2=at[a];// les 2 triangles adjacent
+		register Int1 a1=a,a2=aa[a];// les 2 numero de l arete dans les 2 triangles
+		if(a2/4 !=0) return 0; // arete lock or MarkUnSwap
+
+		register Vertex  *sa=t1->ns[VerticesOfTriangularEdge[a1][0]];
+		register Vertex  *sb=t1->ns[VerticesOfTriangularEdge[a1][1]];
+		register Vertex  *s1=t1->ns[OppositeVertex[a1]];
+		register Vertex  *s2=t2->ns[OppositeVertex[a2]];
+
+		Icoor2 det1=t1->det , det2=t2->det ;
+		Icoor2 detT = det1+det2;
+		Icoor2 detA = Abs(det1) + Abs(det2);
+		Icoor2 detMin = Min(det1,det2);
+
+		int OnSwap = 0;       
+		// si 2 triangle infini (bord) => detT = -2;
+		if (sa == 0) {// les deux triangles sont frontieres
+			det2=bamg::det(s2->i,sb->i,s1->i);
+			OnSwap = det2 >0;}
+		else if (sb == 0) { // les deux triangles sont frontieres
+			det1=bamg::det(s1->i,sa->i,s2->i);
+			OnSwap = det1 >0;}
+		else if(( s1 != 0) && (s2 != 0) ) {
+			det1 = bamg::det(s1->i,sa->i,s2->i);
+			det2 = detT - det1;
+			OnSwap = (Abs(det1) + Abs(det2)) < detA;
+
+			Icoor2 detMinNew=Min(det1,det2);
+			//     if (detMin<0 && (Abs(det1) + Abs(det2) == detA)) OnSwap=BinaryRand();// just for test   
+			if (! OnSwap &&(detMinNew>0)) {
+				OnSwap = detMin ==0;
+				if (! OnSwap) {
+					int  kopt = koption;
+					while (1)
+					 if(kopt) {
+						 // critere de Delaunay pure isotrope
+						 register Icoor2 xb1 = sb->i.x - s1->i.x,
+									 x21 = s2->i.x - s1->i.x,
+									 yb1 = sb->i.y - s1->i.y,
+									 y21 = s2->i.y - s1->i.y,
+									 xba = sb->i.x - sa->i.x, 
+									 x2a = s2->i.x - sa->i.x,
+									 yba = sb->i.y - sa->i.y,
+									 y2a = s2->i.y - sa->i.y;
+						 register double
+							cosb12 =  double(xb1*x21 + yb1*y21),
+									 cosba2 =  double(xba*x2a + yba*y2a) ,
+									 sinb12 = double(det2),
+									 sinba2 = double(t2->det);
+
+
+						 // angle b12 > angle ba2 => cotg(angle b12) < cotg(angle ba2)
+						 OnSwap =  ((double) cosb12 * (double)  sinba2) <  ((double) cosba2 * (double) sinb12);
+						 //  	 if(CurrentTh) 
+						 //  	   cout << "swap " << CurrentTh->Number(sa) << " " << CurrentTh->Number(sb) << " " ;
+						 //  	 cout <<  cosb12 << " " <<  sinba2 << " "  <<  cosba2 << " " << sinb12 
+						 //  	      << " Onswap = " <<  OnSwap << endl;
+						 break;
+					 }
+					 else 
+						{	
+						 // critere de Delaunay anisotrope 
+						 Real8 som;
+						 I2 AB=(I2) *sb - (I2) *sa;
+						 I2 MAB2=((I2) *sb + (I2) *sa);
+						 R2 MAB(MAB2.x*0.5,MAB2.y*0.5);
+						 I2 A1=(I2) *s1 - (I2) *sa;
+						 I2 D = (I2) * s1 - (I2) * sb ;
+						 R2 S2(s2->i.x,s2->i.y);
+						 R2 S1(s1->i.x,s1->i.y);
+							{
+							 Metric M=s1->m;
+							 R2 ABo = M.Orthogonal(AB);
+							 R2 A1o = M.Orthogonal(A1);
+							 // (A+B)+ x ABo = (S1+B)/2+ y A1 
+							 // ABo x - A1o y =  (S1+B)/2-(A+B)/2 = (S1-B)/2 = D/2
+							 double dd = Abs(ABo.x*A1o.y)+Abs(ABo.y*A1o.x);
+							 double d = (ABo.x*A1o.y - ABo.y*A1o.x)*2; // because D/2
+							 if (Abs(d) > dd*1.e-3) {
+								 R2 C(MAB+ABo*((D.x*A1o.y - D.y*A1o.x)/d));
+								 som  = M(C - S2)/M(C - S1);
+							 } else 
+								{kopt=1;continue;}
+
+							}
+							{
+							 Metric M=s2->m;
+							 R2 ABo = M.Orthogonal(AB);
+							 R2 A1o = M.Orthogonal(A1);
+							 // (A+B)+ x ABo = (S1+B)/2+ y A1 
+							 // ABo x - A1o y =  (S1+B)/2-(A+B)/2 = (S1-B)/2 = D/2 
+							 double dd = Abs(ABo.x*A1o.y)+Abs(ABo.y*A1o.x);
+							 double d = (ABo.x*A1o.y - ABo.y*A1o.x)*2; // because D/2
+							 if(Abs(d) > dd*1.e-3) {
+								 R2 C(MAB+ABo*((D.x*A1o.y - D.y*A1o.x)/d));
+								 som  += M(C - S2)/M(C -  S1);
+							 } else 
+								{kopt=1;continue;}
+							}
+						 OnSwap = som < 2;
+						 break;
+						}
+
+				} // OnSwap 
+			} // (! OnSwap &&(det1 > 0) && (det2 > 0) )
+		}
+		if( OnSwap ) 
+		 bamg::swap(t1,a1,t2,a2,s1,s2,det1,det2);
+		else {
+			NbUnSwap ++;
+			t1->SetMarkUnSwap(a1);     
+		}
+		return OnSwap;
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::MetricAt{{{1*/
+	Metric Triangles::MetricAt(const R2 & A) const { 
+		I2 a = toI2(A);
+		Icoor2 deta[3];
+		Triangle * t =FindTriangleContening(a,deta);
+		if (t->det <0) { // outside
+			double ba,bb;
+			TriangleAdjacent edge= CloseBoundaryEdge(a,t,ba,bb) ;
+			return Metric(ba,*edge.EdgeVertex(0),bb,*edge.EdgeVertex(1));}
+		else { // inside
+			Real8   aa[3];
+			Real8 s = deta[0]+deta[1]+deta[2];
+			aa[0]=deta[0]/s;
+			aa[1]=deta[1]/s;
+			aa[2]=deta[2]/s;
+			return Metric(aa,(*t)[0],(*t)[1],(*t)[2]);
+		}
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::Add{{{1*/
+	void Triangles::Add( Vertex & s,Triangle * t, Icoor2 * det3) {
+		// -------------------------------------------
+		//             s2
+		//                                            !
+		//             /|\                            !
+		//            / | \                           !
+		//           /  |  \                          !
+		//    tt1   /   |   \ tt0                     !
+		//         /    |s   \                        !
+		//        /     .     \                       !
+		//       /  .      `   \                      !
+		//      / .           ` \                     !
+		//      ----------------                      !
+		//   s0       tt2       s1
+		//-------------------------------------------- 
+
+		Triangle * tt[3]; // the 3 new Triangles
+		Vertex &s0 = (* t)[0], &s1=(* t)[1], &s2=(* t)[2];
+		Icoor2  det3local[3];
+		int infv = &s0 ?  ((  &s1 ? ( &s2  ? -1 : 2) : 1  )) : 0;
+		// infv = ordre of the infini vertex (null)
+		register int nbd0 =0; // number of zero det3
+		register int izerodet=-1,iedge; // izerodet = egde contening the vertex s
+		Icoor2 detOld = t->det;
+
+		if ( ( infv <0 ) && (detOld <0) ||  ( infv >=0  ) && (detOld >0) ) 
+		  {
+			cerr << "  infv " << infv << " det = " << detOld << endl;
+			cerr << Number(s) << " "<< Number(s0) << " "  
+			  << Number(s1) << " "  << Number(s2) << endl;
+			MeshError(3);
+		  }
+
+		// if det3 do not exist then constuct det3
+		if (!det3) { 
+			det3 = det3local; // alloc 
+			if ( infv<0 ) {
+				det3[0]=bamg::det(s ,s1,s2);
+				det3[1]=bamg::det(s0,s ,s2);
+				det3[2]=bamg::det(s0,s1,s );}
+			else { 
+				// one of &s1  &s2  &s0 is NULL so (&si || &sj) <=> !&sk
+				det3[0]=  &s0 ? -1  : bamg::det(s ,s1,s2) ;
+				det3[1]=  &s1 ? -1 : bamg::det(s0,s ,s2) ;
+				det3[2]=  &s2 ? -1 : bamg::det(s0,s1,s ) ;}}
+
+
+				if (!det3[0]) izerodet=0,nbd0++;
+				if (!det3[1]) izerodet=1,nbd0++;
+				if (!det3[2]) izerodet=2,nbd0++;
+
+				if  (nbd0 >0 ) // point s on a egde or on a vertex 
+				 if (nbd0 == 1) {
+					 iedge = OppositeEdge[izerodet];
+					 TriangleAdjacent ta = t->Adj(iedge);
+
+					 // the point is on the edge 
+					 // if the point is one the boundary 
+					 // add the point in outside part 
+					 if ( t->det >=0) { // inside triangle
+						 if ((( Triangle *) ta)->det < 0 ) {
+							 // add in outside triangle 
+							 Add(s,( Triangle *) ta);
+							 return;}
+					 }}
+				 else {
+					 cerr << " bug  " << nbd0 <<endl;
+					 cerr << " Bug double points in " << endl ;
+					 cerr << " s = " << Number(s) << " " <<  s << endl;
+					 cerr << " s0 = "<< Number(s0) << " "  << s0 << endl;
+					 cerr << " s1 = "<< Number(s1) << " "  << s1 << endl;
+					 cerr << " s2 = "<< Number(s2) << " "  << s2 << endl;
+					 MeshError(5,this);}
+
+					 // remove de MarkUnSwap edge
+					 t->SetUnMarkUnSwap(0);     
+					 t->SetUnMarkUnSwap(1);     
+					 t->SetUnMarkUnSwap(2);
+
+					 tt[0]= t;
+					 tt[1]= &triangles[nbt++];
+					 tt[2]= &triangles[nbt++];
+
+					 if (nbt>nbtx) {
+						 cerr << " No enougth triangles " << endl;
+						 MeshError(999,this);
+					 }
+
+					 *tt[1]=   *tt[2]= *t;
+					 // gestion of the link
+					 tt[0]->link=tt[1];
+					 tt[1]->link=tt[2]; 
+
+					 (* tt[0])(OppositeVertex[0])=&s;
+					 (* tt[1])(OppositeVertex[1])=&s;
+					 (* tt[2])(OppositeVertex[2])=&s;
+
+					 tt[0]->det=det3[0];
+					 tt[1]->det=det3[1];
+					 tt[2]->det=det3[2];         
+
+					 //  update adj des triangles externe 
+					 tt[0]->SetAdjAdj(0);
+					 tt[1]->SetAdjAdj(1);
+					 tt[2]->SetAdjAdj(2);
+					 //  update des adj des 3 triangle interne
+					 const int i0 = 0;
+					 const int i1= NextEdge[i0];
+					 const int i2 = PreviousEdge[i0];
+
+					 tt[i0]->SetAdj2(i2,tt[i2],i0);
+					 tt[i1]->SetAdj2(i0,tt[i0],i1);
+					 tt[i2]->SetAdj2(i1,tt[i1],i2);
+
+					 tt[0]->SetTriangleContainingTheVertex();
+					 tt[1]->SetTriangleContainingTheVertex();
+					 tt[2]->SetTriangleContainingTheVertex();
+
+
+					 // swap if the point s is on a edge
+					 if(izerodet>=0) {
+						 //  cout << " the point s is on a edge =>swap " << iedge << " "  << *tt[izerodet] << endl;
+						 int rswap =tt[izerodet]->swap(iedge);
+
+						 if (!rswap) 
+							{
+							 cout << " Pb swap the point s is on a edge =>swap " << iedge << " "  << *tt[izerodet] << endl;
+							}
+						 assert(rswap);
+					 }
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::SplitInternalEdgeWithBorderVertices{{{1*/
+	Int4  Triangles::SplitInternalEdgeWithBorderVertices(){
+		Int4 NbSplitEdge=0;
+		SetVertexFieldOn();  
+		Int4 it;
+		Int4 nbvold=nbv;
+		long int verbosity=2;
+		for (it=0;it<nbt;it++)
+		  {
+			Triangle &t=triangles[it];
+			if (t.link)
+			 for (int j=0;j<3;j++)
+			  if(!t.Locked(j) && !t.Hidden(j)){
+				  Triangle &tt = *t.TriangleAdj(j);
+				  if ( &tt && tt.link && it < Number(tt)) 
+					 { // an internal edge 
+					  Vertex &v0 = t[VerticesOfTriangularEdge[j][0]];
+					  Vertex &v1 = t[VerticesOfTriangularEdge[j][1]];
+					  if (v0.on && v1.on)
+						 {
+						  R2 P= ((R2) v0 + (R2) v1)*0.5;
+						  if ( nbv<nbvx) {
+							  vertices[nbv].r = P;
+							  vertices[nbv++].m = Metric(0.5,v0.m,0.5,v1.m);
+							  vertices[nbv].ReferenceNumber=0;
+							  vertices[nbv].DirOfSearch = NoDirOfSearch ;
+						  }
+						  NbSplitEdge++;
+						  if (verbosity>7)
+							cout <<" Internal edge with two vertices on boundary" 
+							  << Number(v0) << " " << Number(v1) << " by " <<  endl;
+						 }
+					 }
+			  }
+		  }
+		ReMakeTriangleContainingTheVertex();    
+		if (nbvold!=nbv) 
+		  {
+			Int4  iv = nbvold;
+			Int4 NbSwap = 0;
+			Icoor2 dete[3];  
+			for (Int4 i=nbvold;i<nbv;i++) 
+			  {// for all the new point
+				Vertex & vi = vertices[i];
+				vi.i = toI2(vi.r);
+				vi.r = toR2(vi.i);
+				//      if (!quadtree->ToClose(vi,seuil,hi,hj)) {
+				// a good new point 
+				vi.ReferenceNumber=0; 
+				vi.DirOfSearch =NoDirOfSearch;
+				//	cout << " Add " << Number(vi) << " " << vi 
+				// << "   " <<  Number(vi) << " <--> " << Number(vi) <<endl;
+				Triangle *tcvi = FindTriangleContening(vi.i,dete);
+				if (tcvi && !tcvi->link) {
+					cout << i <<  " PB insert point " << Number(vi) << vi << Number(vi) 
+					  << " tcvi = " << tcvi << " " << tcvi->link << endl;
+					cout << (*tcvi)[1] <<  (*tcvi)[2] << endl;
+					tcvi = FindTriangleContening(vi.i,dete);
+					cout << (*tcvi)[1] <<  (*tcvi)[2] << endl;
+					MeshError(1001,this);
+				}
+
+
+				quadtree->Add(vi);
+				assert (tcvi && tcvi->det >= 0) ;// internal 
+				Add(vi,tcvi,dete);
+				NbSwap += vi.Optim(1);          
+				iv++;
+				//      }
+			  }
+			if (verbosity>3) 
+			  {
+				cout << "    Nb Of New Point " << iv ;
+				cout << " Nb swap = " << NbSwap << " to  split internal edges with border vertices" ;}
+
+				nbv = iv;
+		  }
+		if (NbSplitEdge >  nbv-nbvold)
+		 cout << " Warning not enough vertices  to split all internal edges "  << endl
+			<< "    we lost " << NbSplitEdge - ( nbv-nbvold) << " Edges Sorry " << endl;
+		if (verbosity>2)
+		 cout << "SplitInternalEdgeWithBorderVertices: Number of splited edge " << NbSplitEdge << endl;
+		return  NbSplitEdge;
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::InsertNewPoints{{{1*/
+	Int4 Triangles::InsertNewPoints(Int4 nbvold,Int4 & NbTSwap) {
+		long int verbosity=2;
+		Real8 seuil= 1.414/2 ;// for two close point 
+		Int4 i;
+		// insertion part --- 
+
+		const Int4 nbvnew = nbv-nbvold;
+		if (verbosity>5) 
+		 cout << "    Try to Insert the " <<nbvnew<< " new points " << endl;  
+		Int4 NbSwap=0;
+		Icoor2 dete[3];
+
+		// construction d'un ordre aleatoire 
+		if (! nbvnew) 
+		 return 0; 
+		if (nbvnew) {
+			const Int4 PrimeNumber= AGoodNumberPrimeWith(nbv)  ;
+			Int4 k3 = rand()%nbvnew ; 
+			for (Int4 is3=0; is3<nbvnew; is3++) {
+				register Int4 j = nbvold +(k3 = (k3 + PrimeNumber)% nbvnew);
+				register Int4 i = nbvold+is3; 
+				ordre[i]= vertices + j;
+				ordre[i]->ReferenceNumber=i;
+			}
+			// be carefull 
+			Int4  iv = nbvold;
+			for (i=nbvold;i<nbv;i++) 
+			  {// for all the new point
+				Vertex & vi = *ordre[i];
+				vi.i = toI2(vi.r);
+				vi.r = toR2(vi.i);
+				Real4 hx,hy;
+				vi.m.Box(hx,hy);
+				Icoor1 hi=(Icoor1) (hx*coefIcoor),hj=(Icoor1) (hy*coefIcoor);
+				if (!quadtree->ToClose(vi,seuil,hi,hj)) 
+				  {
+					// a good new point 
+					Vertex & vj = vertices[iv];
+					Int4 j = vj.ReferenceNumber; 
+					assert( &vj== ordre[j]);
+					if(i!=j)
+					  { //  for valgring 
+						Exchange(vi,vj);
+						Exchange(ordre[j],ordre[i]);
+					  }
+					vj.ReferenceNumber=0; 
+					//	cout << " Add " << Number(vj) << " " << vj 
+					// << "   " <<  Number(vi) << " <--> " << Number(vj) <<endl;
+					Triangle *tcvj = FindTriangleContening(vj.i,dete);
+					if (tcvj && !tcvj->link) 
+					  {
+						cerr << i <<  " PB insert point " << Number(vj) << vj << Number(vi) 
+						  << " tcvj = " << tcvj << " " << tcvj->link << endl;
+						cerr << (*tcvj)[1] <<  (*tcvj)[2] << endl;
+						tcvj = FindTriangleContening(vj.i,dete);
+						cout << (*tcvj)[1] <<  (*tcvj)[2] << endl;
+						MeshError(1001,this);
+					  }
+
+
+					quadtree->Add(vj);
+					assert (tcvj && tcvj->det >= 0) ;// internal 
+					Add(vj,tcvj,dete);
+					NbSwap += vj.Optim(1);          
+					iv++;
+				  }
+			  } 
+			if (verbosity>3) {
+				cout << "    Nb Of New Point " << iv << " Nb Of To close Points " << nbv-iv ;
+				cout << " Nb swap = " << NbSwap << " after " ;}
+
+				nbv = iv;
+		}
+
+		for (i=nbvold;i<nbv;i++) 
+		 NbSwap += vertices[i].Optim(1);  
+		if (verbosity>3) 
+		 cout << " NbSwap = " <<  NbSwap << endl;
+
+
+		NbTSwap +=  NbSwap ;
+		return nbv-nbvold;
+
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::NewPoints{{{1*/
+	void  Triangles::NewPoints(Triangles & Bh,int KeepBackVertex) {
+		long int verbosity=2;
+		Int4 nbtold(nbt),nbvold(nbv);
+		if (verbosity>2) 
+		 cout << "  -- Triangles::NewPoints ";
+		if (verbosity>3)cout <<  " nbv (in)  on Boundary  = " << nbv  <<endl;
+		Int4 i,k;
+		int j;
+		Int4 *first_np_or_next_t = new Int4[nbtx];
+		Int4 NbTSwap =0;
+		//    insert old point
+		nbtold = nbt;
+
+		if (KeepBackVertex && (&Bh != this) && (nbv+Bh.nbv< nbvx)) 
+		  {
+			//   Bh.SetVertexFieldOn();
+			for (i=0;i<Bh.nbv;i++)
+			  { 
+				Vertex & bv = Bh[i];
+				if (!bv.on) {
+					vertices[nbv].r = bv.r;
+					vertices[nbv++].m = bv.m;}
+			  }
+			int nbv1=nbv;
+			Bh.ReMakeTriangleContainingTheVertex();     
+			InsertNewPoints(nbvold,NbTSwap)   ;            
+			if (verbosity>2)
+			 cout <<  "      (Nb of Points from background mesh  = " 
+				<< nbv-nbvold  << " / " << nbv1-nbvold << ")" << endl;
+		  }  
+		else 
+		 Bh.ReMakeTriangleContainingTheVertex();     
+
+		Triangle *t;
+		// generation of the list of next Triangle 
+		// at 1 time we test all the triangles
+		Int4 Headt =0,next_t;
+		for(i=0;i<nbt;i++)
+		 first_np_or_next_t[i]=-(i+1);
+		// end list i >= nbt 
+		// the list of test triangle is 
+		// the next traingle on i is  -first_np_or_next_t[i]
+		int iter=0;
+		// Big loop 
+		do {
+			iter++;
+			nbtold = nbt;
+			nbvold = nbv;
+
+			// default size of  IntersectionTriangle
+
+			i=Headt;
+			next_t=-first_np_or_next_t[i];
+			for(t=&triangles[i];i<nbt;t=&triangles[i=next_t],next_t=-first_np_or_next_t[i]) 
+			  { // for each triangle  t
+				// we can change first_np_or_next_t[i]
+				//      cout << " Do the triangle " << i << " Next_t=" << next_t << endl;
+				assert(i>=0 && i < nbt );
+				first_np_or_next_t[i] = iter; 
+				for(j=0;j<3;j++)
+				  { // for each edge 
+					TriangleAdjacent tj(t,j);
+					Vertex & vA = * tj.EdgeVertex(0);
+					Vertex & vB = * tj.EdgeVertex(1);
+
+					if (!t->link) continue;// boundary
+					if (t->det <0) continue;
+					if (t->Locked(j)) continue;
+
+					TriangleAdjacent tadjj = t->Adj(j);	  
+					Triangle * ta= tadjj;
+
+					if (ta->det <0) continue;	  
+
+					R2 A = vA;
+					R2 B = vB;
+
+					k=Number(ta);
+
+					if(first_np_or_next_t[k]==iter)  // this edge is done before 
+					 continue; // next edge of the triangle 
+
+					//const Int4 NbvOld = nbv;
+					lIntTria.SplitEdge(Bh,A,B);
+					lIntTria.NewPoints(vertices,nbv,nbvx);
+				  } // end loop for each edge 
+
+			  }// for triangle   
+
+			if (!InsertNewPoints(nbvold,NbTSwap)) 
+			 break;
+
+			for (i=nbtold;i<nbt;i++)
+			 first_np_or_next_t[i]=iter;
+
+			Headt = nbt; // empty list 
+			for (i=nbvold;i<nbv;i++) 
+			  { // for all the triangle contening the vertex i
+				Vertex * s  = vertices + i;
+				TriangleAdjacent ta(s->t, EdgesVertexTriangle[s->vint][1]);
+				Triangle * tbegin= (Triangle*) ta;
+				Int4 kt;
+				do { 
+					kt = Number((Triangle*) ta);
+					if (first_np_or_next_t[kt]>0) 
+					 first_np_or_next_t[kt]=-Headt,Headt=kt;
+					assert( ta.EdgeVertex(0) == s);
+					ta = Next(Adj(ta));
+				} while ( (tbegin != (Triangle*) ta)); 
+			  }   
+
+		} while (nbv!=nbvold);
+
+		delete []  first_np_or_next_t;
+
+		Int4 NbSwapf =0,NbSwp;
+
+		// bofbof 
+
+
+		NbSwp = NbSwapf;
+		for (i=0;i<nbv;i++)
+		 NbSwapf += vertices[i].Optim(0);
+		/*
+			for (i=0;i<nbv;i++)
+			NbSwapf += vertices[i].Optim(0);
+			for (i=0;i<nbv;i++)
+			NbSwapf += vertices[i].Optim(0);
+			for (i=0;i<nbv;i++)
+			NbSwapf += vertices[i].Optim(0);
+			for (i=0;i<nbv;i++)
+			NbSwapf += vertices[i].Optim(0);
+			*/
+		NbTSwap +=  NbSwapf ;
+		if (verbosity>3) cout << "   " ;
+		if (verbosity>2) 
+		 cout << " Nb Of Vertices =" << nbv << " Nb of triangles = " << nbt-NbOutT 
+			<< " NbSwap final = " << NbSwapf << " Nb Total Of Swap = " << NbTSwap << endl;
+
+
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::NewPointsOld{{{1*/
+	void  Triangles::NewPointsOld(Triangles & Bh) {
+		long int verbosity=2;
+		Real8 seuil= 0.7 ;// for two neart point 
+		if (verbosity>1) 
+		 cout << " begin :  Triangles::NewPointsOld " << endl;
+		Int4 i,k;
+		int j;
+		Int4 BeginNewPoint[3];
+		Int4 EndNewPoint[3];
+#ifdef TRACETRIANGLE
+		Int4 trace=0;
+#endif
+		int step[3];
+		Int4 *first_np_or_next_t = new Int4[nbtx];
+		Int4 ColorEdge[3];
+		Int4 color=-1;
+		Triangle *t;
+		// generation of the list of next Triangle 
+		// at 1 time we test all the triangles
+		Int4 Headt =0,next_t;
+		for(i=0;i<nbt;i++)
+		 first_np_or_next_t[i]=-(i+1);
+		// end list i >= nbt 
+		// the list of test triangle is 
+		// the next Triangle on i is  -first_np_or_next_t[i]
+		Int4 nbtold,nbvold;
+
+		// Big loop 
+		do {
+			nbtold = nbt;
+			nbvold = nbv;
+			// default size of  IntersectionTriangle
+
+			i=Headt;
+			next_t=-first_np_or_next_t[i];
+			for(t=&triangles[i];i<nbt;t=&triangles[i=next_t],next_t=-first_np_or_next_t[i]) 
+			  { // for each triangle  t
+				// we can change first_np_or_next_t[i]
+#ifdef TRACETRIANGLE
+				trace =  TRACETRIANGLE <0 ? 1 : i == TRACETRIANGLE;
+#endif
+				//      cout << " Do the triangle " << i << " Next_t=" << next_t << endl;
+				assert(i>=0 && i < nbt );
+				first_np_or_next_t[i] = nbv; // to save the fist new point of triangle
+				for(j=0;j<3;j++)
+				  { // for each edge 
+					TriangleAdjacent tj(t,j);
+					// color++;// the color is 3i+j
+					color = 3*i + j ;;
+					ColorEdge[j]=color;
+					BeginNewPoint[j]=nbv;
+					EndNewPoint[j]=nbv-1;
+					step[j]=1;// right sens 
+					Vertex & vA = * tj.EdgeVertex(0);
+					Vertex & vB = * tj.EdgeVertex(1);
+
+#ifdef TRACETRIANGLE
+					if(trace) {
+						cout << " i " << Number(vA) <<" j "<<  Number(vB) 
+						  << " "  << t->Locked(j) ;
+					}
+#endif
+					if (!t->link) continue;// boundary
+					if (t->det <0) continue;
+					if (t->Locked(j)) continue;
+
+					TriangleAdjacent tadjj = t->Adj(j);	  
+					Triangle * ta= tadjj;
+
+					if (ta->det <0) continue;	  
+
+					R2 A = vA;
+					R2 B = vB;
+
+					k=Number(ta);
+					// the 2 opposite vertices 
+					const Vertex & vC1  =  *tj.OppositeVertex();
+					const Vertex & vC2 = *tadjj.OppositeVertex();
+
+#ifdef TRACETRIANGLE
+					trace = trace || k == TRACETRIANGLE;
+					if(trace) {
+						cout << "Test Arete " << i << " AB = " << A << B 
+						  << "i "  <<Number(vA)<< "j" <<Number(vB); 
+						cout << " link" <<(int)t->link << " ta=" << Number( ta) 
+						  << " det " <<ta->det ;
+						cout << " hA = " <<vA.m.h << " hB = " <<vB.m.h ;
+						cout << " loc " << ta->Locked(j) << endl;
+					}
+#endif
+
+					if(first_np_or_next_t[k]>0) { // this edge is done before 
+						// find the color of the edge and begin , end of newpoint
+						register int kk = t->NuEdgeTriangleAdj(j);
+						assert ((*t)(VerticesOfTriangularEdge[j][0]) == (*ta)(VerticesOfTriangularEdge[kk][1]));
+						assert ((*t)(VerticesOfTriangularEdge[j][1]) == (*ta)(VerticesOfTriangularEdge[kk][0]));
+						register Int4 kolor =3*k + kk;
+						ColorEdge[j]=kolor;
+						register Int4 kkk= 1;
+						step[j]=-1;// other sens 
+						BeginNewPoint[j]=0;
+						EndNewPoint[j]=-1; // empty list          
+						for (Int4 iv=first_np_or_next_t[k];iv<nbv;iv++) 
+						 if (vertices[iv].color > kolor) 
+						  break; // the color is passed            
+						 else if (vertices[iv].color == kolor) {
+							 EndNewPoint[j]=iv; 
+							 if (kkk) // one time test
+							  kkk=0,BeginNewPoint[j]=iv;}
+							 continue; // next edge of the triangle 
+					} // end  if( k < i) 
+
+
+					const Int4 NbvOld = nbv;
+					lIntTria.SplitEdge(Bh,A,B);
+					// Int4 NbvNp =
+					lIntTria.NewPoints(vertices,nbv,nbvx);
+					Int4 nbvNew=nbv;
+					nbv = NbvOld;
+					for (Int4 iv=NbvOld;iv<nbvNew;iv++) {
+						vertices[nbv].color = color;
+						vertices[nbv].ReferenceNumber=nbv;// circular link
+						R2 C =  vertices[iv].r;
+						vertices[nbv].r =  C;
+						vertices[nbv].m =  vertices[iv].m ;
+						// test if the new point is not to close to the 2 opposite vertex
+						R2 CC1 = C-vC1 , CC2 = C-vC2;
+						if (   (  (vC1.m(CC1) + vertices[nbv].m(CC1)) >  seuil)
+									&& (  (vC2.m(CC2) + vertices[nbv].m(CC2)) >  seuil) )
+						 nbv++;
+					}
+
+					EndNewPoint[j] = nbv-1;
+				  } // end loop for each edge 
+
+#ifdef TRACETRIANGLE
+				if(trace) {
+					// verification des point cree 
+					cout << "\n ------------ " << t->link << " " << t->det 
+					  << " b " << BeginNewPoint[0] << " " << BeginNewPoint[1]
+					  << " " << BeginNewPoint[2] << " " 
+					  << " e " << EndNewPoint[0] << " " << EndNewPoint[1] 
+					  << " " << EndNewPoint[2] << " " 
+					  << " s " << step[0] << " " << step[1] << " " << step[2] << " " 
+					  <<  endl;
+				}
+#endif
+
+				if (!t->link) continue;// boundary
+				if (t->det<=0) continue;// outside 
+				//      continue;
+				for(int j0=0;j0<3;j0++)
+				 for (Int4 i0= BeginNewPoint[j0]; i0 <= EndNewPoint[j0];i0++)
+					{
+					 // find the neart  point one the opposite edge 
+					 // to compute i1
+					 Vertex & vi0 = vertices[i0];
+					 int kstack = 0;
+					 Int4 stack[10];
+					 //   Int4 savRef[10];
+					 int j1 = j0; 
+					 while (j0 != (j1 = NextEdge[j1])) {//loop on the 2 other edge
+						 // computation of the intersection of edge j1 and DOrto
+						 // take the good sens 
+
+						 if (BeginNewPoint[j1]> EndNewPoint[j1])
+						  continue; // 
+						 else if (EndNewPoint[j1] - BeginNewPoint[j1] <1) {
+							 for (Int4 ii1= BeginNewPoint[j1];ii1<=EndNewPoint[j1];ii1++)
+							  stack[kstack++] = ii1;
+							 continue;}
+
+
+							 int k0,k1;
+							 if (step[j1]<0) k0=1,k1=0; // reverse
+							 else k0=0,k1=1; 
+							 R2 V10 = (R2)(*t)[VerticesOfTriangularEdge[j1][k0]];
+							 R2 V11 = (R2)(*t)[VerticesOfTriangularEdge[j1][k1]];
+							 R2 D = V11-V10;
+							 Real8 c0 =  vi0.m(D,(R2) vi0);
+
+							 Real8 c10 =  vi0.m(D,V10);
+							 Real8 c11 =  vi0.m(D,V11);
+
+							 Real8 s;
+							 //cout << " --i0 = " << i0  << D  << V10 << V11 << endl ;
+							 //cout << "   c10 " <<  c10 << " c0 " << c0 << " c11 " << c11 << endl;
+							 if (( c10 < c0 ) && (c0 < c11)) 
+							  s = (c11-c0)/(c11-c10);
+							 else if  (( c11 < c0 ) && (c0 < c10)) 
+							  s = (c11-c0) /(c11-c10);
+							 else break;
+							 R2 VP = V10*s + V11*(1-s);
+							 int sss = (c11-c10) >0 ? 1 : -1;
+							 // find the 2 point by dichotomie
+							 //cout << "   t =" << Number(t) << " c0 " << c0  ;
+							 Int4 ii0 =  BeginNewPoint[j1];
+							 Int4 ii1 =  EndNewPoint[j1];	     
+							 Real8 ciii=-1,cii0=-1,cii1=-1  ;
+							 if ( sss * ((cii0=vi0.m(D,(R2) vertices[ii0]))- c0) >0 )  
+							  stack[kstack++] = ii0;//cout << " add+0 " << ii0;
+							 else if ( sss * ((cii1=  vi0.m(D ,(R2) vertices[ii1]))- c0) < 0 )  
+							  stack[kstack++] = ii1;//cout << " add+1 " << ii1;
+							 else {
+								 while ((ii1-ii0)> 1) {
+									 Int4 iii = (ii0+ii1)/2;
+									 ciii = vi0.m( D ,(R2) vertices[iii]);
+									 //cout << " (iii = " << iii << " " <<  ciii << ") ";
+									 if ( sss * (ciii - c0) <0 )  ii0 = iii;
+									 else ii1 = iii;}	        	      
+									 stack[kstack++] = ii0;// cout << " add0 " << ii0;
+									 if (ii1 != ii0)  stack[kstack++] = ii1;//cout << " add1 " << ii1;
+							 }
+							 if (kstack >5) // bug ?
+							  cout << "NewPoints: bug????? " << kstack << " stack  " << stack[kstack]<< endl;
+					 }
+
+					 stack[kstack++] = -1; // to stop
+					 Int4 i1;
+					 kstack =0; 
+					 while( (i1=stack[kstack++]) >= 0) 
+						{ // the two parameter is i0 and i1 
+						 assert(i1 < nbv && i1 >= 0);
+						 assert(i0 < nbv && i0 >= 0);
+						 assert(i1 != i0);
+						 R2 v01 = (R2) vertices[i1]- (R2) vertices[i0];
+						 Real8 d01 = (vertices[i0].m(v01) + vertices[i1].m(v01));
+
+
+#ifdef TRACETRIANGLE
+						 if(trace) {
+							 cout << "\n test j" << j <<" "  << i0 
+								<< " " << i1 << " d01=" << d01 <<endl;}
+#endif
+						 assert (i0 >= nbvold);
+						 assert (i1 >= nbvold);
+						 assert(i0 != i1);
+						 if (d01 == 0) 
+						  break; 
+						 if ( d01 < seuil) 
+						  if (i1<nbvold) {
+							  // remove all the points i0;
+							  register Int4 ip,ipp;
+							  for  (ip=i0;i0 != (ipp = vertices[ip].ReferenceNumber);ip=ipp)
+								vertices[ip].ReferenceNumber = -1;// mark remove
+							  vertices[ip].ReferenceNumber = -1;// mark remove
+						  }
+						  else {
+							  // remove on of two points
+							  register Int4 ip0, ip1, ipp0,ipp1;
+							  register int kk0=1,kk1=1;
+							  // count the number of common points to compute weight w0,w1
+							  for  (ip0=i0;i0 != (ipp0 = vertices[ip0].ReferenceNumber);ip0=ipp0) kk0++;
+							  for  (ip1=i1;i1 != (ipp1 = vertices[ip1].ReferenceNumber);ip1=ipp1) kk1++;
+
+							  register Real8 w0 = ((Real8) kk0)/(kk0+kk1);
+							  register Real8 w1 = ((Real8) kk1)/(kk0+kk1);
+
+							  // make a circular link
+							  Exchange(vertices[i0].ReferenceNumber,vertices[i1].ReferenceNumber);
+							  // the new coordinate 
+							  R2 C //= vertices[i0] ;
+							  =  vertices[i0].r *w0 + vertices[i1].r* w1;
+
+#ifdef TRACETRIANGLE
+							  if(trace) {
+								  cout << "\n ref = "<< vertices[i0].ref << " " <<vertices[i1].ref <<endl;
+							  }
+#endif    
+							  // update the new point points of the list 
+							  for  (ip0=i0;i0 != (ipp0 = vertices[ip0].ReferenceNumber);ip0=ipp0)
+								vertices[ip0].r = C;	      
+							  vertices[ip0].r = C;
+						  }
+						}
+					} // for (i0= ....
+			  }// for triangle   
+
+			// remove of all the double points
+
+			Int4 ip,ipp,kkk=nbvold;
+			for (i=nbvold;i<nbv;i++) 
+			 if (vertices[i].ReferenceNumber>=0) {// good points
+				 //  cout <<" i = " << i ;
+				 for  (ip=i;i != (ipp = vertices[ip].ReferenceNumber);ip=ipp)
+				  vertices[ip].ReferenceNumber = -1;// mark remove
+				 vertices[ip].ReferenceNumber = -1;// mark remove
+				 // cout << i << " ---> " << kkk << endl;        
+				 vertices[kkk] = vertices[i];
+				 vertices[kkk].i = toI2(vertices[kkk].r);
+				 vertices[kkk++].ReferenceNumber = 0;
+
+			 } 
+
+			// insertion part --- 
+
+			const Int4 nbvnew = kkk-nbvold;
+
+			cout << "    Remove " << nbv - kkk  << " to close  vertex " ;
+			cout << " and   Insert the " <<nbvnew<< " new points " << endl;  
+			nbv = kkk;
+			Int4 NbSwap=0;
+			Icoor2 dete[3];
+
+			// construction d'un ordre aleatoire 
+			if (! nbvnew) 
+			 break; 
+			if (nbvnew) {
+				const Int4 PrimeNumber= AGoodNumberPrimeWith(nbv)  ;
+				Int4 k3 = rand()%nbvnew ; 
+				for (Int4 is3=0; is3<nbvnew; is3++) 
+				 ordre[nbvold+is3]= &vertices[nbvold +(k3 = (k3 + PrimeNumber)% nbvnew)];
+
+				for (i=nbvold;i<nbv;i++) 
+				  { Vertex * vi = ordre[i];
+					Triangle *tcvi = FindTriangleContening(vi->i,dete);
+					//     Vertex * nv =  quadtree->NearestVertex(vi->i.x,vi->i.y);
+					//      cout << " Neart Vertex of "  << Number(vi)<< vi->i << " is " 
+					//   << Number(nv) << nv->i  << endl;
+					// Int4  kt = Number(tcvi);
+					// 
+
+					quadtree->Add(*vi); //
+					assert (tcvi->det >= 0) ;// internal 
+					Add(*vi,tcvi,dete),NbSwap += vi->Optim(1);          
+				  }  
+			}
+			cout << " Nb swap = " << NbSwap << " after " ;
+
+			for (i=nbvold;i<nbv;i++) 
+			 NbSwap += vertices[i].Optim(1);  
+			cout << NbSwap << endl;
+
+			for (i=nbtold;i<nbt;i++)
+			 first_np_or_next_t[i]=1;
+
+			Headt = nbt; // empty list 
+			for (i=nbvold;i<nbv;i++) 
+			  { // for all the triangle contening the vertex i
+				Vertex * s  = vertices + i;
+				TriangleAdjacent ta(s->t, EdgesVertexTriangle[s->vint][1]);
+				Triangle * tbegin= (Triangle*) ta;
+				Int4 kt;
+				do { 
+					kt = Number((Triangle*) ta);
+					if (first_np_or_next_t[kt]>0) 
+					 first_np_or_next_t[kt]=-Headt,Headt=kt;
+					assert( ta.EdgeVertex(0) == s);
+					ta = Next(Adj(ta));
+				} while ( (tbegin != (Triangle*) ta)); 
+			  }
+
+
+		} while (nbv!=nbvold);
+		delete []  first_np_or_next_t;
+		cout << " end :  Triangles::NewPoints old  nbv=" << nbv << endl;
+
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::Insert{{{1*/
+	void Triangles::Insert() {
+		long int verbosity=2;
+		if (verbosity>2) cout << "  -- Insert initial " << nbv << " vertices " << endl ;
+		Triangles * OldCurrentTh =CurrentTh;
+
+		CurrentTh=this;
+		double time0=CPUtime(),time1,time2,time3;
+		SetIntCoor();
+		Int4 i;
+		for (i=0;i<nbv;i++) 
+		 ordre[i]= &vertices[i] ;
+
+		// construction d'un ordre aleatoire 
+		const Int4 PrimeNumber= AGoodNumberPrimeWith(nbv) ;
+		Int4 k3 = rand()%nbv ; 
+		for (int is3=0; is3<nbv; is3++) 
+		 ordre[is3]= &vertices[k3 = (k3 + PrimeNumber)% nbv];
+
+
+
+
+		for (i=2 ; det( ordre[0]->i, ordre[1]->i, ordre[i]->i ) == 0;) 
+		 if  ( ++i >= nbv) {
+			 cerr << " All the vertices are aline " << endl;
+			 MeshError(998,this); }
+
+			 // echange i et 2 dans ordre afin 
+			 // que les 3 premiers ne soit pas aligne
+			 Exchange( ordre[2], ordre[i]);
+
+			 // on ajoute un point a l'infini pour construire le maillage
+			 // afin d'avoir une definition simple des aretes frontieres
+			 nbt = 2;
+
+
+			 // on construit un maillage trivale forme
+			 // d'une arete et de 2 triangles
+			 // construit avec le 2 aretes orientes et 
+			 Vertex *  v0=ordre[0], *v1=ordre[1];
+
+			 triangles[0](0) = 0; // sommet pour infini 
+			 triangles[0](1) = v0;
+			 triangles[0](2) = v1;
+
+			 triangles[1](0) = 0;// sommet pour infini 
+			 triangles[1](2) = v0;
+			 triangles[1](1) = v1;
+			 const int e0 = OppositeEdge[0];
+			 const int e1 = NextEdge[e0];
+			 const int e2 = PreviousEdge[e0];
+			 triangles[0].SetAdj2(e0, &triangles[1] ,e0);
+			 triangles[0].SetAdj2(e1, &triangles[1] ,e2);
+			 triangles[0].SetAdj2(e2, &triangles[1] ,e1);
+
+			 triangles[0].det = -1;  // faux triangles
+			 triangles[1].det = -1;  // faux triangles
+
+			 triangles[0].SetTriangleContainingTheVertex();
+			 triangles[1].SetTriangleContainingTheVertex();
+
+			 triangles[0].link=&triangles[1];
+			 triangles[1].link=&triangles[0];
+
+			 //  nbtf = 2;
+			 if (  !quadtree )  quadtree = new QuadTree(this,0);
+			 quadtree->Add(*v0);
+			 quadtree->Add(*v1);
+
+			 // on ajoute les sommets un Ò un 
+			 Int4 NbSwap=0;
+
+			 time1=CPUtime();
+
+			 if (verbosity>3) cout << "  -- Begin of insertion process " << endl;
+
+			 for (Int4 icount=2; icount<nbv; icount++) {
+				 Vertex *vi  = ordre[icount];
+				 //    cout << " Insert " << Number(vi) << endl;
+				 Icoor2 dete[3];
+				 Triangle *tcvi = FindTriangleContening(vi->i,dete);
+				 quadtree->Add(*vi); 
+				 Add(*vi,tcvi,dete);
+				 NbSwap += vi->Optim(1,0);
+
+			 }// fin de boucle en icount
+			 time2=CPUtime();
+			 if (verbosity>3) 
+			  cout << "    NbSwap of insertion " <<    NbSwap 
+				 << " NbSwap/Nbv " <<  (float) NbSwap / (float) nbv 
+				 << " NbUnSwap " << NbUnSwap << " Nb UnSwap/Nbv " 
+				 << (float)NbUnSwap /(float) nbv 
+				 <<endl;
+			 NbUnSwap = 0;
+			 // construction d'un ordre aleatoire 
+			 //  const int PrimeNumber= (nbv % 999983) ? 1000003: 999983 ;
+#ifdef NBLOOPOPTIM
+
+			 k3 = rand()%nbv ; 
+			 for (int is4=0; is4<nbv; is4++) 
+			  ordre[is4]= &vertices[k3 = (k3 + PrimeNumber)% nbv];
+
+			 double timeloop = time2 ;
+			 for(int Nbloop=0;Nbloop<NBLOOPOPTIM;Nbloop++) 
+				{
+				 double time000 = timeloop;
+				 Int4  NbSwap = 0;
+				 for (int is1=0; is1<nbv; is1++) 
+				  NbSwap += ordre[is1]->Optim(0,0);
+				 timeloop = CPUtime();
+				 if (verbosity>3) 
+				  cout << "    Optim Loop "<<Nbloop<<" NbSwap: " <<  NbSwap 
+					 << " NbSwap/Nbv " 	   <<  (float) NbSwap / (float) nbv 
+					 << " CPU=" << timeloop - time000 << "  s, " 
+					 << " NbUnSwap/Nbv " << (float)NbUnSwap /(float) nbv  
+					 <<  endl;
+				 NbUnSwap = 0;
+				 if(!NbSwap) break;
+				}
+			 ReMakeTriangleContainingTheVertex(); 
+			 // because we break the TriangleContainingTheVertex
+#endif
+			 time3=CPUtime();
+			 if (verbosity>4) 
+			  cout << "    init " << time1 - time0 << " initialisation,  " 
+				 << time2 - time1 << "s, insert point  " 
+				 << time3 -time2 << "s, optim " << endl
+				 << "     Init Total Cpu Time = " << time3 - time0 << "s " << endl;
+
+			 CurrentTh=OldCurrentTh;
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::ForceBoundary{{{1*/
+	void Triangles::ForceBoundary() {
+		long int verbosity=2;
+		if (verbosity > 2)
+		 cout << "  -- ForceBoundary  nb of edge " << nbe << endl;
+		int k=0;
+		Int4  nbfe=0,nbswp=0,Nbswap=0;
+		for (Int4 t = 0; t < nbt; t++)  
+		 if (!triangles[t].det)
+		  k++,cerr << " det T" << t << " = " << 0 << endl;
+		if (k!=0) {
+			cerr << " ther is  " << k << "  triangles of mes = 0 " << endl;
+			MeshError(11,this);}
+
+			TriangleAdjacent ta(0,0);
+			for (Int4 i = 0; i < nbe; i++) 
+			  {
+				nbswp =  ForceEdge(edges[i][0],edges[i][1],ta);
+
+				if ( nbswp < 0) 	k++;
+				else Nbswap += nbswp;
+				if (nbswp) nbfe++;
+				if ( nbswp < 0 && k < 5)
+				  {
+					cerr << " Missing  Edge " << i << " v0 =  " << Number(edges[i][0]) << edges[i][0].r
+					  <<" v1= " << Number(edges[i][1]) << edges[i][1].r << " " << edges[i].on->Cracked() << "  " << (Triangle *) ta ;
+					if(ta.t)
+					  {
+						Vertex *aa = ta.EdgeVertex(0), *bb = ta.EdgeVertex(1);  
+						cerr << " crossing with  [" << Number(aa) << ", " << Number(bb) << "]\n";
+					  }
+					else cerr << endl;
+
+				  }
+				if ( nbswp >=0 && edges[i].on->Cracked())
+				 ta.SetCracked();
+			  }
+
+
+			if (k!=0) {
+				cerr << " they is " << k << " lost edges " << endl;
+				cerr << " The boundary is crossing may be!" << endl;
+				MeshError(10,this);
+			}
+			for (Int4 j=0;j<nbv;j++)
+			 Nbswap +=  vertices[j].Optim(1,0);
+			if (verbosity > 3)
+			 cout << "     Nb of inforced edge = " << nbfe << " Nb of Swap " << Nbswap << endl;
+
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::FindSubDomain{{{1*/
+	void Triangles::FindSubDomain(int OutSide=0) {
+		long int verbosity=0;
+
+		if (verbosity >2)
+		  {
+			if (OutSide)
+			 cout << "  -- Find all external sub-domain ";	
+			else
+			 cout << "  -- Find all internal sub-domain ";
+			if(verbosity>99)
+			  {
+
+				for(int i=0;i<nbt;++i)
+				 cout << i<< " " << triangles[i] << endl;
+			  }
+
+		  }
+		// if (verbosity > 4) cout << " OutSide=" << OutSide << endl;
+		short * HeapArete = new short[nbt];
+		Triangle  **  HeapTriangle = new Triangle*  [nbt];
+		Triangle *t,*t1;
+		Int4 k,it;
+
+		for (Int4 itt=0;itt<nbt;itt++) 
+		 triangles[itt].link=0; // par defaut pas de couleur
+
+		Int4  NbSubDomTot =0;
+		for ( it=0;it<nbt;it++)  { 
+			if ( ! triangles[it].link  ) {
+				t = triangles + it;
+				NbSubDomTot++;; // new composante connexe
+				Int4 i = 0; // niveau de la pile 
+				t->link = t ; // sd forme d'un triangle cicular link
+
+				HeapTriangle[i] =t ; 
+				HeapArete[i] = 3;
+
+				while (i >= 0) // boucle sur la pile
+				  { while ( HeapArete[i]--) // boucle sur les 3 aretes 
+					  { 
+						int na =  HeapArete[i];
+						Triangle * tc =  HeapTriangle[i]; // triangle courant
+						if( ! tc->Locked(na)) // arete non frontiere
+						  {
+							Triangle * ta = tc->TriangleAdj(na) ; // næ triangle adjacent
+							if (ta->link == 0 ) // non deja chainer => on enpile
+							  { 
+								i++;
+								ta->link = t->link ;  // on chaine les triangles
+								t->link = ta ;  // d'un meme sous domaine          
+								HeapArete[i] = 3; // pour les 3 triangles adjacents
+								HeapTriangle[i] = ta;
+							  }}
+					  } // deplie fin de boucle sur les 3 adjacences
+					i--;
+				  }          
+			}      
+		}
+
+		// supression de tous les sous domaine infini <=>  contient le sommet NULL
+		it =0;
+		NbOutT = 0;
+		while (it<nbt) {
+			if (triangles[it].link) 
+			  { 
+				if (!( triangles[it](0) &&  triangles[it](1) &&  triangles[it](2) )) 
+				  {
+					// infini triangle 
+					NbSubDomTot --;
+					//  cout << " triangle infini " << it << triangles[it] << endl;
+					t=&triangles[it];
+					NbOutT--;  // on fait un coup de trop. 
+					while  (t){ // cout << Number(t) << " " << endl;
+						NbOutT++;
+						t1=t;
+						t=t->link;
+						t1->link=0;}//while (t)
+				  }
+			  }   
+			it++;} // end while (it<nbt)
+			if (nbt == NbOutT ||  !NbSubDomTot) 
+			  {
+				cout << "\n error : " <<  NbOutT << " " << NbSubDomTot <<" " << nbt << endl;
+				cerr << "Error: The boundary is not close => All triangles are outside " << endl;
+				MeshError(888,this);
+			  }
+
+			delete [] HeapArete;
+			delete [] HeapTriangle;
+
+
+			if (OutSide|| !Gh.subdomains || !Gh.NbSubDomains ) 
+			  { // No geom sub domain
+				Int4 i;
+				if (subdomains) delete [] subdomains;
+				subdomains = new SubDomain[ NbSubDomTot];
+				NbSubDomains=  NbSubDomTot;
+				for ( i=0;i<NbSubDomains;i++) {
+					subdomains[i].head=NULL;
+					subdomains[i].ref=i+1;
+				}
+				Int4 * mark = new Int4[nbt];
+				for (it=0;it<nbt;it++)
+				 mark[it]=triangles[it].link ? -1 : -2;
+
+				it =0;
+				k = 0;
+				while (it<nbt) {
+					if (mark[it] == -1) {
+						t1 = & triangles[it];
+						t = t1->link;
+						mark[it]=k;
+						subdomains[k].head = t1;
+						// cout << " New -- " << Number(t1) << " " << it << endl;
+						do {// cout << " k " << k << " " << Number(t) << endl;
+							mark[Number(t)]=k;
+							t=t->link;
+						} while (t!=t1);
+						mark[it]=k++;}
+						//    else if(mark[it] == -2 ) triangles[it].Draw(999);
+						it++;} // end white (it<nbt)
+						assert(k== NbSubDomains);
+						if(OutSide) 
+						  {
+							//  to remove all the sub domain by parity adjacents
+							//  because in this case we have only the true boundary edge
+							// so teh boundary is manifold
+							Int4 nbk = NbSubDomains;
+							while (nbk)
+							 for (it=0;it<nbt && nbk ;it++)
+							  for (int na=0;na<3 && nbk ;na++)
+								 {
+								  Triangle *ta = triangles[it].TriangleAdj(na);
+								  Int4 kl = ta ? mark[Number(ta)] : -2;
+								  Int4 kr = mark[it];
+								  if(kr !=kl) {
+									  //cout << kl << " " << kr << " rl "  << subdomains[kl].ref
+									  // << " rr " << subdomains[kr].ref ;
+									  if (kl >=0 && subdomains[kl].ref <0 && kr >=0 && subdomains[kr].ref>=0)
+										nbk--,subdomains[kr].ref=subdomains[kl].ref-1;
+									  if (kr >=0 && subdomains[kr].ref <0 && kl >=0 && subdomains[kl].ref>=0)
+										nbk--,subdomains[kl].ref=subdomains[kr].ref-1;
+									  if(kr<0 && kl >=0 && subdomains[kl].ref>=0)
+										nbk--,subdomains[kl].ref=-1;
+									  if(kl<0 && kr >=0 && subdomains[kr].ref>=0)
+										nbk--,subdomains[kr].ref=-1;
+									  //   cout << " after \t "   
+									  //	 << kl << subdomains[kl].ref << " rr " << kr 
+									  // << subdomains[kr].ref << endl;
+								  }
+								 }
+							//  cout << subdomains[0].ref << subdomains[1].ref << endl;
+							Int4  j=0;
+							for ( i=0;i<NbSubDomains;i++)
+							 if((-subdomains[i].ref) %2) { // good 
+								 //cout << " sudom ok  = " << i << " " << subdomains[i].ref
+								 // << " " << (-subdomains[i].ref) %2 << endl;
+								 if(i != j) 
+								  Exchange(subdomains[i],subdomains[j]);
+								 j++;}
+							 else
+								{ //cout << " remove sub domain " << i << endl;
+								 t= subdomains[i].head;
+								 while  (t){// cout << Number(t) << " " << endl;
+									 NbOutT++;
+									 t1=t;
+									 t=t->link;
+									 t1->link=0;}//while (t)
+								}
+
+							if(verbosity>4)
+							 cout << " Number of remove sub domain (OutSideMesh) =" << NbSubDomains-j << endl;
+							NbSubDomains=j;
+						  }
+
+						delete []  mark; 
+
+			  }
+			else
+			  { // find the head for all sub domaine
+				if (Gh.NbSubDomains != NbSubDomains && subdomains)
+				 delete [] subdomains, subdomains=0;
+				if (! subdomains  ) 
+				 subdomains = new SubDomain[ Gh.NbSubDomains];
+				NbSubDomains =Gh.NbSubDomains;
+				if(verbosity>4)
+				 cout << "     find the " << NbSubDomains << " sub domain " << endl;
+				Int4 err=0;
+				ReMakeTriangleContainingTheVertex();
+				Int4 * mark = new Int4[nbt];
+				Edge **GeometricalEdgetoEdge = MakeGeometricalEdgeToEdge();
+
+				for (it=0;it<nbt;it++)
+				 mark[it]=triangles[it].link ? -1 : -2;
+				Int4 inew =0;
+				for (Int4 i=0;i<NbSubDomains;i++) 
+				  {
+					GeometricalEdge &eg = *Gh.subdomains[i].edge;
+					subdomains[i].ref = Gh.subdomains[i].ref;
+					int ssdlab = subdomains[i].ref;
+					// by carefull is not easy to find a edge create from a GeometricalEdge 
+					// see routine MakeGeometricalEdgeToEdge
+					Edge &e = *GeometricalEdgetoEdge[Gh.Number(eg)];
+					assert(&e);
+					Vertex * v0 =  e(0),*v1 = e(1);
+					Triangle *t  = v0->t;
+					int sens = Gh.subdomains[i].sens;
+					// test if ge and e is in the same sens 
+					//	cout << " geom edge = " <<  Gh.Number(eg) <<" @" << &eg << " ref = " << subdomains[i].ref 
+					//     << " ref edge =" << eg.ref << " sens " << sens ;
+					if (((eg[0].r-eg[1].r),(e[0].r-e[1].r))<0)
+					 sens = -sens ;
+					subdomains[i].sens = sens;
+					subdomains[i].edge = &e;
+					//	cout << " sens " << sens << " in geom " << eg[0].r << eg[1].r << " in mesh  " << e[0].r << e[1].r << endl;
+					//	cout << "  v0 , v1 = " << Number(v0) << " "  << Number(v1) << endl;
+					assert(t && sens);
+
+					TriangleAdjacent  ta(t,EdgesVertexTriangle[v0->vint][0]);// previous edges
+
+					while (1) 
+					  {
+						assert( v0 == ta.EdgeVertex(1) );
+						//	 cout << " recherche " << Number( ta.EdgeVertex(0)) << endl;
+						if (ta.EdgeVertex(0) == v1) { // ok we find the edge
+							if (sens>0)  
+							 subdomains[i].head=t=Adj(ta);
+							else 
+							 subdomains[i].head=t=ta;
+							//cout << "      triangle  =" << Number(t) << " = " << (*t)[0].r <<  (*t)[1].r <<  (*t)[2].r << endl;
+							if(t<triangles || t >= triangles+nbt || t->det < 0 
+										|| t->link == 0) // Ajoute aout 200 
+							  {
+								cerr << " Error in the def of sub domain "<<i
+								  << " form border " << NbSubDomains - i  << "/" << NbSubDomains
+								  << ": Bad sens  " << Gh.Number(eg) <<" "<< sens <<  endl;  
+								err++;
+								break;}
+								Int4 it = Number(t);
+								if (mark[it] >=0) {
+									if(verbosity>10)
+									 cerr << "     Warning: the sub domain " << i << " ref = " << subdomains[i].ref 
+										<< " is previouly defined with "  <<mark[it] << " ref = " << subdomains[mark[it]].ref
+										<< " skip this def " << endl;
+									break;}
+									if(i != inew) 
+									 Exchange(subdomains[i],subdomains[inew]);
+									inew++;
+									Triangle *tt=t;
+									Int4 kkk=0;
+									do 
+									  {
+										kkk++;
+										assert(mark[Number(tt)]<0);
+										mark[Number(tt)]=i;
+										tt=tt->link;
+									  } while (tt!=t);
+									if(verbosity>7)
+									 cout << "     Nb de triangles dans le sous domaine " << i << " de ref " << subdomains[i].ref << " = " << kkk << endl;
+									break;}
+									ta = Previous(Adj(ta));         
+									if(t == (Triangle *) ta) {
+										err++;
+										cerr << " Error in the def of sub domain " << i 
+										  << " edge=" << Gh.Number(eg) << " " << sens << endl;
+										break;}
+										//         cout << " NB of remove subdomain " << NbSubDomTot-NbSubDomains<< endl;
+
+					  }
+
+				  }
+				if (err) MeshError(777,this);
+
+				if (inew < NbSubDomains) {
+					if (verbosity>5) 
+					 cout << "     Warning: We remove " << NbSubDomains-inew << " SubDomains " << endl;
+					NbSubDomains=inew;}
+
+
+					for (it=0;it<nbt;it++)
+					 if ( mark[it] ==-1 ) 
+					  NbOutT++,triangles[it].link =0;
+					delete [] GeometricalEdgetoEdge;
+					delete [] mark;
+
+			  }
+			NbOutT=0;
+			for (it=0;it<nbt;it++) 
+			 if(!triangles[it].link)  NbOutT++;
+			if (verbosity> 4)
+			 cout << "    " ;
+			if (verbosity> 2)
+			 cout << " Nb of Sub borned Domain  = " <<  NbSubDomTot << " NbOutTriangles = " << NbOutT <<endl;
+
+
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::ReNumberingVertex{{{1*/
+	void Triangles::ReNumberingVertex(Int4 * renu) {
+		// warning be carfull because pointeur
+		// from on mesh to over mesh 
+		//  --  so do ReNumbering a the beginning
+		Vertex * ve = vertices+nbv;
+		Int4 it,ie,i;
+
+		for ( it=0;it<nbt;it++) 
+		 triangles[it].ReNumbering(vertices,ve,renu);
+
+		for ( ie=0;ie<nbe;ie++) 
+		 edges[ie].ReNumbering(vertices,ve,renu);
+
+		for (i=0;i< NbVerticesOnGeomVertex;i++)
+		  {
+			Vertex *v = VerticesOnGeomVertex[i].mv;
+			if (v>=vertices && v < ve)
+			 VerticesOnGeomVertex[i].mv=vertices+renu[Number(v)];
+		  }
+
+		for (i=0;i< NbVerticesOnGeomEdge;i++)
+		  {
+			Vertex *v =VerticesOnGeomEdge[i].mv;
+			if (v>=vertices && v < ve)
+			 VerticesOnGeomEdge[i].mv=vertices+renu[Number(v)];
+		  }
+
+		for (i=0;i< NbVertexOnBThVertex;i++)
+		  {
+			Vertex *v=VertexOnBThVertex[i].v;
+			if (v>=vertices && v < ve)
+			 VertexOnBThVertex[i].v=vertices+renu[Number(v)];
+		  }
+
+		for (i=0;i< NbVertexOnBThEdge;i++)
+		  {
+			Vertex *v=VertexOnBThEdge[i].v;
+			if (v>=vertices && v < ve)
+			 VertexOnBThEdge[i].v=vertices+renu[Number(v)];
+		  }
+
+		// move the Vertices without a copy of the array 
+		// be carefull not trivial code 
+		Int4 j;
+		for ( it=0;it<nbv;it++) // for all sub cycles of the permutation renu
+		 if (renu[it] >= 0) // a new sub cycle
+			{ 
+			 i=it;
+			 Vertex ti=vertices[i],tj;
+			 while ( (j=renu[i]) >= 0) 
+				{ // i is old, and j is new 
+				 renu[i] = -1-renu[i]; // mark 
+				 tj = vertices[j]; // save new
+				 vertices[j]= ti; // new <- old
+				 i=j;     // next 
+				 ti = tj;
+				}  
+			}
+		if (quadtree) 
+		  {  delete quadtree;
+			quadtree = new QuadTree(this);
+		  }
+		for ( it=0;it<nbv;it++)
+		 renu[i]= -renu[i]-1;
+
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::ReNumberingTheTriangleBySubDomain{{{1*/
+	void Triangles::ReNumberingTheTriangleBySubDomain(bool justcompress) {
+		long int verbosity=0;
+		Int4 *renu= new Int4[nbt];
+		register Triangle *t0,*t,*te=triangles+nbt;
+		register Int4 k=0,it,i,j;
+
+		for ( it=0;it<nbt;it++) 
+		 renu[it]=-1; // outside triangle 
+		for ( i=0;i<NbSubDomains;i++)
+		  { 
+			t=t0=subdomains[i].head;
+			assert(t0); // no empty sub domain
+			do { 
+				Int4 kt = Number(t);
+				assert(kt>=0 && kt < nbt );
+				assert(renu[kt]==-1);
+				renu[kt]=k++;
+			}
+			while (t0 != (t=t->link));
+		  }
+		if (verbosity>9)
+		 cout << " number of inside triangles " << k << " nbt = " << nbt << endl;
+		// take is same numbering if possible    
+		if(justcompress)
+		 for ( k=0,it=0;it<nbt;it++) 
+		  if(renu[it] >=0 ) 
+			renu[it]=k++;
+
+		// put the outside triangles at the end
+		for ( it=0;it<nbt;it++) 
+		 if (renu[it]==-1) 
+		  renu[it]=k++;
+
+		assert(k == nbt);
+		// do the change on all the pointeur 
+		for ( it=0;it<nbt;it++)
+		 triangles[it].ReNumbering(triangles,te,renu);
+
+		for ( i=0;i<NbSubDomains;i++)
+		 subdomains[i].head=triangles+renu[Number(subdomains[i].head)];
+
+		// move the Triangles  without a copy of the array 
+		// be carefull not trivial code 
+		for ( it=0;it<nbt;it++) // for all sub cycles of the permutation renu
+		 if (renu[it] >= 0) // a new sub cycle
+			{ 
+			 i=it;
+			 Triangle ti=triangles[i],tj;
+			 while ( (j=renu[i]) >= 0) 
+				{ // i is old, and j is new 
+				 renu[i] = -1; // mark 
+				 tj = triangles[j]; // save new
+				 triangles[j]= ti; // new <- old
+				 i=j;     // next 
+				 ti = tj;
+				}  
+			}
+		delete [] renu;
+		nt = nbt - NbOutT;
+
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::ConsRefTriangle{{{1*/
+	Int4  Triangles::ConsRefTriangle(Int4 *reft) const {
+		long int verbosity=0;
+		assert(reft);
+		register Triangle *t0,*t;
+		register Int4 k=0, num;   
+		for (Int4 it=0;it<nbt;it++) 
+		 reft[it]=-1; // outside triangle 
+		for (Int4 i=0;i<NbSubDomains;i++)
+		  { 
+			t=t0=subdomains[i].head;
+			assert(t0); // no empty sub domain
+			// register Int4 color=i+1;// because the color 0 is outside triangle
+			do { k++;
+				num = Number(t);
+				assert(num>=0 &&num < nbt);
+				reft[num]=i;
+				//  cout << Number(t0) << " " <<Number(t)<< " "  << i << endl;
+			}
+			while (t0 != (t=t->link));
+		  }
+		//  NbOutT = nbt - k;
+		if (verbosity>5) 
+		 cout << " Nb of Sub Domain =" << NbSubDomains  << " Nb of In Triangles " << k 
+			<< " Nbt = " << nbt << " Out Triangles = " << nbt - k <<  endl;
+
+		return k;   
+
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::GeomToTriangles1{{{1*/
+	void Triangles::GeomToTriangles1(Int4 inbvx,int KeepBackVertices) { 
+		Gh.NbRef++;// add a ref to Gh
+
+
+		/************************************************************************* 
+		// methode in 2 step
+		// 1 - compute the number of new edge to allocate
+		// 2 - construct the edge
+remark: 
+in this part we suppose to have a background mesh with the same
+geometry 
+
+To construct the discretisation of the new mesh we have to 
+rediscretize the boundary of background Mesh 
+because we have only the pointeur from the background mesh to the geometry.
+We need the abcisse of the background mesh vertices on geometry
+so a vertex is 
+0 on GeometricalVertex ;
+1 on GeometricalEdge + abcisse
+2 internal 
+
+		 *************************************************************************/
+		assert(&BTh.Gh == &Gh);
+
+		long int verbosity=0;
+		BTh.NbRef++; // add a ref to BackGround Mesh
+		PreInit(inbvx);
+		BTh.SetVertexFieldOn();
+		int * bcurve = new int[Gh.NbOfCurves]; // 
+
+		// we have 2 ways to make the loop 
+		// 1) on the geometry 
+		// 2) on the background mesh
+		//  if you do the loop on geometry, we don't have the pointeur on background,
+		//  and if you do the loop in background we have the pointeur on geometry
+		// so do the walk on  background
+		//  Int4 NbVerticesOnGeomVertex;
+		//  VertexOnGeom * VerticesOnGeomVertex;  
+		//  Int4 NbVerticesOnGeomEdge;
+		//  VertexOnGeom * VerticesOnGeomEdge;
+
+
+		NbVerticesOnGeomVertex=0;
+		NbVerticesOnGeomEdge=0;
+		//1 copy of the  Required vertex
+		int i; 
+		for ( i=0;i<Gh.nbv;i++)
+		 if (Gh[i].Required()) NbVerticesOnGeomVertex++;
+
+		VerticesOnGeomVertex = new VertexOnGeom[NbVerticesOnGeomVertex];
+		VertexOnBThVertex = new VertexOnVertex[NbVerticesOnGeomVertex];
+		//
+		if( NbVerticesOnGeomVertex >= nbvx) 
+		  {
+			cerr << " Too much vertices on geometry " << NbVerticesOnGeomVertex << " >= " << nbvx << endl; 
+			MeshError(1,this);
+		  }
+		assert(vertices);
+		for (i=0;i<Gh.nbv;i++)
+		 if (Gh[i].Required()) {//Gh  vertices Required
+			 vertices[nbv] =  Gh[i];
+			 vertices[nbv].i = I2(0,0);
+			 Gh[i].to = vertices + nbv;// save Geom -> Th
+			 VerticesOnGeomVertex[nbv]= VertexOnGeom(vertices[nbv],Gh[i]);
+			 // cout << "--------- "  <<Number(Gh[i].to) << " " << Gh[i].to << " " << i << endl;
+			 nbv++;}
+		 else Gh[i].to=0;
+		// 
+		for (i=0;i<BTh.NbVerticesOnGeomVertex;i++)
+		  { 
+			VertexOnGeom & vog = BTh.VerticesOnGeomVertex[i];
+			if (vog.IsRequiredVertex()) {
+				GeometricalVertex * gv = vog;
+				Vertex *bv = vog;
+				assert(gv->to);// use of Geom -> Th
+				VertexOnBThVertex[NbVertexOnBThVertex++] = VertexOnVertex(gv->to,bv);
+				gv->to->m = bv->m; // for taking the metrix of the background mesh
+				;}
+		  }
+		assert(NbVertexOnBThVertex == NbVerticesOnGeomVertex);
+		// new stuff FH with curve
+		//  find the begin of the curve in BTh
+		  {
+			Gh.UnMarkEdges();	
+			int bfind=0;
+			/*
+				cout << " nb curves = " << Gh.NbOfCurves << endl;
+				for(int i=0;i<Gh.NbOfCurves ;i++)
+				{
+				cout << " Curve " << i << " begin e=" << Gh.Number(Gh.curves[i].be) << " k=" << Gh.curves[i].kb 
+				<< "  end e= " << Gh.Number(Gh.curves[i].ee) << " k=" << Gh.curves[i].ke << endl;
+				}*/
+			for (int i=0;i<Gh.NbOfCurves;i++)
+			  {
+				bcurve[i]=-1; 
+			  }
+
+			for (int iedge=0;iedge<BTh.nbe;iedge++) 
+			  {      
+				Edge & ei = BTh.edges[iedge];
+				for(int je=0;je<2;je++) // for the 2 extremites
+				 if (!ei.on->Mark() && ei[je].on->IsRequiredVertex() )
+					{
+					 // a begin of curve 
+					 int nc = ei.on->CurveNumber;
+
+					 //cout << "curve " <<  nc << " v " << Gh.Number((GeometricalVertex *) *ei[je].on) << " "
+					 //     << " e "  << " " << Gh.Number(ei.on) << " vc " << Gh.Number((*Gh.curves[nc].be)[Gh.curves[nc].kb]) << endl;
+					 if(
+								 ei.on==Gh.curves[nc].be    && 
+								 (GeometricalVertex *) *ei[je].on == &(*Gh.curves[nc].be)[Gh.curves[nc].kb] //  same extremity 
+						)     
+						{ 
+						 // cout << " find " << endl;
+						 bcurve[nc]=iedge*2+je;
+						 bfind++;	
+						}      
+					}
+			  } 
+			assert( bfind==Gh.NbOfCurves);
+		  }          
+		// method in 2 + 1 step 
+		//  0.0) compute the length and the number of vertex to do allocation
+		//  1.0)  recompute the length
+		//  1.1)   compute the  vertex 
+		Int4 nbex=0,NbVerticesOnGeomEdgex=0;
+		for (int step=0; step <2;step++)
+		  {
+			Int4 NbOfNewPoints=0;
+			Int4 NbOfNewEdge=0;
+			Int4 iedge;
+			Gh.UnMarkEdges();	
+			/*   add Curve loop  FH    
+			// find a starting back groud edges to walk 
+			for (iedge=0;iedge<BTh.nbe;iedge++) {      
+			Edge & ei = BTh.edges[iedge];
+			for(int jedge=0;jedge<2;jedge++) // for the 2 extremites
+			if (!ei.on->Mark() && ei[jedge].on->IsRequiredVertex() )
+			{
+			*/  
+			// new code FH 2004 
+			Real8 L=0;
+			for (int icurve=0;icurve<Gh.NbOfCurves;icurve++)
+			  { 
+				iedge=bcurve[icurve]/2;
+				int jedge=bcurve[icurve]%2;
+				if( ! Gh.curves[icurve].master) continue; // we skip all equi curve
+				Edge & ei = BTh.edges[iedge];
+				// warning: ei.on->Mark() can be change in
+				// loop for(jedge=0;jedge<2;jedge++) 
+				// new curve  
+				// good the find a starting edge 
+				Real8 Lstep=0,Lcurve=0;// step between two points   (phase==1) 
+				Int4 NbCreatePointOnCurve=0;// Nb of new points on curve     (phase==1) 
+
+
+				//    cout.precision(16);
+				for(int phase=0;phase<=step;phase++) 
+				  {
+
+					for(Curve * curve= Gh.curves+icurve;curve;curve= curve->next)
+					  {
+
+						int icurveequi= Gh.Number(curve);
+
+						if( phase == 0 &&  icurveequi != icurve)  continue;
+
+						int k0=jedge,k1;
+						Edge * pe=  BTh.edges+iedge;
+						//GeometricalEdge *ong = ei.on;
+						int iedgeequi=bcurve[icurveequi]/2;
+						int jedgeequi=bcurve[icurveequi]%2;
+
+						int k0equi=jedgeequi,k1equi;		  
+						Edge * peequi= BTh.edges+iedgeequi;
+						GeometricalEdge *ongequi = peequi->on;
+
+						Real8 sNew=Lstep;// abcisse of the new points (phase==1) 
+						L=0;// length of the curve
+						Int4 i=0;// index of new points on the curve
+						register GeometricalVertex * GA0 = *(*peequi)[k0equi].on;
+						Vertex *A0;
+						A0 = GA0->to;  // the vertex in new mesh
+						Vertex *A1;
+						VertexOnGeom *GA1;
+						Edge * PreviousNewEdge = 0;
+						//  cout << "  --------------New Curve phase " << phase 
+						//       << "---------- A0=" << *A0 << ei[k0]  <<endl;
+						assert (A0-vertices>=0 && A0-vertices <nbv);
+						if(ongequi->Required() ) 
+						  {
+							GeometricalVertex *GA1 = *(*peequi)[1-k0equi].on;
+							A1 = GA1->to;  //
+						  }       
+						else 
+						 for(;;) 
+							{
+							 //   assert(pe && BTh.Number(pe)>=0 && BTh.Number(pe)<=BTh.nbe);
+							 Edge &ee=*pe; 
+							 Edge &eeequi=*peequi; 
+							 k1 = 1-k0; // next vertex of the edge 
+							 k1equi= 1 - k0equi;
+
+							 assert(pe  && ee.on);
+							 ee.on->SetMark();
+							 Vertex & v0=ee[0], & v1=ee[1];
+							 R2 AB= (R2) v1 - (R2) v0;
+							 Real8 L0=L,LAB;
+							 LAB =  LengthInterpole(v0.m,v1.m,AB);
+							 L+= LAB;    
+							 if (phase) {// computation of the new points
+								 while ((i!=NbCreatePointOnCurve) && sNew <= L) { 
+									 //    cout  << " L0= " << L0 << " L " << L << " sN=" 
+									 //         << sNew << " LAB=" << LAB << " NBPC =" <<NbCreatePointOnCurve<< " i " << i  << endl;
+									 assert (sNew >= L0);
+									 assert(LAB);
+
+
+									 assert(vertices && nbv<nbvx);
+									 assert(edges && nbe < nbex);
+									 assert(VerticesOnGeomEdge && NbVerticesOnGeomEdge < NbVerticesOnGeomEdgex);
+									 // new vertex on edge
+									 A1=vertices+nbv++;
+									 GA1=VerticesOnGeomEdge+NbVerticesOnGeomEdge;
+									 Edge *e = edges + nbe++;
+									 Real8 se= (sNew-L0)/LAB;
+									 assert(se>=0 && se < 1.000000001);
+									 se =  abscisseInterpole(v0.m,v1.m,AB,se,1);
+									 assert(se>=0 && se <= 1);
+									 //((k1==1) != (k1==k1equi))
+									 se = k1 ? se : 1. - se;
+									 se = k1==k1equi ? se : 1. - se;
+									 VertexOnBThEdge[NbVerticesOnGeomEdge++] = VertexOnEdge(A1,&eeequi,se); // save 
+									 ongequi = Gh.ProjectOnCurve(eeequi,se,*A1,*GA1); 
+									 A1->ReferenceNumber = eeequi.ref;
+									 A1->DirOfSearch =NoDirOfSearch;
+									 //cout << icurveequi << " " << i << " " <<  *A1 << endl;
+									 e->on = ongequi;
+									 e->v[0]=  A0;
+									 e->v[1]=  A1;
+									 if(verbosity>99)
+									  cout << i << "+ New P "<< nbv-1 << " "  <<sNew<< " L0=" << L0 
+										 << " AB=" << LAB << " s=" << (sNew-L0)/LAB << " se= "  
+										 << se <<" B edge " << BTh.Number(ee) << " signe = " << k1 <<" " << A1->r <<endl;
+
+									 e->ref = eeequi.ref;
+									 e->adj[0]=PreviousNewEdge;
+
+									 if (PreviousNewEdge)
+									  PreviousNewEdge->adj[1] =  e;
+									 PreviousNewEdge = e;
+									 A0=A1;
+									 sNew += Lstep;
+									 //   cout << " sNew = " << sNew << " L = " << L 
+									 //        << "  ------" <<NbCreatePointOnCurve << " " << i <<  endl;
+									 if (++i== NbCreatePointOnCurve) break;
+								 }
+
+							 }               
+							 assert(ee.on->CurveNumber==ei.on->CurveNumber);
+							 if(verbosity>98) cout <<  BTh.Number(ee) << " " << " on=" << *ee[k1].on << " "<< ee[k1].on->IsRequiredVertex() <<  endl;
+							 if ( ee[k1].on->IsRequiredVertex()) {
+								 assert(eeequi[k1equi].on->IsRequiredVertex());
+								 register GeometricalVertex * GA1 = *eeequi[k1equi].on;
+								 A1=GA1->to;// the vertex in new mesh
+								 assert (A1-vertices>=0 && A1-vertices <nbv);
+								 break;}
+								 if (!ee.adj[k1])
+									{cerr << "Error adj edge " << BTh.Number(ee) << ", nbe = "  << nbe 
+									 << " Gh.vertices " << Gh.vertices 
+										<< " k1 = " << k1 << " on=" << *ee[k1].on << endl;
+									 cerr << ee[k1].on->gv-Gh.vertices << endl;
+									}
+								 pe = ee.adj[k1]; // next edge
+								 k0 = pe->Intersection(ee); 
+								 peequi= eeequi.adj[k1equi];  // next edge
+								 k0equi=peequi->Intersection(eeequi);            
+							}// for(;;) end of the curve
+
+
+						if (phase) // construction of the last edge
+						  {
+							Edge *e = edges + nbe++;
+							if (verbosity>10) 
+							 cout << " Fin curve A1" << *A1 << " " << icurve << " <=> " << icurveequi <<"-----" <<
+								NbCreatePointOnCurve << " == " <<i<<endl;
+							e->on  = ongequi;
+							e->v[0]=  A0;
+							e->v[1]=	A1;
+							e->ref = peequi->ref;
+							e->adj[0]=PreviousNewEdge;
+							e->adj[1]=0;
+							if (PreviousNewEdge)
+							 PreviousNewEdge->adj[1] =  e;
+							PreviousNewEdge = e;
+
+							assert(i==NbCreatePointOnCurve);
+
+						  }
+					  } //  end loop on equi curve 
+
+					if (!phase)  { // 
+						Int4 NbSegOnCurve = Max((Int4)(L+0.5),(Int4) 1);// nb of seg
+						Lstep = L/NbSegOnCurve; 
+						Lcurve = L;
+						NbCreatePointOnCurve = NbSegOnCurve-1;
+
+						for(Curve * curve= Gh.curves+icurve;curve;curve= curve->next)
+						  {
+							NbOfNewEdge += NbSegOnCurve;
+							NbOfNewPoints += NbCreatePointOnCurve;
+						  }
+						if(verbosity>5)
+						 cout << icurve << " NbSegOnCurve = " <<  NbSegOnCurve << " Lstep=" 
+							<< Lstep <<" " << NbOfNewPoints<< " NBPC= " << NbCreatePointOnCurve <<endl;
+						// do'nt 
+						//  if(NbCreatePointOnCurve<1) break;
+					}
+				  }//for(phase;;)
+				/*  modif FH add Curve class  		  
+					 }}//for (iedge=0;iedge<BTh.nbe;iedge++) 
+					 */
+				// new code Curve class  	
+		  } //  end of curve loop 
+		// end new code	    
+		// do the allocation
+		if(step==0) 
+		  {
+			//if(!NbOfNewPoints) break;// nothing ????? bug 
+			if(nbv+NbOfNewPoints > nbvx) 
+			  {
+				cerr << " Too much vertices on geometry " << nbv+NbOfNewPoints  << " >= " << nbvx << endl;
+				MeshError(3,this);
+			  }
+			//cout << " NbOfNewEdge" << NbOfNewEdge << " NbOfNewPoints " << NbOfNewPoints << endl;
+			edges = new Edge[NbOfNewEdge];
+			nbex = NbOfNewEdge;
+			if(NbOfNewPoints) { // 
+				VerticesOnGeomEdge = new VertexOnGeom[NbOfNewPoints];
+				NbVertexOnBThEdge =NbOfNewPoints;
+				VertexOnBThEdge = new  VertexOnEdge[NbOfNewPoints];
+				NbVerticesOnGeomEdgex = NbOfNewPoints; }
+				NbOfNewPoints =0;
+				NbOfNewEdge = 0;
+		  }
+		  } // for(step;;)
+		assert(nbe);
+
+		delete [] bcurve;
+
+
+		Insert();
+		ForceBoundary();
+		FindSubDomain();
+
+		NewPoints(BTh,KeepBackVertices) ;
+		CurrentTh = 0;
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::GeomToTriangles0{{{1*/
+	void Triangles::GeomToTriangles0(Int4 inbvx) {
+		Gh.NbRef++;// add a ref to GH
+
+
+		Int4 i,NbOfCurves=0,NbNewPoints,NbEdgeCurve;
+		Real8 lcurve, lstep,s;
+
+		R2 AB;
+		GeometricalVertex *a,*b;
+		Vertex *va,*vb;
+		GeometricalEdge * e;
+		PreInit(inbvx);
+		int  background = &BTh != this;
+		//  int  SameGeom = background && (&BTh.Gh == &Gh);
+		nbv = 0;
+		NbVerticesOnGeomVertex=0;
+		NbVerticesOnGeomEdge=0;
+		for (i=0;i<Gh.nbv;i++)
+		 if (Gh[i].Required() && Gh[i].IsThe() ) NbVerticesOnGeomVertex++;
+		VerticesOnGeomVertex = new VertexOnGeom[NbVerticesOnGeomVertex];  
+		//
+		if( NbVerticesOnGeomVertex >= nbvx) 
+		  {
+			cerr << " Too much vertices on geometry " << NbVerticesOnGeomVertex << " >= " << nbvx << endl;
+			MeshError(1,this);
+		  }
+		for (i=0;i<Gh.nbv;i++)
+		 if (Gh[i].Required()&& Gh[i].IsThe()  ) {//Gh  vertices Required
+			 if (nbv < nbvx)
+			  vertices[nbv] = Gh[i];
+			 Gh[i].to = vertices + nbv;// save Geom -> Th
+			 VerticesOnGeomVertex[nbv]= VertexOnGeom(*Gh[i].to,Gh[i]);
+			 //  cout << "--------- "  <<Number(Gh[i].to) << " " << Gh[i].to << " " << i << endl;
+			 nbv++;
+		 }
+		//  assert( Gh.nbv < nbvx);
+
+		// Method in 2 step:  0 and 1 
+		// 1) compute de nb of edge 
+		// 2) construct the edge    
+		// generation of the curves
+		assert(! edges);
+		// 2 step 
+		// --step=0 to compute the number of edges + alloc at end
+		// --step=1 to construct the edges
+		for (int step=0;step<2;step++) 
+		  {//  for (int step=0;step<2;step++) 
+			Int4 nbex = 0;
+			nbe = 0;
+			Int4 NbVerticesOnGeomEdge0=NbVerticesOnGeomEdge;
+			//  cout <<  "  -------------- step =" << step << endl;
+			Gh.UnMarkEdges();	
+			NbOfCurves = 0;
+			for (i=0;i<Gh.nbe;i++) {
+				GeometricalEdge & ei = Gh.edges[i];   
+				if (!ei.Dup()) // a good curve (not dup )
+				 for(int j=0;j<2;j++) 
+				  if (!ei.Mark() && ei[j].Required()) { 
+					  // warning ei.Mark() can be change in loop for(j=0;j<2;j++) 
+					  //  cout << " New curve = " << NbOfCurves << endl;
+					  Int4 nbvend  =0;
+
+					  Edge * PreviousNewEdge=0;
+
+					  lstep = -1;//to do not create points
+					  if(ei.Required())
+						 {
+						  if (j==0)
+							if(step==0)
+							 nbe++;
+							else
+							  { 
+								e = & ei;
+								a=ei(0)->The();
+								b=ei(1)->The();
+								assert(edges);
+								edges[nbe].v[0]=a->to;
+								edges[nbe].v[1]=b->to;;
+								edges[nbe].ref = e->ref;
+								edges[nbe].on = e;
+								edges[nbe].adj[0] = 0;
+								edges[nbe].adj[1] = 0;
+								nbe++;}
+						 }
+					  else 
+						 { // on curve ------
+						  for ( int kstep=0;kstep<= step;kstep++)
+							 { // begin  for ( int kstep=0;kstep<= step;kstep++)
+							  // if 2nd step where 2 step
+							  // -- 1 compute le length of the curve
+							  // -- create the points and edge
+							  PreviousNewEdge=0;
+							  NbNewPoints=0;
+							  NbEdgeCurve=0;
+							  assert(nbvend < nbvx); 
+							  lcurve =0;
+							  s = lstep;
+							  int k=j;
+							  e = & ei;
+							  a=ei(k)->The();
+							  va = a->to;
+							  e->SetMark();
+							  //  cout << " New curve " ;
+
+							  // if SameGeo  We have go in the background geometry 
+							  // to find the discretisation of the curve
+
+							  for(;;) 
+								 { 
+								  k = 1-k;
+								  b= (*e)(k)->The();
+								  AB = b->r - a->r;
+								  Metric MA = background ? BTh.MetricAt(a->r) :a->m ;
+								  Metric MB =  background ? BTh.MetricAt(b->r) :b->m ;
+								  Real8 ledge = (MA(AB) + MB(AB))/2;
+								  // 
+								  const int MaxSubEdge = 10;
+								  int NbSubEdge = 1;
+								  Real8 lSubEdge[MaxSubEdge];
+								  R2 A,B;
+								  if (ledge < 1.5) 
+									lSubEdge[0] = ledge;
+								  else {
+									  NbSubEdge = Min( MaxSubEdge, (int) (ledge +0.5));
+									  A= a->r;
+									  Metric MAs =MA,MBs;
+									  // cout << " lSubEdge old=" << ledge 
+									  //      << " new " << A << MA << endl;
+									  ledge = 0; 
+									  Real8 x =0, xstep= 1. /  NbSubEdge;
+									  for (int kk=0; kk < NbSubEdge; kk++,A=B,MAs=MBs ) {
+										  x += xstep;
+										  B =  e->F(k ? x : 1-x);
+										  MBs= background ? BTh.MetricAt(B) :Metric(1-x, MA, x ,MB);
+										  AB = A-B;
+										  lSubEdge[kk]= (ledge += (MAs(AB)+MBs(AB))/2);
+										  // cout << "     " << lSubEdge[kk] << " x " << x  
+										  //      << " " << A << B << MA << MB<< endl ;
+									  }
+									  //  cout << endl;
+								  }
+
+								  Real8 lcurveb = lcurve+ ledge ;
+								  while (lcurve<=s && s <= lcurveb && nbv < nbvend)
+									 {
+									  // New points
+
+									  // Real8 aa=(lcurveb-s)/ledge;
+									  // Real8 bb=(s-lcurve)/ledge;
+
+									  Real8 ss = s-lcurve;
+									  // 1) find the SubEdge containing ss by dichotomie
+									  int kk0=-1,kk1=NbSubEdge-1,kkk;
+									  Real8 ll0=0,ll1=ledge,llk;
+									  while (kk1-kk0>1)
+										 {
+										  if (ss < (llk=lSubEdge[kkk=(kk0+kk1)/2]))
+											kk1=kkk,ll1=llk;
+										  else
+											kk0=kkk,ll0=llk;}
+										  assert(kk1 != kk0);
+
+										  Real8 sbb = (ss-ll0  )/(ll1-ll0);
+										  Real8 bb = (kk1+sbb)/NbSubEdge, aa=1-bb;
+
+										  // new vertex on edge
+										  vb = &vertices[nbv++];
+										  vb->m = Metric(aa,a->m,bb,b->m);
+										  vb->ReferenceNumber = e->ref;
+										  vb->DirOfSearch =NoDirOfSearch;
+										  Real8 abcisse = k ? bb : aa;
+										  vb->r =  e->F( abcisse );
+										  VerticesOnGeomEdge[NbVerticesOnGeomEdge++]= VertexOnGeom(*vb,*e,abcisse);        
+
+										  // to take in account the sens of the edge
+
+										  s += lstep;
+										  edges[nbe].v[0]=va;
+										  edges[nbe].v[1]=vb;
+										  edges[nbe].ref = e->ref;
+										  edges[nbe].on = e;
+										  edges[nbe].adj[0] = PreviousNewEdge;
+										  if(PreviousNewEdge)
+											PreviousNewEdge->adj[1] = &edges[nbe];
+										  PreviousNewEdge = edges + nbe;
+										  nbe++;
+										  va = vb;
+									 }
+								  lcurve = lcurveb;
+								  e->SetMark();
+								  // cout << e-Gh.edges << ", " << k << " " 
+								  //      <<(*e)[k].r <<" " <<(*e)[1-k].r <<" " 
+								  //      << lcurve<< ";; " ;                          
+								  a=b;
+								  if (b->Required() ) break;
+								  int kprev=k;
+								  k = e->SensAdj[kprev];// next vertices
+								  e = e->Adj[kprev];
+								  assert(e);
+								 }// for(;;)
+							  vb = b->to;
+							  //            cout << endl;
+							  NbEdgeCurve = Max((Int4) (lcurve +0.5), (Int4) 1);
+							  NbNewPoints = NbEdgeCurve-1;
+							  if(!kstep)
+								 { NbVerticesOnGeomEdge0 += NbNewPoints;
+								  NbOfCurves++;}
+
+								  nbvend=nbv+NbNewPoints; 
+
+								  lstep = lcurve / NbEdgeCurve;
+								  //   cout <<"lstep " << lstep << " lcurve " 
+								  //    << lcurve << " NbEdgeCurve " << NbEdgeCurve << " " <<NbVerticesOnGeomEdge0<<" " <<NbVerticesOnGeomEdge<<" step =" <<step<<  endl;
+							 } 
+						  // end of curve --
+						  if (edges) { // last edges of the curves 
+							  edges[nbe].v[0]=va;
+							  edges[nbe].v[1]=vb;
+							  edges[nbe].ref = e->ref;
+							  edges[nbe].on = e;
+							  edges[nbe].adj[0] = PreviousNewEdge;
+							  edges[nbe].adj[1] = 0;
+							  if(PreviousNewEdge)
+								PreviousNewEdge->adj[1] = & edges[nbe];
+
+							  nbe++;}
+						  else
+							nbe += NbEdgeCurve;
+						 } // end on  curve ---
+				  } // if (edges[i][j].Corner())  
+			} // for (i=0;i<nbe;i++)
+			if(!step) {
+				// cout << "edges " << edges << " VerticesOnGeomEdge " <<VerticesOnGeomEdge << endl;
+				assert(!edges);
+				assert(!VerticesOnGeomEdge);
+				edges = new Edge[nbex=nbe];
+				if(NbVerticesOnGeomEdge0)
+				 VerticesOnGeomEdge = new VertexOnGeom[NbVerticesOnGeomEdge0];
+				assert(edges);
+				assert(VerticesOnGeomEdge || NbVerticesOnGeomEdge0 ==0);
+				// do the vertex on a geometrical vertex
+				NbVerticesOnGeomEdge0 = NbVerticesOnGeomEdge;       
+			}
+			else 
+			 assert(NbVerticesOnGeomEdge == NbVerticesOnGeomEdge0);
+			//     cout << " Nb of Curves = " << NbOfCurves << "nbe = " << nbe 
+			//	  << "== " << nbex << "  nbv = " << nbv <<  endl;
+			assert(nbex=nbe);
+		  } // for (step=0;step<2;step++)
+
+		Insert();
+		ForceBoundary();
+		FindSubDomain();
+
+		// NewPointsOld(*this) ;
+		NewPoints(*this,0) ;
+		CurrentTh = 0;
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::MakeGeometricalEdgeToEdge{{{1*/
+	Edge** Triangles::MakeGeometricalEdgeToEdge() {
+		assert(Gh.nbe);
+		Edge **e= new (Edge* [Gh.nbe]);
+
+		Int4 i;
+		for ( i=0;i<Gh.nbe ; i++)
+		 e[i]=NULL;
+		for ( i=0;i<nbe ; i++) 
+		  { 
+			Edge * ei = edges+i;
+			GeometricalEdge *on = ei->on; 
+			e[Gh.Number(on)] = ei;    
+		  }
+		for ( i=0;i<nbe ; i++) 
+		 for (int ii=0;ii<2;ii++) { 
+			 Edge * ei = edges+i;
+			 GeometricalEdge *on = ei->on;
+			 int j= ii;
+			 while (!(*on)[j].Required()) { 
+				 //	cout << i << " " << ii << " j= " << j << " curve = " 
+				 //           <<  on->CurveNumber << "  " << Gh.Number(on) << " on " << j 
+				 //   << " s0 " << Gh.Number( (*on)[0]) << " s1  " << Gh.Number( (*on)[1]) 
+				 //   << " ->  " ;
+				 Adj(on,j); // next geom edge
+				 j=1-j;
+				 //       cout << Gh.Number(on) << "  " << j  << " e[ON] =  " <<  e[Gh.Number(on)] 
+				 //    << " s0 " << Gh.Number( (*on)[0]) << " s1  " << Gh.Number( (*on)[1]) << endl; 
+				 if (e[Gh.Number(on)])  break; // optimisation     
+				 e[Gh.Number(on)] = ei; 
+			 }
+		 }
+
+		int kk=0;
+		for ( i=0;i<Gh.nbe ; i++)
+		 if (!e[i]) 
+		  if(kk++<10) {
+			  cerr << " Bug -- the geometrical edge " << i << " is on no edge curve = " << Gh.edges[i].CurveNumber 
+				 << " s0 " << Gh.Number( Gh.edges[i][0]) << " s1  " << Gh.Number( Gh.edges[i][1]) << endl; 
+			  //	 assert( e[i]);
+		  }
+		if(kk) MeshError(997,this);
+
+		return e;
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::SetIntCoor{{{1*/
+	void Triangles::SetIntCoor(const char * strfrom) {
+		pmin =  vertices[0].r;
+		pmax =  vertices[0].r;
+
+		// recherche des extrema des vertices pmin,pmax
+		Int4 i;
+		for (i=0;i<nbv;i++) {
+			pmin.x = Min(pmin.x,vertices[i].r.x);
+			pmin.y = Min(pmin.y,vertices[i].r.y);
+			pmax.x = Max(pmax.x,vertices[i].r.x);
+			pmax.y = Max(pmax.y,vertices[i].r.y);
+		}
+		R2 DD = (pmax-pmin)*0.05;
+		pmin = pmin-DD;
+		pmax = pmax+DD; 
+		coefIcoor= (MaxICoor)/(Max(pmax.x-pmin.x,pmax.y-pmin.y));
+		assert(coefIcoor >0);
+
+		// generation of integer coord  
+		for (i=0;i<nbv;i++) {
+			vertices[i].i = toI2(vertices[i].r);    
+		}
+
+		// computation of the det 
+		int Nberr=0;
+		for (i=0;i<nbt;i++)
+		  {
+			Vertex & v0 = triangles[i][0];
+			Vertex & v1 = triangles[i][1];
+			Vertex & v2 = triangles[i][2];
+			if ( &v0 && &v1 &&  &v2 ) // a good triangles;
+			  {
+				triangles[i].det= det(v0,v1,v2);
+				if (triangles[i].det <=0 && Nberr++ <10)
+				  {
+					if(Nberr==1)
+					 if (strfrom)
+					  cerr << "+++ Fatal Error " << strfrom << "(SetInCoor)  Error :  area of Triangle < 0 " << endl; 
+					 else 
+					  cerr << "+++  Fatal Error Triangle (in SetInCoor) area of Triangle < 0" << endl;
+					cerr << " Triangle " << i << "  det  (I2) = " << triangles[i].det ;
+					cerr << " (R2) " << Det(v1.r-v0.r,v2.r-v0.r);
+					cerr << "; The 3  vertices " << endl;
+					cerr << Number(v0) << " "  << Number(v1) << " " 
+					  << Number(v2) << " : " ;
+					cerr << v0.r << v1.r << v2.r << " ; ";
+					cerr << v0.i << v1.i << v2.i << endl;
+				  }
+			  }
+			else
+			 triangles[i].det= -1; // Null triangle; 
+		  }
+		if (Nberr) MeshError(899,this);
+
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::FillHoleInMesh{{{1*/
+	void Triangles::FillHoleInMesh() {
+
+		Triangles* OldCurrentTh =CurrentTh;
+		CurrentTh=this;
+
+		int verbosity=0;
+
+		// generation of the integer coordinate
+		  {
+
+			// find extrema coordinates of vertices pmin,pmax
+			Int4 i;
+			if(verbosity>2) printf("      Filling holes in mesh of %i vertices\n",nbv); 
+
+			//initialize ordre
+			assert(ordre);
+			for (i=0;i<nbv;i++) ordre[i]=0;
+
+			NbSubDomains =0;
+
+			/* generation of the adjacence of the triangles*/
+
+			SetOfEdges4* edge4= new SetOfEdges4(nbt*3,nbv);
+
+			//initialize st
+			Int4* st = new Int4[nbt*3];
+			for (i=0;i<nbt*3;i++) st[i]=-1;
+
+			//check number of edges
+			Int4 kk =0;
+			for (i=0;i<nbe;i++){
+				kk=kk+(i == edge4->addtrie(Number(edges[i][0]),Number(edges[i][1])));
+			}
+			if (kk != nbe) { 
+				throw ErrorException(__FUNCT__,exprintf("Some Double edge in the mesh, the number is %i",kk-nbe));
+			}
+
+			//
+			for (i=0;i<nbt;i++){
+				for (int j=0;j<3;j++) {
+					Int4 k =edge4->addtrie(Number(triangles[i][VerticesOfTriangularEdge[j][0]]),
+								Number(triangles[i][VerticesOfTriangularEdge[j][1]]));
+					Int4 invisible = triangles[i].Hidden(j);
+					if(st[k]==-1){
+						st[k]=3*i+j;
+					}
+					else if(st[k]>=0) {
+						assert( ! triangles[i].TriangleAdj(j) && !triangles[st[k] / 3].TriangleAdj((int) (st[k]%3)));
+
+						triangles[i].SetAdj2(j,triangles + st[k] / 3,(int) (st[k]%3));
+						if (invisible)  triangles[i].SetHidden(j);
+						if (k<nbe) {
+							triangles[i].SetLocked(j);
+						}
+						st[k]=-2-st[k]; 
+					}
+					else {
+						throw ErrorException(__FUNCT__,exprintf("The edge (%i , %i) belongs to more than 2 triangles",
+										Number(triangles[i][VerticesOfTriangularEdge[j][0]]),Number(triangles[i][VerticesOfTriangularEdge[j][1]])));
+					}
+				}
+			}
+			if(verbosity>5) {
+				printf("         info on Mesh %s:\n",name);
+				printf("            - number of vertices    = %i \n",nbv); 
+				printf("            - number of triangles   = %i \n",nbt); 
+				printf("            - number of given edges = %i \n",nbe); 
+				printf("            - number of all edges   = %i \n"  ,edge4->nb()); 
+				printf("            - Euler number 1 - nb of holes = %i \n"  ,nbt-edge4->nb()+nbv); 
+			}
+
+			// check the consistant of edge[].adj and the geometrical required  vertex
+			Int4 k=0;
+			for (i=0;i<edge4->nb();i++){
+				if (st[i] >=0){ // edge alone 
+					if (i < nbe) {
+						Int4 i0=edge4->i(i);
+						ordre[i0] = vertices+i0;
+						Int4 i1=edge4->j(i);
+						ordre[i1] = vertices+i1;
+					}
+					else {
+						k=k+1;
+						if (k <20) {
+							throw ErrorException(__FUNCT__,exprintf("Lost boundary edges %i : %i %i",i,edge4->i(i),edge4->j(i)));
+						}
+					}
+				}
+			}
+			if(k != 0) {
+				throw ErrorException(__FUNCT__,exprintf("%i boundary edges  are not defined as edges",k));
+			}
+
+			/* mesh generation with boundary points*/
+			Int4 nbvb = 0;
+			for (i=0;i<nbv;i++){ 
+				vertices[i].t=0;
+				vertices[i].vint=0;
+				if (ordre[i]){ 
+					ordre[nbvb++] = ordre[i];
+				}
+			}
+
+			Triangle* savetriangles= triangles;
+			Int4 savenbt=nbt;
+			Int4 savenbtx=nbtx;
+			SubDomain * savesubdomains = subdomains;
+			subdomains = 0;
+
+			Int4  Nbtriafillhole = 2*nbvb;
+			Triangle* triafillhole =new Triangle[Nbtriafillhole];
+			triangles =  triafillhole;
+
+			nbt=2;
+			nbtx= Nbtriafillhole;
+
+			for (i=2 ; det( ordre[0]->i, ordre[1]->i, ordre[i]->i ) == 0;) 
+			 if  ( ++i >= nbvb) {
+				 cerr << "FillHoleInMesh: All the vertices are aline " << nbvb << endl;
+				 MeshError(998,this); }
+				 Exchange( ordre[2], ordre[i]);
+
+				 Vertex *  v0=ordre[0], *v1=ordre[1];
+
+
+				 triangles[0](0) = 0; // sommet pour infini 
+				 triangles[0](1) = v0;
+				 triangles[0](2) = v1;
+
+				 triangles[1](0) = 0;// sommet pour infini 
+				 triangles[1](2) = v0;
+				 triangles[1](1) = v1;
+				 const int e0 = OppositeEdge[0];
+				 const int e1 = NextEdge[e0];
+				 const int e2 = PreviousEdge[e0];
+				 triangles[0].SetAdj2(e0, &triangles[1] ,e0);
+				 triangles[0].SetAdj2(e1, &triangles[1] ,e2);
+				 triangles[0].SetAdj2(e2, &triangles[1] ,e1);
+
+				 triangles[0].det = -1;  // faux triangles
+				 triangles[1].det = -1;  // faux triangles
+
+				 triangles[0].SetTriangleContainingTheVertex();
+				 triangles[1].SetTriangleContainingTheVertex();
+
+				 triangles[0].link=&triangles[1];
+				 triangles[1].link=&triangles[0];
+
+				 if (!quadtree ) 
+				  delete  quadtree; // ->ReInitialise();
+
+				 quadtree = new QuadTree(this,0);
+				 quadtree->Add(*v0);
+				 quadtree->Add(*v1);
+
+				 // We add the vertices one by one
+				 Int4 NbSwap=0;
+				 for (Int4 icount=2; icount<nbvb; icount++) {
+					 Vertex *vi  = ordre[icount];
+					 //	  cout << " Add vertex " <<  Number(vi) << endl;
+					 Icoor2 dete[3];
+					 Triangle *tcvi = FindTriangleContening(vi->i,dete);
+					 quadtree->Add(*vi); 
+					 Add(*vi,tcvi,dete);
+					 NbSwap += vi->Optim(1,1);
+				 }
+
+				 // inforce the boundary 
+				 TriangleAdjacent ta(0,0);
+				 Int4 nbloss = 0,knbe=0;
+				 for ( i = 0; i < nbe; i++){
+					 if (st[i] >=0){  // edge alone => on border ...  FH oct 2009
+						 Vertex & a=edges[i][0], & b =    edges[i][1];
+						 if (a.t && b.t) // le bug est la si maillage avec des bod non raffine 1.
+							{
+							 knbe++;
+							 if (ForceEdge(a,b,ta)<0)
+							  nbloss++;
+							}
+					 }
+				 }
+				 if(nbloss) {
+					 cerr << " we loss some  " << nbloss << " "  << " edges other " << knbe << endl;
+					 MeshError(1100,this);
+				 }
+
+				 FindSubDomain(1);
+				 // remove all the hole 
+				 // remove all the good sub domain
+				 Int4 krm =0;
+				 for (i=0;i<nbt;i++){
+					 if (triangles[i].link){ // remove triangles
+						 krm++;
+						 for (int j=0;j<3;j++)
+							{
+							 TriangleAdjacent ta =  triangles[i].Adj(j);
+							 Triangle & tta = * (Triangle *) ta;
+							 if(! tta.link) // edge between remove and not remove 
+								{ // change the link of ta;
+								 int ja = ta;
+								 Vertex *v0= ta.EdgeVertex(0);
+								 Vertex *v1= ta.EdgeVertex(1);
+								 Int4 k =edge4->addtrie(v0?Number(v0):nbv,v1? Number(v1):nbv);
+								 assert(st[k] >=0); 
+								 tta.SetAdj2(ja,savetriangles + st[k] / 3,(int) (st[k]%3));
+								 ta.SetLock();
+								 st[k]=-2-st[k]; 
+								}
+							}
+					 }
+				 }
+				 Int4 NbTfillHoll =0;
+				 for (i=0;i<nbt;i++){
+					 if (triangles[i].link) {
+						 triangles[i]=Triangle((Vertex *) NULL,(Vertex *) NULL,(Vertex *) NULL);
+						 triangles[i].color=-1;
+					 }
+					 else
+						{
+						 triangles[i].color= savenbt+ NbTfillHoll++;
+						}
+				 }
+				 // cout <<      savenbt+NbTfillHoll << " " <<  savenbtx  << endl;
+				 assert(savenbt+NbTfillHoll <= savenbtx );
+				 // copy of the outside triangles in saveTriangles 
+				 for (i=0;i<nbt;i++){
+					 if(triangles[i].color>=0) {
+						 savetriangles[savenbt]=triangles[i];
+						 savetriangles[savenbt].link=0;
+						 savenbt++;
+					 }
+				 }
+				 // gestion of the adj
+				 k =0;
+				 Triangle * tmax = triangles + nbt;
+				 for (i=0;i<savenbt;i++)  
+					{ 
+					 Triangle & ti = savetriangles[i];
+					 for (int j=0;j<3;j++)
+						{
+						 Triangle * ta = ti.TriangleAdj(j);
+						 int aa = ti.NuEdgeTriangleAdj(j);
+						 int lck = ti.Locked(j);
+						 if (!ta) k++; // bug 
+						 else if ( ta >= triangles && ta < tmax) 
+							{
+							 ta= savetriangles + ta->color;
+							 ti.SetAdj2(j,ta,aa);
+							 if(lck) ti.SetLocked(j);
+							}
+						}
+					}
+				 //	 OutSidesTriangles = triangles;
+				 //	Int4 NbOutSidesTriangles = nbt;
+
+				 // restore triangles;
+				 nbt=savenbt;
+				 nbtx=savenbtx;
+				 delete [] triangles;
+				 delete [] subdomains;
+				 triangles = savetriangles;
+				 subdomains = savesubdomains;
+				 //	 cout <<  triangles << " <> " << OutSidesTriangles << endl; 
+				 /*	 k=0;
+						 for (i=0;i<nbt;i++)
+						 for (int j=0;j<3;j++)
+						 if (!triangles[i].TriangleAdj(j))
+						 k++;
+						 */
+				 if (k) {
+					 cerr << "Error Nb of triangles edge alone = " << k << endl;
+					 MeshError(9997,this);
+				 }
+				 FindSubDomain();
+				 // cout << " NbTOld = " << NbTold << " ==  " << nbt - NbOutT << " " << nbt << endl;
+
+				 delete edge4;
+				 delete [] st;
+				 for (i=0;i<nbv;i++)
+				  quadtree->Add(vertices[i]);
+
+				 SetVertexFieldOn();
+
+				 for (i=0;i<nbe;i++)
+				  if(edges[i].on) 
+					for(int j=0;j<2;j++)
+					 if (!edges[i].adj[j])
+					  if(!edges[i][j].on->IsRequiredVertex()) {
+						  cerr << " Erreur adj et sommet requis edges [" << i <<  "][ " << j << "]= "
+							 <<  Number(edges[i][j]) << " : "  << " on = " << Gh.Number(edges[i].on) ;
+						  if (edges[i][j].on->OnGeomVertex())
+							cerr << " vertex " << Gh.Number(edges[i][j].on->gv);
+						  else if (edges[i][j].on->OnGeomEdge())
+							cerr << "Edges " << Gh.Number(edges[i][j].on->ge);
+						  else
+							cerr << " = " << edges[i][j].on ;
+						  cerr << endl;
+					  }
+		  }
+		CurrentTh=OldCurrentTh;
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::Optim{{{1*/
+	Int4  Triangle::Optim(Int2 i,int koption) {
+		// turne around in positif sens
+		Int4 NbSwap =0;
+		Triangle  *t = this;
+		int k=0,j =OppositeEdge[i];
+		int jp = PreviousEdge[j];
+		// initialise   tp, jp the previous triangle & edge
+		Triangle *tp= at[jp];
+		jp = aa[jp]&3;
+		do {
+			//    cout << *t << " " <<  j  << "\n\t try swap " ;
+			while (t->swap(j,koption))
+			  {
+				NbSwap++;
+				assert(k++<20000);
+				t=  tp->at[jp];      // set unchange t qnd j for previous triangles
+				j=  NextEdge[tp->aa[jp]&3];
+				//   cout << "\n\t s  " <<  *t << " " << j << endl;
+			  }
+			// end on this  Triangle 
+			tp = t;
+			jp = NextEdge[j];
+
+			t=  tp->at[jp];      // set unchange t qnd j for previous triangles
+			j=  NextEdge[tp->aa[jp]&3];
+
+		} while( t != this);
+		return NbSwap;
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::SmoothingVertex{{{1*/
+	void Triangles::SmoothingVertex(int nbiter,Real8 omega ) { 
+		long int verbosity=0;
+		//  if quatree exist remove it end reconstruct
+		if (quadtree) delete quadtree;
+		quadtree=0;
+		ReMakeTriangleContainingTheVertex();
+		Triangle vide; // a triangle to mark the boundary vertex
+		Triangle   ** tstart= new Triangle* [nbv];
+		Int4 i,j,k;
+		//   attention si Background == Triangle alors on ne peut pas utiliser la rechech rapide 
+		if ( this == & BTh)
+		 for ( i=0;i<nbv;i++)
+		  tstart[i]=vertices[i].t;     
+		else 
+		 for ( i=0;i<nbv;i++)
+		  tstart[i]=0;
+		for ( j=0;j<NbVerticesOnGeomVertex;j++ ) 
+		 tstart[ Number(VerticesOnGeomVertex[j].mv)]=&vide;
+		for ( k=0;k<NbVerticesOnGeomEdge;k++ ) 
+		 tstart[ Number(VerticesOnGeomEdge[k].mv)]=&vide;
+		if(verbosity>2) 
+		 cout << "  -- SmoothingVertex: nb Iteration = " << nbiter << " Omega = " << omega << endl;
+		for (k=0;k<nbiter;k++)
+		  {
+			Int4 i,NbSwap =0;
+			Real8 delta =0;
+			for ( i=0;i<nbv;i++)
+			 if (tstart[i] != &vide) // not a boundary vertex 
+			  delta=Max(delta,vertices[i].Smoothing(*this,BTh,tstart[i],omega));
+			if (!NbOfQuad)
+			 for ( i=0;i<nbv;i++)
+			  if (tstart[i] != &vide) // not a boundary vertex 
+				NbSwap += vertices[i].Optim(1);
+			if (verbosity>3)
+			 cout << "    Move max = " <<  sqrt(delta) << " iteration = " 
+				<< k << " Nb of Swap = " << NbSwap << endl;
+		  }
+
+		delete [] tstart;
+		if (quadtree) quadtree= new QuadTree(this);
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::MakeQuadTree{{{1*/
+	void Triangles::MakeQuadTree() {  
+		long int verbosity=0;
+		if(verbosity>8)
+		 cout << "      MakeQuadTree" << endl;
+		if (  !quadtree )  quadtree = new QuadTree(this);
+
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::ShowRegulaty{{{1*/
+	void  Triangles::ShowRegulaty() const {
+		const  Real8  sqrt32=sqrt(3.)*0.5; 
+		const Real8  aireKh=sqrt32*0.5;
+		D2  Beq(1,0),Heq(0.5,sqrt32);
+		D2xD2 Br(D2xD2(Beq,Heq).t());
+		D2xD2 B1r(Br.inv());
+		/*   D2xD2 BB = Br.t()*Br;
+			  cout << " BB = " << BB << " " << Br*B1r <<  endl; 
+			  MetricAnIso MMM(BB.x.x,BB.x.y,BB.y.y);
+			  MatVVP2x2 VMM(MMM);
+			  cout << " " << VMM.lambda1 << " " << VMM.lambda2 <<  endl; 
+			  */
+		double gammamn=1e100,hmin=1e100;
+		double gammamx=0,hmax=0;
+		double beta=1e100;
+		double beta0=0;
+		double  alpha2=0;
+		double area=0,Marea=0;
+		// Real8 cf= Real8(coefIcoor);
+		// Real8 cf2= 6.*cf*cf;
+		int nt=0;
+		for (int it=0;it<nbt;it++)
+		 if ( triangles[it].link) 
+			{
+			 nt++;
+			 Triangle &K=triangles[it];
+			 Real8  area3= Area2((R2) K[0],(R2) K[1],(R2) K[2])/6.;
+			 area+= area3;
+			 D2xD2 B_Kt(K[0],K[1],K[2]);
+			 D2xD2 B_K(B_Kt.t());
+			 D2xD2 B1K = Br*B_K.inv();
+			 D2xD2 BK =  B_K*B1r;
+			 D2xD2 B1B1 = B1K.t()*B1K;
+			 MetricAnIso MK(B1B1.x.x,B1B1.x.y,B1B1.y.y);
+			 MatVVP2x2 VMK(MK);
+			 alpha2 = Max(alpha2,Max(VMK.lambda1/VMK.lambda2,VMK.lambda2/VMK.lambda1));
+			 // cout << B_K << " * " << B1r << " == " << BK << " " << B_K*B_K.inv() << endl;
+			 Real8 betaK=0;
+
+			 for (int j=0;j<3;j++)
+				{
+				 Real8 he= Norme2(R2(K[j],K[(j+1)%3]));
+				 hmin=Min(hmin,he);
+				 hmax=Max(hmax,he);
+				 Vertex & v=K[j];
+				 D2xD2 M((MetricAnIso)v);
+				 betaK += sqrt(M.det());
+
+				 D2xD2 BMB = BK.t()*M*BK;
+				 MetricAnIso M1(BMB.x.x,BMB.x.y,BMB.y.y);
+				 MatVVP2x2 VM1(M1);
+				 //cout << B_K <<" " <<  M << " " <<  he << " " << BMB << " " << VM1.lambda1 << " " << VM1.lambda2<<   endl; 
+				 gammamn=Min3(gammamn,VM1.lambda1,VM1.lambda2);
+				 gammamx=Max3(gammamx,VM1.lambda1,VM1.lambda2);		
+				}
+			 betaK *= area3;//  1/2 (somme sqrt(det))* area(K)
+			 Marea+= betaK;
+			 // cout << betaK << " " << area3 << " " << beta << " " << beta0 << " " << area3*3*3*3 <<endl;
+			 beta=min(beta,betaK);
+			 beta0=max(beta0,betaK);
+			}   
+		area*=3; 
+		gammamn=sqrt(gammamn);
+		gammamx=sqrt(gammamx);    
+		cout << "  -- adaptmesh Regulary:  Nb triangles " << nt <<  " , h  min " << hmin  << " , h max " << hmax << endl;  
+		cout << "     area =  " << area << " , M area = " << Marea << " , M area/( |Khat| nt) " << Marea/(aireKh*nt) << endl; 
+		cout << "     infiny-regulaty:  min " << gammamn << "  max " << gammamx << endl;  
+		cout << "     anisomax  "<< sqrt(alpha2) << ", beta max = " << 1./sqrt(beta/aireKh) 
+		  << " min  "<<  1./sqrt(beta0/aireKh)  << endl;
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::ShowHistogram{{{1*/
+	void  Triangles::ShowHistogram() const {
+
+		const Int4 kmax=10;
+		const Real8 llmin = 0.5,llmax=2;
+		const Real8 lmin=log(llmin),lmax=log(llmax),delta= kmax/(lmax-lmin);
+		Int4 histo[kmax+1];
+		Int4 i,it,k, nbedges =0;
+		for (i=0;i<=kmax;i++) histo[i]=0;
+		for (it=0;it<nbt;it++)
+		 if ( triangles[it].link) 
+			{
+
+			 for (int j=0;j<3;j++)
+				{
+				 Triangle *ta = triangles[it].TriangleAdj(j);
+				 if ( !ta || !ta->link || Number(ta) >= it) 
+					{ 
+					 Vertex & vP = triangles[it][VerticesOfTriangularEdge[j][0]];
+					 Vertex & vQ = triangles[it][VerticesOfTriangularEdge[j][1]];
+					 if ( !& vP || !&vQ) continue;
+					 R2 PQ = vQ.r - vP.r;
+					 Real8 l = log(LengthInterpole(vP,vQ,PQ));
+					 nbedges++;
+					 k = (int) ((l - lmin)*delta);
+					 k = Min(Max(k,0L),kmax);
+					 histo[k]++;
+					}
+				}
+			}  
+		cout << "  -- Histogram of the unit mesh,  nb of edges" << nbedges << endl <<endl;
+
+		cout << "        length of edge in   | % of edge  | Nb of edges " << endl;
+		cout << "        ------------------- | ---------- | ----------- " << endl;
+		for   (i=0;i<=kmax;i++)
+		  { 
+			cout << "    " ;
+			cout.width(10);
+			if (i==0) cout  << " 0 " ;
+			else cout  << exp(lmin+i/delta) ;
+			cout.width(); cout << "," ;
+			cout.width(10);
+			if (i==kmax) cout << " +infty " ;
+			else cout  << exp(lmin+(i+1)/delta) ;
+			cout.width();cout << "   |   " ;
+
+			cout.precision(4);
+			cout.width(6);
+			cout <<  ((long)  ((10000.0 * histo[i])/ nbedges))/100.0 ;
+			cout.width();
+			cout.precision();
+			cout <<  "   |   " << histo[i] <<endl;
+		  }
+		cout << "        ------------------- | ---------- | ----------- " << endl <<endl;
+
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::Crack{{{1*/
+	int  Triangles::Crack() { 
+		assert(NbCrackedEdges ==0 || NbCrackedVertices >0); 
+		for (int i=0;i<NbCrackedEdges;i++)
+		 CrackedEdges[i].Crack();
+		return NbCrackedEdges;
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::UnCrack{{{1*/
+	int Triangles::UnCrack() { 
+		assert(NbCrackedEdges ==0 || NbCrackedVertices >0); 
+		for (int i=0;i<NbCrackedEdges;i++)
+		 CrackedEdges[i].UnCrack();
+		return NbCrackedEdges;
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::CrackMesh{{{1*/
+	int Triangles::CrackMesh() {
+		long int verbosity=0;
+		Triangles *CurrentThOld = CurrentTh;
+		//  computed the number of cracked edge
+		int i,k;
+		for (k=i=0;i<nbe;i++)
+		 if(edges[i].on->Cracked()) k++;
+		if( k==0) return 0;
+		CurrentTh = this;
+		cout << " Nb of Cracked Edges = " << k << endl;
+		NbCrackedEdges =k;
+		CrackedEdges = new  CrackedEdge[k];
+		//  new edge
+		Edge * e = new Edge[ nbe + k];
+
+		// copy
+		for (i=0;i<nbe;i++) 
+		 e[i] = edges[i];
+		delete edges;
+		edges = e;
+
+		const int  nbe0  = nbe;
+		for (k=i=0;i<nbe0;i++) // on double les arete cracked 
+		 if(edges[i].on->Cracked())
+			{
+			 e[nbe] = e[i];
+			 //  return the edge 
+			 e[nbe].v[0] =  e[i].v[1];
+			 e[nbe].v[1] =  e[i].v[0];
+			 e[nbe].on = e[i].on->link ; // fqux 
+			 CrackedEdges[k++]=CrackedEdge(edges,i,nbe);
+			 nbe++;
+			}
+		ReMakeTriangleContainingTheVertex() ; 
+		//  
+		int nbcrakev  =0;
+		Vertex *vlast = vertices + nbv;
+		Vertex *vend = vertices + nbvx; // end of array
+		for (int iv=0;iv<nbv;iv++) // vertex 
+		  {
+			Vertex & v= vertices[iv];
+			Vertex * vv = & v;  
+			int kk=0; // nb cracked
+			int kc=0; 
+			int kkk =0; // nb triangle  with same number 
+			Triangle * tbegin = v.t;
+			int i  = v.vint;       
+			assert(tbegin && (i >= 0 ) && (i <3));
+			// turn around the vertex v
+			TriangleAdjacent ta(tbegin,EdgesVertexTriangle[i][0]);// previous edge
+			int k=0;
+			do {
+				int kv = VerticesOfTriangularEdge[ta][1];
+				k++; 
+				Triangle * tt (ta);
+				if ( ta.Cracked() ) 
+				  {   
+					TriangleAdjacent tta=(ta.Adj());
+					assert(tta.Cracked());
+					if ( kk == 0) tbegin=ta,kkk=0;  //  begin by a cracked edge  => restart                
+					if (  kkk ) { kc =1;vv = vlast++;  kkk = 0; } // new vertex if use 
+					kk++;// number of cracked edge view                 
+				  }
+				if ( tt->link ) { // if good triangles store the value 
+					int it = Number(tt);
+					assert(it < nt);
+					(*tt)(kv)= vv; //   Change the vertex of triangle 
+					if(vv<vend) {*vv= v;vv->ReferenceNumber=iv;} // copy the vertex value + store the old vertex number in ref 
+					//	  tt->SetTriangleContainingTheVertex();
+					kkk++;
+				} else if (kk) { // crack + boundary 
+					if (  kkk ) { kc =1;vv = vlast++;  kkk = 0; } // new vertex if use 
+				}
+
+				ta = Next(ta).Adj(); 
+			} while ( (tbegin != ta)); 
+			assert(k);
+			if (kc)  nbcrakev++;
+		  }
+
+		if ( nbcrakev ) 
+		 for (int iec =0;iec < NbCrackedEdges; iec ++)
+		  CrackedEdges[iec].Set();
+
+		//  set the ref 
+		cout << " set the ref " <<  endl ;
+		NbCrackedVertices =   nbcrakev;
+		// int nbvo = nbv;
+		nbv = vlast - vertices;
+		int nbnewv =  nbv - nbv; // nb of new vrtices 
+		if (nbcrakev && verbosity > 1 )
+		 cout << " Nb of craked vertices = " << nbcrakev << " Nb of created vertices " <<   nbnewv<< endl;
+		// all the new vertices are on geometry 
+		//  BOFBO--  A VOIR
+		if (nbnewv)
+		  { // 
+			Int4 n = nbnewv+NbVerticesOnGeomVertex;
+			Int4 i,j,k;
+			VertexOnGeom * vog = new VertexOnGeom[n];
+			for ( i =0; i<NbVerticesOnGeomVertex;i++) 
+			 vog[i]=VerticesOnGeomVertex[i];
+			delete [] VerticesOnGeomVertex;
+			VerticesOnGeomVertex = vog;
+			// loop on cracked edge 
+			Vertex * LastOld = vertices + nbv - nbnewv;
+			for (int iec =0;iec < NbCrackedEdges; iec ++)
+			 for (k=0;k<2;k++)
+				{
+				 Edge & e = *( k ? CrackedEdges[iec].a.edge : CrackedEdges[iec].b.edge);
+				 for (j=0;j<2;j++) 
+					{
+					 Vertex * v = e(j);
+					 if ( v >=  LastOld)
+						{ // a new vertex 
+						 Int4 old = v->ReferenceNumber ; // the old same vertex 
+						 Int4 i  = ( v - LastOld);
+						 //  if the old is on vertex => warning
+						 // else the old is on edge => ok 
+						 vog[i] = vog[old];
+						 //  		    vog[i].mv = v;
+						 //g[i].ge = ;
+						 //og[i].abcisse = ;
+						}
+
+					}
+				}
+
+			NbVerticesOnGeomVertex = n;
+		  }
+		SetVertexFieldOn();
+
+
+		if (vlast >= vend)
+		  {  
+			cerr << " Not enougth vertices to crack the mesh we need " << nbv << " vertices " << endl;
+			MeshError(555,this);
+		  }
+		cout << "  NbCrackedVertices " <<  NbCrackedVertices << endl;
+		CurrentTh = CurrentThOld;
+		return  NbCrackedVertices;
+	}
+	/*}}}1*/
+	/*FUNCTION Triangles::FindTriangleContening{{{1*/
+	Triangle * Triangles::FindTriangleContening(const I2 & B,Icoor2 dete[3], Triangle *tstart) const {
+		Triangle * t=0;	
+		int j,jp,jn,jj;
+		if (tstart) 
+		 t=tstart;
+		else 
+		  {
+			assert(quadtree);
+			Vertex *a = quadtree->NearestVertex(B.x,B.y) ;
+
+			if (! a || !a->t ) {
+				if (a) 
+				  {cerr << " Attention PB TriangleConteningTheVertex  vertex number=" << Number(a) << endl;
+					cerr  << "We forget a call to ReMakeTriangleContainingTheVertex" << endl;}
+					cerr << " Pb with " << B << toR2(B) << endl;
+					MeshError(7777);
+			}
+			assert(a>= vertices && a < vertices+nbv);
+			//  int k=0;
+			t = a->t;
+			assert(t>= triangles && t < triangles+nbt);
+
+		  }
+		Icoor2  detop ;
+		int kkkk =0; // number of test triangle 
+
+		while ( t->det < 0) 
+		  { // the initial triangles is outside  
+			int k0=(*t)(0) ?  ((  (*t)(1) ? ( (*t)(2) ? -1 : 2) : 1  )) : 0;
+			assert(k0>=0); // k0 the NULL  vertex 
+			int k1=NextVertex[k0],k2=PreviousVertex[k0];
+			dete[k0]=det(B,(*t)[k1],(*t)[k2]);
+			dete[k1]=dete[k2]=-1;     
+			if (dete[k0] > 0) // outside B 
+			 return t; 
+			t = t->TriangleAdj(OppositeEdge[k0]);
+			assert(kkkk++ < 2);
+		  }
+
+		jj=0;
+		detop = det(*(*t)(VerticesOfTriangularEdge[jj][0]),*(*t)(VerticesOfTriangularEdge[jj][1]),B);
+
+		while(t->det  > 0 ) 
+		  { 
+			assert( kkkk++ < 2000 ); 
+			j= OppositeVertex[jj];
+			dete[j] = detop;  //det(*b,*s1,*s2);
+			jn = NextVertex[j];
+			jp = PreviousVertex[j];
+			dete[jp]= det(*(*t)(j),*(*t)(jn),B);
+			dete[jn] = t->det-dete[j] -dete[jp];
+
+			// count the number k of  dete <0
+			int k=0,ii[3];
+			if (dete[0] < 0 ) ii[k++]=0; 
+			if (dete[1] < 0 ) ii[k++]=1;
+			if (dete[2] < 0 ) ii[k++]=2;
+			// 0 => ok
+			// 1 => go in way 1
+			// 2 => two way go in way 1 or 2 randomly
+
+			if (k==0) 
+			 break;
+			if (k == 2 && BinaryRand())
+			 Exchange(ii[0],ii[1]);
+			assert ( k  < 3);
+			TriangleAdjacent t1 = t->Adj(jj=ii[0]);
+			if ((t1.det() < 0 ) && (k == 2))
+			 t1 = t->Adj(jj=ii[1]);
+			t=t1;
+			j=t1;// for optimisation we now the -det[OppositeVertex[j]];
+			detop = -dete[OppositeVertex[jj]];
+			jj = j;
+		  }
+
+		if (t->det<0) // outside triangle 
+		 dete[0]=dete[1]=dete[2]=-1,dete[OppositeVertex[jj]]=detop;
+		//  NbOfTriangleSearchFind += kkkk;  
+		return t;
+	}
+	/*}}}1*/
 
 } // end of namespace bamg