tetrahedralization.hpp 25.1 KB
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/*******************************************************************************
 * CGoGN: Combinatorial and Geometric modeling with Generic N-dimensional Maps  *
 * version 0.1                                                                  *
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 * Copyright (C) 2009-2012, IGG Team, LSIIT, University of Strasbourg           *
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 *                                                                              *
 * 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.           *
 *                                                                              *
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 * Web site: http://cgogn.unistra.fr/                                           *
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 * Contact information: cgogn@unistra.fr                                        *
 *                                                                              *
 *******************************************************************************/

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#include "Topology/generic/traversor3.h"

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namespace CGoGN
{

namespace Algo
{

namespace Modelisation
{

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namespace Tetrahedralization
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{
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template <typename PFP>
void hexahedronToTetrahedron(typename PFP::MAP& map, Dart d)
{
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	//Splitting Path
	std::vector<Dart> sp;
	sp.reserve(32);
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	Traversor3VE<typename PFP::MAP> tra(map, d);
	for (Dart d = tra.begin() ; d != tra.end() ; d = tra.next())
	{
		map.splitFace(map.phi1(d), map.phi_1(d));
		sp.push_back(map.phi1(d));
	}

	map.splitVolume(sp);
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}


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/************************************************************************************************
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 * 									Collapse / Split Operators
 ************************************************************************************************/
template <typename PFP>
Dart splitVertex(typename PFP::MAP& map, std::vector<Dart>& vd)
{
	//split the vertex
	Dart dres = map.splitVertex(vd);

	//split the faces incident to the new vertex
	Dart dbegin = map.phi1(map.phi2(vd.front()));
	Dart dit = dbegin;
	do
	{
		map.splitFace(map.phi1(dit),map.phi_1(dit));
		dit = map.alpha2(dit);
	}
	while(dbegin != dit);

	//split the volumes incident to the new vertex
	for(unsigned int i = 0; i < vd.size(); ++i)
	{
		Dart dit = vd[i];

		std::vector<Dart> v;
		v.push_back(map.phi1(map.phi1(map.phi2(dit))));
		std::cout << "[" << v.back();
		v.push_back(map.phi1(dit));
		std::cout << " - " << v.back();
		v.push_back(map.phi1(map.phi2(map.phi_1(dit))));
		std::cout << " - " << v.back() << "]" << std::endl;
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		map.splitVolume(v);
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	}

	return dres;
}

/************************************************************************************************
 * 								Tetrahedron functions															   *
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 ************************************************************************************************/
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template <typename PFP>
bool isTetrahedron(typename PFP::MAP& the_map, Dart d)
{
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	unsigned int nbFaces = 0;
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	//Test the number of faces end its valency
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	Traversor3WF<typename PFP::MAP> travWF(the_map, d);
	for(Dart dit = travWF.begin() ; dit != travWF.end(); dit = travWF.next())
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	{
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		//increase the number of faces
		nbFaces++;
		if(nbFaces > 4)	//too much faces
			return false;

		//test the valency of this face
		if(the_map.faceDegree(dit) != 3)
			return false;
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	}

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	return true;
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}

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template <typename PFP>
bool isTetrahedralization(typename PFP::MAP& map, const FunctorSelect& selected)
{
	TraversorV<typename PFP::MAP> travV(map, selected);
	for(Dart dit = travV.begin() ; dit != travV.end() ; dit = travV.next())
	{
		if(!isTetrahedron<PFP>(map, dit))
			return false;
	}

	return true;
}

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/************************************************************************************************
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 * 									Topological functions															   *
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 ************************************************************************************************/
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//sew a face into the edge
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template <typename PFP>
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Dart linkIntoEdge(typename PFP::MAP& map, Dart d, Dart e)
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{
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	Dart e2 = map.phi2(e);
	Dart d3 = map.phi3(d);

	//Decoud les 2 brins
	map.unsewFaces(e);
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	//Coudre la nouvelle face au milieu de l'ancienne arête
	map.sewFaces(e2,d3);
	map.sewFaces(e,d);
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	map.setDartEmbedding<VERTEX>(d, map.getEmbedding<VERTEX>(e2)) ;
	map.setDartEmbedding<VERTEX>(d3, map.getEmbedding<VERTEX>(e)) ;
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	return e2;
}
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//unsew a face from the edge
template <typename PFP>
void unlinkFromEdge(typename PFP::MAP& map, Dart d)
{
	Dart d3 = map.phi3(d);

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//	if(map.isOrbitEmbedded<VERTEX>())
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//	{
//		//Si la face n'est pas libre en phi2
//		if(map.phi2(d) != d && map.phi2(d3) != d3)
//		{
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//			unsigned int dVEmb = map.getEmbedding<VERTEX>(d) ;
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//			if(dVEmb != EMBNULL)
//			{
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//				map.embedOrbit<VERTEX>(d, dVEmb) ;
//				map.setDartEmbedding<VERTEX>(d, EMBNULL) ;
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//			}
//
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//			unsigned int d3VEmb = map.getEmbedding<VERTEX>(d3) ;
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//			if(d3VEmb != EMBNULL)
//			{
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//				map.embedOrbit<VERTEX>(d3, d3VEmb) ;
//				map.setDartEmbedding<VERTEX>(d3, EMBNULL) ;
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//			}
//		}
//		//Si la face est libre en phi2
//		else
//		{
//
//		}
//	}
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	Dart e2 = map.phi2(d3);
	Dart d2 = map.phi2(d);
	map.unsewFaces(e2);
	map.unsewFaces(d2);
	map.sewFaces(d2,e2);
}

template <typename PFP>
void unlinkFace(typename PFP::MAP& map, Dart d)
{
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	Dart e = d;
	do
	{
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		unlinkFromEdge<PFP>(map, e);
		e = map.phi1(e);
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	}
	while (e != d);
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}
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template <typename PFP>
void insertFace(typename PFP::MAP& map, Dart d, Dart nF)
{
	Dart dd = d;
	Dart nFd = nF;
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	do {
		//TODO linkIntoEdge
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		Dart d2 = map.phi2(dd);
		map.unsewFaces(dd);
		map.sewFaces(dd,nFd);
		map.sewFaces(d2,map.phi3(nFd));
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		map.setDartEmbedding<VERTEX>(nFd, map.getEmbedding<VERTEX>(d2)) ;
		map.setDartEmbedding<VERTEX>(map.phi3(nFd), map.getEmbedding<VERTEX>(dd)) ;
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		dd = map.phi_1(map.phi2(map.phi_1(dd)));
		nFd = map.phi1(nFd);
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	} while (nFd != nF);
}

/***********************************************************************************************
 * 										swap functions										   *
 ***********************************************************************************************/
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//ok
template <typename PFP>
void swap2To2(typename PFP::MAP& map, Dart d)
{
	//save a dart from a non-modifed-face of one tetrahedron
	Dart r = map.phi2(d);

	//detach common face from tetrahedron from the rest of the faces
	unlinkFace<PFP>(map, d);

	//flip the middle edge
	map.flipEdge(r);
	Dart e = map.phi2(r);

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	unsigned int dVEmb = map.getEmbedding<VERTEX>(r) ;
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	if(dVEmb != EMBNULL)
	{
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		map.setDartEmbedding<VERTEX>(map.phi_1(r), dVEmb) ;
		map.setDartEmbedding<VERTEX>(r, EMBNULL) ;
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	}

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	unsigned int eVEmb = map.getEmbedding<VERTEX>(e) ;
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	if(eVEmb != EMBNULL)
	{
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		map.setDartEmbedding<VERTEX>(map.phi_1(e), eVEmb) ;
		map.setDartEmbedding<VERTEX>(e, EMBNULL) ;
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	}

	//insert the face in the flipped edge
	insertFace<PFP>(map, r, d);
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	Dart dd = d;
	do {
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		Dart e = map.phi2(dd);
		Dart e2= map.phi2(map.phi3(dd));

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		map.setDartEmbedding<VERTEX>(dd, map.getEmbedding<VERTEX>(e2)) ;
		map.setDartEmbedding<VERTEX>(map.phi3(dd), map.getEmbedding<VERTEX>(e)) ;
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		dd = map.phi1(dd);
	} while( dd!=d);
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}

//ok
template <typename PFP>
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void swap4To4(typename PFP::MAP& map, Dart d)
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{
	//!! 4 decouture inutile, seule l'intersection du centre doit etre decousu puis recousu

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	Dart e = map.phi2(map.phi3(d));
	Dart dd = map.phi2(d);
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	//unsew middle crossing darts
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	map.unsewVolumes(d);
	map.unsewVolumes(map.phi2(map.phi3(dd)));
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	Algo::Modelisation::Tetrahedralization::swap2To2<PFP>(map, dd);
	Algo::Modelisation::Tetrahedralization::swap2To2<PFP>(map, e);
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	//sew middle darts so that they do not cross
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	map.sewVolumes(d,map.phi2(map.phi3(e)));
	map.sewVolumes(map.phi2(map.phi3(dd)),map.phi2(e));
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}

template <typename PFP>
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void swap3To2(typename PFP::MAP& map, Dart d)
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{
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	Dart en1 = map.phi_1(map.phi2(d));
	Dart en2 = map.phi1(d);
	Dart fi = map.phi2(en1);
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	//Decouture de la premiere face
	unlinkFromEdge<PFP>(map, map.phi2(en1));
	unlinkFromEdge<PFP>(map, map.phi2(en2));
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	//Decouture de la seconde face
	en1 = map.phi1(map.phi2(en1));
	en2 = map.phi_1(map.phi2(en2));
	unlinkFromEdge<PFP>(map, map.phi2(en1));
	unlinkFromEdge<PFP>(map, map.phi2(en2));
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	//Decouture de la troisieme face
	en1 = map.phi1(map.phi2(en1));
	en2 = map.phi_1(map.phi2(en2));
	unlinkFromEdge<PFP>(map, map.phi2(en1));
	unlinkFromEdge<PFP>(map, map.phi2(en2));
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	//Faces interieurs
	Dart fi2 = map.phi2(map.phi1(fi));
	Dart fi3 = map.phi2(map.phi3(map.phi1(fi)));
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	map.deleteFace(fi);
	map.deleteFace(fi2);
	map.deleteFace(fi3);
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	    //Couture de cette face au milieu des 2 tetraedres
	    Dart f = map.newFace(3);
	    Dart fprim = map.newFace(3);
	    map.sewVolumes(f,fprim);
	//     Dart en = linkIntoEdge(f,d);
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	    Dart ff=f;
	    Dart en= d;
	    do {
	        Dart e2 = map.phi2(en);
	        Dart d3 = map.phi3(ff);
	        map.unsewFaces(en);
	        map.sewFaces(e2,d3);
	        map.sewFaces(en,ff);

	        en = map.phi_1(map.phi2(map.phi_1(en)));

	        ff = map.phi1(ff);
	    } while(ff!=f);


		Dart dd = d;

		do {
			Dart e = map.phi2(map.phi3(map.phi2(dd)));

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			unsigned int eVEmb = map.getEmbedding<VERTEX>(e) ;
			unsigned int ddVEmb = map.getEmbedding<VERTEX>(dd) ;
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			map.setDartEmbedding<VERTEX>(map.phi2(dd), eVEmb) ;
			map.setDartEmbedding<VERTEX>(map.phi2(e), ddVEmb) ;
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			dd = map.phi1(map.phi2(map.phi1(dd)));
		} while( dd!=d);
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}

//[precond] le brin doit venir d'une face partagé par 2 tetraèdres
// renvoie un brin de l'ancienne couture entre les 2 tetras qui est devenu une arête
template <typename PFP>
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Dart swap2To3(typename PFP::MAP& map, Dart d)
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{
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	Dart e = map.phi1(map.phi2(map.phi3(d)));

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	unsigned int p1 = map.getEmbedding<VERTEX>(map.phi_1(map.phi2(d))) ;
	unsigned int p2 = map.getEmbedding<VERTEX>(map.phi2(map.phi1(map.phi2(map.phi3(d))))) ;
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	//détachement des demi-faces du milieu
	//garde la relation volumique qui les lies
	//relie les faces de bords des 2 tetraèdres
	//renvoie le brin de base d'un des 2 tétraèdres
	unlinkFace<PFP>(map, d);

	//Couture de la premiere face
	Dart en1 = linkIntoEdge<PFP>(map,d,e);
	Dart en2 = linkIntoEdge<PFP>(map, map.phi1(d), map.phi_1(map.phi2(map.phi_1(e))));
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	map.setDartEmbedding<VERTEX>(map.phi_1(d), p1);
	map.setDartEmbedding<VERTEX>(map.phi1(map.phi3(d)), p2);
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	///Couture de la seconde face
	en1 = map.phi1(map.phi1(en1));
	en2 = map.phi_1(map.phi_1(en2));

	Dart f1 = map.newFace(3);
	Dart f1prim = map.newFace(3);
	map.sewVolumes(f1,f1prim);
	en1 = linkIntoEdge<PFP>(map, f1,en1);
	en2 = linkIntoEdge<PFP>(map, map.phi1(f1),en2);

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	map.setDartEmbedding<VERTEX>(map.phi_1(f1), p1);
	map.setDartEmbedding<VERTEX>(map.phi1(map.phi3(f1)), p2);
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	///Couture de la troisieme face
	en1 = map.phi1(map.phi1(en1));
	en2 = map.phi_1(map.phi_1(en2));

	Dart f2 = map.newFace(3);
	Dart f2prim = map.newFace(3);
	map.sewVolumes(f2,f2prim);
	en1 = linkIntoEdge<PFP>(map, f2,en1);
	en2 = linkIntoEdge<PFP>(map, map.phi1(f2),en2);

	//couture des 3 faces du milieu
	map.sewFaces(map.phi_1(d), map.phi1(map.phi3(f2)));
	map.sewFaces(map.phi1(map.phi3(d)), map.phi_1(f1));
	map.sewFaces(map.phi1(map.phi3(f1)), map.phi_1(f2));

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	map.setDartEmbedding<VERTEX>(map.phi_1(f2), p1);
	map.setDartEmbedding<VERTEX>(map.phi1(map.phi3(f2)), p2);
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	return map.phi_1(d);
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}

template <typename PFP>
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void swap5To4(typename PFP::MAP& map, Dart d, VertexAttribute<typename PFP::VEC3>& positions)
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{


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}

/************************************************************************************************
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 *							Flip Functions 																	   *
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 ************************************************************************************************/

template <typename PFP>
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void flip1To4(typename PFP::MAP& map, Dart d, VertexAttribute<typename PFP::VEC3>& position)
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{
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//	typedef typename PFP::TVEC3 TVEC3;
//	typedef typename PFP::VEC3 VEC3;
//
//
//	//parcourir le tetra est sauvegarder un brin de chaque face + calcul du centroid
//	VEC3 volCenter;
//	unsigned count = 0 ;
//
//	DartMarkerStore mf(map);		// Lock a face marker to save one dart per face
//	DartMarkerStore mv(map);		// Lock a vertex marker to compute volume center
//
//	std::vector<Dart> visitedFaces;
//	visitedFaces.reserve(4);
//	visitedFaces.push_back(d);
//
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//	mf.markOrbit<FACE>(d) ;
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//
//	//TODO diminuer complexite avec boucle specifique aux tetras
//	for(unsigned int i = 0; i < visitedFaces.size(); ++i)
//	{
//		Dart e = visitedFaces[i] ;
//		do
//		{
//			//compute volume centroid
//			if(!mv.isMarked(e))
//			{
//				volCenter += position[e];
//				++count;
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//				mv.markOrbit<VERTEX>(e);
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//			}
//
//			// add all face neighbours to the table
//			Dart ee = map.phi2(e) ;
//			if(!mf.isMarked(ee)) // not already marked
//			{
//				visitedFaces.push_back(ee) ;
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//				mf.markOrbit<FACE>(ee) ;
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//			}
//
//			e = map.phi1(e) ;
//		} while(e != visitedFaces[i]) ;
//	}
//
//	volCenter /= typename PFP::REAL(count) ;
//
//	//store the new faces to 3-sew
//	std::vector<std::pair<Dart,Dart> > nFaces;
//	nFaces.reserve(6);
//
//	//triangule chaque face avec plongement au centroid
//	for (std::vector<Dart>::iterator face = visitedFaces.begin(); face != visitedFaces.end(); ++face)
//	{
//		// on decoud et on ferme le trou
//		Dart temp = *face;
//		do
//		{
//			nFaces.push_back(std::pair<Dart,Dart>(temp, map.phi2(temp)));
//			map.unsewFaces(temp);
//			temp = map.phi1(temp);
//		}
//		while(temp != *face);
//
//		map.closeHole(*face);
//
//		Dart fi = map.phi2(*face);
//
//		Dart cd = Algo::Modelisation::trianguleFace<PFP>(map, fi);
//		position[cd] = volCenter;
//	}
//
//	//coudre les nouveaux brins entre eux par phi3
//	for (std::vector<std::pair<Dart,Dart> >::iterator face =nFaces.begin(); face != nFaces.end(); ++face)
//	{
//
//		if(map.phi3(map.phi2((*face).first)) == map.phi2((*face).first))
//			map.sewVolumes(map.phi2((*face).first), map.phi2((*face).second));
//	}
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}

/************************************************************************************************
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 *                 Bisection Functions                                                          *
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 ************************************************************************************************/
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template <typename PFP>
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void edgeBisection(typename PFP::MAP& map, Dart d, VertexAttribute<typename PFP::VEC3>& position)
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{
	//coupe l'arete en 2
	Dart f = map.phi1(d);
	map.cutEdge(d);
	Dart e = map.phi1(d);
	position[e] = position[d];
	position[e] += position[f];
	position[e] *= 0.5;


	//split de la face de d
	map.splitFace(map.phi_1(d), map.phi1(d));

	//alpha2(d)
	Dart dd = map.alpha2(d);

	//si alpha2 == d
	if(dd == d)
	{
		map.splitFace(map.phi2(d), map.phi1(map.phi1(map.phi2(d))));
		std::cout << "dd == d" << std::endl;
	}
	else
	{
		Dart prev = d;

		while (dd!=d)
		{
			prev = dd;
			dd = map.alpha2(dd);

			std::cout << "plop" << std::endl;
			map.splitFace(map.phi_1(prev), map.phi1(prev));
		}

		if(map.phi3(map.phi2(dd)) == map.phi2(dd))
		{
			map.splitFace(map.phi2(dd), map.phi1(map.phi1(map.phi2(dd))));
		}

	}

	Dart temp = d;
	do{


		//insertion de la face
		//decouture des 2 bouts
		Dart etemp = map.phi2(map.phi1(temp));

		map.unsewFaces(map.phi1(temp));
		map.unsewFaces(map.phi_1(map.phi2(temp)));
		map.unsewFaces(map.phi1(map.phi2(map.phi_1(temp))));

		//fermture des 2 trous
		map.closeHole(map.phi1(temp));
		map.closeHole(etemp);

		//recouture par phi3
		map.sewVolumes(map.phi2(map.phi1(temp)), map.phi2(etemp));


		temp = map.alpha2(temp);
	}
	while(temp != d);

//	if(map.phi3(d) == d)
//	{
//		map.splitFace(map.phi_1(d), map.phi1(d));
//		d = map.phi2(d);
//	}
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//
//
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//	Dart prev = d;
//	Dart dd = map.alpha2(d);
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//
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//	//
//	map.splitFace(d, map.phi1(map.phi1(d)));
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//
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//	//si phi3(d) != d
//	map.splitFace(map.phi_1(d), map.phi1(d));
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//
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//	//map.splitFace(map.phi2(d), map.phi1(map.phi1(map.phi2(d))));
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//
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//	//map.Map2::splitFace(map.phi_1(d), map.phi1(d));
//	//map.Map2::splitFace(map.phi2(d), map.phi1(map.phi1(map.phi2(d))));
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//
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//	//		if(map.phi3(d) == d)
//	//		{
//	//			map.splitFace(map.phi2(d), map.phi1(map.phi1(map.phi2(d))));
//	//		}
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//
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//	while (dd!=d)
//	{
//		prev = dd;
//		dd = map.alpha2(dd);
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//
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//		map.splitFace(map.phi_1(prev), map.phi1(prev));
//	}
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//	DartMarkerStore mf(map);
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//
//
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//	//tout autour de l'arete
//	Dart temp = d;
//	do{
//
//		if(!mf.isMarked(temp))
//		{
//			//split les 2 faces le long
//			map.splitFace(map.phi_1(temp), map.phi1(temp));
//			map.splitFace(map.phi2(temp), map.phi1(map.phi1(map.phi2(temp))));
//
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//			mf.markOrbit<FACE>(temp);
//			mf.markOrbit<FACE>(map.phi2(temp));
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//		}
//			//insertion de la face
//			//decouture des 2 bouts
//			Dart etemp = map.phi2(map.phi1(temp));
//
//			map.unsewFaces(map.phi1(temp));
//			map.unsewFaces(map.phi_1(map.phi2(temp)));
//			map.unsewFaces(map.phi1(map.phi2(map.phi_1(temp))));
//
//			//fermture des 2 trous
//			map.closeHole(map.phi1(temp));
//			map.closeHole(etemp);
//
//			//recouture par phi3
//			map.sewVolumes(map.phi2(map.phi1(temp)), map.phi2(etemp));
//
//
//
//		temp = map.alpha2(temp);
//	}
//	while(temp != d);
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}

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///**
// * create a tetra based on the two triangles that have a common dart and phi2(dart)
// * return a new dart inside the tetra
// */
//template<typename PFP>
//Dart extractTetra(typename PFP::MAP& the_map, Dart d)
//{
//
//
//	Dart e = the_map.phi2(d);
//
//	//create the new faces
//	Dart dd = the_map.newFace(3);
//	Dart ee = the_map.newFace(3);
//
//	//update their sew
//	the_map.sewFaces(dd,ee);
//	the_map.sewFaces(the_map.phi3(dd),the_map.phi3(ee));
//
//	//add the two new faces in the mesh to obtain a tetra
//	Dart s2d = the_map.phi2(the_map.phi_1(d));
//	the_map.unsewFaces(the_map.phi_1(d));
//	the_map.sewFaces(the_map.phi_1(d),the_map.phi_1(dd));
//	the_map.sewFaces(s2d,the_map.phi3(the_map.phi_1(dd)));
//
//	Dart s2e = the_map.phi2(the_map.phi_1(e));
//	the_map.unsewFaces(the_map.phi_1(e));
//	the_map.sewFaces(the_map.phi_1(e),the_map.phi_1(ee));
//	the_map.sewFaces(s2e,the_map.phi3(the_map.phi_1(ee)));
//
//	Dart ss2d = the_map.phi2(the_map.phi1(d));
//	the_map.unsewFaces(the_map.phi1(d));
//	the_map.sewFaces(the_map.phi1(d),the_map.phi1(ee));
//	the_map.sewFaces(ss2d,the_map.phi3(the_map.phi1(ee)));
//
//	Dart ss2e = the_map.phi2(the_map.phi1(e));
//	the_map.unsewFaces(the_map.phi1(e));
//	the_map.sewFaces(the_map.phi1(e),the_map.phi1(dd));
//	the_map.sewFaces(ss2e,the_map.phi3(the_map.phi1(dd)));
//
//	//embed the coords
//	the_map.setVertexEmb(d,the_map.getVertexEmb(d));
//	the_map.setVertexEmb(e,the_map.getVertexEmb(e));
//	the_map.setVertexEmb(the_map.phi_1(d),the_map.getVertexEmb(the_map.phi_1(d)));
//	the_map.setVertexEmb(the_map.phi_1(e),the_map.getVertexEmb(the_map.phi_1(e)));
//
//	return dd;
//}
//
///**
// * tetrahedrization of the volume
// * @param the map
// * @param a dart of the volume
// * @param true if the faces are in CCW order
// * @return success of the tetrahedrization
// */
//template<typename PFP>
//bool smartVolumeTetrahedrization(typename PFP::MAP& the_map, Dart d, bool CCW=true)
//{
//
//	typedef typename PFP::EMB EMB;
//
//	bool ret=true;
//
//	if (!the_map.isTetrahedron(d))
//	{
//		//only works on a 3-map
//		assert(Dart::nbInvolutions()>=2 || "cannot be applied on this map, nbInvolutions must be at least 2");
//
//		if (Geometry::isConvex<PFP>(the_map,d,CCW))
//		{
//			the_map.tetrahedrizeVolume(d);
//		}
//		else
//		{
//
//			//get all the dart of the volume
//			std::vector<Dart> vStore;
//			FunctorStore fs(vStore);
//			the_map.foreach_dart_of_volume(d,fs);
//
//			if (vStore.size()==0)
//			{
//				if (the_map.phi1(d)==d)
//					CGoGNout << "plop" << CGoGNendl;
//				if (the_map.phi2(d)==d)
//					CGoGNout << "plip" << CGoGNendl;
//
//				CGoGNout << the_map.getVertexEmb(d)->getPosition() << CGoGNendl;
//				CGoGNout << "tiens tiens, c'est etrange" << CGoGNendl;
//			}
//			//prepare the list of embeddings of the current volume
//			std::vector<EMB *> lstEmb;
//
//			//get a marker
//			DartMarker m(the_map);
//
//			//all the darts from a vertex that can generate a tetra (3 adjacent faces)
//			std::vector<Dart> allowTetra;
//
//			//all the darts that are not in otherTetra
//			std::vector<Dart> otherTetra;
//
//			//for each dart of the volume
//			for (typename std::vector<Dart>::iterator it = vStore.begin() ; it != vStore.end() ; ++it )
//			{
//				Dart e = *it;
//				//if the vertex is not treated
//				if (!m.isMarked(e))
//				{
//					//store the embedding
//					lstEmb.push_back(reinterpret_cast<EMB*>(the_map.getVertexEmb(e)));
//					Dart ee=e;
//
//					//count the number of adjacent faces and mark the darts
//					int nbe=0;
//					do
//					{
//						nbe++;
//						m.markOrbit(DART,e);
//						ee=the_map.phi1(the_map.phi2(ee));
//					}
//					while (ee!=e);
//
//					//if 3 adjacents faces, we can create a tetra on this vertex
//					if (nbe==3)
//						allowTetra.push_back(e);
//					else
//						otherTetra.push_back(e);
//				}
//			}
//
//			//we haven't created a tetra yet
//			bool decoupe=false;
//
//			//if we have vertex that can be base
//			if (allowTetra.size()!=0)
//			{
//				//foreach possible vertex while we haven't done any cut
//				for (typename std::vector<Dart>::iterator it=allowTetra.begin();it!=allowTetra.end() && !decoupe ;++it)
//				{
//					//get the dart
//					Dart s=*it;
//					//store the emb
//					std::vector<EMB*> lstCurEmb;
//					lstCurEmb.push_back(reinterpret_cast<EMB*>(the_map.getVertexEmb(s)));
//					lstCurEmb.push_back(reinterpret_cast<EMB*>(the_map.getVertexEmb(the_map.phi1(s))));
//					lstCurEmb.push_back(reinterpret_cast<EMB*>(the_map.getVertexEmb(the_map.phi_1(s))));
//					lstCurEmb.push_back(reinterpret_cast<EMB*>(the_map.getVertexEmb(the_map.phi_1(the_map.phi2(s)))));
//
//					//store the coords of the point
//					gmtl::Vec3f points[4];
//					for (int i=0;i<4;++i)
//					{
//						points[i] = lstCurEmb[i]->getPosition();
//					}
//
//					//test if the future tetra is well oriented (concave case)
//					if (Geometry::isTetrahedronWellOriented(points,CCW))
//					{
//						//test if we haven't any point inside the future tetra
//						bool isEmpty=true;
//						for (typename std::vector<EMB *>::iterator iter = lstEmb.begin() ; iter != lstEmb.end() && isEmpty ; ++iter)
//						{
//							//we don't test the vertex that composes the new tetra
//							if (std::find(lstCurEmb.begin(),lstCurEmb.end(),*iter)==lstCurEmb.end())
//							{
//								isEmpty = !Geometry::isPointInTetrahedron(points, (*iter)->getPosition(), CCW);
//							}
//						}
//
//						//if no point inside the new tetra
//						if (isEmpty)
//						{
//							//cut the spike to make a tet
//							Dart dRes = the_map.cutSpike(*it);
//							decoupe=true;
//							//and continue with the rest of the volume
//							ret = ret && smartVolumeTetrahedrization<PFP>(the_map,the_map.phi3(dRes),CCW);
//						}
//					}
//				}
//			}
//
//			if (!decoupe)
//			{
//				//foreach other vertex while we haven't done any cut
//				for (typename std::vector<Dart>::iterator it=otherTetra.begin();it!=otherTetra.end() && !decoupe ;++it)
//				{
//					//get the dart
//					Dart s=*it;
//					//store the emb
//					std::vector<EMB*> lstCurEmb;
//					lstCurEmb.push_back(reinterpret_cast<EMB*>(the_map.getVertexEmb(s)));
//					lstCurEmb.push_back(reinterpret_cast<EMB*>(the_map.getVertexEmb(the_map.phi1(s))));
//					lstCurEmb.push_back(reinterpret_cast<EMB*>(the_map.getVertexEmb(the_map.phi_1(s))));
//					lstCurEmb.push_back(reinterpret_cast<EMB*>(the_map.getVertexEmb(the_map.phi_1(the_map.phi2(s)))));
//
//					//store the coords of the point
//					gmtl::Vec3f points[4];
//					for (int i=0;i<4;++i)
//					{
//						points[i] = lstCurEmb[i]->getPosition();
//					}
//
//					//test if the future tetra is well oriented (concave case)
//					if (Geometry::isTetrahedronWellOriented(points,CCW))
//					{
//						//test if we haven't any point inside the future tetra
//						bool isEmpty=true;
//						for (typename std::vector<EMB *>::iterator iter = lstEmb.begin() ; iter != lstEmb.end() && isEmpty ; ++iter)
//						{
//							//we don't test the vertex that composes the new tetra
//							if (std::find(lstCurEmb.begin(),lstCurEmb.end(),*iter)==lstCurEmb.end())
//							{
//								isEmpty = !Geometry::isPointInTetrahedron(points, (*iter)->getPosition(), CCW);
//							}
//						}
//
//						//if no point inside the new tetra
//						if (isEmpty)
//						{
//							//cut the spike to make a tet
//							Dart dRes = extractTetra<PFP>(the_map,*it);
//							decoupe=true;
//							//and continue with the rest of the volume
//							smartVolumeTetrahedrization<PFP>(the_map,the_map.phi3(dRes),CCW);
//						}
//					}
//				}
//			}
//
//			if (!decoupe)
//				ret=false;
//		}
//	}
//	return ret;
//}

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} // namespace Tetrahedralization
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} // namespace Modelisation
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} // namespace Algo
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} // namespace CGoGN