diff --git a/include/Topology/generic/genericmap.h b/include/Topology/generic/genericmap.h
index ec94d52bd1f61d9d97c5a05f5787c8c4e27f914b..c3f0cf4741190ee51a04da13a0cd4a2e5991553a 100644
--- a/include/Topology/generic/genericmap.h
+++ b/include/Topology/generic/genericmap.h
@@ -168,7 +168,7 @@ public:
 
 	virtual unsigned int dimension() const = 0 ;
 
-	static const unsigned int DIMENSION = 0 ;
+//	static const unsigned int DIMENSION = 0 ;
 	/**
 	 * Clear the map
 	 * @param removeAttrib
@@ -741,6 +741,7 @@ public:
 
 	bool isBoundaryMarked2(Dart d) const ;
 	bool isBoundaryMarked3(Dart d) const ;
+	bool isBoundaryMarkedCurrent(Dart d) const ;
 
 protected:
 	/**
diff --git a/include/Topology/generic/genericmap.hpp b/include/Topology/generic/genericmap.hpp
index 7410eecd9adccd0719e899635bf7d7a0e65684db..6976bfa60eef5755167faa5abeb157178bd35c86 100644
--- a/include/Topology/generic/genericmap.hpp
+++ b/include/Topology/generic/genericmap.hpp
@@ -705,6 +705,12 @@ inline bool GenericMap::isBoundaryMarked(Dart d) const
 }
 
 
+inline bool GenericMap::isBoundaryMarkedCurrent(Dart d) const
+{
+	return m_markTables[DART][0]->operator[](dartIndex(d)).testMark(m_boundaryMarkers[this->dimension()-2]);
+}
+
+
 inline void GenericMap::boundaryMark2(Dart d)
 {
 	boundaryMark<2>(d);
diff --git a/include/Topology/generic/traversorCell.h b/include/Topology/generic/traversorCell.h
index bfcd88c73a897db8e4feef11ad220a9cb316b3c5..76f6fbf8ffb719dda0957e09dfb8bebd06272442 100644
--- a/include/Topology/generic/traversorCell.h
+++ b/include/Topology/generic/traversorCell.h
@@ -64,6 +64,39 @@ public:
 	void skip(Dart d);
 } ;
 
+
+template <unsigned int ORBIT>
+class TraversorCell<GenericMap,ORBIT> : public Traversor<GenericMap>
+{
+private:
+	GenericMap& m ;
+
+	AttributeContainer* cont ;
+	unsigned int qCurrent ;
+
+	DartMarker* dmark ;
+	CellMarker<ORBIT>* cmark ;
+	AttributeMultiVector<Dart>* quickTraversal ;
+
+	Dart current ;
+	bool firstTraversal ;
+	const FunctorSelect& m_good ;
+
+public:
+	TraversorCell(GenericMap& map, const FunctorSelect& good = allDarts, bool forceDartMarker = false, unsigned int thread = 0) ;
+
+	~TraversorCell() ;
+
+	Dart begin() ;
+
+	Dart end() ;
+
+	Dart next() ;
+
+	void skip(Dart d);
+} ;
+
+
 template <typename MAP>
 class TraversorV : public TraversorCell<MAP, VERTEX>
 {
diff --git a/include/Topology/generic/traversorCell.hpp b/include/Topology/generic/traversorCell.hpp
index ffebee9a7fb1d8c779166ccc06368652098d4214..bc0f3b70b7f47eff25099112ab83ad68c589ee2a 100644
--- a/include/Topology/generic/traversorCell.hpp
+++ b/include/Topology/generic/traversorCell.hpp
@@ -155,4 +155,140 @@ void TraversorCell<MAP, ORBIT>::skip(Dart d)
 		cmark->mark(d) ;
 }
 
+
+
+//special version (partial specialization) for Genric Map
+template <unsigned int ORBIT>
+TraversorCell<GenericMap, ORBIT>::TraversorCell(GenericMap& map, const FunctorSelect& good, bool forceDartMarker, unsigned int thread) :
+	m(map), dmark(NULL), cmark(NULL), quickTraversal(NULL), current(NIL), firstTraversal(true), m_good(good)
+{
+	if(forceDartMarker)
+		dmark = new DartMarker(map, thread) ;
+	else
+	{
+		quickTraversal = map.template getQuickTraversal<ORBIT>() ;
+		if(quickTraversal != NULL)
+		{
+			cont = &(m.template getAttributeContainer<ORBIT>()) ;
+		}
+		else
+		{
+			if(map.template isOrbitEmbedded<ORBIT>())
+				cmark = new CellMarker<ORBIT>(map, thread) ;
+			else
+				dmark = new DartMarker(map, thread) ;
+		}
+	}
+}
+
+template <unsigned int ORBIT>
+TraversorCell<GenericMap, ORBIT>::~TraversorCell()
+{
+	if(dmark)
+		delete dmark ;
+	else if(cmark)
+		delete cmark ;
+}
+
+template <unsigned int ORBIT>
+Dart TraversorCell<GenericMap, ORBIT>::begin()
+{
+	if(quickTraversal != NULL)
+	{
+		qCurrent = cont->begin() ;
+		current = (*quickTraversal)[qCurrent] ;
+	}
+	else
+	{
+		if(!firstTraversal)
+		{
+			if(dmark)
+				dmark->unmarkAll() ;
+			else
+				cmark->unmarkAll() ;
+		}
+
+		current = m.begin() ;
+		while(current != m.end() && (m.isBoundaryMarkedCurrent(current) || !m_good(current)))
+			m.next(current) ;
+
+		if(current == m.end())
+			current = NIL ;
+		else
+		{
+			if(dmark)
+				dmark->markOrbit<ORBIT>(current) ;
+			else
+				cmark->mark(current) ;
+		}
+
+		firstTraversal = false ;
+	}
+
+	return current ;
+}
+
+template <unsigned int ORBIT>
+Dart TraversorCell<GenericMap, ORBIT>::end()
+{
+	return NIL ;
+}
+
+template <unsigned int ORBIT>
+Dart TraversorCell<GenericMap, ORBIT>::next()
+{
+	if(current != NIL)
+	{
+		if(quickTraversal != NULL)
+		{
+			cont->next(qCurrent) ;
+			current = (*quickTraversal)[qCurrent] ;
+		}
+		else
+		{
+			if(dmark)
+			{
+				bool ismarked = dmark->isMarked(current) ;
+				while(current != NIL && (ismarked || m.isBoundaryMarkedCurrent(current) || !m_good(current)))
+				{
+					m.next(current) ;
+					if(current == m.end())
+						current = NIL ;
+					else
+						ismarked = dmark->isMarked(current) ;
+				}
+				if(current != NIL)
+					dmark->markOrbit<ORBIT>(current) ;
+			}
+			else
+			{
+				bool ismarked = cmark->isMarked(current) ;
+				while(current != NIL && (ismarked || m.isBoundaryMarkedCurrent(current) || !m_good(current)))
+				{
+					m.next(current) ;
+					if(current == m.end())
+						current = NIL ;
+					else
+						ismarked = cmark->isMarked(current) ;
+				}
+				if(current != NIL)
+					cmark->mark(current) ;
+			}
+		}
+	}
+	return current ;
+}
+
+template <unsigned int ORBIT>
+void TraversorCell<GenericMap, ORBIT>::skip(Dart d)
+{
+	if(dmark)
+		dmark->markOrbit<ORBIT>(d) ;
+	else
+		cmark->mark(d) ;
+}
+
+
+
+
 } // namespace CGoGN