diff --git a/include/Algo/Import/importMRDAT.h b/include/Algo/Import/importMRDAT.h
index 7b64a0d3abd011a52d7a49002c4c6af8279c6b8d..ed72b880fd583b2924db73e97ae9461c82f3ee90 100644
--- a/include/Algo/Import/importMRDAT.h
+++ b/include/Algo/Import/importMRDAT.h
@@ -104,7 +104,7 @@ public:
 //				if(oldEmb == EMBNULL)
 //				{
 					//std::cout << "oldEmb == NULL"<< std::endl;
-					map.template setOrbitEmbedding<VERTEX>(dd, newEmb) ;
+					Algo::Topo::setOrbitEmbedding<VERTEX>(map,dd,newEmb);
 
 					//needed because the darts are duplicated at each level
 					//and the vertex orbits are initialized at the creation of each level with wrong embedding indices
@@ -114,7 +114,8 @@ public:
 					for(unsigned int i = map.getCurrentLevel() + 1; i <= map.getMaxLevel(); ++i)
 					{
 						map.setCurrentLevel(i) ;
-						map.template setOrbitEmbedding<VERTEX>(dd, newEmb) ;
+						Algo::Topo::setOrbitEmbedding<VERTEX>(map,dd,newEmb);
+
 					}
 					//map.popLevel() ;
 					map.setCurrentLevel(cur);
diff --git a/include/Algo/Import/importMRDAT.hpp b/include/Algo/Import/importMRDAT.hpp
index 46a6c6042d358a6097521c09e5c42222225a65c4..e9878a1cb8201431870dd179bb8fea95e55a99ea 100644
--- a/include/Algo/Import/importMRDAT.hpp
+++ b/include/Algo/Import/importMRDAT.hpp
@@ -44,9 +44,9 @@ inline void nextNonEmptyLine(std::ifstream& fp, std::string& line)
 template <typename PFP>
 bool importMRDAT(typename PFP::MAP& map, const std::string& filename, std::vector<std::string>& attrNames, QuadTree& qt)
 {
-	VertexAttribute<typename PFP::VEC3, typename PFP::MAP> position = map.template getAttribute<typename PFP::VEC3, VERTEX>("position") ;
+	VertexAttribute<typename PFP::VEC3, typename PFP::MAP> position = map.template getAttribute<typename PFP::VEC3, VERTEX, typename PFP::MAP>("position") ;
 	if (!position.isValid())
-		position = map.template addAttribute<typename PFP::VEC3, VERTEX>("position") ;
+		position = map.template addAttribute<typename PFP::VEC3, VERTEX, typename PFP::MAP>("position") ;
 
 	attrNames.push_back(position.name()) ;
 
@@ -197,7 +197,6 @@ bool importMRDAT(typename PFP::MAP& map, const std::string& filename, std::vecto
 	DartMarkerNoUnmark<typename PFP::MAP> m(map) ;
 
 	unsigned int vemb = EMBNULL;
-	auto fsetemb = [&] (Dart d) { map.template setDartEmbedding<VERTEX>(d, vemb); };
 
 	unsigned nbf = qt.roots.size() ;
 
@@ -211,7 +210,7 @@ bool importMRDAT(typename PFP::MAP& map, const std::string& filename, std::vecto
 			unsigned int idx = qt.roots[i]->indices[j] ;
 			vemb = qt.verticesID[idx] ;
 
-			map.template foreach_dart_of_orbit<PFP::MAP::VERTEX_OF_PARENT>(d, fsetemb) ;
+			map.template foreach_dart_of_orbit<PFP::MAP::VERTEX_OF_PARENT>(d, [&] (Dart dd) { map.template initDartEmbedding<VERTEX>(dd, vemb); });
 
 			m.mark(d) ;								// mark on the fly to unmark on second loop
 			vecDartsPerVertex[vemb].push_back(d) ;	// store incident darts for fast adjacency reconstruction
diff --git a/include/Algo/Modelisation/subdivision.hpp b/include/Algo/Modelisation/subdivision.hpp
index f99ada42d9e27a3b04e2dda38cd322a07f54c84d..80b7134a90ed02c289f83c6f0e7bbe6124de6b62 100644
--- a/include/Algo/Modelisation/subdivision.hpp
+++ b/include/Algo/Modelisation/subdivision.hpp
@@ -582,8 +582,8 @@ void DooSabin(typename PFP::MAP& map, EMBV& position)
 					// take care of edge embedding
 					if(map.template isOrbitEmbedded<EDGE>())
 					{
-						map.template setOrbitEmbedding<EDGE>(nf, map.template getEmbedding<EDGE>(e));
-						map.template setOrbitEmbedding<EDGE>(map.template phi<11>(nf), map.template getEmbedding<EDGE>(e2));
+						Algo::Topo::setOrbitEmbedding<VERTEX>(map, nf, map.template getEmbedding<EDGE>(e));
+						Algo::Topo::setOrbitEmbedding<VERTEX>(map, map.template phi<11>(nf), map.template getEmbedding<EDGE>(e2));
 					}
 
 					dm.markOrbit<FACE>(nf);
@@ -608,7 +608,8 @@ void DooSabin(typename PFP::MAP& map, EMBV& position)
 				Dart d = df;
 				do
 				{
-					map.template setOrbitEmbedding<EDGE>(d,map.template getEmbedding<EDGE>(map.phi2(d)));
+//					map.template setOrbitEmbedding<EDGE>(d,map.template getEmbedding<EDGE>(map.phi2(d)));
+					Algo::Topo::setOrbitEmbedding<VERTEX>(map, d, map.template getEmbedding<EDGE>(map.phi2(d)));
 					d = map.phi1(d);
 				} while (d != df);
 			}
@@ -646,7 +647,8 @@ void DooSabin(typename PFP::MAP& map, EMBV& position)
 					P+= c2*buffer[j];
 				}
 			}
-			map.template setOrbitEmbeddingOnNewCell<VERTEX>(e);
+//			map.template setOrbitEmbeddingOnNewCell<VERTEX>(e);
+			Algo::Topo::setOrbitEmbeddingOnNewCell<VERTEX>(map,e);
 			position[e] = P;
 			e = map.phi1(e);
 		}
@@ -730,9 +732,9 @@ void computeDual(typename PFP::MAP& map, VertexAttribute<typename PFP::VEC3, typ
 	typedef typename PFP::VEC3 VEC3 ;
 
 	// Face Attribute -> after dual new Vertex Attribute
-	FaceAttribute<VEC3, MAP> positionF  = map.template getAttribute<VEC3, FACE>("position") ;
+	FaceAttribute<VEC3, MAP> positionF  = map.template getAttribute<VEC3, FACE,MAP>("position") ;
 	if(!positionF.isValid())
-		positionF = map.template addAttribute<VEC3, FACE>("position") ;
+		positionF = map.template addAttribute<VEC3, FACE,MAP>("position") ;
 
 	// Compute Centroid for the faces
 	Algo::Surface::Geometry::computeCentroidFaces<PFP>(map, position, positionF) ;
@@ -752,9 +754,9 @@ void computeBoundaryConstraintDual(typename PFP::MAP& map, VertexAttribute<typen
 	typedef typename PFP::REAL REAL ;
 
 	// Face Attribute -> after dual new Vertex Attribute
-	FaceAttribute<VEC3, MAP> positionF  = map.template getAttribute<VEC3, FACE>("position") ;
+	FaceAttribute<VEC3, MAP> positionF  = map.template getAttribute<VEC3, FACE,MAP>("position") ;
 	if(!positionF.isValid())
-		positionF = map.template addAttribute<VEC3, FACE>("position") ;
+		positionF = map.template addAttribute<VEC3, FACE,MAP>("position") ;
 
 	//Triangule boundary faces & compute for each new face the centroid
 	std::vector<Dart> boundsDart;
@@ -823,9 +825,9 @@ void computeBoundaryConstraintKeepingOldVerticesDual(typename PFP::MAP& map, Ver
 	typedef typename PFP::REAL REAL ;
 
 	// Face Attribute -> after dual new Vertex Attribute
-	FaceAttribute<VEC3, MAP> positionF  = map.template getAttribute<VEC3, FACE>("position") ;
+	FaceAttribute<VEC3, MAP> positionF  = map.template getAttribute<VEC3, FACE,MAP>("position") ;
 	if(!positionF.isValid())
-		positionF = map.template addAttribute<VEC3, FACE>("position") ;
+		positionF = map.template addAttribute<VEC3, FACE,MAP>("position") ;
 
 	//Triangule boundary faces & compute for each new face the centroid
 	std::vector<Dart> boundsDart;
diff --git a/include/Algo/Multiresolution/Map2MR/map2MR_DualRegular.hpp b/include/Algo/Multiresolution/Map2MR/map2MR_DualRegular.hpp
index 7516087f7f53ab7958b20822caaeafe6831932ee..3faf811a58357c1f85ea2b1f9959959651589dba 100644
--- a/include/Algo/Multiresolution/Map2MR/map2MR_DualRegular.hpp
+++ b/include/Algo/Multiresolution/Map2MR/map2MR_DualRegular.hpp
@@ -22,6 +22,8 @@
 *                                                                              *
 *******************************************************************************/
 
+#include "Algo/Topo/embedding.h"
+
 namespace CGoGN
 {
 
@@ -87,8 +89,10 @@ void Map2MR<PFP>::addNewLevel(bool embedNewVertices)
 		// take care of edge embedding
 		if(m_map.template isOrbitEmbedded<EDGE>())
 		{
-			m_map.template setOrbitEmbedding<EDGE>(nf, m_map.template getEmbedding<EDGE>(d));
-			m_map.template setOrbitEmbedding<EDGE>(m_map.phi1(m_map.phi1(nf)), m_map.template getEmbedding<EDGE>(d2));
+//			m_map.template setOrbitEmbedding<EDGE>(nf, m_map.template getEmbedding<EDGE>(d));
+//			m_map.template setOrbitEmbedding<EDGE>(m_map.phi1(m_map.phi1(nf)), m_map.template getEmbedding<EDGE>(d2));
+			Algo::Topo::setOrbitEmbedding<EDGE>(m_map, nf, m_map.template getEmbedding<EDGE>(d));
+			Algo::Topo::setOrbitEmbedding<EDGE>(m_map, m_map.phi1(m_map.phi1(nf)), m_map.template getEmbedding<EDGE>(d2));
 		}
 
 		m_map.decCurrentLevel();
@@ -109,13 +113,15 @@ void Map2MR<PFP>::addNewLevel(bool embedNewVertices)
 		{
 			if(m_map.template isOrbitEmbedded<EDGE>())
 			{
-				m_map.template setOrbitEmbedding<EDGE>(temp, m_map.template getEmbedding<EDGE>(	m_map.phi2(temp)));
+//				m_map.template setOrbitEmbedding<EDGE>(temp, m_map.template getEmbedding<EDGE>(	m_map.phi2(temp)));
+				Algo::Topo::setOrbitEmbedding<EDGE>(m_map, temp, m_map.template getEmbedding<EDGE>(	m_map.phi2(temp)));
 			}
 
 			if(!shareVertexEmbeddings)
 			{
 				//if(m_map.template getEmbedding<VERTEX>(d) == EMBNULL)
-				m_map.template setOrbitEmbeddingOnNewCell<VERTEX>(temp) ;
+				Algo::Topo::setOrbitEmbeddingOnNewCell<VERTEX>(m_map, temp);
+
 				//m_map.template setOrbitEmbeddingOnNewCell<VERTEX>(d2) ;
 			}
 
diff --git a/include/Topology/generic/mapImpl/mapMulti.h b/include/Topology/generic/mapImpl/mapMulti.h
index 30f525b162cfb9b56038e9fb2b71aca0b762fe5e..de3e9c30078b91d3476fc3fe001e5f411c6add6d 100644
--- a/include/Topology/generic/mapImpl/mapMulti.h
+++ b/include/Topology/generic/mapImpl/mapMulti.h
@@ -30,6 +30,8 @@
 namespace CGoGN
 {
 
+class MapMono;
+
 class MapMulti : public GenericMap
 {
 	template<typename MAP> friend class DartMarkerTmpl ;
@@ -301,6 +303,8 @@ public:
 
 	bool copyFrom(const GenericMap& map);
 
+	bool copyFromOtherType(const MapMono& map);
+
 	void restore_topo_shortcuts();
 } ;
 
diff --git a/include/Topology/map/map2.hpp b/include/Topology/map/map2.hpp
index 9ea582d3dc0767115eb92de4c719667401ad4eed..fb04d8acb7a80995bcf2acc056c53a4224022eb8 100644
--- a/include/Topology/map/map2.hpp
+++ b/include/Topology/map/map2.hpp
@@ -243,7 +243,7 @@ template <typename MAP_IMPL>
 void Map2<MAP_IMPL>::createHole(Dart d)
 {
 	assert(!isBoundaryEdge(d)) ;
-	this->template boundaryMarkOrbit<2,FACE>(d) ;
+	Algo::Topo::boundaryMarkOrbit<2,FACE>(*this, d) ;
 }
 
 /*! @name Topological Operators
diff --git a/src/Topology/generic/mapMono.cpp b/src/Topology/generic/mapMono.cpp
index 0550cf5a07efb2ec68ac7c2f61753eb34560633b..5eb36920d90ee21164e06f5c3704a9c11154b041 100644
--- a/src/Topology/generic/mapMono.cpp
+++ b/src/Topology/generic/mapMono.cpp
@@ -193,6 +193,9 @@ void MapMono::restore_topo_shortcuts()
 
 void MapMono::compactTopo()
 {
+	if (fragmentation(DART)==1.0)
+		return;
+
 	std::vector<unsigned int> oldnew;
 	m_attribs[DART].compact(oldnew);
 
diff --git a/src/Topology/generic/mapMulti.cpp b/src/Topology/generic/mapMulti.cpp
index d36251eb545da673868eb6ee930fb5ba74ed03d9..f79ba47199146fa8fa6de085320b383f4afc4fcf 100644
--- a/src/Topology/generic/mapMulti.cpp
+++ b/src/Topology/generic/mapMulti.cpp
@@ -23,6 +23,7 @@
 *******************************************************************************/
 
 #include "Topology/generic/mapImpl/mapMulti.h"
+#include "Topology/generic/mapImpl/mapMono.h"
 
 namespace CGoGN
 {
@@ -313,31 +314,77 @@ bool MapMulti::loadMapBin(const std::string& filename)
 	return true;
 }
 
+
+bool MapMulti::copyFromOtherType(const MapMono& mapMR)
+{
+//	map.compactIfNeeded(1.0);
+
+	// clear the map but do not insert boundary markers dart attribute
+	GenericMap::init(false);
+
+	// init MR data
+	initMR();
+
+	// copy attrib containers from MapMono
+	for (unsigned int i = 0; i < NB_ORBITS; ++i)
+		m_attribs[i].copyFrom(mapMR.getAttributeContainer(i));
+
+	// restore shortcuts
+	GenericMap::restore_shortcuts();
+	restore_topo_shortcuts();
+
+	AttributeContainer darts = m_attribs[DART];
+	for(unsigned int xd = darts.begin(); xd != darts.end(); darts.next(xd))
+	{
+		unsigned int mrdi = m_mrattribs.insertLine() ;
+		assert(mrdi==xd);
+		(*m_mrDarts[0])[mrdi] = xd ;
+	}
+
+	return true;
+}
+
+
 bool MapMulti::copyFrom(const GenericMap& map)
 {
-	const MapMulti& mapMR = reinterpret_cast<const MapMulti&>(map);
+	const MapMulti* mapMR = dynamic_cast<const MapMulti*>(&map);
+
 
-	if (mapTypeName() != map.mapTypeName())
+	if (mapMR == NULL)
 	{
-		CGoGNerr << "try to copy from incompatible type map" << CGoGNendl;
-		return false;
+		const MapMono* mapmono = dynamic_cast<const MapMono*>(mapMR);
+		if (mapmono == NULL)
+		{
+			CGoGNerr << "try to copy from incompatible type map" << CGoGNendl;
+			return false;
+		}
+		copyFromOtherType(*mapmono);
 	}
 
 	// clear the map but do not insert boundary markers dart attribute
 	GenericMap::init(false);
 
+	// init MR data without adding the attributes
+	m_mrattribs.clear(true) ;
+	m_mrattribs.setRegistry(m_attributes_registry_map) ;
+	m_mrDarts.clear() ;
+	m_mrDarts.reserve(16) ;
+	m_mrNbDarts.clear();
+	m_mrNbDarts.reserve(16);
+	m_mrLevelStack.clear() ;
+	m_mrLevelStack.reserve(16) ;
 
-	// load attrib container
+	// copy attrib containers
 	for (unsigned int i = 0; i < NB_ORBITS; ++i)
-		m_attribs[i].copyFrom(mapMR.m_attribs[i]);
+		m_attribs[i].copyFrom(mapMR->m_attribs[i]);
 
-	m_mrattribs.copyFrom(mapMR.m_mrattribs);
-	m_mrCurrentLevel = mapMR.m_mrCurrentLevel;
+	m_mrattribs.copyFrom(mapMR->m_mrattribs);
 
-	unsigned int nb = mapMR.m_mrNbDarts.size();
-	m_mrNbDarts.resize(nb);
-	for (unsigned int i = 0; i < nb; ++i)
-		m_mrNbDarts[i] = mapMR.m_mrNbDarts[i];
+	m_mrCurrentLevel = mapMR->m_mrCurrentLevel;
+
+	m_mrNbDarts.assign(mapMR->m_mrNbDarts.begin(), mapMR->m_mrNbDarts.end());
+
+	m_mrLevelStack.assign(mapMR->m_mrLevelStack.begin(), mapMR->m_mrLevelStack.end());  // ??
 
 	// restore shortcuts
 	GenericMap::restore_shortcuts();