diff --git a/include/Algo/Geometry/curvature.hpp b/include/Algo/Geometry/curvature.hpp
index e27323cebaa6fccf18700b3b984a326fb228c5f5..611629a752af4f5fc3a40662928ee571c24bf4db 100644
--- a/include/Algo/Geometry/curvature.hpp
+++ b/include/Algo/Geometry/curvature.hpp
@@ -440,17 +440,17 @@ void computeCurvatureVertices_NormalCycles(
 	if (!map. template isOrbitEmbedded<VERTEX>())
 	{
 		CellMarkerNoUnmark<VERTEX> cm(map);
-		map. template initOrbitEmbedding<VERTEX>();
+		map. template initAllOrbitsEmbedding<VERTEX>();
 	}
 	if (!map. template isOrbitEmbedded<EDGE>())
 	{
 		CellMarkerNoUnmark<EDGE> cm(map);
-		map. template initOrbitEmbedding<EDGE>();
+		map. template initAllOrbitsEmbedding<EDGE>();
 	}
 	if (!map. template isOrbitEmbedded<FACE>())
 	{
 		CellMarkerNoUnmark<FACE> cm(map);
-		map. template initOrbitEmbedding<FACE>();
+		map. template initAllOrbitsEmbedding<FACE>();
 	}
 
 	FunctorComputeCurvatureVertices_NormalCycles<PFP> funct(map, radius, position, normal, edgeangle, kmax, kmin, Kmax, Kmin, Knormal);
diff --git a/include/Topology/generic/genericmap.h b/include/Topology/generic/genericmap.h
index 7d379046921e285eed5236b7641c67138931a1d6..efae06e449ff7d87c9b378dc7653b268b8e4158f 100644
--- a/include/Topology/generic/genericmap.h
+++ b/include/Topology/generic/genericmap.h
@@ -438,6 +438,14 @@ public:
 	template <unsigned int ORBIT>
 	void initCell(unsigned int i) ;
 
+	/**
+	 * Traverse the map and embed all orbits of the given dimension with a new cell
+	 * @param realloc if true -> all the orbits are embedded on new cells, if false -> already embedded orbits are not impacted
+	 */
+	template <unsigned int ORBIT>
+	void initAllOrbitsEmbedding(bool realloc = false) ;
+
+
 	/****************************************
 	 *     QUICK TRAVERSAL MANAGEMENT       *
 	 ****************************************/
diff --git a/include/Topology/generic/genericmap.hpp b/include/Topology/generic/genericmap.hpp
index 890821a579d276c1df7048c9f5356fac199a1183..cda01ae56f01531a2c4ac821306b365a9edc0458 100644
--- a/include/Topology/generic/genericmap.hpp
+++ b/include/Topology/generic/genericmap.hpp
@@ -397,12 +397,12 @@ inline void GenericMap::copyCell(Dart d, Dart e)
 	assert(isOrbitEmbedded<ORBIT>() || !"Invalid parameter: orbit not embedded");
 	unsigned int dE = getEmbedding<ORBIT>(d) ;
 	unsigned int eE = getEmbedding<ORBIT>(e) ;
-//	if(eE != EMBNULL)	// if the source is NULL, nothing to copy
-//	{
-//		if(dE == EMBNULL)	// if the dest is NULL, create a new cell
-//			dE = setOrbitEmbeddingOnNewCell<ORBIT>(d) ;
+	if(eE != EMBNULL)	// if the source is NULL, nothing to copy
+	{
+		if(dE == EMBNULL)	// if the dest is NULL, create a new cell
+			dE = setOrbitEmbeddingOnNewCell<ORBIT>(d) ;
 		m_attribs[ORBIT].copyLine(dE, eE) ;	// copy the data
-//	}
+	}
 }
 
 template <unsigned int ORBIT>
@@ -419,6 +419,23 @@ inline void GenericMap::initCell(unsigned int i)
 	m_attribs[ORBIT].initLine(i) ;
 }
 
+
+template <unsigned int ORBIT>
+void GenericMap::initAllOrbitsEmbedding(bool realloc)
+{
+	assert(isOrbitEmbedded<ORBIT>() || !"Invalid parameter: orbit not embedded") ;
+	DartMarker mark(*this) ;
+	for(Dart d = begin(); d != end(); next(d))
+	{
+		if(!mark.isMarked(d))
+		{
+			mark.markOrbit<ORBIT>(d) ;
+			if(realloc || getEmbedding<ORBIT>(d) == EMBNULL)
+				setOrbitEmbeddingOnNewCell<ORBIT>(d) ;
+		}
+	}
+}
+
 /****************************************
  *     QUICK TRAVERSAL MANAGEMENT       *
  ****************************************/
@@ -538,18 +555,9 @@ void GenericMap::addEmbedding()
 	AttributeMultiVector<unsigned int>* amv = dartCont.addAttribute<unsigned int>(oss.str()) ;
 	m_embeddings[ORBIT] = amv ;
 
-	FunctorInitEmb<GenericMap, ORBIT> fsetemb(*this);
-	DartMarker dm(*this);
-	for(Dart d = this->begin(); d != this->end(); this->next(d))
-	{
-		if(!dm.isMarked(d))
-		{
-			dm.markOrbit<ORBIT>(d);
-			unsigned int em = newCell<ORBIT>();
-			fsetemb.changeEmb(em);
-			foreach_dart_of_orbit<ORBIT>(d, fsetemb);
-		}
-	}
+	// set new embedding to EMBNULL for all the darts of the map
+	for(unsigned int i = dartCont.begin(); i < dartCont.end(); dartCont.next(i))
+		(*amv)[i] = EMBNULL ;
 }
 
 /****************************************
diff --git a/include/Topology/generic/traversor2_closed.h b/include/Topology/generic/traversor2_closed.h
new file mode 100644
index 0000000000000000000000000000000000000000..ba2d497ccb515c454d780fdebf908c0843425ea6
--- /dev/null
+++ b/include/Topology/generic/traversor2_closed.h
@@ -0,0 +1,260 @@
+/*******************************************************************************
+* CGoGN: Combinatorial and Geometric modeling with Generic N-dimensional Maps  *
+* version 0.1                                                                  *
+* Copyright (C) 2009-2012, IGG Team, LSIIT, University of Strasbourg           *
+*                                                                              *
+* This library is free software; you can redistribute it and/or modify it      *
+* under the terms of the GNU Lesser General Public License as published by the *
+* Free Software Foundation; either version 2.1 of the License, or (at your     *
+* option) any later version.                                                   *
+*                                                                              *
+* This library is distributed in the hope that it will be useful, but WITHOUT  *
+* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or        *
+* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License  *
+* for more details.                                                            *
+*                                                                              *
+* You should have received a copy of the GNU Lesser General Public License     *
+* along with this library; if not, write to the Free Software Foundation,      *
+* Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301 USA.           *
+*                                                                              *
+* Web site: http://cgogn.unistra.fr/                                           *
+* Contact information: cgogn@unistra.fr                                        *
+*                                                                              *
+*******************************************************************************/
+
+#ifndef __TRAVERSOR2_CLOSED_H__
+#define __TRAVERSOR2_CLOSED_H__
+
+#include "Topology/generic/dart.h"
+#include "Topology/generic/traversorGen.h"
+
+namespace CGoGN
+{
+
+namespace ClosedMap
+{
+
+
+/*******************************************************************************
+					VERTEX CENTERED TRAVERSALS
+*******************************************************************************/
+
+// Traverse the edges incident to a given vertex
+template <typename MAP>
+class Traversor2VE: public Traversor<MAP>
+{
+private:
+	MAP& m ;
+	Dart start ;
+	Dart current ;
+
+public:
+	Traversor2VE(MAP& map, Dart dart) ;
+
+	Dart begin() ;
+	Dart end() ;
+	Dart next() ;
+} ;
+
+// Traverse the faces incident to a given vertex
+template <typename MAP>
+class Traversor2VF : public Traversor<MAP>
+{
+private:
+	MAP& m ;
+	Dart start ;
+	Dart current ;
+
+public:
+	Traversor2VF(MAP& map, Dart dart) ;
+
+	Dart begin() ;
+	Dart end() ;
+	Dart next() ;
+} ;
+
+// Traverse the vertices adjacent to a given vertex through sharing a common edge
+template <typename MAP>
+class Traversor2VVaE : public Traversor<MAP>
+{
+private:
+	MAP& m ;
+	Dart start ;
+	Dart current ;
+
+public:
+	Traversor2VVaE(MAP& map, Dart dart) ;
+
+	Dart begin() ;
+	Dart end() ;
+	Dart next() ;
+} ;
+
+// Traverse the vertices adjacent to a given vertex through sharing a common face
+template <typename MAP>
+class Traversor2VVaF : public Traversor<MAP>
+{
+private:
+	MAP& m ;
+	Dart start ;
+	Dart current ;
+
+	Dart stop ;
+
+public:
+	Traversor2VVaF(MAP& map, Dart dart) ;
+
+	Dart begin() ;
+	Dart end() ;
+	Dart next() ;
+} ;
+
+/*******************************************************************************
+					EDGE CENTERED TRAVERSALS
+*******************************************************************************/
+
+// Traverse the vertices incident to a given edge
+template <typename MAP>
+class Traversor2EV : public Traversor<MAP>
+{
+private:
+	MAP& m ;
+	Dart start ;
+	Dart current ;
+
+public:
+	Traversor2EV(MAP& map, Dart dart) ;
+
+	Dart begin() ;
+	Dart end() ;
+	Dart next() ;
+} ;
+
+// Traverse the faces incident to a given edge
+template <typename MAP>
+class Traversor2EF : public Traversor<MAP>
+{
+private:
+	MAP& m ;
+	Dart start ;
+	Dart current ;
+
+public:
+	Traversor2EF(MAP& map, Dart dart) ;
+
+	Dart begin() ;
+	Dart end() ;
+	Dart next() ;
+} ;
+
+// Traverse the edges adjacent to a given edge through sharing a common vertex
+template <typename MAP>
+class Traversor2EEaV : public Traversor<MAP>
+{
+private:
+	MAP& m ;
+	Dart start ;
+	Dart current ;
+
+	Dart stop1, stop2 ;
+
+public:
+	Traversor2EEaV(MAP& map, Dart dart) ;
+
+	Dart begin() ;
+	Dart end() ;
+	Dart next() ;
+} ;
+
+// Traverse the edges adjacent to a given edge through sharing a common face
+template <typename MAP>
+class Traversor2EEaF : public Traversor<MAP>
+{
+private:
+	MAP& m ;
+	Dart start ;
+	Dart current ;
+
+	Dart stop1, stop2 ;
+
+public:
+	Traversor2EEaF(MAP& map, Dart dart) ;
+
+	Dart begin() ;
+	Dart end() ;
+	Dart next() ;
+} ;
+
+/*******************************************************************************
+					FACE CENTERED TRAVERSALS
+*******************************************************************************/
+
+// Traverse the vertices incident to a given face
+template <typename MAP>
+class Traversor2FV : public Traversor<MAP>
+{
+private:
+	MAP& m ;
+	Dart start ;
+	Dart current ;
+
+public:
+	Traversor2FV(MAP& map, Dart dart) ;
+
+	Dart begin() ;
+	Dart end() ;
+	Dart next() ;
+} ;
+
+
+// Traverse the edges incident to a given face (equivalent to vertices)
+template <typename MAP>
+class Traversor2FE: public Traversor2FV<MAP>
+{
+public:
+	Traversor2FE(MAP& map, Dart dart):Traversor2FV<MAP>(map,dart){}
+} ;
+
+// Traverse the faces adjacent to a given face through sharing a common vertex
+template <typename MAP>
+class Traversor2FFaV : public Traversor<MAP>
+{
+private:
+	MAP& m ;
+	Dart start ;
+	Dart current ;
+
+	Dart stop ;
+
+public:
+	Traversor2FFaV(MAP& map, Dart dart) ;
+
+	Dart begin() ;
+	Dart end() ;
+	Dart next() ;
+} ;
+
+// Traverse the faces adjacent to a given face through sharing a common edge
+template <typename MAP>
+class Traversor2FFaE : public Traversor<MAP>
+{
+private:
+	MAP& m ;
+	Dart start ;
+	Dart current ;
+
+public:
+	Traversor2FFaE(MAP& map, Dart dart) ;
+
+	Dart begin() ;
+	Dart end() ;
+	Dart next() ;
+} ;
+
+} // namespace ClosedMap
+
+} // namespace CGoGN
+
+#include "Topology/generic/traversor2_closed.hpp"
+
+#endif
diff --git a/include/Topology/generic/traversor2_closed.hpp b/include/Topology/generic/traversor2_closed.hpp
new file mode 100644
index 0000000000000000000000000000000000000000..472c927991adf21aa1957faccdae083d2495b175
--- /dev/null
+++ b/include/Topology/generic/traversor2_closed.hpp
@@ -0,0 +1,438 @@
+/*******************************************************************************
+* CGoGN: Combinatorial and Geometric modeling with Generic N-dimensional Maps  *
+* version 0.1                                                                  *
+* Copyright (C) 2009-2012, IGG Team, LSIIT, University of Strasbourg           *
+*                                                                              *
+* This library is free software; you can redistribute it and/or modify it      *
+* under the terms of the GNU Lesser General Public License as published by the *
+* Free Software Foundation; either version 2.1 of the License, or (at your     *
+* option) any later version.                                                   *
+*                                                                              *
+* This library is distributed in the hope that it will be useful, but WITHOUT  *
+* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or        *
+* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License  *
+* for more details.                                                            *
+*                                                                              *
+* You should have received a copy of the GNU Lesser General Public License     *
+* along with this library; if not, write to the Free Software Foundation,      *
+* Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301 USA.           *
+*                                                                              *
+* Web site: http://cgogn.unistra.fr/                                           *
+* Contact information: cgogn@unistra.fr                                        *
+*                                                                              *
+*******************************************************************************/
+
+namespace CGoGN
+{
+
+namespace ClosedMap
+{
+
+/*******************************************************************************
+					VERTEX CENTERED TRAVERSALS
+*******************************************************************************/
+
+// Traversor2VE
+
+template <typename MAP>
+Traversor2VE<MAP>::Traversor2VE(MAP& map, Dart dart) : m(map), start(dart)
+{}
+
+template <typename MAP>
+Dart Traversor2VE<MAP>::begin()
+{
+	current = start ;
+	return current ;
+}
+
+template <typename MAP>
+Dart Traversor2VE<MAP>::end()
+{
+	return NIL ;
+}
+
+template <typename MAP>
+Dart Traversor2VE<MAP>::next()
+{
+	if(current != NIL)
+	{
+		current = m.phi2(m.phi_1(current)) ;
+		if(current == start)
+			current = NIL ;
+	}
+	return current ;
+}
+
+// Traversor2VF
+
+template <typename MAP>
+Traversor2VF<MAP>::Traversor2VF(MAP& map, Dart dart) : m(map), start(dart)
+{
+}
+
+template <typename MAP>
+Dart Traversor2VF<MAP>::begin()
+{
+	current = start ;
+	return current ;
+}
+
+template <typename MAP>
+Dart Traversor2VF<MAP>::end()
+{
+	return NIL ;
+}
+
+template <typename MAP>
+Dart Traversor2VF<MAP>::next()
+{
+	if(current != NIL)
+	{
+		current = m.phi2(m.phi_1(current)) ;
+		if(current == start)
+			current = NIL ;
+	}
+	return current ;
+}
+
+// Traversor2VVaE
+
+template <typename MAP>
+Traversor2VVaE<MAP>::Traversor2VVaE(MAP& map, Dart dart) : m(map)
+{
+	start = m.phi2(dart) ;
+}
+
+template <typename MAP>
+Dart Traversor2VVaE<MAP>::begin()
+{
+	current = start ;
+	return current ;
+}
+
+template <typename MAP>
+Dart Traversor2VVaE<MAP>::end()
+{
+	return NIL ;
+}
+
+template <typename MAP>
+Dart Traversor2VVaE<MAP>::next()
+{
+	if(current != NIL)
+	{
+		current = m.phi_1(m.phi2(current)) ;
+		if(current == start)
+			current = NIL ;
+	}
+	return current ;
+}
+
+// Traversor2VVaF
+
+template <typename MAP>
+Traversor2VVaF<MAP>::Traversor2VVaF(MAP& map, Dart dart) : m(map)
+{
+	if(m.isBoundaryMarked(dart))
+		dart = m.phi2(m.phi_1(dart)) ;
+	start = m.phi1(m.phi1(dart)) ;
+	if(start == dart)
+		start = m.phi1(dart) ;
+	stop = dart ;
+}
+
+template <typename MAP>
+Dart Traversor2VVaF<MAP>::begin()
+{
+	current = start ;
+	return current ;
+}
+
+template <typename MAP>
+Dart Traversor2VVaF<MAP>::end()
+{
+	return NIL ;
+}
+
+template <typename MAP>
+Dart Traversor2VVaF<MAP>::next()
+{
+	if(current != NIL)
+	{
+		current = m.phi1(current) ;
+		if(current == stop)
+		{
+			Dart d = m.phi2(m.phi_1(current)) ;
+			current = m.phi1(m.phi1(d)) ;
+			if(current == d)
+				current = m.phi1(d) ;
+			stop = d ;
+		}
+		if(current == start)
+			current = NIL ;
+	}
+	return current ;
+}
+
+/*******************************************************************************
+					EDGE CENTERED TRAVERSALS
+*******************************************************************************/
+
+// Traversor2EV
+
+template <typename MAP>
+Traversor2EV<MAP>::Traversor2EV(MAP& map, Dart dart) : m(map), start(dart)
+{}
+
+template <typename MAP>
+Dart Traversor2EV<MAP>::begin()
+{
+	current = start ;
+	return current ;
+}
+
+template <typename MAP>
+Dart Traversor2EV<MAP>::end()
+{
+	return NIL ;
+}
+
+template <typename MAP>
+Dart Traversor2EV<MAP>::next()
+{
+	if(current != NIL)
+	{
+		current = m.phi2(current) ;
+		if(current == start)
+			current = NIL ;
+	}
+	return current ;
+}
+
+// Traversor2EF
+
+template <typename MAP>
+Traversor2EF<MAP>::Traversor2EF(MAP& map, Dart dart) : m(map), start(dart)
+{
+}
+
+template <typename MAP>
+Dart Traversor2EF<MAP>::begin()
+{
+	current = start ;
+	return current ;
+}
+
+template <typename MAP>
+Dart Traversor2EF<MAP>::end()
+{
+	return NIL ;
+}
+
+template <typename MAP>
+Dart Traversor2EF<MAP>::next()
+{
+	if(current != NIL)
+	{
+		current = m.phi2(current) ;
+		if(current == start) // do not consider a boundary face
+			current = NIL ;
+	}
+	return current ;
+}
+
+// Traversor2EEaV
+
+template <typename MAP>
+Traversor2EEaV<MAP>::Traversor2EEaV(MAP& map, Dart dart) : m(map)
+{
+	start = m.phi2(m.phi_1(dart)) ;
+	stop1 = dart ;
+	stop2 = m.phi2(dart) ;
+}
+
+template <typename MAP>
+Dart Traversor2EEaV<MAP>::begin()
+{
+	current = start ;
+	return current ;
+}
+
+template <typename MAP>
+Dart Traversor2EEaV<MAP>::end()
+{
+	return NIL ;
+}
+
+template <typename MAP>
+Dart Traversor2EEaV<MAP>::next()
+{
+	if(current != NIL)
+	{
+		current = m.phi2(m.phi_1(current)) ;
+		if(current == stop1)
+			current = m.phi2(m.phi_1(stop2)) ;
+		else if(current == stop2)
+			current = NIL ;
+	}
+	return current ;
+}
+
+// Traversor2EEaF
+
+template <typename MAP>
+Traversor2EEaF<MAP>::Traversor2EEaF(MAP& map, Dart dart) : m(map)
+{
+	start = m.phi1(dart) ;
+	stop1 = dart ;
+	stop2 = m.phi2(dart) ;
+}
+
+template <typename MAP>
+Dart Traversor2EEaF<MAP>::begin()
+{
+	current = start ;
+	return current ;
+}
+
+template <typename MAP>
+Dart Traversor2EEaF<MAP>::end()
+{
+	return NIL ;
+}
+
+template <typename MAP>
+Dart Traversor2EEaF<MAP>::next()
+{
+	if(current != NIL)
+	{
+		current = m.phi1(current) ;
+		if(current == stop1)
+			current = m.phi1(stop2) ;
+		else if(current == stop2)
+			current = NIL ;
+	}
+	return current ;
+}
+
+/*******************************************************************************
+					FACE CENTERED TRAVERSALS
+*******************************************************************************/
+
+// Traversor2FV
+
+template <typename MAP>
+Traversor2FV<MAP>::Traversor2FV(MAP& map, Dart dart) : m(map), start(dart)
+{}
+
+template <typename MAP>
+Dart Traversor2FV<MAP>::begin()
+{
+	current = start ;
+	return current ;
+}
+
+template <typename MAP>
+Dart Traversor2FV<MAP>::end()
+{
+	return NIL ;
+}
+
+template <typename MAP>
+Dart Traversor2FV<MAP>::next()
+{
+	if(current != NIL)
+	{
+		current = m.phi1(current) ;
+		if(current == start)
+			current = NIL ;
+	}
+	return current ;
+}
+
+// Traversor2FFaV
+
+template <typename MAP>
+Traversor2FFaV<MAP>::Traversor2FFaV(MAP& map, Dart dart) : m(map)
+{
+	start = m.phi2(m.phi_1(m.phi2(m.phi_1(dart)))) ;
+	current = start ;
+	if(start == dart)
+	{
+		stop = m.phi2(m.phi_1(dart)) ;
+		start = next() ;
+	}
+	stop = dart ;
+}
+
+template <typename MAP>
+Dart Traversor2FFaV<MAP>::begin()
+{
+	current = start ;
+	return current ;
+}
+
+template <typename MAP>
+Dart Traversor2FFaV<MAP>::end()
+{
+	return NIL ;
+}
+
+template <typename MAP>
+Dart Traversor2FFaV<MAP>::next()
+{
+	if(current != NIL)
+	{
+		current = m.phi2(m.phi_1(current)) ;
+		if(current == stop)
+		{
+			Dart d = m.phi1(current) ;
+			current = m.phi2(m.phi_1(m.phi2(m.phi_1(d)))) ;
+			if(current == d)
+			{
+				stop = m.phi2(m.phi_1(d)) ;
+				return next() ;
+			}
+			stop = d ;
+		}
+		if(current == start)
+			current = NIL ;
+	}
+	return current ;
+}
+
+// Traversor2FFaE
+
+template <typename MAP>
+Traversor2FFaE<MAP>::Traversor2FFaE(MAP& map, Dart dart) : m(map)
+{
+	start = m.phi2(dart) ;
+}
+
+template <typename MAP>
+Dart Traversor2FFaE<MAP>::begin()
+{
+	current = start ;
+	return current ;
+}
+
+template <typename MAP>
+Dart Traversor2FFaE<MAP>::end()
+{
+	return NIL ;
+}
+
+template <typename MAP>
+Dart Traversor2FFaE<MAP>::next()
+{
+	if(current != NIL)
+	{
+		current = m.phi2(m.phi1(m.phi2(current))) ;
+		if(current == start)
+			current = NIL ;
+	}
+	return current ;
+}
+
+} // namespace ClosedMap
+} // namespace CGoGN