map2.cpp 23.8 KB
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/*******************************************************************************
* CGoGN: Combinatorial and Geometric modeling with Generic N-dimensional Maps  *
* version 0.1                                                                  *
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* Copyright (C) 2009-2011, 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.u-strasbg.fr/                                         *
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* Contact information: cgogn@unistra.fr                                        *
*                                                                              *
*******************************************************************************/

#include "Topology/map/map2.h"

namespace CGoGN
{

/*! @name Generator and Deletor
 *  To generate or delete faces in a 2-map
 *************************************************************************/

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void Map2::mergeBoundaryFaces(Dart dd, Dart ee)
{
	if (ee != phi_1(dd))
		phi1sew(ee, phi_1(dd)) ;
	if (ee != phi_1(dd))
		phi1sew(ee, phi_1(dd)) ;
	Map1::deleteOrientedFace(dd) ;
}

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void Map2::mergeFacewithBoundary(Dart d)
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{
	Dart e = d ;
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	do									// foreach edge of face
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	{
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		Dart f = phi2(e);
		if (isBoundaryMarked(f))		// if sewed to boundary
		{
			phi2unsew(e);// ?? not necessary
			Dart ff = phi_1(f);
			if (e != ff)
				phi1sew(e, ff) ;		//    merge with it
			Dart ee = phi_1(e);
			if (f != ee)
				phi1sew(f, ee) ;
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			Map1::deleteOrientedFace(e) ;
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		}
		e = phi1(e) ;
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	} while (e != d) ;
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}


void Map2::deleteOrientedFace(Dart d)
{
	// tag face in boundary
	boundaryMarkOrbit(FACE,d);
	mergeFacewithBoundary(d);

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}

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void Map2::sewOrientedFaces(Dart d, Dart e)
{
	assert(phi2(d)==d && phi2(e)==e);
	// sewing the faces
	phi2sew(d, e);
}

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/*! @name Topological Operators
 *  Topological operations on 2-maps
 *************************************************************************/

void Map2::splitVertex(Dart d, Dart e)
{
	assert(sameOrientedVertex(d, e));
	Dart dd = phi2(d) ;
	Dart ee = phi2(e) ;
	Map1::cutEdge(dd);			// Cut the edge of dd (make a new half edge)
	Map1::cutEdge(ee);			// Cut the edge of ee (make a new half edge)
	phi2sew(phi1(dd), phi1(ee));// Sew the two faces along the new edge
}

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bool Map2::deleteVertex(Dart d)
{
	if(isBoundaryVertex(d))
		return false ;

	Dart vit = d ;
	do
	{
		Dart f = phi_1(phi2(vit)) ;
		phi1sew(vit, f) ;
		vit = alpha1(vit) ;
	} while(vit != d) ;
	Map1::deleteFace(d) ;

	return true ;
}

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void Map2::linkVertices(Dart d, Dart e)
{
	Map1::linkVertices(d, e);			// Split the face
	phi2sew(phi_1(d), phi_1(e));	// Sew the two resulting faces along the new edge
}

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void Map2::cutEdge(Dart d)
{
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//	Map1::cutEdge(d);		// Cut the edge of d
//	Dart nd = phi1(d);
//	Dart e = phi2(d);
//	if (e != d)				// Test if an opposite edge exists
//	{
//		Map1::cutEdge(e);	// Cut the opposite edge
//		Dart ne = phi1(e);
//		phi2unsew(d);		// Correct the phi2 links
//		phi2sew(d, ne);
//		phi2sew(e, nd);
//	}

	Map1::cutEdge(d);		// Cut the 1-edge of d
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	Dart e = phi2(d);
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	Map1::cutEdge(e);		// Cut the 1-edge of phi2(d)

	phi2unsew(d);			// remove old phi2 links

	Dart nd = phi1(d);
	Dart ne = phi1(e);

	phi2sew(d, ne);			// Correct the phi2 links
	phi2sew(e, nd);

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}

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void Map2::uncutEdge(Dart d)
{
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//	assert(vertexDegree(phi1(d)) == 2) ;
//	Dart ne = phi2(d) ;
//	if(ne == d)
//		collapseEdge(d) ;
//	else
//	{
//		Dart nd = phi1(d) ;
//		Dart e = phi_1(ne) ;
//		phi2unsew(e) ;
//		phi2unsew(d) ;
//		Map1::collapseEdge(nd) ;
//		Map1::collapseEdge(ne) ;
//		phi2sew(d, e) ;
//	}

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	assert(vertexDegree(phi1(d)) == 2) ;
	Dart ne = phi2(d) ;
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	Dart nd = phi1(d) ;
	Dart e = phi_1(ne) ;
	phi2unsew(e) ;
	phi2unsew(d) ;
	Map1::collapseEdge(nd) ;
	Map1::collapseEdge(ne) ;
	phi2sew(d, e) ;
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}

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Dart Map2::collapseEdge(Dart d, bool delDegenerateFaces)
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{
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//	Dart resV ;
//
//	Dart e = phi2(d);
//	if (e != d)			// Test if an opposite edge exists
//	{
//		phi2unsew(d);	// Unlink the opposite edges
//		Dart f = phi1(e) ;
//		Dart g = phi_1(e) ;
//
//		if(f != d && !isFaceTriangle(e))
//			resV = f ;
//		else if(phi2(g) != g)
//			resV = phi2(g) ;
//		else if(f != d && phi2(f) != f)
//			resV = phi1(phi2(f)) ;
//
//		if (f != e && delDegenerateFaces)
//		{
//			Map1::collapseEdge(e) ;		// Collapse edge e
//			collapseDegeneratedFace(f) ;// and collapse its face if degenerated
//		}
//		else
//			Map1::collapseEdge(e) ;	// Just collapse edge e
//	}
//
//	Dart f = phi1(d) ;
//	Dart g = phi_1(d) ;
//
//	if(resV == Dart::nil())
//	{
//		if(!isFaceTriangle(d))
//			resV = f ;
//		else if(phi2(g) != g)
//			resV = phi2(g) ;
//		else if(phi2(f) != f)
//			resV = phi1(phi2(f)) ;
//	}
//
//	if (f != d && delDegenerateFaces)
//	{
//		Map1::collapseEdge(d) ;		// Collapse edge d
//		collapseDegeneratedFace(f) ;// and collapse its face if degenerated
//	}
//	else
//		Map1::collapseEdge(d) ;	// Just collapse edge d
//
//	return resV ;

	Dart resV=Dart::nil() ;
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	Dart e = phi2(d);
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	phi2unsew(d);	// Unlink the opposite edges

	if (isBoundaryMarked(e))
	{
		Dart f = phi1(e) ;
		Map1::collapseEdge(e) ;		// Collapse edge e
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		if (f!=e)
			collapseDegeneratedFace(f) ;// and collapse its face if degenerated
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	}
	else
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	{
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		Dart f = phi1(e) ;
		Dart g = phi_1(e) ;

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		if(f != d && !isFaceTriangle(e))
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			resV = f ;
		else if(phi2(g) != g)
			resV = phi2(g) ;
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		else if(f != d && phi2(f) != f)
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			resV = phi1(phi2(f)) ;

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		if (f != e && delDegenerateFaces)
		{
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			Map1::collapseEdge(e) ;		// Collapse edge e
			collapseDegeneratedFace(f) ;// and collapse its face if degenerated
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		}
		else
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			Map1::collapseEdge(e) ;	// Just collapse edge e
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	}
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	if (isBoundaryMarked(d))
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	{
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		Dart f = phi1(d) ;
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		Map1::collapseEdge(d) ;		// Collapse edge d
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		if (f!=d)
			collapseDegeneratedFace(f) ;// and collapse its face if degenerated
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	}
	else
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	{
		Dart f = phi1(d) ;
		Dart g = phi_1(d) ;

		if(resV == Dart::nil())
		{
			if(f != e && !isFaceTriangle(d))
				resV = f ;
			else if(phi2(g) != g)
				resV = phi2(g) ;
			else if(f != e && phi2(f) != f)
				resV = phi1(phi2(f)) ;
		}

		if (f != d && delDegenerateFaces)
		{
			Map1::collapseEdge(d) ;		// Collapse edge d
			collapseDegeneratedFace(f) ;// and collapse its face if degenerated
		}
		else
			Map1::collapseEdge(d) ;	// Just collapse edge d
	}
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	return resV ;
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}

bool Map2::flipEdge(Dart d)
{
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	if (!isBoundaryEdge(d))
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	{
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		Dart e = phi2(d);
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		Dart dNext = phi1(d);
		Dart eNext = phi1(e);
		Dart dPrev = phi_1(d);
		Dart ePrev = phi_1(e);
		phi1sew(d, ePrev);		// Detach the two
		phi1sew(e, dPrev);		// vertices of the edge
		phi1sew(d, dNext);		// Insert the edge in its
		phi1sew(e, eNext);		// new vertices after flip
		return true ;
	}
	return false ; // cannot flip a border edge
}

bool Map2::flipBackEdge(Dart d)
{
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	if (!isBoundaryEdge(d))
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	{
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		Dart e = phi2(d);
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		Dart dNext = phi1(d);
		Dart eNext = phi1(e);
		Dart dPrev = phi_1(d);
		Dart ePrev = phi_1(e);
		phi1sew(d, ePrev);			// Detach the two
		phi1sew(e, dPrev);			// vertices of the edge
		phi1sew(e, phi_1(dPrev));	// Insert the edge in its
		phi1sew(d, phi_1(ePrev));	// new vertices after flip
		return true ;
	}
	return false ; // cannot flip a border edge
}

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void Map2::insertEdgeInVertex(Dart d, Dart e)
{
	assert(!sameVertex(d,e) && phi2(e)==phi_1(e));

	phi1sew(phi_1(d),phi_1(e));
}

void Map2::removeEdgeFromVertex(Dart d)
{
	assert(phi2(d)!=d);

	phi1sew(phi_1(d),phi2(d));
}

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void Map2::sewFaces(Dart d, Dart e)
{
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	Dart dd = phi2(d);
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	Dart ee = phi2(e);
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	// unsew from boundary
	phi2unsew(d);
	phi2unsew(e);

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	// remove boundary edge (could be a Map1::mergeFaces without assert ?)
	mergeBoundaryFaces(dd,ee);
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	// sewing the faces
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	phi2sew(d, e);
}

void Map2::unsewFaces(Dart d)
{
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	Dart dd = phi2(d);


	Dart e = newBoundaryFace(2);

	if (isBoundaryVertex(d))
	{
		Dart f = findBoundaryVertex(d);
		phi1sew(e,phi_1(f));
	}

	if (isBoundaryVertex(dd))
	{
		Dart f = findBoundaryVertex(dd);
		phi1sew(phi_1(e),phi_1(f));
	}

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	phi2unsew(d);
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	// sew faces to the boundary
	phi2sew(d,e);
	phi2sew(dd,phi1(e));

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}

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bool Map2::collapseDegeneratedFace(Dart d)
{
	Dart e = phi1(d);				// Check if the face is a loop
	if (phi1(e) == d)				// Yes: it contains one or two edge(s)
	{
		Dart d2 = phi2(d);			// Check opposite edges
		Dart e2 = phi2(e);
		if (d2 != d) phi2unsew(d);	// Update phi2-links if needed
		if (e2 != e) phi2unsew(e);
		if (d2 != d && e2 != e)
			phi2sew(d2, e2);
		Map1::deleteOrientedFace(d);// Delete the single edge or two edges of the loop
		return true ;
	}
	return false ;
}

void Map2::splitFace(Dart d, Dart e)
{
	Map1::splitFace(d, e);			// Split the face
	phi2sew(phi_1(d), phi_1(e));	// Sew the two resulting faces along the new edge
}

bool Map2::mergeFaces(Dart d)
{
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	if (!isBoundaryEdge(d))
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	{
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		Dart e = phi2(d) ;
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		phi2unsew(d);			// unsew the face of d
		Map1::mergeFaces(d, e); // merge the two faces along edges of d and e
		return true ;
	}
	return false ;
}

void Map2::extractTrianglePair(Dart d)
{
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//	assert(isFaceTriangle(d)) ;
//	Dart e = phi2(d) ;
//	if(e != d)
//	{
//		assert(isFaceTriangle(e)) ;
//		Dart e1 = phi2(phi1(e)) ;
//		Dart e2 = phi2(phi_1(e)) ;
//		phi2unsew(e1) ;
//		phi2unsew(e2) ;
//		phi2sew(e1, e2) ;
//	}
//	Dart d1 = phi2(phi1(d)) ;
//	Dart d2 = phi2(phi_1(d)) ;
//	phi2unsew(d1) ;
//	phi2unsew(d2) ;
//	phi2sew(d1, d2) ;

	if (!isBoundaryMarked(d))
	{
		assert(isFaceTriangle(d)) ;
		Dart d1 = phi2(phi1(d)) ;
		Dart d2 = phi2(phi_1(d)) ;
		phi2unsew(d1) ;
		phi2unsew(d2) ;
		phi2sew(d1, d2) ;
	}

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	Dart e = phi2(d) ;
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	if (!isBoundaryMarked(e))
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	{
		assert(isFaceTriangle(e)) ;
		Dart e1 = phi2(phi1(e)) ;
		Dart e2 = phi2(phi_1(e)) ;
		phi2unsew(e1) ;
		phi2unsew(e2) ;
		phi2sew(e1, e2) ;
	}
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}

void Map2::insertTrianglePair(Dart d, Dart v1, Dart v2)
{
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//	assert(sameOrientedVertex(v1, v2)) ;
//	assert((v1 != v2 && phi2(d) != d) || (v1 == v2 && phi2(d) == d)) ;
//	assert(isFaceTriangle(d) && phi2(phi1(d)) == phi1(d) && phi2(phi_1(d)) == phi_1(d)) ;
//	Dart e = phi2(d) ;
//	if(e != d && v1 != v2)
//	{
//		assert(isFaceTriangle(e) && phi2(phi1(e)) == phi1(e) && phi2(phi_1(e)) == phi_1(e)) ;
//		Dart vv2 = phi2(v2) ;
//		phi2unsew(v2) ;
//		phi2sew(phi_1(e), v2) ;
//		phi2sew(phi1(e), vv2) ;
//	}
//	Dart vv1 = phi2(v1) ;
//	phi2unsew(v1) ;
//	phi2sew(phi_1(d), v1) ;
//	phi2sew(phi1(d), vv1) ;


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	assert(sameOrientedVertex(v1, v2)) ;
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	assert((v1 != v2 && !isBoundaryMarked(d)) || (v1 == v2 && isBoundaryMarked(d))) ;
	assert(isFaceTriangle(d) && isBoundaryMarked(phi1(d)) && isBoundaryMarked(phi_1(d)) ) ;
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	Dart e = phi2(d) ;
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	if (!isBoundaryEdge(d) && v1 != v2)
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	{
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		assert( isFaceTriangle(e) && isBoundaryMarked(phi1(e)) && isBoundaryMarked(phi_1(e)) ) ;
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		Dart vv2 = phi2(v2) ;
		phi2unsew(v2) ;
		phi2sew(phi_1(e), v2) ;
		phi2sew(phi1(e), vv2) ;
	}
	Dart vv1 = phi2(v1) ;
	phi2unsew(v1) ;
	phi2sew(phi_1(d), v1) ;
	phi2sew(phi1(d), vv1) ;
}

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void Map2::unsewAroundVertex(Dart d)
{
	Dart e = d;

	do
	{
		Dart temp = phi1(e);
		Dart e_1 = phi_1(e);

		do
		{
			unsewFaces(temp);
			temp = phi1(temp);
		}while(temp != e_1);

		e = alpha1(e);
	}
	while(e != d);
}

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//void Map2::explodPolyhedron(Dart d)
//{
//	unsewAroundVertex(d);
////	closeHole(phi1(d));
//
//	//Recherche du (ou un des) sommet oppose
//		//tourner autour du sommet
//			//si quad  alors sommet oppose
//			//
//		//si pas de quad alors un sommet du trian
//
//	//
//}
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bool Map2::mergeVolumes(Dart d, Dart e)
{
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//	// First traversal of both faces to check the face sizes
//	// and stored their edges to efficiently access them further
//	std::vector<Dart> dDarts;
//	std::vector<Dart> eDarts;
//	dDarts.reserve(16);		// usual faces have less than 16 edges
//	eDarts.reserve(16);
//
//	Dart dFit = d ;
//	Dart eFit = phi1(e) ;	// must take phi1 because of the use
//	do						// of reverse iterator for sewing loop
//	{
//		dDarts.push_back(dFit) ;
//		dFit = phi1(dFit) ;
//	} while(dFit != d) ;
//	do
//	{
//		eDarts.push_back(eFit) ;
//		eFit = phi1(eFit) ;
//	} while(eFit != phi1(e)) ;
//
//	if(dDarts.size() != eDarts.size())
//		return false ;
//
//	// Make the sewing: take darts in initial order (clockwise) in first face
//	// and take darts in reverse order (counter-clockwise) in the second face
//	std::vector<Dart>::iterator dIt;
//	std::vector<Dart>::reverse_iterator eIt;
//	for (dIt = dDarts.begin(), eIt = eDarts.rbegin(); dIt != dDarts.end(); ++dIt, ++eIt)
//	{
//		Dart d2 = phi2(*dIt);			// Search the faces adjacent to dNext and eNext
//		Dart e2 = phi2(*eIt);
//		if (d2 != *dIt) phi2unsew(d2);	// Unlink the two adjacent faces from dNext and eNext
//		if (e2 != *eIt) phi2unsew(e2);
//		if (d2 != *dIt && e2 != *eIt) phi2sew(d2,e2); // Link the two adjacent faces together if they exists
//	}
//	Map1::deleteOrientedFace(d);	// Delete the two alone faces
//	Map1::deleteOrientedFace(e);
//
//	return true ;

	if (isBoundaryMarked(d) || isBoundaryMarked(e))
		return false;

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	// First traversal of both faces to check the face sizes
	// and stored their edges to efficiently access them further
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	std::vector<Dart> dDarts;
	std::vector<Dart> eDarts;
	dDarts.reserve(16);		// usual faces have less than 16 edges
	eDarts.reserve(16);

	Dart dFit = d ;
	Dart eFit = phi1(e) ;	// must take phi1 because of the use
	do						// of reverse iterator for sewing loop
	{
		dDarts.push_back(dFit) ;
		dFit = phi1(dFit) ;
	} while(dFit != d) ;
	do
	{
		eDarts.push_back(eFit) ;
		eFit = phi1(eFit) ;
	} while(eFit != phi1(e)) ;

	if(dDarts.size() != eDarts.size())
		return false ;

	// Make the sewing: take darts in initial order (clockwise) in first face
	// and take darts in reverse order (counter-clockwise) in the second face
	std::vector<Dart>::iterator dIt;
	std::vector<Dart>::reverse_iterator eIt;
	for (dIt = dDarts.begin(), eIt = eDarts.rbegin(); dIt != dDarts.end(); ++dIt, ++eIt)
	{
		Dart d2 = phi2(*dIt);			// Search the faces adjacent to dNext and eNext
		Dart e2 = phi2(*eIt);
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		phi2unsew(d2);	// Unlink the two adjacent faces from dNext and eNext
		phi2unsew(e2);
		phi2sew(d2,e2); // Link the two adjacent faces together
		if (isBoundaryMarked(d2) && isBoundaryMarked(e2))
			mergeBoundaryFaces(d2,e2);
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	}
	Map1::deleteOrientedFace(d);	// Delete the two alone faces
	Map1::deleteOrientedFace(e);

	return true ;
}

unsigned int Map2::closeHole(Dart d)
{
	assert(phi2(d) == d);		// Nothing to close

	Dart first = newDart();		// First edge of the face that will fill the hole
	unsigned int countEdges = 1;

	phi2sew(d, first);	// phi2-link the new edge to the hole

	Dart dNext = d;	// Turn around the hole
	Dart dPhi1;		// to complete the face
	do
	{
		do
		{
			dPhi1 = phi1(dNext);	// Search and put in dNext
			dNext = phi2(dPhi1);	// the next dart of the hole
		} while (dNext != dPhi1 && dPhi1 != d);

		if (dPhi1 != d)
		{
			Dart next = newDart();	// Add a new edge there and link it to the face
			++countEdges;
			phi1sew(first, next);	// the edge is linked to the face
			phi2sew(dNext, next);	// the face is linked to the hole
		}
	} while (dPhi1 != d);

	if (countEdges == 2)
	{
		countEdges = 0 ;
		collapseDegeneratedFace(first); // if the closing face is 2-sided, collapse it
	}

	return countEdges ;
}

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//void Map2::closeMap(DartMarker& marker)
//{
//	// Search the map for topological holes (fixed point for phi2)
//	for (Dart d = begin(); d != end(); next(d))
//	{
//		if (phi2(d) == d)
//		{
//			closeHole(d);
//			marker.markOrbit(FACE, phi2(d)) ;
//		}
//	}
//
void Map2::closeMap()
{	// Search the map for topological holes (fixed point for phi2)
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	for (Dart d = begin(); d != end(); next(d))
	{
		if (phi2(d) == d)
		{
			closeHole(d);
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			boundaryMarkOrbit(FACE,phi2(d));
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		}
	}
}

/*! @name Topological Queries
 *  Return or set various topological information
 *************************************************************************/

bool Map2::sameOrientedVertex(Dart d, Dart e)
{
	Dart dNext = d;				// Foreach dart dNext in the vertex of d
	do
	{
		if (dNext == e)			// Test equality with e
			return true;
		dNext = alpha1(dNext);
	} while (dNext != d);
	return false;				// None is equal to e => vertices are distinct
}

unsigned int Map2::vertexDegree(Dart d)
{
	unsigned int count = 0 ;
	Dart dNext = d ;
	do
	{
		++count ;
		if(phi2(dNext) == dNext)
			++count ;
		dNext = alpha1(dNext) ;
	} while (dNext != d) ;
	return count ;
}

unsigned int Map2::volumeDegree(Dart d)
{
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//	unsigned int count = 0;
//	DartMarkerStore mark(*this);		// Lock a marker
//
//	std::vector<Dart> visitedFaces;		// Faces that are traversed
//	visitedFaces.reserve(16);
//	visitedFaces.push_back(d);			// Start with the face of d
//	std::vector<Dart>::iterator face;
//
//	// For every face added to the list
//	for (face = visitedFaces.begin(); face != visitedFaces.end(); ++face)
//	{
//		if (!mark.isMarked(*face))		// Face has not been visited yet
//		{
//			++count;
//
//			Dart dNext = *face ;
//			do
//			{
//				mark.mark(dNext);					// Mark
//				Dart adj = phi2(dNext);				// Get adjacent face
//				if (adj != dNext && !mark.isMarked(adj))
//					visitedFaces.push_back(adj);	// Add it
//				dNext = phi1(dNext);
//			} while(dNext != *face);
//		}
//	}
//
//	return count;


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	unsigned int count = 0;
	DartMarkerStore mark(*this);		// Lock a marker

	std::vector<Dart> visitedFaces;		// Faces that are traversed
	visitedFaces.reserve(16);
	visitedFaces.push_back(d);			// Start with the face of d
	std::vector<Dart>::iterator face;

	// For every face added to the list
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	for (unsigned int i=0; i != visitedFaces.size(); ++i)
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	{
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		Dart df = visitedFaces[i];
		if (!isBoundaryMarked(df) && !mark.isMarked(df))		// Face has not been visited yet
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		{
			++count;

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			Dart dNext = df ;
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			do
			{
				mark.mark(dNext);					// Mark
				Dart adj = phi2(dNext);				// Get adjacent face
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				if ( !isBoundaryMarked(adj) && !mark.isMarked(adj) )
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					visitedFaces.push_back(adj);	// Add it
				dNext = phi1(dNext);
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			} while(dNext != df);
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		}
	}

	return count;
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}

bool Map2::isBoundaryVertex(Dart d)
{
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//	Dart dNext = d ;
//	do
//	{
//		if(phi2(dNext) == dNext)
//			return true ;
//		dNext = alpha1(dNext) ;
//	} while (dNext != d) ;
//	return false ;

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	Dart dNext = d ;
	do
	{
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		if (isBoundaryMarked(dNext))
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			return true ;
		dNext = alpha1(dNext) ;
	} while (dNext != d) ;
	return false ;
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}

Dart Map2::findBoundaryVertex(Dart d)
{
	Dart dNext = d ;
	do
	{
		if (isBoundaryMarked(dNext))
			return dNext ;
		dNext = alpha1(dNext) ;
	} while (dNext != d) ;
	return Dart::nil();
}

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bool Map2::isBoundaryEdge(Dart d)
{
	Dart e = phi2(d);
	return  isBoundaryMarked(e) || isBoundaryMarked(d);
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}

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Dart Map2::nextOnBoundary(Dart d)
{
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//	assert(phi2(d) == d);	// Only work on boundary dart
//	Dart dPhi1;
//	Dart dNext = d;
//	do
//	{						// Loop inside the vertex
//		dPhi1 = phi1(dNext);
//		dNext = phi2(dPhi1);
//	} while (dNext != dPhi1);
//	return dNext;

	assert( isBoundaryMarked(phi2(d)) );	// Only work on boundary dart
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	Dart dPhi1;
	Dart dNext = d;
	do
	{						// Loop inside the vertex
		dPhi1 = phi1(dNext);
		dNext = phi2(dPhi1);
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	} while (! isBoundaryMarked(dNext));
	return dPhi1;
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}

bool Map2::isTriangular()
{
	DartMarker m(*this) ;
	for(Dart d = begin(); d != end(); next(d))
	{
		if(!m.isMarked(d))
		{
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			m.markOrbit(FACE, d) ;
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			Dart dd = d ; // ???

			if (!isBoundaryMarked(d))
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			{
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				bool t = isFaceTriangle(d) ;
				if(!t)
				{
					return false ;
				}
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			}
		}
	}
	return true ;
}

bool Map2::check()
{
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	CGoGNout << "Check: topology begin" << CGoGNendl;
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	DartMarker m(*this);
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	for(Dart d = Map2::begin(); d != Map2::end(); Map2::next(d))
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	{
		Dart d2 = phi2(d);
		if (phi2(d2) != d)	// phi2 involution ?
		{
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			CGoGNout << "Check: phi2 is not an involution" << CGoGNendl;
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			return false;
		}

		Dart d1 = phi1(d);
		if (phi_1(d1) != d)	// phi1 a une image correcte ?
		{
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			CGoGNout << "Check: inconsistent phi_1 link" << CGoGNendl;
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			return false;
		}

		if (m.isMarked(d1))	// phi1 a un seul antécédent ?
		{
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			CGoGNout << "Check: dart with two phi1 predecessors" << CGoGNendl;
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			return false;
		}
		m.mark(d1);

		if (d1 == d)
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			CGoGNout << "Check: (warning) face loop (one edge)" << CGoGNendl;
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		if (phi1(d1) == d)
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			CGoGNout << "Check: (warning) face with only two edges" << CGoGNendl;
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		if (phi2(d1) == d)
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			CGoGNout << "Check: (warning) dangling edge" << CGoGNendl;
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	}
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	for(Dart d = Map2::begin(); d != Map2::end(); Map2::next(d))
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	{
		if (!m.isMarked(d))	// phi1 a au moins un antécédent ?
		{
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			CGoGNout << "Check: dart with no phi1 predecessor" << CGoGNendl;
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			return false;
		}
	}
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	CGoGNout << "Check: topology ok" << CGoGNendl;
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	return true;
}

/*! @name Cell Functors
 *  Apply functors to all darts of a cell
 *************************************************************************/

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bool Map2::foreach_dart_of_vertex(Dart d, FunctorType& f, unsigned int thread)
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{
	Dart dNext = d;
	do
	{
		if (f(dNext))
			return true;
		dNext = alpha1(dNext);
 	} while (dNext != d);
 	return false;
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}

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bool Map2::foreach_dart_of_edge(Dart d, FunctorType& fonct, unsigned int thread)
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{
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//	if (fonct(d))
//		return true;
//
//	Dart d2 = phi2(d);
//	if (d2 != d)
//		return fonct(d2);
//	else
//		return false;

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	if (fonct(d))
		return true;
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	return fonct(phi2(d));
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}

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bool Map2::foreach_dart_of_oriented_volume(Dart d, FunctorType& f, unsigned int thread)
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{
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	DartMarkerStore mark(*this,thread);	// Lock a marker
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	bool found = false;				// Last functor return value

	std::list<Dart> visitedFaces;	// Faces that are traversed
	visitedFaces.push_back(d);		// Start with the face of d
	std::list<Dart>::iterator face;

	// For every face added to the list
	for (face = visitedFaces.begin(); !found && face != visitedFaces.end(); ++face)
	{
		if (!mark.isMarked(*face))		// Face has not been visited yet
		{
			// Apply functor to the darts of the face
			found = foreach_dart_of_oriented_face(*face, f);

			// If functor returns false then mark visited darts (current face)
			// and add non visited adjacent faces to the list of face
			if (!found)
			{
				Dart dNext = *face ;
				do
				{
					mark.mark(dNext);					// Mark
					Dart adj = phi2(dNext);				// Get adjacent face
					if (adj != dNext && !mark.isMarked(adj))
						visitedFaces.push_back(adj);	// Add it
					dNext = phi1(dNext);
				} while(dNext != *face);
			}
		}
	}
	return found;
}

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bool Map2::foreach_dart_of_star(Dart d, unsigned int orbit, FunctorType& f, unsigned int thread)
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{
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	if(orbit == VERTEX)
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	{

		Dart dNext = d;
		do
		{
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			if(Map1::foreach_dart_of_face(dNext,f,thread))
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				return true;

			dNext = alpha1(dNext);
		} while (dNext != d);

		return false;
	}
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	else if(orbit == FACE)
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	{
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		if(Map1::foreach_dart_of_face(d,f,thread))
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			return true;

		if(phi2(d) != d)
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			return Map1::foreach_dart_of_face(phi2(d),f,thread);
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		else
			return false;
	}

	return false;
}

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bool Map2::foreach_dart_of_link(Dart d, unsigned int orbit, FunctorType& f, unsigned int thread)
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{
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	if(orbit == VERTEX)
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	{
		Dart dNext = d;
		do
		{
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			if(Map2::foreach_dart_of_edge(phi1(dNext),f,thread))
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				return true;

			dNext = alpha1(dNext);
		} while (dNext != d);

		return false;
	}
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	else if(orbit == FACE)
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	{
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		if(Map2::foreach_dart_of_vertex(phi_1(d),f,thread))
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			return true;

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		if(Map2::foreach_dart_of_vertex(phi_1(phi2(d)),f,thread))
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			return true;

		return false;
	}

	return false;
}


} // namespace CGoGN