diff --git a/include/Algo/Export/exportPov.h b/include/Algo/Export/exportPov.h
index 0b97ad352cc8e66acf72e1ac1dc846d6c52a56a7..0120d51f546edc8f0c95c4ee106dfdc25d66b3fc 100644
--- a/include/Algo/Export/exportPov.h
+++ b/include/Algo/Export/exportPov.h
@@ -3,6 +3,7 @@
 
 #include "Topology/generic/attributeHandler.h"
 #include "Utils/cgognStream.h"
+#include "Algo/Geometry/normal.h"
 
 namespace CGoGN
 {
@@ -45,7 +46,7 @@ void exportMeshPlain(std::ofstream& out, typename PFP::MAP& map, typename PFP::T
 			unsigned int nb=0;
 			Dart dd=d;
 			do {
-				traite.markOrbit(DART,dd);
+				traite.mark(dd);
 				dd = map.phi1(dd);
 				nb++;
 			} while(dd!=d);
@@ -69,6 +70,104 @@ void exportMeshPlain(std::ofstream& out, typename PFP::MAP& map, typename PFP::T
 	out << "}" << std::endl;
 }
 
+template <typename PFP>
+void export3MeshPlainSmooth(std::ofstream& out, typename PFP::MAP& map, typename PFP::TVEC3& position, const std::string& meshName, const FunctorSelect& good = SelectorTrue())
+{
+	typedef typename PFP::VEC3 VEC3;
+
+	out << "#declare " << meshName << "= mesh2 {" << std::endl;
+
+	unsigned int nbDarts = map.getNbDarts() ;
+
+	//vector containing the degree of faces
+	std::vector<unsigned int> facesSize ;
+	//vector containing the list of index of vertices
+	std::vector<std::vector<unsigned int> > facesIdx ;
+	facesSize.reserve(nbDarts/3) ;
+	facesIdx.reserve(nbDarts/3) ;
+
+	//map : attribute place / index in declaration (for vertices and normals)
+	std::map<unsigned int, unsigned int> vIndex ;
+	//index : start from 0 and increase (used to ignore the gaps potentially present in the container)
+	unsigned int vCpt = 0 ;
+
+	//remember the attribute lines
+	std::vector<unsigned int> vertices ;
+
+	std::vector<VEC3> normals ;
+	vertices.reserve(nbDarts/6) ;
+	normals.reserve(nbDarts/6) ;
+
+	CellMarker markV(map, VERTEX) ;
+	DartMarker markF(map) ;
+	for(Dart d = map.begin(); d != map.end(); map.next(d))
+	{
+
+		if(good(d) && !markF.isMarked(d) && map.phi3(d)==d)
+		{
+			markF.markOrbit(FACE, d) ;
+			std::vector<unsigned int> fidx ;
+			fidx.reserve(4) ;
+			Dart dd = d ;
+			do
+			{
+				unsigned int vNum = map.getEmbedding(VERTEX, dd) ;
+				if(!markV.isMarked(dd))
+				{
+					markV.mark(dd) ;
+					VEC3 norm = Algo::Geometry::vertexBorderNormal<PFP>(map,dd,position);
+
+					vIndex[vNum] = vCpt++ ;
+					vertices.push_back(vNum) ;
+
+					normals.push_back(norm) ;
+				}
+
+				fidx.push_back(vIndex[vNum]) ;
+
+				dd = map.phi1(dd) ;
+			} while(dd != d) ;
+
+			facesSize.push_back(map.faceDegree(d)) ;
+			facesIdx.push_back(fidx) ;
+		}
+	}
+
+	//export all vertices
+	out << "vertex_vectors {" << std::endl;
+	out << vertices.size() << "," << std::endl;
+	for(unsigned int i = 0; i < vertices.size(); ++i)
+	{
+		const VEC3& v = position[vertices[i]] ;
+		out << "<" << v[0] << ", " << v[1] << ", " << v[2] << ">"<< std::endl ;
+	}
+	out << "}" << std::endl;
+
+	//export all normals
+	out << "normal_vectors {" << std::endl;
+	out << normals.size() << "," << std::endl;
+	for(unsigned int i = 0; i < normals.size(); ++i)
+	{
+		const VEC3& v = normals[i];
+		out << "<" << v[0] << ", " << v[1] << ", " << v[2] << ">"<< std::endl ;
+	}
+	out << "}" << std::endl;
+
+	//export all faces
+	out << "face_indices {" << std::endl;
+	out << facesSize.size() << "," << std::endl;
+	for(unsigned int i = 0; i < facesSize.size(); ++i)
+	{
+		out << "<" << facesIdx[i][0];
+		for(unsigned int j = 1; j < facesIdx[i].size(); ++j)
+			out << ", " << facesIdx[i][j] ;
+		out << ">" << std::endl ;
+	}
+	out << "}" << std::endl;
+
+	out << "}" << std::endl;
+}
+
 template <typename PFP>
 void exportMeshWire(std::ofstream& out, typename PFP::MAP& map, typename PFP::TVEC3& position, const std::string& meshName, const FunctorSelect& good = SelectorTrue())
 {
@@ -134,7 +233,8 @@ bool exportScenePov(typename PFP::MAP& map, typename PFP::TVEC3& position, const
 	out << "global_settings {" << std::endl;
 	out << "radiosity {" << std::endl;
 	out << "pretrace_start 0.08 pretrace_end 0.04" << std::endl;
-	out << "count 100 nearest_count 10 error_bound 0.15 recursion_limit 1 low_error_factor 0.2 gray_threshold 0.0 minimum_reuse 0.015 brightness 1 adc_bailout 0.01/2 normal off media off} max_trace_level 255}" << std::endl;
+	out << "count 100 nearest_count 10 error_bound 0.15 recursion_limit 1 low_error_factor 0.2 gray_threshold 0.0 minimum_reuse 0.015 brightness 1 adc_bailout 0.01/2 normal off media off}" << std::endl;
+	out << "max_trace_level 255}" << std::endl;
 
 	Algo::ExportPov::exportMeshPlain<PFP>(out,map,position,"myMesh",good);
 
@@ -147,6 +247,51 @@ bool exportScenePov(typename PFP::MAP& map, typename PFP::TVEC3& position, const
 	return true;
 }
 
+template <typename PFP>
+bool exportScenePovSmooth(typename PFP::MAP& map, typename PFP::TVEC3& position, const std::string& filename, typename PFP::VEC3 cameraPos, typename PFP::VEC3 cameraLook, typename PFP::VEC3 translate, float angle_X, float angle_Y, float angle_Z,const FunctorSelect& good = SelectorTrue())
+{
+	std::ofstream out(filename.c_str(), std::ios::out);
+	if (!out.good()) {
+		CGoGNerr << "(export) Unable to open file " << filename << CGoGNendl;
+		return false;
+	}
+
+	float angleX = angle_X;
+	float angleY = angle_Y;
+	float angleZ = angle_Z;
+
+	//define the camera position
+	out << "camera { location <" << cameraPos[0] << "," << cameraPos[1] << "," << cameraPos[2] << "> look_at <" << cameraLook[0] << "," << cameraLook[1] << "," << cameraLook[2] <<">}" << std::endl;
+
+	//set a "infinite" plane
+// 	out << "plane { y, -1 pigment { color rgb 1 } }" << std::endl;
+
+	//set a sky sphere
+	out << "sphere { <0, 0, 0>, 5000";
+	out << "texture{ pigment { color rgb <1, 1, 1>}	finish { ambient 1 diffuse 0 } } }" << std::endl;
+
+	//put some lights
+	out << "light_source { <" << cameraPos[0] << "," << cameraPos[1] << "," << cameraPos[2] << "> color rgb 0.45}" << std::endl;
+
+	//set a high quality rendering
+	out << "global_settings {" << std::endl;
+//	out << "radiosity {" << std::endl;
+//	out << "pretrace_start 0.08 pretrace_end 0.04" << std::endl;
+//	out << "count 300 nearest_count 10 error_bound 0.15 recursion_limit 1 low_error_factor 0.2 gray_threshold 0.0 minimum_reuse 0.015 brightness 1 adc_bailout 0.01/2 normal off media off}" << std::endl;
+	out << "max_trace_level 60}" << std::endl;
+
+	Algo::ExportPov::export3MeshPlainSmooth<PFP>(out,map,position,"myMesh",good);
+
+	out << "object {myMesh" << std::endl;
+ 	out << "translate <" << translate[0] << "," << translate[1] << "," << translate[2] << ">" << std::endl;
+ 	out << "rotate <" << angleX << "," << angleY << "," << angleZ << "> " << std::endl;
+ 	out << "double_illuminate" << std::endl;
+ 	out << "texture{ pigment{ color rgb <0.5,1.0,0.5>} finish { ambient 0.5 roughness 0.2 } } }" << std::endl;
+
+	out.close();
+	return true;
+}
+
 }
 
 }
diff --git a/include/Algo/Geometry/normal.h b/include/Algo/Geometry/normal.h
index d17f60f87b19c19be14c330882d02ceb8af69af6..34b1ad2b0aa5f13949382522c0e9cf7894bd88c2 100644
--- a/include/Algo/Geometry/normal.h
+++ b/include/Algo/Geometry/normal.h
@@ -39,12 +39,18 @@ namespace Geometry
 template <typename PFP>
 typename PFP::VEC3 triangleNormal(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& position) ;
 
+template <typename PFP>
+typename PFP::VEC3 newellNormal(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& position);
+
 template <typename PFP>
 typename PFP::VEC3 faceNormal(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& position) ;
 
 template <typename PFP>
 typename PFP::VEC3 vertexNormal(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& position) ;
 
+template <typename PFP>
+typename PFP::VEC3 vertexBorderNormal(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& position) ;
+
 template <typename PFP>
 void computeNormalFaces(typename PFP::MAP& map, const typename PFP::TVEC3& position, typename PFP::TVEC3& face_normal, const FunctorSelect& select = SelectorTrue(), unsigned int thread = 0) ;
 
diff --git a/include/Algo/Geometry/normal.hpp b/include/Algo/Geometry/normal.hpp
index e6bc5855af2d8d78c8e45b598e1947ac929919f1..d33ff29f20a978c197421f16e8a401a3a28ca78d 100644
--- a/include/Algo/Geometry/normal.hpp
+++ b/include/Algo/Geometry/normal.hpp
@@ -116,6 +116,40 @@ typename PFP::VEC3 vertexNormal(typename PFP::MAP& map, Dart d, const typename P
 	return N ;
 }
 
+template <typename PFP>
+typename PFP::VEC3 vertexBorderNormal(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& position)
+{
+	assert(map.dimension() == 3);
+
+	typedef typename PFP::VEC3 VEC3 ;
+
+	VEC3 N(0) ;
+	std::vector<Dart> faces;
+	CellMarker f(map,FACE);
+
+	FunctorStore fs(faces);
+	map.foreach_dart_of_oriented_vertex(d,fs);
+
+	for(std::vector<Dart>::iterator it = faces.begin() ; it != faces.end() ; ++it)
+	{
+		if(!f.isMarked(*it) && map.phi3(*it)==*it)
+		{
+			f.mark(*it);
+			VEC3 n = faceNormal<PFP>(map, *it, position);
+			if(!n.hasNan())
+			{
+				VEC3 v1 = vectorOutOfDart<PFP>(map, *it, position);
+				VEC3 v2 = vectorOutOfDart<PFP>(map, map.phi_1(*it), position);
+				n *= convexFaceArea<PFP>(map, *it, position) / (v1.norm2() * v2.norm2());
+				N += n ;
+			}
+		}
+	}
+
+	N.normalize() ;
+	return N ;
+}
+
 template <typename PFP>
 void computeNormalFaces(typename PFP::MAP& map, const typename PFP::TVEC3& position, typename PFP::TVEC3& face_normal, const FunctorSelect& select, unsigned int thread)
 {
diff --git a/include/Topology/gmap/gmap1.hpp b/include/Topology/gmap/gmap1.hpp
index 9e1de3f14b7377041cf63bb0f0ff4607de9933ac..8e365accead745a3ee908a34cceda1b37969da9c 100644
--- a/include/Topology/gmap/gmap1.hpp
+++ b/include/Topology/gmap/gmap1.hpp
@@ -213,6 +213,10 @@ inline void GMap1::collapseEdge(Dart d)
 inline void GMap1::splitFace(Dart d, Dart e)
 {
 	assert(d != e && sameFace(d, e)) ;
+
+	if(!sameOrientedFace(d,e))
+		e = beta1(e);
+
 	Dart d1 = beta1(d) ;
 	Dart e1 = beta1(e) ;
 	Dart dd = newEdge() ;
diff --git a/include/Topology/gmap/gmap2.h b/include/Topology/gmap/gmap2.h
index 229e6ab17d9e2383af90d89fadaddd56af05138e..f4f64e2724659a61bcb8e5fdc854251e7148a899 100644
--- a/include/Topology/gmap/gmap2.h
+++ b/include/Topology/gmap/gmap2.h
@@ -336,14 +336,6 @@ public:
 	* @param fonct functor obj ref
 	*/
 	bool foreach_dart_of_cc(Dart d, FunctorType& fonct, unsigned int thread=0);
-
-	//!
-	/*! TODO Ajout a valider
-	 * restreint aux complexes simpliciaux
-	 * Apply a functor on the all darts in the set of the link from orbit
-	 */
-	bool foreach_dart_of_link(Dart d, unsigned int orbit, FunctorType& f, unsigned int thread=0);
-	//@}
 };
 
 } // namespace CGoGN
diff --git a/include/Topology/gmap/gmap3.h b/include/Topology/gmap/gmap3.h
index 26d49c3c852fcc46382c79c587c7218aa0188e03..545c9cecec3e70d2bf485a7ae92664085d840bf6 100644
--- a/include/Topology/gmap/gmap3.h
+++ b/include/Topology/gmap/gmap3.h
@@ -200,7 +200,14 @@ public:
 
 	//@{
 	/**
-	* Apply a functor on each dart of a face
+	* Apply a functor on each dart of a vertex
+	* @param d a dart of the face
+	* @param fonct functor obj ref
+	*/
+	bool foreach_dart_of_oriented_vertex(Dart d, FunctorType& fonct, unsigned int thread=0);
+
+	/**
+	* Apply a functor on each dart of a vertex
 	* @param d a dart of the face
 	* @param fonct functor obj ref
 	*/
diff --git a/include/Topology/map/map2.h b/include/Topology/map/map2.h
index 14cd0f513fdcc8d5068d944d3d9a82c994ac4d78..733e4e3fd676e301fd94048c3c4999a26bf07a5b 100644
--- a/include/Topology/map/map2.h
+++ b/include/Topology/map/map2.h
@@ -286,33 +286,53 @@ public:
 	 */
 	bool sameOrientedVertex(Dart d, Dart e) ;
 
+	//! Test if dart d and e belong to the same vertex
+	/*! @param d a dart
+	 *  @param e a dart
+	 */
+	bool sameVertex(Dart d, Dart e) ;
+
+	//! Compute the number of edges of the vertex of d
+	/*! @param d a dart
+	 */
+	unsigned int vertexDegree(Dart d) ;
+
+	//! Tell if the vertex of d is on the boundary of the map
+	/*! @param d a dart
+	 */
+	bool isBoundaryVertex(Dart d) ;
+
 	//!Test if dart d and e belong to the same oriented face
 	/*! @param d a dart
 	 *  @param e a dart
 	 */
 	bool sameOrientedFace(Dart d, Dart e);
 
-	//! Test if dart d and e belong to the same vertex
+	// TODO a mettre en algo
+	/**
+	 * check if the mesh is triangular or not
+	 * @return a boolean indicating if the mesh is triangular
+	 */
+	bool isTriangular() ;
+
+	//@{
+	//! Test if dart d and e belong to the same oriented volume
 	/*! @param d a dart
 	 *  @param e a dart
 	 */
-	bool sameVertex(Dart d, Dart e) ;
+	bool sameOrientedVolume(Dart d, Dart e) ;
 
-	//! Compute the number of edges of the vertex of d
+	//! Test if dart d and e belong to the same volume
 	/*! @param d a dart
+	 *  @param e a dart
 	 */
-	unsigned int vertexDegree(Dart d) ;
+	bool sameVolume(Dart d, Dart e) ;
 
 	//! Compute the number of faces in the volume of d
 	/*! @param d a dart
 	 */
 	unsigned int volumeDegree(Dart d);
 
-	//! Tell if the vertex of d is on the boundary of the map
-	/*! @param d a dart
-	 */
-	bool isBoundaryVertex(Dart d) ;
-
 	//! Follow the boundary of a surface as if it was a oriented face.
 	/*! This operation alternate phi1 and phi2 operator until another
 	 *  boudary dart is reached.
@@ -320,12 +340,6 @@ public:
 	 */
 	Dart nextOnBoundary(Dart d);
 
-	// TODO a mettre en algo
-	/**
-	 * check if the mesh is triangular or not
-	 * @return a boolean indicating if the mesh is triangular
-	 */
-	bool isTriangular() ;
 
 	// TODO a mettre en algo
 	/**
@@ -339,7 +353,6 @@ public:
 	 *  Apply functors to all darts of a cell
 	 *************************************************************************/
 
-	//@{
 	//! Apply a functor on every dart of a vertex
 	/*! @param d a dart of the vertex
 	 *  @param f the functor to apply
diff --git a/include/Topology/map/map2.hpp b/include/Topology/map/map2.hpp
index 6ec61a88122cdde0ec45f94eba897541a4359371..04d4afb6bbc9f4d127294d36bbb8d6bc56c0ebc1 100644
--- a/include/Topology/map/map2.hpp
+++ b/include/Topology/map/map2.hpp
@@ -181,6 +181,11 @@ inline bool Map2::sameVertex(Dart d, Dart e)
 	return sameOrientedVertex(d, e) ;
 }
 
+inline bool Map2::sameVolume(Dart d, Dart e)
+{
+	return sameOrientedVolume(d, e) ;
+}
+
 /*! @name Cell Functors
  *  Apply functors to all darts of a cell
  *************************************************************************/
diff --git a/include/Topology/map/map3.h b/include/Topology/map/map3.h
index 23db8a4ae1bb36b1c47a1dc645fb465921b6ce67..2f95252acf9cbfb7dfd13cc22cbb65f451af51ed 100644
--- a/include/Topology/map/map3.h
+++ b/include/Topology/map/map3.h
@@ -236,6 +236,12 @@ public:
 	 *************************************************************************/
 
 	//@{
+	//! Apply a functor on each dart of a vertex
+	/*! @param d a dart of the vertex
+	 *  @param fonct the functor
+	 */
+	bool foreach_dart_of_oriented_vertex(Dart d, FunctorType& f, unsigned int thread=0);
+
 	//! Apply a functor on each dart of a vertex
 	/*! @param d a dart of the vertex
 	 *  @param fonct the functor
diff --git a/include/Topology/map/map3.hpp b/include/Topology/map/map3.hpp
index 12169f7c3fd215a10e4f4b029496a534d6b8016e..9c0fd0b074ddd92d7dca1767022b50cde174ad1a 100644
--- a/include/Topology/map/map3.hpp
+++ b/include/Topology/map/map3.hpp
@@ -178,6 +178,11 @@ inline void Map3::phi3unsew(Dart d)
 	(*m_phi3)[e.index] = e ;
 }
 
+inline bool Map3::foreach_dart_of_vertex(Dart d, FunctorType& f, unsigned int thread)
+{
+	return foreach_dart_of_oriented_vertex(d, f, thread);
+}
+
 //template<typename TMAP>
 //bool Map3::foreach_dart_of_parent_cell(int dim, Dart d, FunctorType& f)
 //{
diff --git a/src/Topology/gmap/gmap2.cpp b/src/Topology/gmap/gmap2.cpp
index 772c65da936bd7ac823d23513828f8abe98dda9e..d6a7693e2062db47ed9231e139eeeb1e86d26c70 100644
--- a/src/Topology/gmap/gmap2.cpp
+++ b/src/Topology/gmap/gmap2.cpp
@@ -664,33 +664,4 @@ bool GMap2::foreach_dart_of_cc(Dart d, FunctorType& f, unsigned int thread)
 	return found;
 }
 
-bool GMap2::foreach_dart_of_link(Dart d, unsigned int orbit, FunctorType& f, unsigned int thread)
-{
-	if(orbit == VERTEX)
-	{
-		Dart dNext = d;
-		do
-		{
-			if(GMap2::foreach_dart_of_edge(phi1(dNext),f,thread))
-				return true;
-
-			dNext = alpha1(dNext);
-		} while (dNext != d);
-
-		return false;
-	}
-	else if(orbit == FACE)
-	{
-		if(GMap2::foreach_dart_of_vertex(phi_1(d),f,thread))
-			return true;
-
-		if(GMap2::foreach_dart_of_vertex(phi_1(phi2(d)),f,thread))
-			return true;
-
-		return false;
-	}
-
-	return false;
-}
-
 } // namespace CGoGN
diff --git a/src/Topology/gmap/gmap3.cpp b/src/Topology/gmap/gmap3.cpp
index 40db040d6ad2e6634a34d8fd42a8832459ca82b6..16e7d22ce94d94b5e4c2d627ad34ef4a483d8d19 100644
--- a/src/Topology/gmap/gmap3.cpp
+++ b/src/Topology/gmap/gmap3.cpp
@@ -500,6 +500,46 @@ bool GMap3::check()
  *  Apply functors to all darts of a cell
  *************************************************************************/
 
+bool GMap3::foreach_dart_of_oriented_vertex(Dart d, FunctorType& f, unsigned int thread)
+{
+	DartMarkerStore mv(*this,thread);	// Lock a marker
+	bool found = false;					// Last functor return value
+
+	std::vector<Dart> darts_list;			//Darts that are traversed
+	darts_list.reserve(512);
+	darts_list.push_back(d);			//Start with the dart d
+	mv.mark(d);
+
+	for(std::vector<Dart>::iterator darts = darts_list.begin(); !found && darts != darts_list.end() ; ++darts)
+	{
+		Dart dc = *darts;
+
+		//add phi21 and phi23 successor if they are not marked yet
+		Dart d2 = phi2(dc);
+		if(d2 != dc)
+		{
+			Dart d21 = phi1(d2); // turn in volume
+			Dart d23 = phi3(d2); // change volume
+
+			if(!mv.isMarked(d21))
+			{
+				darts_list.push_back(d21);
+				mv.mark(d21);
+			}
+
+			if((d23!=d2) && !mv.isMarked(d23))
+			{
+				darts_list.push_back(d23);
+				mv.mark(d23);
+			}
+		}
+
+		found = f(dc);
+	}
+
+	return found;
+}
+
 bool GMap3::foreach_dart_of_vertex(Dart d, FunctorType& f, unsigned int thread)
 {
 	DartMarkerStore mv(*this,thread);	// Lock a marker
diff --git a/src/Topology/map/map2.cpp b/src/Topology/map/map2.cpp
index 1ca6ba4ab70d8506aeafd9a927f3ac7bd242bcc6..728cb513d4d6d32dd2d1808da080fb4b837ea40a 100644
--- a/src/Topology/map/map2.cpp
+++ b/src/Topology/map/map2.cpp
@@ -427,6 +427,32 @@ bool Map2::sameOrientedVertex(Dart d, Dart e)
 	return false;				// None is equal to e => vertices are distinct
 }
 
+unsigned int Map2::vertexDegree(Dart d)
+{
+	unsigned int count = 0 ;
+	Dart dNext = d ;
+	do
+	{
+		++count ;
+		if(phi2(dNext) == dNext)
+			++count ;
+		dNext = alpha1(dNext) ;
+	} while (dNext != d) ;
+	return count ;
+}
+
+bool Map2::isBoundaryVertex(Dart d)
+{
+	Dart dNext = d ;
+	do
+	{
+		if(phi2(dNext) == dNext)
+			return true ;
+		dNext = alpha1(dNext) ;
+	} while (dNext != d) ;
+	return false ;
+}
+
 bool Map2::sameOrientedFace(Dart d, Dart e)
 {
 	Dart dNext = d;
@@ -439,18 +465,35 @@ bool Map2::sameOrientedFace(Dart d, Dart e)
 	return false;				// None is equal to e => faces are distinct
 }
 
-unsigned int Map2::vertexDegree(Dart d)
+bool Map2::sameOrientedVolume(Dart d, Dart e)
 {
-	unsigned int count = 0 ;
-	Dart dNext = d ;
-	do
+	DartMarkerStore mark(*this);	// Lock a marker
+	bool found = false;				// Last functor return value
+
+	std::list<Dart> visitedFaces;	// Faces that are traversed
+	visitedFaces.push_back(d);		// Start with the face of d
+	std::list<Dart>::iterator face;
+
+	// For every face added to the list
+	for (face = visitedFaces.begin(); !found && face != visitedFaces.end(); ++face)
 	{
-		++count ;
-		if(phi2(dNext) == dNext)
-			++count ;
-		dNext = alpha1(dNext) ;
-	} while (dNext != d) ;
-	return count ;
+		if (!mark.isMarked(*face))		// Face has not been visited yet
+		{
+			Dart dNext = *face ;
+			do
+			{
+				if(dNext==e)
+					return true;
+
+				mark.mark(dNext);					// Mark
+				Dart adj = phi2(dNext);				// Get adjacent face
+				if (adj != dNext && !mark.isMarked(adj))
+					visitedFaces.push_back(adj);	// Add it
+				dNext = phi1(dNext);
+			} while(dNext != *face);
+		}
+	}
+	return false;
 }
 
 unsigned int Map2::volumeDegree(Dart d)
@@ -485,18 +528,6 @@ unsigned int Map2::volumeDegree(Dart d)
 	return count;
 }
 
-bool Map2::isBoundaryVertex(Dart d)
-{
-	Dart dNext = d ;
-	do
-	{
-		if(phi2(dNext) == dNext)
-			return true ;
-		dNext = alpha1(dNext) ;
-	} while (dNext != d) ;
-	return false ;
-}
-
 Dart Map2::nextOnBoundary(Dart d)
 {
 	assert(phi2(d) == d);	// Only work on boundary dart
diff --git a/src/Topology/map/map3.cpp b/src/Topology/map/map3.cpp
index 06b31e901ee6fe52e79418d2e94bc654f9fecb99..af2c8a446dbb61412a664af14f22b3f7d5972e5b 100644
--- a/src/Topology/map/map3.cpp
+++ b/src/Topology/map/map3.cpp
@@ -535,7 +535,7 @@ bool Map3::check()
  *  Apply functors to all darts of a cell
  *************************************************************************/
 
-bool Map3::foreach_dart_of_vertex(Dart d, FunctorType& f, unsigned int thread)
+bool Map3::foreach_dart_of_oriented_vertex(Dart d, FunctorType& f, unsigned int thread)
 {
 	DartMarkerStore mv(*this,thread);	// Lock a marker
 	bool found = false;					// Last functor return value