diff --git a/Triangulation_on_sphere_2/include/CGAL/Regular_triangulation_on_sphere_2.h b/Triangulation_on_sphere_2/include/CGAL/Regular_triangulation_on_sphere_2.h
index c929e540981..5508284308d 100644
--- a/Triangulation_on_sphere_2/include/CGAL/Regular_triangulation_on_sphere_2.h
+++ b/Triangulation_on_sphere_2/include/CGAL/Regular_triangulation_on_sphere_2.h
@@ -181,12 +181,13 @@ void set_radius(double radius){
   Vertex_handle insert(const Point &p, Face_handle f = Face_handle() );
   Vertex_handle insert_first(const Point &p);
   Vertex_handle insert_second(const Point &p);
-  Vertex_handle insert_outside_affine_hull_regular(const Point& p,bool plane=false);
+  //Vertex_handle insert_outside_affine_hull_regular(const Point& p,bool plane=false);
+	Vertex_handle insert_outside_affine_hull_regular(const Point& p);
   //Vertex_handle insert_hole_approach_2(const Point &p, Locate_type lt, Face_handle loc, int li) ;
   Vertex_handle insert_in_plane_triangulation(const Point &p, Locate_type lt, Face_handle loc);
 	
   bool test_conflict(const Point  &p, Face_handle fh) const;
-  bool update_ghost_faces(Vertex_handle v=Vertex_handle());
+  bool update_ghost_faces(Vertex_handle v=Vertex_handle(), bool first = false);
 	
   //REMOVAL
   void remove_degree_3(Vertex_handle v, Face_handle f = Face_handle());
@@ -568,7 +569,8 @@ is_valid(bool verbose, int level ) const //int level
    case 2 :
     for(All_faces_iterator it=all_faces_begin(); it!=all_faces_end(); it++) {
       Orientation s = orientation(it->vertex(0)->point(),  it->vertex(1)->point(), it->vertex(2)->point());
-	  result = result && ( s == LEFT_TURN || it->is_ghost());	
+	  //result = result && ( s == LEFT_TURN || it->is_ghost());	
+		result = result && (s != NEGATIVE || it->is_ghost());
 	CGAL_triangulation_assertion(result);
 	}
    
@@ -661,48 +663,7 @@ insert_in_plane_triangulation(const Point &p, Locate_type lt, Face_handle loc){
 	CGAL_triangulation_precondition(!test_dim_up(p));
 	CGAL_triangulation_precondition(dimension()==1);
 	
-	/*
-	Face_handle f = edges_begin()->first;
-	Face_handle loc;
-	//existing points coplanar with sphere?
-	Orientation pqr = orientation(f->vertex(0)->point(), 
-								  f->vertex(1)->point(),
-								  f->neighbor(0)->vertex(1)->point());
-	if( pqr != ON_ORIENTED_BOUNDARY ){
-		Edges_iterator eit=edges_begin();
-		do{
-			Face_handle f=eit->first;
-			Vertex_handle v1 = f->vertex(0);
-			Vertex_handle v2 = f -> vertex(1);
-			if(orientation(v1->point(), v2->point(), p)==RIGHT_TURN){
-				loc = f;
-			break;
-				
-			} eit++;
-		}while( eit!=edges_end());
-	}
-	else {
-		
-		Edges_iterator eit=edges_begin();
-		Point po = Point(0,0,0);
-		
-		do{
-			Face_handle f=eit->first;
-			Vertex_handle v1 = f->vertex(0);
-			Vertex_handle v2 = f -> vertex(1);
 			
-			//ERROR
-			bool conflict = Base::collinear_between(v1->point(), v2->point(), p);
-			//Orientation o=coplanar_orientation(v1->point(), v2->point(), p);
-			//if(o ==RIGHT_TURN){
-			if(conflict){
-				loc = f;
-				break;
-				
-			} eit++;
-		}while( eit!=edges_end());
-	}*/
-		
 		Vertex_handle v0 = loc->vertex(0);
 		Vertex_handle v1 = loc->vertex(1);
 		Vertex_handle v=this->_tds.create_vertex();
@@ -722,7 +683,7 @@ insert_in_plane_triangulation(const Point &p, Locate_type lt, Face_handle loc){
 		
 		delete_face(loc);
 		
-		
+	   update_ghost_faces(v);
 		return v;
 }
 	
@@ -756,9 +717,8 @@ typename Regular_triangulation_on_sphere_2<Gt,Tds>::Vertex_handle
 Regular_triangulation_on_sphere_2<Gt,Tds>::
 insert(const Point &p, Locate_type lt, Face_handle loc, int li) {
 		
-	//!!!!!!!!!!!!TODO point is valide!!!!!!!!!!!!!!!!!!!!!!!!
-	
 	Vertex_handle v;
+	
 	switch (dimension()){
 		case -2 :
 			return insert_first(p);
@@ -770,22 +730,19 @@ insert(const Point &p, Locate_type lt, Face_handle loc, int li) {
 			return insert_outside_affine_hull_regular(p);
 				
 		
-		case 1:
-			if(test_dim_up(p)){
+		case 1:{
+		  if(test_dim_up(p)){
 			Face_handle f=all_edges_begin()->first;
 			Vertex_handle v1=f->vertex(0);
 			Vertex_handle v2=f->vertex(1);
 			Vertex_handle v3=f->neighbor(0)->vertex(1);
-			Orientation orient=orientation(v1->point(),v2->point(),v3->point()) ;
-			v = insert_outside_affine_hull_regular(p,orient==COLLINEAR);
-			return v;
+			return insert_outside_affine_hull_regular(p);
 			} 
-			else {
-			 v= insert_in_plane_triangulation(p,lt,loc);	
-			return v;
-		    }
+		   else 
+			return insert_in_plane_triangulation(p,lt,loc);	
+		}
 			
-		case 2:
+		case 2:{
 			std::vector<Face_handle> faces;
 			std::vector<Edge> edges;
 			faces.reserve(32);
@@ -795,164 +752,129 @@ insert(const Point &p, Locate_type lt, Face_handle loc, int li) {
 			v =this->_tds.star_hole(edges.begin(), edges.end());
 			v->set_point(p);
 			delete_faces(faces.begin(), faces.end());
-			
-					
-			//if( lt != FACE )
+							
+			if( lt != FACE )
 				update_ghost_faces(v);
 												
 			return v;		
 	      }
+	}
+	CGAL_assertion(false);
+	return v;
 }	
 	
 template <class Gt, class Tds >
 typename Triangulation_on_sphere_2<Gt,Tds>::Vertex_handle
 Regular_triangulation_on_sphere_2<Gt,Tds>::
-insert_outside_affine_hull_regular(const Point& p,bool plane)
+insert_outside_affine_hull_regular(const Point& p)
 {
+ if(dimension()==0){
+	Vertex_handle v = vertices_begin();			
+	Vertex_handle u=v->face()->neighbor(0)->vertex(0);
+	Vertex_handle nv;
+			
+	//orientation is given by the 2 first points
+	if( collinear_between(v->point(),u->point(),p) || orientation(u->point(),v->point(),p) == LEFT_TURN ) 
+		nv=Base::tds().insert_dim_up(v,false);
+	else 
+		nv=Base::tds().insert_dim_up(v,true); 
+	
+	nv->set_point(p);
 		
-		if(dimension()==0){
-			Vertex_handle v = vertices_begin();			
-			Vertex_handle u=v->face()->neighbor(0)->vertex(0);
-			Vertex_handle nv;
+	Face_handle f=all_edges_begin()->first; 
+	CGAL_triangulation_assertion( orientation(f->vertex(0)->point(), f->vertex(1)->point(),
+											   f->neighbor(0)->vertex(1)->point()) != RIGHT_TURN );
 			
-			//orientation is given by the 2 first points
-			if( collinear_between(v->point(),u->point(),p) || orientation(u->point(),v->point(),p) == LEFT_TURN ) 
-				nv=Base::tds().insert_dim_up(v,false);
-			else 
-				nv=Base::tds().insert_dim_up(v,true);           
-			nv->set_point(p);
-			
-			
-			CGAL_triangulation_assertion( orientation(all_edges_begin()->first->vertex(0)->point(),
-													  all_edges_begin()->first->vertex(1)->point(),
-													  all_edges_begin()->first->neighbor(0)->vertex(1)->point())
-										 != RIGHT_TURN ); 
-			
-			//seting ghost edge if needed
-			bool done=false;
-			All_edges_iterator eit=all_edges_begin();
-			do{
-				Face_handle f=eit->first;
-				Face_handle fn=f->neighbor(0);
-				Point q=fn->vertex(1)->point();
-				if(collinear_between(f->vertex(0)->point(),f->vertex(1)->point(),q)){
-					f->ghost()=true;
-				}
-				else{
-					f->ghost()=false;
-				}
-				++eit;
-			}while( eit!=all_edges_end() && !done );
-			
-			return nv;
-		}
+	 update_ghost_faces(nv);
+	 return nv;
+   }
 		
-		else{ //dimension=1
-			bool conform = false;
-			Face_handle f = (all_edges_begin())->first;
-			
-			if(plane){//points coplanar with geom_traits->sphere
-				Vertex_handle v1 = f->vertex(0);
-				Vertex_handle v2 = f->vertex(1);
-				Orientation orient = orientation( f->vertex(0)->point(),f->vertex(1)->point(),p);
-				//conform = ( orient == COUNTERCLOCKWISE);
-				conform = (orient != CLOCKWISE);
-			}
-			
-			else{//three vertices non-coplanar with geom_traits->sphere
-				Face_handle fn=f->neighbor(0);
+ else{ 	//dimension 1	
+	bool conform = false;
+	Face_handle f = (all_edges_begin())->first;
+	Face_handle fn=f->neighbor(0);
+	const Point p0=f->vertex(0)->point();
+	const Point p1=f->vertex(1)->point();
+	const Point p2=fn->vertex(1)->point();
+	Orientation orient = orientation(p0, p1, p2);
+	Orientation orient2 = power_test(p0, p1, p2, p);
+	CGAL_triangulation_assertion(orient!=NEGATIVE);
+	 
+	if(orient2==POSITIVE)
+	  conform =true;
 				
-				const Point p0=f->vertex(0)->point();
-				const Point p1=f->vertex(1)->point();
-				const Point p2=fn->vertex(1)->point();
-				
-				Orientation orient = orientation(p0, p1, p2);
-				Orientation orient2 = power_test(p0, p1, p2, p);
-				CGAL_triangulation_assertion(orient);
-				if(orient2==POSITIVE)
-					conform =true;
-				
-			}
-			
-			//find smalest vertex
-			Vertex_handle w=vertices_begin();
-			All_vertices_iterator vi;
-			for( vi = vertices_begin(); vi != vertices_end(); vi++){
-				if(compare_xyz(w->point(), vi->point())<0)
-					w=vi;
-			}
-			
-			
-			
-			//Vertex_handle v = this->_tds.insert_dim_up( f->vertex(0), conform);
-			Vertex_handle v = this->_tds.insert_dim_up( w, conform);
-			v->set_point(p);
-	  		
-			this->_ghost=all_faces_begin();
-			
-			
-			//seting ghost faces if needed
-			All_faces_iterator fit;
-			for(fit =all_faces_begin(); fit !=all_faces_end(); fit++) {
-				//if(orientation(fit)==NEGATIVE){
-				if(orientation(fit)!=POSITIVE){
-					fit->ghost()=true;
-					this->_ghost=fit;
-				}
-			}
-			
-			return v; 
-		}
-		
+	//find smalest vertex
+	Vertex_handle w=vertices_begin();
+	All_vertices_iterator vi;
+	for( vi = vertices_begin(); vi != vertices_end(); vi++){
+	 if(compare_xyz(w->point(), vi->point())<0)
+		w=vi;
 	}
+			
+			
+	Vertex_handle v = this->_tds.insert_dim_up( w, conform);
+	v->set_point(p);
+	this->_ghost=all_faces_begin();
+	update_ghost_faces(v, true);
+			
+	return v; 
+  }
+}
 	
 	
 template < class Gt, class Tds >
 bool
 Regular_triangulation_on_sphere_2<Gt,Tds>::
-update_ghost_faces(Vertex_handle v)
+update_ghost_faces(Vertex_handle v, bool first)
 {
 	bool neg_found=false;
   if(dimension()==1){
-    All_edges_iterator eit=all_edges_begin();
-    do{
-      Face_handle f=eit->first;
-      Face_handle fn=f->neighbor(0);
-      Point q=fn->vertex(1)->point();
-		if(collinear_between(f->vertex(0)->point(),f->vertex(1)->point(),q)){
-	 f->ghost()=true;
-			neg_found = true;
-		}
-      else 
-	f->ghost()=false;
-      ++eit;
-    }while( eit!=all_edges_end());
-  }
+	 All_edges_iterator eit=all_edges_begin();
+	  for (; eit!=all_edges_end(); eit++){
+       Face_handle f=eit->first;
+       Face_handle fn=f->neighbor(0);
+       Point q=fn->vertex(1)->point();
+		 if(collinear_between(f->vertex(0)->point(),f->vertex(1)->point(),q)){
+	        f->ghost()=true;
+		    neg_found = true;
+		 } 
+          else 
+	        f->ghost()=false;
+        }
+	}
   else{//dimension==2
-
-    Face_circulator fc=incident_faces(v,v->face());
-    Face_circulator done(fc);
-    	
-    do{
-      //if(orientation(fc)==NEGATIVE){
+	if (first){ //first time dimension 2
+		 All_faces_iterator fi = all_faces_begin();
+		for(;fi!=all_faces_end();fi++){
+			if(orientation(fi)!=POSITIVE){
+				fi->ghost()=true;
+				neg_found=true;
+				this->_ghost=fi;
+			  }
+			  else
+				  fi->ghost()=false;
+		 }
+	}
+			  
+	else { //not first
+	  Face_circulator fc=incident_faces(v,v->face());
+	  Face_circulator done(fc);
+       do{
 		if(orientation(fc)!=POSITIVE){
-	     fc->ghost()=true;
-	     neg_found=true;
+	      fc->ghost()=true;
+	      neg_found=true;
 	     this->_ghost=fc;
-      }
-      else{
-	     fc->ghost()=false;
-      }
-    }while(++fc!=done);
-	
-  }
-    return neg_found;
-	  
- 
+        }
+        else
+	      fc->ghost()=false;
+	   }while(++fc!=done);
+	 }
+    
+   }
+	return neg_found;
+
 }
 
-
-
 //-------------------------------------------------------------------------------REMOVAL----------------------------------------------------//
 template < class Gt, class Tds >
 void
diff --git a/Triangulation_on_sphere_2/include/CGAL/Triangulation_on_sphere_2.h b/Triangulation_on_sphere_2/include/CGAL/Triangulation_on_sphere_2.h
index 67a607ffac5..488620da219 100644
--- a/Triangulation_on_sphere_2/include/CGAL/Triangulation_on_sphere_2.h
+++ b/Triangulation_on_sphere_2/include/CGAL/Triangulation_on_sphere_2.h
@@ -356,6 +356,11 @@ Orientation coplanar_orientation(const Point& p, const Point& q,const Point& r,
 		return _tds.mirror_index(v,i);
 	}
 	
+	Edge mirror_edge(const Edge e) const
+	{
+		return _tds.mirror_edge(e);
+	}
+	
 	
 	
    /*---------------------------------------------------------------------TEMPLATE MEMBERS--------------------------------------*/
@@ -561,15 +566,15 @@ locate_edge(const Point& p, Locate_type& lt, int& li, bool plane)const
 	 f=eit->first;
 	 Vertex_handle v1 = f->vertex(0);
 	 Vertex_handle v2 = f -> vertex(1);
-	 if(!f->is_ghost())
+	 //if(!f->is_ghost())
 	  if(orientation(v1->point(), v2->point(), p)==RIGHT_TURN){
 		lt=EDGE;
 		li=2;
 		test_distance( p, (*eit).first, lt, li);
 		return (*eit).first;
 	   }	
-	if(f->is_ghost())
-		loc = f;
+	//if(f->is_ghost())
+		//loc = f;
 	}//end for
 		
 	test_distance(p, loc, lt, li);
@@ -591,8 +596,7 @@ switch (dimension()){
 		
 	case 0:
 	case 1:{
-		show_face(f);
-	 Vertex_handle v0 = f->vertex(0);
+		Vertex_handle v0 = f->vertex(0);
 	 Vertex_handle v1= f->neighbor(0)->vertex(0);
 	 if (is_too_close(v0->point(),p)||is_too_close(v1->point(),p) )
 		lt = TOO_CLOSE;
diff --git a/Triangulation_on_sphere_2/test/bugs_minimal_examples.cpp b/Triangulation_on_sphere_2/test/bugs_minimal_examples.cpp
index 16b0fd77c32..a25835337ee 100644
--- a/Triangulation_on_sphere_2/test/bugs_minimal_examples.cpp
+++ b/Triangulation_on_sphere_2/test/bugs_minimal_examples.cpp
@@ -88,17 +88,6 @@ bool are_equal(RTOS triA, RTOS triB){
 
 
 
-
-
-
-
-
-
-
-
-
-
-
 int main(int argc, char* argv[]) 
 {
 	
@@ -131,14 +120,9 @@ int main(int argc, char* argv[])
 	points.resize(5);
 
  Vertex_handle v1 = rtos.insert(p1);
-	rtos.is_valid();
-	Vertex_handle v4 = rtos.insert(p4);
-	rtos.is_valid();
+Vertex_handle v4 = rtos.insert(p4);
 Vertex_handle v2 = rtos.insert(p2);
-	rtos.show_all();
-	
-	Vertex_handle v5 = rtos.insert(p5);
-	rtos.show_all();
+Vertex_handle v5 = rtos.insert(p5);
 Vertex_handle v3 = rtos.insert(p3);
 	rtos.is_valid();
 	
@@ -156,7 +140,7 @@ std::random_shuffle(points.begin(), points.end());
 		std::cout<<points.at(i)<<std::endl;
 		rtos2.insert(points.at(i));
 	}
-	
+	rtos2.is_valid();
 	are_equal(rtos, rtos2);
 	//rtos.remove(v1);
 	//rtos.remove(v2);
@@ -188,19 +172,23 @@ std::random_shuffle(points.begin(), points.end());
 	
 	Point_3 p27 = Point_3(radius, 0 ,0);
 	points2.push_back(p27);
-	Vertex_handle v0 = rtos.insert(p0);
+	
+	//	Vertex_handle v0 = rtos.insert(p0);
 	
 	
 	Vertex_handle v21 = rtos.insert(p21);
 	Vertex_handle v22 = rtos.insert(p22);
 	Vertex_handle v23 = rtos.insert(p23);
-	rtos.show_vertex(v23);
+	rtos.show_all();
+	Vertex_handle v26 = rtos.insert(p26); 
 	
 	
 	
 	Vertex_handle v24 = rtos.insert(p24); 
 	Vertex_handle v25 = rtos.insert(p25);
-	Vertex_handle v26 = rtos.insert(p26); 			
+	rtos.is_valid();
+	//Vertex_handle v = rtos.insert(p26); 	
+	Vertex_handle v0 = rtos.insert(p0);
 	//Vertex_handle v27 = rtos.insert(p27);
 	rtos.is_valid();
 
diff --git a/Triangulation_on_sphere_2/test/test_random.cpp b/Triangulation_on_sphere_2/test/test_random.cpp
index 84458d17c42..f9d887d76d5 100644
--- a/Triangulation_on_sphere_2/test/test_random.cpp
+++ b/Triangulation_on_sphere_2/test/test_random.cpp
@@ -33,18 +33,6 @@ typedef RTOS::Edge                                               Edge;
 
 
 
-bool is_ok(K::Point_3 p, std::vector<K::Point_3> po, double minDist2, int ind)
-{
-	bool ok= true;
-	for(int j= 0; j<ind; j++){
-		
-		if( squared_distance(p, po.at(j))<=minDist2 ){
-		ok = false;
-		}
-		
-	}
-	return ok;
-}
 
 
 bool has_face(Face_handle fh, Vertex_handle v0, Vertex_handle v1, Vertex_handle v2){
@@ -52,8 +40,6 @@ bool has_face(Face_handle fh, Vertex_handle v0, Vertex_handle v1, Vertex_handle
 	
 	
 	for(int i=0;i<=2; i++){
-		std::cout<<v0->point()<<std::endl;
-		std::cout<<fh->vertex(i)->point()<<std::endl;
 		test1 = (v0->point()==fh->vertex(i)->point());
 		if(test1) 
 			break;
@@ -104,7 +90,7 @@ bool are_equal(RTOS triA, RTOS triB){
 int main(){
 	int nu_of_pts;
 	double radius;
-	nu_of_pts =100000;
+	nu_of_pts =10000;
 	radius=6000000;
 	//radius = 1;
 	//double minDist = radius*2e-25;
@@ -165,18 +151,15 @@ int main(){
 	
 	t.start();
 	//====insert new points============
-		
-		
-	for (int count=0; count<nu_of_pts; count++) {
-		//std::cout<< "================= point number   "<< count+1 <<" =================="<<std::endl;
-		K::Point_3 p = points.at(count);
-		Vertex_handle v = rtos.insert(p);
-		vertices.push_back(v);			
-			
-	}
-	//rtos.is_valid();
+		rtos.insert(points.begin(),points.end());
 	
 	
+	t.stop();
+	std::cout<<"running time"<< t.time()<<std::endl;
+
+	rtos.is_valid();
+
+	/*
 	
 	//*****second triangulation*******
 	std::random_shuffle(points.begin(), points.end());