diff --git a/include/Algo/Multiresolution/Map3MR/Filters/bertramBoundary.h b/include/Algo/Multiresolution/Map3MR/Filters/bertramBoundary.h
new file mode 100644
index 0000000000000000000000000000000000000000..1683dc008b1cced95f57f50fe8ea4c67fdadcbc6
--- /dev/null
+++ b/include/Algo/Multiresolution/Map3MR/Filters/bertramBoundary.h
@@ -0,0 +1,782 @@
+/*******************************************************************************
+* 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 __3MR_BERTRAM_BOUNDARY_FILTER__
+#define __3MR_BERTRAM_BOUNDARY_FILTER__
+
+#include <cmath>
+#include "Algo/Geometry/centroid.h"
+#include "Algo/Modelisation/tetrahedralization.h"
+#include "Algo/Multiresolution/filter.h"
+#include "Topology/generic/traversor2_closed.h"
+
+namespace CGoGN
+{
+
+namespace Algo
+{
+
+namespace Volume
+{
+
+namespace MR
+{
+
+namespace Primal
+{
+
+namespace Filters
+{
+
+/*******************************************************************************
+ *							Without features preserving
+ *******************************************************************************/
+
+//
+// Analysis
+//
+
+//w-lift(a)
+template <typename PFP>
+class Ber02OddAnalysisFilter : public Algo::MR::Filter
+{
+protected:
+	typename PFP::MAP& m_map ;
+	VertexAttribute<typename PFP::VEC3>& m_position ;
+	typename PFP::VEC3::DATA_TYPE m_a;
+
+public:
+	Ber02OddAnalysisFilter(typename PFP::MAP& m, VertexAttribute<typename PFP::VEC3>& p, typename PFP::VEC3::DATA_TYPE a) : m_map(m), m_position(p), m_a(a)
+	{}
+
+	void operator() ()
+	{
+		TraversorE<typename PFP::MAP> travE(m_map) ;
+		for (Dart d = travE.begin(); d != travE.end(); d = travE.next())
+		{
+			typename PFP::VEC3 ve = (m_position[d] + m_position[m_map.phi1(d)]) * typename PFP::REAL(0.5);
+			ve *= 2.0 * m_a;
+
+			m_map.incCurrentLevel() ;
+			Dart midV = m_map.phi1(d) ;
+			m_position[midV] -= ve;
+			m_map.decCurrentLevel() ;
+		}
+
+		TraversorF<typename PFP::MAP> travF(m_map) ;
+		for (Dart d = travF.begin(); d != travF.end(); d = travF.next())
+		{
+			typename PFP::VEC3 vf(0.0);
+			typename PFP::VEC3 ef(0.0);
+
+			unsigned int count = 0;
+			Traversor3FE<typename PFP::MAP> travFE(m_map, d);
+			for (Dart dit = travFE.begin(); dit != travFE.end(); dit = travFE.next())
+			{
+				vf += m_position[dit];
+				m_map.incCurrentLevel();
+				ef += m_position[m_map.phi1(dit)];
+				m_map.decCurrentLevel();
+				++count;
+			}
+			ef /= count;
+			ef *= 4.0 * m_a;
+
+			vf /= count;
+			vf *= 4.0 * m_a * m_a;
+
+			m_map.incCurrentLevel() ;
+			Dart midF = m_map.phi1(m_map.phi1(d));
+			m_position[midF] -= vf + ef ;
+			m_map.decCurrentLevel() ;
+		}
+
+		TraversorW<typename PFP::MAP> travW(m_map) ;
+		for (Dart d = travW.begin(); d != travW.end(); d = travW.next())
+		{
+			typename PFP::VEC3 vc = Algo::Surface::Geometry::volumeCentroid<PFP>(m_map, d, m_position);
+			vc *= 8 * m_a * m_a * m_a;
+
+			unsigned int count = 0;
+			typename PFP::VEC3 ec(0.0);
+			Traversor3WE<typename PFP::MAP> travWE(m_map, d);
+			for (Dart dit = travWE.begin(); dit != travWE.end(); dit = travWE.next())
+			{
+				m_map.incCurrentLevel();
+				ec += m_position[m_map.phi1(dit)];
+				m_map.decCurrentLevel();
+				++count;
+			}
+			ec /= count;
+			ec *= 12 * m_a * m_a;
+
+			count = 0;
+			typename PFP::VEC3 fc(0.0);
+			Traversor3WF<typename PFP::MAP> travWF(m_map, d);
+			for (Dart dit = travWF.begin(); dit != travWF.end(); dit = travWF.next())
+			{
+				m_map.incCurrentLevel();
+				fc += m_position[m_map.phi1(m_map.phi1(dit))];
+				m_map.decCurrentLevel();
+				++count;
+			}
+			fc /= count;
+			fc *= 6 * m_a;
+
+			m_map.incCurrentLevel() ;
+			Dart midV = m_map.phi_1(m_map.phi2(m_map.phi1(d)));
+			m_position[midV] -= vc + ec + fc;
+			m_map.decCurrentLevel() ;
+		}
+	}
+} ;
+
+// s-lift(a)
+template <typename PFP>
+class Ber02EvenAnalysisFilter : public Algo::MR::Filter
+{
+protected:
+	typename PFP::MAP& m_map ;
+	VertexAttribute<typename PFP::VEC3>& m_position ;
+	typename PFP::VEC3::DATA_TYPE m_a;
+
+public:
+	Ber02EvenAnalysisFilter(typename PFP::MAP& m, VertexAttribute<typename PFP::VEC3>& p, typename PFP::VEC3::DATA_TYPE a) : m_map(m), m_position(p), m_a(a)
+	{}
+
+	void operator() ()
+	{
+		TraversorF<typename PFP::MAP> travF(m_map) ;
+		for (Dart d = travF.begin(); d != travF.end(); d = travF.next())
+		{
+			if(!m_map.isBoundaryFace(d))
+			{
+				unsigned int count = 0;
+
+				typename PFP::VEC3 cf(0.0);
+				Traversor3FW<typename PFP::MAP> travFW(m_map, d);
+				for(Dart dit = travFW.begin() ; dit != travFW.end() ; dit = travFW.next())
+				{
+					m_map.incCurrentLevel();
+					Dart midV = m_map.phi_1(m_map.phi2(m_map.phi1(dit)));
+					cf += m_position[midV];
+					m_map.decCurrentLevel();
+					++count;
+				}
+				cf /= count;
+				cf *= 2 * m_a;
+
+				m_map.incCurrentLevel() ;
+				Dart midF = m_map.phi1(m_map.phi1(d));
+				m_position[midF] -= cf;
+				m_map.decCurrentLevel() ;
+			}
+		}
+
+		TraversorE<typename PFP::MAP> travE(m_map);
+		for(Dart d = travE.begin() ; d != travE.end() ; d = travE.next())
+		{
+			if(m_map.isBoundaryEdge(d))
+			{
+				Dart db = m_map.findBoundaryFaceOfEdge(d);
+				typename PFP::VEC3 fe(0.0);
+
+//				unsigned int count = 2;
+//				m_map.incCurrentLevel() ;
+//				Dart midV = m_map.phi1(m_map.phi1(db));
+//				fe += m_position[midV];
+//				midV = m_map.phi_1(m_map.phi2(db));
+//				fe += m_position[midV];
+//				m_map.decCurrentLevel() ;
+
+				//TODO Replace do--while with a Traversor2 on Boundary
+				unsigned int count = 0;
+				Traversor2EF<typename PFP::MAP> travEF(m_map, db);
+				for(Dart dit = travEF.begin() ; dit != travEF.end() ; dit = travEF.next())
+				{
+					m_map.incCurrentLevel() ;
+					Dart midV = m_map.phi1(m_map.phi1(dit));
+					fe += m_position[midV];
+					m_map.decCurrentLevel() ;
+					++count;
+				}
+
+				fe /= count;
+				fe *= 2 * m_a;
+
+				m_map.incCurrentLevel() ;
+				Dart midE = m_map.phi1(db);
+				m_position[midE] -= fe;
+				m_map.decCurrentLevel() ;
+			}
+			else
+			{
+				unsigned int count = 0;
+
+				typename PFP::VEC3 ce(0.0);
+				Traversor3EW<typename PFP::MAP> travEW(m_map, d);
+				for(Dart dit = travEW.begin() ; dit != travEW.end() ; dit = travEW.next())
+				{
+					m_map.incCurrentLevel() ;
+					Dart midV = m_map.phi_1(m_map.phi2(m_map.phi1(dit)));
+					ce += m_position[midV];
+					m_map.decCurrentLevel() ;
+					++count;
+				}
+				ce /= count;
+				ce *= 4 * m_a * m_a;
+
+				typename PFP::VEC3 fe(0.0);
+				count = 0;
+				Traversor3EF<typename PFP::MAP> travEF(m_map, d);
+				for(Dart dit = travEF.begin() ; dit != travEF.end() ; dit = travEF.next())
+				{
+					m_map.incCurrentLevel() ;
+					Dart midV = m_map.phi1(m_map.phi1(dit));
+					fe += m_position[midV];
+					m_map.decCurrentLevel() ;
+					++count;
+				}
+				fe /= count;
+				fe *= 4 * m_a;
+
+				m_map.incCurrentLevel() ;
+				Dart midE = m_map.phi1(d);
+				m_position[midE] -= ce + fe;
+				m_map.decCurrentLevel() ;
+			}
+		}
+
+		TraversorV<typename PFP::MAP> travV(m_map);
+		for(Dart d = travV.begin() ; d != travV.end() ; d = travV.next())
+		{
+			if(m_map.isBoundaryVertex(d))
+			{
+				Dart db = m_map.findBoundaryFaceOfVertex(d);
+
+				unsigned int count = 0;
+				typename PFP::VEC3 ev(0.0);
+				typename PFP::VEC3 fv(0.0);
+
+//				Dart dit = db;
+//				do
+//				{
+//					m_map.incCurrentLevel() ;
+//
+//					Dart midEdgeV = m_map.phi1(dit);
+//					ev += m_position[midEdgeV];
+//					fv += m_position[m_map.phi1(midEdgeV)];
+//
+//					m_map.decCurrentLevel() ;
+//					++count;
+//
+//					dit = m_map.phi2(m_map.phi_1(dit));
+//
+//				}while(dit != db);
+
+				Traversor2VF<typename PFP::MAP> travVF(m_map,db);
+				for(Dart dit = travVF.begin(); dit != travVF.end() ; dit = travVF.next())
+				{
+					m_map.incCurrentLevel() ;
+
+					Dart midEdgeV = m_map.phi1(dit);
+					ev += m_position[midEdgeV];
+					fv += m_position[m_map.phi1(midEdgeV)];
+
+					m_map.decCurrentLevel() ;
+					++count;
+				}
+
+				fv /= count;
+				fv *= 4 * m_a * m_a;
+
+				ev /= count;
+				ev *= 4 * m_a;
+
+				m_position[d] -= fv + ev;
+
+			}
+			else
+			{
+				unsigned int count = 0;
+
+				typename PFP::VEC3 cv(0.0);
+				Traversor3VW<typename PFP::MAP> travVW(m_map,d);
+				for(Dart dit = travVW.begin(); dit != travVW.end() ; dit = travVW.next())
+				{
+					m_map.incCurrentLevel() ;
+					Dart midV = m_map.phi_1(m_map.phi2(m_map.phi1(dit)));
+					cv += m_position[midV];
+					m_map.decCurrentLevel() ;
+					++count;
+				}
+				cv /= count;
+				cv *= 8 * m_a * m_a * m_a;
+
+				typename PFP::VEC3 fv(0.0);
+				count = 0;
+				Traversor3VF<typename PFP::MAP> travVF(m_map,d);
+				for(Dart dit = travVF.begin(); dit != travVF.end() ; dit = travVF.next())
+				{
+					m_map.incCurrentLevel() ;
+					Dart midV = m_map.phi1(m_map.phi1(dit));
+					fv += m_position[midV];
+					m_map.decCurrentLevel() ;
+					++count;
+				}
+				fv /= count;
+				fv *= 12 * m_a * m_a;
+
+				typename PFP::VEC3 ev(0.0);
+				count = 0;
+				Traversor3VE<typename PFP::MAP> travVE(m_map,d);
+				for(Dart dit = travVE.begin(); dit != travVE.end() ; dit = travVE.next())
+				{
+					m_map.incCurrentLevel() ;
+					Dart midV = m_map.phi1(dit);
+					ev += m_position[midV];
+					m_map.decCurrentLevel() ;
+					++count;
+				}
+				ev /= count;
+				ev *= 6 * m_a;
+
+				m_position[d] -= cv + fv + ev;
+			}
+		}
+	}
+} ;
+
+// s-scale(a)
+template <typename PFP>
+class Ber02ScaleAnalysisFilter : public Algo::MR::Filter
+{
+protected:
+	typename PFP::MAP& m_map ;
+	VertexAttribute<typename PFP::VEC3>& m_position ;
+	typename PFP::VEC3::DATA_TYPE m_a;
+
+public:
+	Ber02ScaleAnalysisFilter(typename PFP::MAP& m, VertexAttribute<typename PFP::VEC3>& p, typename PFP::VEC3::DATA_TYPE a) : m_map(m), m_position(p), m_a(a)
+	{}
+
+	void operator() ()
+	{
+		TraversorF<typename PFP::MAP> travF(m_map) ;
+		for (Dart d = travF.begin(); d != travF.end(); d = travF.next())
+		{
+				m_map.incCurrentLevel() ;
+				Dart midF = m_map.phi1(m_map.phi1(d));
+				if(!m_map.isBoundaryVertex(midF))
+					m_position[midF] /= m_a ;
+				m_map.decCurrentLevel() ;
+
+		}
+
+		TraversorE<typename PFP::MAP> travE(m_map) ;
+		for (Dart d = travE.begin(); d != travE.end(); d = travE.next())
+		{
+
+			m_map.incCurrentLevel() ;
+			Dart midE = m_map.phi1(d);
+			if(m_map.isBoundaryVertex(midE))
+				m_position[midE] /= m_a;
+			else
+				m_position[midE] /= m_a * m_a;
+			m_map.decCurrentLevel() ;
+
+		}
+
+		TraversorV<typename PFP::MAP> travV(m_map) ;
+		for (Dart d = travV.begin(); d != travV.end(); d = travV.next())
+		{
+			if(m_map.isBoundaryVertex(d))
+				m_position[d] /= m_a * m_a;
+			else
+				m_position[d] /= m_a *m_a * m_a;
+		}
+	}
+} ;
+
+
+//
+// Synthesis
+//
+
+//w-lift(a)
+template <typename PFP>
+class Ber02OddSynthesisFilter : public Algo::MR::Filter
+{
+protected:
+	typename PFP::MAP& m_map ;
+	VertexAttribute<typename PFP::VEC3>& m_position ;
+	typename PFP::VEC3::DATA_TYPE m_a;
+
+public:
+	Ber02OddSynthesisFilter(typename PFP::MAP& m, VertexAttribute<typename PFP::VEC3>& p, typename PFP::VEC3::DATA_TYPE a) : m_map(m), m_position(p), m_a(a)
+	{}
+
+	void operator() ()
+	{
+		TraversorW<typename PFP::MAP> travW(m_map) ;
+		for (Dart d = travW.begin(); d != travW.end(); d = travW.next())
+		{
+			typename PFP::VEC3 vc = Algo::Surface::Geometry::volumeCentroid<PFP>(m_map, d, m_position);
+			vc *= 8 * m_a * m_a * m_a;
+
+			unsigned int count = 0;
+			typename PFP::VEC3 ec(0.0);
+			Traversor3WE<typename PFP::MAP> travWE(m_map, d);
+			for (Dart dit = travWE.begin(); dit != travWE.end(); dit = travWE.next())
+			{
+				m_map.incCurrentLevel();
+				ec += m_position[m_map.phi1(dit)];
+				m_map.decCurrentLevel();
+				++count;
+			}
+			ec /= count;
+			ec *= 12 * m_a * m_a;
+
+			count = 0;
+			typename PFP::VEC3 fc(0.0);
+			Traversor3WF<typename PFP::MAP> travWF(m_map, d);
+			for (Dart dit = travWF.begin(); dit != travWF.end(); dit = travWF.next())
+			{
+				m_map.incCurrentLevel();
+				fc += m_position[m_map.phi1(m_map.phi1(dit))];
+				m_map.decCurrentLevel();
+				++count;
+			}
+			fc /= count;
+			fc *= 6 * m_a;
+
+			m_map.incCurrentLevel() ;
+			Dart midV = m_map.phi_1(m_map.phi2(m_map.phi1(d)));
+			m_position[midV] += vc; // + ec + fc;
+			m_map.decCurrentLevel() ;
+		}
+
+		TraversorF<typename PFP::MAP> travF(m_map) ;
+		for (Dart d = travF.begin(); d != travF.end(); d = travF.next())
+		{
+			typename PFP::VEC3 vf(0.0);
+			typename PFP::VEC3 ef(0.0);
+
+			unsigned int count = 0;
+			Traversor3FE<typename PFP::MAP> travFE(m_map, d);
+			for (Dart dit = travFE.begin(); dit != travFE.end(); dit = travFE.next())
+			{
+				vf += m_position[dit];
+				m_map.incCurrentLevel();
+				ef += m_position[m_map.phi1(dit)];
+				m_map.decCurrentLevel();
+				++count;
+			}
+			ef /= count;
+			ef *= 4.0 * m_a;
+
+			vf /= count;
+			vf *= 4.0 * m_a * m_a;
+
+			m_map.incCurrentLevel() ;
+			Dart midF = m_map.phi1(m_map.phi1(d));
+			m_position[midF] += vf; // + ef ;
+			m_map.decCurrentLevel() ;
+		}
+
+		TraversorE<typename PFP::MAP> travE(m_map) ;
+		for (Dart d = travE.begin(); d != travE.end(); d = travE.next())
+		{
+			typename PFP::VEC3 ve = (m_position[d] + m_position[m_map.phi1(d)]) * typename PFP::REAL(0.5);
+			ve *= 2.0 * m_a;
+
+			m_map.incCurrentLevel() ;
+			Dart midV = m_map.phi1(d) ;
+			m_position[midV] += ve;
+			m_map.decCurrentLevel() ;
+		}
+	}
+} ;
+
+// s-lift(a)
+template <typename PFP>
+class Ber02EvenSynthesisFilter : public Algo::MR::Filter
+{
+protected:
+	typename PFP::MAP& m_map ;
+	VertexAttribute<typename PFP::VEC3>& m_position ;
+	typename PFP::VEC3::DATA_TYPE m_a;
+
+public:
+	Ber02EvenSynthesisFilter(typename PFP::MAP& m, VertexAttribute<typename PFP::VEC3>& p, typename PFP::VEC3::DATA_TYPE a) : m_map(m), m_position(p), m_a(a)
+	{}
+
+	void operator() ()
+	{
+		TraversorV<typename PFP::MAP> travV(m_map);
+		for(Dart d = travV.begin() ; d != travV.end() ; d = travV.next())
+		{
+			if(m_map.isBoundaryVertex(d))
+			{
+				Dart db = m_map.findBoundaryFaceOfVertex(d);
+
+				unsigned int count = 0;
+				typename PFP::VEC3 ev(0.0);
+				typename PFP::VEC3 fv(0.0);
+
+
+				//TODO Replace do--while with a Traversor2 on Boundary
+				Traversor2VF<typename PFP::MAP> travVF(m_map,db);
+				for(Dart dit = travVF.begin(); dit != travVF.end() ; dit = travVF.next())
+				{
+					m_map.incCurrentLevel() ;
+
+					Dart midEdgeV = m_map.phi1(dit);
+					ev += m_position[midEdgeV];
+					fv += m_position[m_map.phi1(midEdgeV)];
+
+					m_map.decCurrentLevel() ;
+					++count;
+				}
+
+				fv /= count;
+				fv *= 4 * m_a * m_a;
+
+				ev /= count;
+				ev *= 4 * m_a;
+
+				m_position[d] += fv + ev;
+
+			}
+			else
+			{
+//				unsigned int count = 0;
+//
+//				typename PFP::VEC3 cv(0.0);
+//				Traversor3VW<typename PFP::MAP> travVW(m_map,d);
+//				for(Dart dit = travVW.begin(); dit != travVW.end() ; dit = travVW.next())
+//				{
+//					m_map.incCurrentLevel() ;
+//					Dart midV = m_map.phi_1(m_map.phi2(m_map.phi1(dit)));
+//					cv += m_position[midV];
+//					m_map.decCurrentLevel() ;
+//					++count;
+//				}
+//				cv /= count;
+//				cv *= 8 * m_a * m_a * m_a;
+//
+//				typename PFP::VEC3 fv(0.0);
+//				count = 0;
+//				Traversor3VF<typename PFP::MAP> travVF(m_map,d);
+//				for(Dart dit = travVF.begin(); dit != travVF.end() ; dit = travVF.next())
+//				{
+//					m_map.incCurrentLevel() ;
+//					Dart midV = m_map.phi1(m_map.phi1(dit));
+//					fv += m_position[midV];
+//					m_map.decCurrentLevel() ;
+//					++count;
+//				}
+//				fv /= count;
+//				fv *= 12 * m_a * m_a;
+//
+//				typename PFP::VEC3 ev(0.0);
+//				count = 0;
+//				Traversor3VE<typename PFP::MAP> travVE(m_map,d);
+//				for(Dart dit = travVE.begin(); dit != travVE.end() ; dit = travVE.next())
+//				{
+//					m_map.incCurrentLevel() ;
+//					Dart midV = m_map.phi1(dit);
+//					ev += m_position[midV];
+//					m_map.decCurrentLevel() ;
+//					++count;
+//				}
+//				ev /= count;
+//				ev *= 6 * m_a;
+//
+//				m_position[d] += cv + fv + ev;
+			}
+		}
+
+		TraversorE<typename PFP::MAP> travE(m_map);
+		for(Dart d = travE.begin() ; d != travE.end() ; d = travE.next())
+		{
+			if(m_map.isBoundaryEdge(d))
+			{
+				Dart db = m_map.findBoundaryFaceOfEdge(d);
+				typename PFP::VEC3 fe(0.0);
+
+				//TODO Replace do--while with a Traversor2 on Boundary
+				unsigned int count = 0;
+				Traversor2EF<typename PFP::MAP> travEF(m_map, db);
+				for(Dart dit = travEF.begin() ; dit != travEF.end() ; dit = travEF.next())
+				{
+					m_map.incCurrentLevel() ;
+					Dart midV = m_map.phi1(m_map.phi1(dit));
+					fe += m_position[midV];
+					m_map.decCurrentLevel() ;
+					++count;
+				}
+
+				fe /= count;
+				fe *= 2 * m_a;
+
+				m_map.incCurrentLevel() ;
+				Dart midE = m_map.phi1(db);
+				m_position[midE] += fe;
+				m_map.decCurrentLevel() ;
+			}
+			else
+			{
+//				unsigned int count = 0;
+//
+//				typename PFP::VEC3 ce(0.0);
+//				Traversor3EW<typename PFP::MAP> travEW(m_map, d);
+//				for(Dart dit = travEW.begin() ; dit != travEW.end() ; dit = travEW.next())
+//				{
+//					m_map.incCurrentLevel() ;
+//					Dart midV = m_map.phi_1(m_map.phi2(m_map.phi1(dit)));
+//					ce += m_position[midV];
+//					m_map.decCurrentLevel() ;
+//					++count;
+//				}
+//				ce /= count;
+//				ce *= 4 * m_a * m_a;
+//
+//				typename PFP::VEC3 fe(0.0);
+//				count = 0;
+//				Traversor3EF<typename PFP::MAP> travEF(m_map, d);
+//				for(Dart dit = travEF.begin() ; dit != travEF.end() ; dit = travEF.next())
+//				{
+//					m_map.incCurrentLevel() ;
+//					Dart midV = m_map.phi1(m_map.phi1(dit));
+//					fe += m_position[midV];
+//					m_map.decCurrentLevel() ;
+//					++count;
+//				}
+//				fe /= count;
+//				fe *= 4 * m_a;
+//
+//				m_map.incCurrentLevel() ;
+//				Dart midE = m_map.phi1(d);
+//				m_position[midE] += ce + fe;
+//				m_map.decCurrentLevel() ;
+			}
+		}
+
+//		TraversorF<typename PFP::MAP> travF(m_map) ;
+//		for (Dart d = travF.begin(); d != travF.end(); d = travF.next())
+//		{
+//			if(!m_map.isBoundaryFace(d))
+//			{
+//				unsigned int count = 0;
+//
+//				typename PFP::VEC3 cf(0.0);
+//				Traversor3FW<typename PFP::MAP> travFW(m_map, d);
+//				for(Dart dit = travFW.begin() ; dit != travFW.end() ; dit = travFW.next())
+//				{
+//					m_map.incCurrentLevel();
+//					Dart midV = m_map.phi_1(m_map.phi2(m_map.phi1(dit)));
+//					cf += m_position[midV];
+//					m_map.decCurrentLevel();
+//					++count;
+//				}
+//				cf /= count;
+//				cf *= 2 * m_a;
+//
+//				m_map.incCurrentLevel() ;
+//				Dart midF = m_map.phi1(m_map.phi1(d));
+//				m_position[midF] += cf;
+//				m_map.decCurrentLevel() ;
+//			}
+//		}
+	}
+} ;
+
+// s-scale(a)
+template <typename PFP>
+class Ber02ScaleSynthesisFilter : public Algo::MR::Filter
+{
+protected:
+	typename PFP::MAP& m_map ;
+	VertexAttribute<typename PFP::VEC3>& m_position ;
+	typename PFP::VEC3::DATA_TYPE m_a;
+
+public:
+	Ber02ScaleSynthesisFilter(typename PFP::MAP& m, VertexAttribute<typename PFP::VEC3>& p, typename PFP::VEC3::DATA_TYPE a) : m_map(m), m_position(p), m_a(a)
+	{}
+
+	void operator() ()
+	{
+		TraversorV<typename PFP::MAP> travV(m_map) ;
+		for (Dart d = travV.begin(); d != travV.end(); d = travV.next())
+		{
+			if(m_map.isBoundaryVertex(d))
+				m_position[d] *= m_a * m_a;
+			//else
+			//	m_position[d] *= m_a *m_a * m_a;
+		}
+
+		TraversorE<typename PFP::MAP> travE(m_map) ;
+		for (Dart d = travE.begin(); d != travE.end(); d = travE.next())
+		{
+
+			m_map.incCurrentLevel() ;
+			Dart midE = m_map.phi1(d);
+			if(m_map.isBoundaryVertex(midE))
+				m_position[midE] *= m_a;
+			//else
+			//	m_position[midE] *= m_a * m_a;
+			m_map.decCurrentLevel() ;
+
+		}
+
+//		TraversorF<typename PFP::MAP> travF(m_map) ;
+//		for (Dart d = travF.begin(); d != travF.end(); d = travF.next())
+//		{
+//				m_map.incCurrentLevel() ;
+//				Dart midF = m_map.phi1(m_map.phi1(d));
+//				if(!m_map.isBoundaryVertex(midF))
+//					m_position[midF] *= m_a ;
+//				m_map.decCurrentLevel() ;
+//
+//		}
+	}
+} ;
+
+
+
+} // namespace Filters
+
+} // namespace Primal
+
+} // namespace MR
+
+} // namespace Volume
+
+} // namespace Algo
+
+} // namespace CGoGN
+
+
+#endif /* __3MR_BERTRAM_BOUNDARY_FILTER__ */