halfEdgeSelector.hpp 51.6 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                                        *
*                                                                              *
*******************************************************************************/

#include <time.h>
#include "Algo/Geometry/basic.h"
#include "Algo/Decimation/geometryApproximator.h"

namespace CGoGN
{

namespace Algo
{

namespace Decimation
{

/************************************************************************************
 *                            QUADRIC ERROR METRIC (Memoryless version)             *
 ************************************************************************************/

template <typename PFP>
bool HalfEdgeSelector_QEMml<PFP>::init()
{
	MAP& m = this->m_map ;

	bool ok = false ;
	for(typename std::vector<ApproximatorGen<PFP>*>::iterator it = this->m_approximators.begin();
		it != this->m_approximators.end() && !ok;
		++it)
	{
		if((*it)->getApproximatedAttributeName() == "position")
		{
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			assert((*it)->getType() == A_hQEM || (*it)->getType() == A_hHalfCollapse || (*it)->getType() != A_Lightfield || !"Approximator for selector (HalfEdgeSelector_QEMml) must be of a half-edge approximator") ;
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			m_positionApproximator = reinterpret_cast<Approximator<PFP, VEC3,DART>* >(*it) ;
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			ok = true ;
		}
	}

	if(!ok)
		return false ;

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	CellMarker<VERTEX> vMark(m) ;
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	for(Dart d = m.begin(); d != m.end(); m.next(d))
	{
		if(!vMark.isMarked(d))
		{
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			Utils::Quadric<REAL> q ;	// create one quadric
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			quadric[d] = q ;	// per vertex
			vMark.mark(d) ;
		}
	}

	DartMarker mark(m) ;
	for(Dart d = m.begin(); d != m.end(); m.next(d))
	{
		if(!mark.isMarked(d))
		{
			Dart d1 = m.phi1(d) ;				// for each triangle,
			Dart d_1 = m.phi_1(d) ;				// initialize the quadric of the triangle
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			Utils::Quadric<REAL> q(this->m_position[d], this->m_position[d1], this->m_position[d_1]) ;
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			quadric[d] += q ;					// and add the contribution of
			quadric[d1] += q ;					// this quadric to the ones
			quadric[d_1] += q ;					// of the 3 incident vertices
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			mark.markOrbit<FACE>(d) ;
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		}
	}

	// Init multimap for each Half-edge
	halfEdges.clear() ;

	for(Dart d = m.begin(); d != m.end(); m.next(d))
	{
		initHalfEdgeInfo(d) ;	// init the edges with their optimal info
	}							// and insert them in the multimap according to their error

	cur = halfEdges.begin() ; 	// init the current edge to the first one

	return true ;
}

template <typename PFP>
bool HalfEdgeSelector_QEMml<PFP>::nextEdge(Dart& d)
{
	if(cur == halfEdges.end() || halfEdges.empty())
		return false ;
	d = (*cur).second ;
	return true ;
}

template <typename PFP>
void HalfEdgeSelector_QEMml<PFP>::updateBeforeCollapse(Dart d)
{
	MAP& m = this->m_map ;

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	HalfEdgeInfo* edgeE = &(halfEdgeInfo[d]) ;
	if(edgeE->valid)
		halfEdges.erase(edgeE->it) ;
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	edgeE = &(halfEdgeInfo[m.phi1(d)]) ;
	if(edgeE->valid)						// remove all
		halfEdges.erase(edgeE->it) ;
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	edgeE = &(halfEdgeInfo[m.phi_1(d)]) ;	// the halfedges that will disappear
	if(edgeE->valid)
		halfEdges.erase(edgeE->it) ;
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										// from the multimap
	Dart dd = m.phi2(d) ;
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	assert(dd != d) ;
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	if(dd != d)
	{
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		edgeE = &(halfEdgeInfo[dd]) ;
		if(edgeE->valid)
			halfEdges.erase(edgeE->it) ;
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		edgeE = &(halfEdgeInfo[m.phi1(dd)]) ;
		if(edgeE->valid)
			halfEdges.erase(edgeE->it) ;
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		edgeE = &(halfEdgeInfo[m.phi_1(dd)]) ;
		if(edgeE->valid)
			halfEdges.erase(edgeE->it) ;
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	}
}

/**
 * Update quadric of a vertex
 * Discards quadrics of d and assigns freshly calculated
 * quadrics depending on the actual planes surrounding d
 * @param dart d
 */
template <typename PFP>
void HalfEdgeSelector_QEMml<PFP>::recomputeQuadric(const Dart d, const bool recomputeNeighbors) {
	Dart dFront,dBack ;
	Dart dInit = d ;

	// Init Front
	dFront = dInit ;

	quadric[d].zero() ;

   	do {
   		// Make step
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   		dBack = this->m_map.phi1(dFront) ;
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       	dFront = this->m_map.phi2_1(dFront) ;
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       	if (this->m_map.phi2(dFront) != dFront) { // if dFront is no border
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           	quadric[d] += Utils::Quadric<REAL>(this->m_position[d],this->m_position[dBack],this->m_position[this->m_map.phi1(dFront)]) ;
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       	}
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       	if (recomputeNeighbors)
       		recomputeQuadric(dBack, false) ;

    } while(dFront != dInit) ;
}

template <typename PFP>
void HalfEdgeSelector_QEMml<PFP>::updateAfterCollapse(Dart d2, Dart dd2)
{
	MAP& m = this->m_map ;

	recomputeQuadric(d2, true) ;

	Dart vit = d2 ;
	do
	{
		updateHalfEdgeInfo(vit, true) ;
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		Dart d = m.phi2(vit) ;
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		if (d != vit)
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			updateHalfEdgeInfo(d, true) ;

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		updateHalfEdgeInfo(m.phi1(vit), true) ;
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		d = m.phi2(m.phi1(vit)) ;
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		if (d != m.phi1(vit))
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			updateHalfEdgeInfo(d, true) ;
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		Dart stop = m.phi2(vit) ;
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		assert (stop != vit) ;
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		Dart vit2 = m.phi12(m.phi1(vit)) ;
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		do {
			updateHalfEdgeInfo(vit2, true) ;
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			d = m.phi2(vit2) ;
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			if (d != vit2)
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				updateHalfEdgeInfo(d, true) ;

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			updateHalfEdgeInfo(m.phi1(vit2), false) ;
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			d = m.phi2(m.phi1(vit2)) ;
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			if (d != m.phi1(vit2))
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				updateHalfEdgeInfo(d, false) ;
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			vit2 = m.phi12(vit2) ;
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		} while (stop != vit2) ;
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		vit = m.phi2_1(vit) ;
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	} while(vit != d2) ;

	cur = halfEdges.begin() ; // set the current edge to the first one
}

template <typename PFP>
void HalfEdgeSelector_QEMml<PFP>::initHalfEdgeInfo(Dart d)
{
	MAP& m = this->m_map ;
	HalfEdgeInfo heinfo ;
	if(m.edgeCanCollapse(d))
		computeHalfEdgeInfo(d, heinfo) ;
	else
		heinfo.valid = false ;

	halfEdgeInfo[d] = heinfo ;
}

template <typename PFP>
void HalfEdgeSelector_QEMml<PFP>::updateHalfEdgeInfo(Dart d, bool recompute)
{
	MAP& m = this->m_map ;
	HalfEdgeInfo& heinfo = halfEdgeInfo[d] ;
	if(recompute)
	{
		if(heinfo.valid)
			halfEdges.erase(heinfo.it) ;			// remove the edge from the multimap
		if(m.edgeCanCollapse(d))
			computeHalfEdgeInfo(d, heinfo) ;
		else
			heinfo.valid = false ;
	}
	else
	{
		if(m.edgeCanCollapse(d))
		{								 	// if the edge can be collapsed now
			if(!heinfo.valid)				 // but it was not before
				computeHalfEdgeInfo(d, heinfo) ;
		}
		else
		{								 // if the edge cannot be collapsed now
			if(heinfo.valid)				 // and it was before
			{
				halfEdges.erase(heinfo.it) ;
				heinfo.valid = false ;
			}
		}
	}
}

template <typename PFP>
void HalfEdgeSelector_QEMml<PFP>::computeHalfEdgeInfo(Dart d, HalfEdgeInfo& heinfo)
{
	MAP& m = this->m_map ;
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	Dart dd = m.phi1(d) ;
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	Utils::Quadric<REAL> quad ;
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	quad += quadric[d] ;	// compute the sum of the
	quad += quadric[dd] ;	// two vertices quadrics

	m_positionApproximator->approximate(d) ;

	REAL err = quad(m_positionApproximator->getApprox(d)) ;
	heinfo.it = halfEdges.insert(std::make_pair(err, d)) ;
	heinfo.valid = true ;
}

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/************************************************************************************
 *                        EDGESELECTOR QEMext for Color                             *
 ************************************************************************************/

template <typename PFP>
bool HalfEdgeSelector_QEMextColor<PFP>::init()
{
	MAP& m = this->m_map ;

	// Verify availability of required approximators
	unsigned int ok = 0 ;
	for (unsigned int approxindex = 0 ; approxindex < this->m_approximators.size() ; ++approxindex)
	{
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		assert(this->m_approximators[approxindex]->getType() == A_hQEM
				|| this->m_approximators[approxindex]->getType() == A_hHalfCollapse
				|| !"Approximator for selector (HalfEdgeSelector_QEMextColor) must be of a half-edge approximator") ;

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		bool saved = false ;
		for (unsigned int attrindex = 0 ; attrindex < this->m_approximators[approxindex]->getNbApproximated() ; ++ attrindex)
		{
			// constraint : 2 approximators in specific order
			if(ok == 0 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == "position")
			{
				++ok ;
				m_approxindex_pos = approxindex ;
				m_attrindex_pos = attrindex ;
				m_pos = this->m_position ;
				if (!saved)
				{
					m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
					saved = true ;
				}
			}
			else if(ok == 1 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == "color")
			{
				++ok ;
				m_approxindex_color = approxindex ;
				m_attrindex_color = attrindex ;
				m_color = m.template getAttribute<typename PFP::VEC3, VERTEX>("color") ;
				assert(m_color.isValid() || !"EdgeSelector_QEMextColor: color attribute is not valid") ;
				if (!saved)
				{
					m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
					saved = true ;
				}
			}
		}
	}

	if(ok != 2)
		return false ;

	TraversorV<MAP> travV(m);
	for(Dart dit = travV.begin() ; dit != travV.end() ; dit = travV.next())
	{
		Utils::QuadricNd<REAL,6> q ;		// create one quadric
		m_quadric[dit] = q ;		// per vertex
	}

	// Compute quadric per vertex
	TraversorF<MAP> travF(m) ;
	for(Dart dit = travF.begin() ; dit != travF.end() ; dit = travF.next()) // init QEM quadrics
	{
		Dart d1 = m.phi1(dit) ;					// for each triangle,
		Dart d_1 = m.phi_1(dit) ;					// initialize the quadric of the triangle

   		VEC6 p0, p1, p2 ;
   		for (unsigned int i = 0 ; i < 3 ; ++i)
   		{
   			p0[i] = this->m_position[dit][i] ;
   			p0[i+3] = this->m_color[dit][i] ;
   			p1[i] = this->m_position[d1][i] ;
   			p1[i+3] = this->m_color[d1][i] ;
   			p2[i] = this->m_position[d_1][i] ;
   			p2[i+3] = this->m_color[d_1][i] ;
   		}
		Utils::QuadricNd<REAL,6> q(p0,p1,p2) ;
		m_quadric[dit] += q ;						// and add the contribution of
		m_quadric[d1] += q ;						// this quadric to the ones
		m_quadric[d_1] += q ;						// of the 3 incident vertices
	}


	// Init multimap for each Half-edge
	halfEdges.clear() ;

	for(Dart d = m.begin(); d != m.end(); m.next(d))
	{
		initHalfEdgeInfo(d) ;	// init the edges with their optimal info
	}							// and insert them in the multimap according to their error

	cur = halfEdges.begin() ; 	// init the current edge to the first one

	return true ;
}

template <typename PFP>
bool HalfEdgeSelector_QEMextColor<PFP>::nextEdge(Dart& d)
{
	if(cur == halfEdges.end() || halfEdges.empty())
		return false ;
	d = (*cur).second ;
	return true ;
}

template <typename PFP>
void HalfEdgeSelector_QEMextColor<PFP>::updateBeforeCollapse(Dart d)
{
	MAP& m = this->m_map ;

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	HalfEdgeInfo* edgeE = &(halfEdgeInfo[d]) ;
	if(edgeE->valid)
		halfEdges.erase(edgeE->it) ;
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	edgeE = &(halfEdgeInfo[m.phi1(d)]) ;
	if(edgeE->valid)						// remove all
		halfEdges.erase(edgeE->it) ;
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	edgeE = &(halfEdgeInfo[m.phi_1(d)]) ;	// the halfedges that will disappear
	if(edgeE->valid)
		halfEdges.erase(edgeE->it) ;
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										// from the multimap
	Dart dd = m.phi2(d) ;
	assert(dd != d) ;
	if(dd != d)
	{
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		edgeE = &(halfEdgeInfo[dd]) ;
		if(edgeE->valid)
			halfEdges.erase(edgeE->it) ;
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		edgeE = &(halfEdgeInfo[m.phi1(dd)]) ;
		if(edgeE->valid)
			halfEdges.erase(edgeE->it) ;
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		edgeE = &(halfEdgeInfo[m.phi_1(dd)]) ;
		if(edgeE->valid)
			halfEdges.erase(edgeE->it) ;
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	}
}

/**
 * Update quadric of a vertex
 * Discards quadrics of d and assigns freshly calculated
 * quadrics depending on the actual planes surrounding d
 * @param dart d
 */
template <typename PFP>
void HalfEdgeSelector_QEMextColor<PFP>::recomputeQuadric(const Dart d, const bool recomputeNeighbors) {
	Dart dFront,dBack ;
	Dart dInit = d ;

	// Init Front
	dFront = dInit ;

	m_quadric[d].zero() ;

 	do
   	{
   		// Make step
   		dBack = this->m_map.phi2(dFront) ;
       	dFront = this->m_map.phi2_1(dFront) ;

       	if (dBack != dFront)
       	{ // if dFront is no border
   			Dart d2 = this->m_map.phi2(dFront) ;

       		VEC6 p0, p1, p2 ;
       		for (unsigned int i = 0 ; i < 3 ; ++i)
       		{

       			p0[i] = this->m_position[d][i] ;
       			p0[i+3] = this->m_color[d][i] ;
       			p1[i] = this->m_position[d2][i] ;
       			p1[i+3] = this->m_color[d2][i] ;
       			p2[i] = this->m_position[dBack][i] ;
       			p2[i+3] = this->m_color[dBack][i] ;
       		}
       		m_quadric[d] += Utils::QuadricNd<REAL,6>(p0,p1,p2) ;
       	}
       	if (recomputeNeighbors)
       		recomputeQuadric(dBack, false) ;

    } while(dFront != dInit) ;
}

template <typename PFP>
void HalfEdgeSelector_QEMextColor<PFP>::updateAfterCollapse(Dart d2, Dart dd2)
{
	MAP& m = this->m_map ;

	recomputeQuadric(d2, true) ;

	Dart vit = d2 ;
	do
	{
		updateHalfEdgeInfo(vit, true) ;
		Dart d = m.phi2(vit) ;
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		if (d != vit)
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			updateHalfEdgeInfo(d, true) ;

		updateHalfEdgeInfo(m.phi1(vit), true) ;
		d = m.phi2(m.phi1(vit)) ;
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		if (d != m.phi1(vit))
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			updateHalfEdgeInfo(d, true) ;

		Dart stop = m.phi2(vit) ;
		assert (stop != vit) ;
		Dart vit2 = m.phi12(m.phi1(vit)) ;
		do {
			updateHalfEdgeInfo(vit2, true) ;
			d = m.phi2(vit2) ;
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			if (d != vit2)
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				updateHalfEdgeInfo(d, true) ;

			updateHalfEdgeInfo(m.phi1(vit2), false) ;
			d = m.phi2(m.phi1(vit2)) ;
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			if (d != m.phi1(vit2))
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				updateHalfEdgeInfo(d, false) ;

			vit2 = m.phi12(vit2) ;
		} while (stop != vit2) ;
		vit = m.phi2_1(vit) ;
	} while(vit != d2) ;

	cur = halfEdges.begin() ; // set the current edge to the first one
}

template <typename PFP>
void HalfEdgeSelector_QEMextColor<PFP>::initHalfEdgeInfo(Dart d)
{
	MAP& m = this->m_map ;
	HalfEdgeInfo heinfo ;
	if(m.edgeCanCollapse(d))
		computeHalfEdgeInfo(d, heinfo) ;
	else
		heinfo.valid = false ;

	halfEdgeInfo[d] = heinfo ;
}

template <typename PFP>
void HalfEdgeSelector_QEMextColor<PFP>::updateHalfEdgeInfo(Dart d, bool recompute)
{
	MAP& m = this->m_map ;
	HalfEdgeInfo& heinfo = halfEdgeInfo[d] ;
	if(recompute)
	{
		if(heinfo.valid)
			halfEdges.erase(heinfo.it) ;			// remove the edge from the multimap
		if(m.edgeCanCollapse(d))
			computeHalfEdgeInfo(d, heinfo) ;
		else
			heinfo.valid = false ;
	}
	else
	{
		if(m.edgeCanCollapse(d))
		{								 	// if the edge can be collapsed now
			if(!heinfo.valid)				 // but it was not before
				computeHalfEdgeInfo(d, heinfo) ;
		}
		else
		{								 // if the edge cannot be collapsed now
			if(heinfo.valid)				 // and it was before
			{
				halfEdges.erase(heinfo.it) ;
				heinfo.valid = false ;
			}
		}
	}
}

template <typename PFP>
void HalfEdgeSelector_QEMextColor<PFP>::computeHalfEdgeInfo(Dart d, HalfEdgeInfo& heinfo)
{
	MAP& m = this->m_map ;
	Dart dd = m.phi1(d) ;

	// New position
	Utils::QuadricNd<REAL,6> quad ;
	quad += m_quadric[d] ;	// compute the sum of the
	quad += m_quadric[dd] ;	// two vertices quadrics

	// compute all approximated attributes
	for(typename std::vector<ApproximatorGen<PFP>*>::iterator it = this->m_approximators.begin() ;
			it != this->m_approximators.end() ;
			++it)
	{
		(*it)->approximate(d) ;
	}

	// get pos
	const VEC3& newPos = this->m_approx[m_approxindex_pos]->getApprox(d,m_attrindex_pos) ; // get newPos
	// get col
	const VEC3& newCol = this->m_approx[m_approxindex_color]->getApprox(d,m_attrindex_color) ; // get newCol

	// compute error
	VEC6 newEmb ;
	for (unsigned int i = 0 ; i < 3 ; ++i)
	{
		newEmb[i] = newPos[i] ;
		newEmb[i+3] = newCol[i] ;
	}

	const REAL& err = quad(newEmb) ;

	// Check if errated values appear
	if (err < -1e-6)
		heinfo.valid = false ;
	else
	{
		heinfo.it = this->halfEdges.insert(std::make_pair(std::max(err,REAL(0)), d)) ;
		heinfo.valid = true ;
	}
}

/************************************************************************************
 *              HALF EDGE LIGHTFIELD SELECTOR (using QEMml half-edge)               *
 ************************************************************************************/

template <typename PFP>
bool HalfEdgeSelector_Lightfield<PFP>::init()
{
	MAP& m = this->m_map ;

	// Verify availability of required approximators
	unsigned int ok = 0 ;
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	unsigned int k = 0 ;
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	for (unsigned int approxindex = 0 ; approxindex < this->m_approximators.size() ; ++approxindex)
	{
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		assert(this->m_approximators[approxindex]->getType() == A_hQEM
				|| this->m_approximators[approxindex]->getType() == A_hHalfCollapse
				|| this->m_approximators[approxindex]->getType() != A_Lightfield
				|| !"Approximator for selector (HalfEdgeSelector_Lightfield) must be of a half-edge approximator") ;

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		bool saved = false ;
		for (unsigned int attrindex = 0 ; attrindex < this->m_approximators[approxindex]->getNbApproximated() ; ++ attrindex)
		{
			// constraint : 2 approximators in specific order
			if(ok == 0 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == "position")
			{
				++ok ;
				m_approxindex_pos = approxindex ;
				m_attrindex_pos = attrindex ;
				m_pos = this->m_position ;
				if (!saved)
				{
					m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
					saved = true ;
				}
			}
			else if(ok == 1 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == "frameT")
			{
				++ok ;
//				m_approxindex_FT = approxindex ;
//				m_attrindex_FT = attrindex ;
				m_frameT = m.template getAttribute<typename PFP::VEC3, VERTEX>("frameT") ;
				if (!saved)
				{
					m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
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					assert(m_frameT.isValid() || !"HalfEdgeSelector_Lightfield: frameT attribute is not valid") ;
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					saved = true ;
				}
			}
			else if(ok == 2 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == "frameB")
			{
				++ok ;
//				m_approxindex_FB = approxindex ;
//				m_attrindex_FB = attrindex ;
				m_frameB = m.template getAttribute<typename PFP::VEC3, VERTEX>("frameB") ;
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				assert(m_frameB.isValid() || !"HalfEdgeSelector_Lightfield: frameB attribute is not valid") ;
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				if (!saved)
				{
					m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
					saved = true ;
				}
			}
			else if(ok == 3 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == "frameN")
			{
				++ok ;
				m_approxindex_FN = approxindex ;
				m_attrindex_FN = attrindex ;
				m_frameN = m.template getAttribute<typename PFP::VEC3, VERTEX>("frameN") ;
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				assert(m_frameN.isValid() || !"HalfEdgeSelector_Lightfield: frameN attribute is not valid") ;
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				if (!saved)
				{
					m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
					saved = true ;
				}
			}
			else
			{
				std::stringstream s ;
				s << "PBcoefs" << k ;
				if(ok > 3 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == s.str().c_str())
				{
					++ok ;
					m_HF.push_back(m.template getAttribute<typename PFP::VEC3, VERTEX>(s.str().c_str())) ;
					if (m_HF[k++].isValid())
					{
						m_approxindex_HF.push_back(approxindex) ;
						m_attrindex_HF.push_back(attrindex) ;
						if (!saved)
						{
							m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
							saved = true ;
						}
					}
				}
			}
		}
	}
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	m_K = k ;
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	if(ok < 5)
		return false ;

	TraversorV<MAP> travV(m);
	for(Dart dit = travV.begin() ; dit != travV.end() ; dit = travV.next())
	{
		Utils::Quadric<REAL> q ;		// create one quadric
		m_quadricGeom[dit] = q ;		// per vertex
	}

	// Compute quadric per vertex
	TraversorF<MAP> travF(m) ;
	for(Dart dit = travF.begin() ; dit != travF.end() ; dit = travF.next()) // init QEM quadrics
	{
		Dart d1 = m.phi1(dit) ;					// for each triangle,
		Dart d_1 = m.phi_1(dit) ;					// initialize the quadric of the triangle

		Utils::Quadric<REAL> q(this->m_position[dit], this->m_position[d1], this->m_position[d_1]) ;
		m_quadricGeom[dit] += q ;						// and add the contribution of
		m_quadricGeom[d1] += q ;						// this quadric to the ones
		m_quadricGeom[d_1] += q ;						// of the 3 incident vertices
	}

	// Init multimap for each Half-edge
	halfEdges.clear() ;

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	for(Dart d = m.begin(); d != m.end(); m.next(d))
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	{
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		initHalfEdgeInfo(d) ;	// init the edges with their optimal info
	}							// and insert them in the multimap according to their error

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	cur = halfEdges.begin() ; 	// init the current edge to the first one

	return true ;
}

template <typename PFP>
bool HalfEdgeSelector_Lightfield<PFP>::nextEdge(Dart& d)
{
	if(cur == halfEdges.end() || halfEdges.empty())
		return false ;
	d = (*cur).second ;
	return true ;
}

template <typename PFP>
void HalfEdgeSelector_Lightfield<PFP>::updateBeforeCollapse(Dart d)
{
	MAP& m = this->m_map ;

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	HalfEdgeInfo* edgeE = &(halfEdgeInfo[d]) ;
	if(edgeE->valid)
		halfEdges.erase(edgeE->it) ;
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	edgeE = &(halfEdgeInfo[m.phi1(d)]) ;
	if(edgeE->valid)						// remove all
		halfEdges.erase(edgeE->it) ;
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	edgeE = &(halfEdgeInfo[m.phi_1(d)]) ;	// the halfedges that will disappear
	if(edgeE->valid)
		halfEdges.erase(edgeE->it) ;
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										// from the multimap
	Dart dd = m.phi2(d) ;
	assert(dd != d) ;
	if(dd != d)
	{
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		edgeE = &(halfEdgeInfo[dd]) ;
		if(edgeE->valid)
			halfEdges.erase(edgeE->it) ;
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		edgeE = &(halfEdgeInfo[m.phi1(dd)]) ;
		if(edgeE->valid)
			halfEdges.erase(edgeE->it) ;
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		edgeE = &(halfEdgeInfo[m.phi_1(dd)]) ;
		if(edgeE->valid)
			halfEdges.erase(edgeE->it) ;
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	}
}

/**
 * Update quadric of a vertex
 * Discards quadrics of d and assigns freshly calculated
 * quadrics depending on the actual planes surrounding d
 * @param dart d
 */
template <typename PFP>
void HalfEdgeSelector_Lightfield<PFP>::recomputeQuadric(const Dart d, const bool recomputeNeighbors)
{
	Dart dFront,dBack ;
	Dart dInit = d ;

	// Init Front
	dFront = dInit ;

	m_quadricGeom[d].zero() ;

   	do {
   		// Make step
   		dBack = this->m_map.phi2(dFront) ;
   		dFront = this->m_map.phi2_1(dFront) ;

   		if (dBack != dFront)
   		{ // if dFront is no border
   			m_quadricGeom[d] += Utils::Quadric<REAL>(m_pos[d],m_pos[this->m_map.phi1(dFront)],m_pos[dBack]) ;
   		}
   		if (recomputeNeighbors)
   			recomputeQuadric(dBack, false) ;

    } while(dFront != dInit) ;
}

template <typename PFP>
void HalfEdgeSelector_Lightfield<PFP>::updateAfterCollapse(Dart d2, Dart dd2)
{
	MAP& m = this->m_map ;

	recomputeQuadric(d2, true) ;

	Dart vit = d2 ;
	do
	{
		updateHalfEdgeInfo(vit, true) ;
		Dart d = m.phi2(vit) ;
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		if (d != vit)
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			updateHalfEdgeInfo(d, true) ;

		updateHalfEdgeInfo(m.phi1(vit), true) ;
		d = m.phi2(m.phi1(vit)) ;
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		if (d != m.phi1(vit))
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			updateHalfEdgeInfo(d, true) ;

		Dart stop = m.phi2(vit) ;
		assert (stop != vit) ;
		Dart vit2 = m.phi12(m.phi1(vit)) ;
		do {
			updateHalfEdgeInfo(vit2, true) ;
			d = m.phi2(vit2) ;
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			if (d != vit2)
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				updateHalfEdgeInfo(d, true) ;

			updateHalfEdgeInfo(m.phi1(vit2), false) ;
			d = m.phi2(m.phi1(vit2)) ;
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			if (d != m.phi1(vit2))
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				updateHalfEdgeInfo(d, false) ;

			vit2 = m.phi12(vit2) ;
		} while (stop != vit2) ;
		vit = m.phi2_1(vit) ;
	} while(vit != d2) ;

	cur = halfEdges.begin() ; // set the current edge to the first one
}

template <typename PFP>
void HalfEdgeSelector_Lightfield<PFP>::initHalfEdgeInfo(Dart d)
{
	MAP& m = this->m_map ;
	HalfEdgeInfo heinfo ;
	if(m.edgeCanCollapse(d))
		computeHalfEdgeInfo(d, heinfo) ;
	else
		heinfo.valid = false ;

	halfEdgeInfo[d] = heinfo ;
}

template <typename PFP>
void HalfEdgeSelector_Lightfield<PFP>::updateHalfEdgeInfo(Dart d, bool recompute)
{
	MAP& m = this->m_map ;
	HalfEdgeInfo& heinfo = halfEdgeInfo[d] ;
	if(recompute)
	{
		if(heinfo.valid)
			halfEdges.erase(heinfo.it) ;			// remove the edge from the multimap
		if(m.edgeCanCollapse(d))
			computeHalfEdgeInfo(d, heinfo) ;
		else
			heinfo.valid = false ;
	}
	else
	{
		if(m.edgeCanCollapse(d))
		{								 	// if the edge can be collapsed now
			if(!heinfo.valid)				 // but it was not before
				computeHalfEdgeInfo(d, heinfo) ;
		}
		else
		{								 // if the edge cannot be collapsed now
			if(heinfo.valid)				 // and it was before
			{
				halfEdges.erase(heinfo.it) ;
				heinfo.valid = false ;
			}
		}
	}
}

template <typename PFP>
void HalfEdgeSelector_Lightfield<PFP>::computeHalfEdgeInfo(Dart d, HalfEdgeInfo& heinfo)
{
	MAP& m = this->m_map ;
	Dart dd = m.phi1(d) ;

	// New position
	Utils::Quadric<REAL> quad ;
	quad += m_quadricGeom[d] ;	// compute the sum of the
	quad += m_quadricGeom[dd] ;	// two vertices quadrics

	// compute all approximated attributes
	for(typename std::vector<ApproximatorGen<PFP>*>::iterator it = this->m_approximators.begin() ;
			it != this->m_approximators.end() ;
			++it)
	{
		(*it)->approximate(d) ;
	}

	// Get all approximated attributes
	// New position
	const VEC3& newPos = this->m_approx[m_approxindex_pos]->getApprox(d,m_attrindex_pos) ; // get newPos
	// New normal
	const VEC3& newFN = this->m_approx[m_approxindex_FN]->getApprox(d,m_attrindex_FN) ; // get new frameN

	// New function
	std::vector<VEC3> newHF ;
	newHF.resize(m_K) ;
	for (unsigned int k = 0 ; k < m_K ; ++k)
		newHF[k] = this->m_approx[m_approxindex_HF[k]]->getApprox(d,m_attrindex_HF[k]) ; // get newHFcoefsK

	// Compute errors
	// Position
	Utils::Quadric<REAL> quadGeom ;
	quadGeom += m_quadricGeom[d] ;	// compute the sum of the
	quadGeom += m_quadricGeom[dd] ;	// two vertices quadrics

	// hemisphere difference error
	double scal1 = double(m_frameN[d] * newFN) ;
	double alpha1 = acos(std::max(std::min(scal1, double(1)),double(-1))) ; // for epsilon normalization of newFN errors
	// angle 2
	double scal2 = double(m_frameN[dd] * newFN) ;
	double alpha2 = acos(std::max(std::min(scal2, double(1)),double(-1))) ; // for epsilon normalization of newFN errors

	double alpha = alpha1 + alpha2 ;

	assert(m_quadricHF.isValid() | !"EdgeSelector_Lightfield<PFP>::computeEdgeInfo: quadricHF is not valid") ;
	Utils::QuadricHF<REAL> quadHF = m_quadricHF[d] ;

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	//std::cout << quadGeom(newPos) / (alpha/M_PI + quadHF(newHF)) << std::endl ;
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	// sum of QEM metric and frame orientation difference
	const REAL& err =
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			quadGeom(newPos) + // geom
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			alpha / M_PI + // frame
			quadHF(newHF) // function coefficients
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			 ;

	// Check if errated values appear
	if (err < -1e-6)
		heinfo.valid = false ;
	else
	{
		heinfo.it = this->halfEdges.insert(std::make_pair(std::max(err,REAL(0)), d)) ;
		heinfo.valid = true ;
	}
}

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/************************************************************************************
 *              HALF EDGE LIGHTFIELD SELECTOR (using QEMml half-edge) experimental  *
 ************************************************************************************/

template <typename PFP>
bool HalfEdgeSelector_LightfieldExp<PFP>::init()
{
	MAP& m = this->m_map ;

	// Verify availability of required approximators
	unsigned int ok = 0 ;
	unsigned int k = 0 ;
	for (unsigned int approxindex = 0 ; approxindex < this->m_approximators.size() ; ++approxindex)
	{
		assert(this->m_approximators[approxindex]->getType() == A_hQEM
				|| this->m_approximators[approxindex]->getType() == A_hHalfCollapse
				|| this->m_approximators[approxindex]->getType() != A_Lightfield
				|| !"Approximator for selector (HalfEdgeSelector_Lightfield) must be of a half-edge approximator") ;

		bool saved = false ;
		for (unsigned int attrindex = 0 ; attrindex < this->m_approximators[approxindex]->getNbApproximated() ; ++ attrindex)
		{
			// constraint : 2 approximators in specific order
			if(ok == 0 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == "position")
			{
				++ok ;
				m_approxindex_pos = approxindex ;
				m_attrindex_pos = attrindex ;
				m_pos = this->m_position ;
				if (!saved)
				{
					m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
					saved = true ;
				}
			}
			else if(ok == 1 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == "frameT")
			{
				++ok ;
//				m_approxindex_FT = approxindex ;
//				m_attrindex_FT = attrindex ;
				m_frameT = m.template getAttribute<typename PFP::VEC3, VERTEX>("frameT") ;
				if (!saved)
				{
					m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
					assert(m_frameT.isValid() || !"HalfEdgeSelector_LightfieldExp: frameT attribute is not valid") ;
					saved = true ;
				}
			}
			else if(ok == 2 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == "frameB")
			{
				++ok ;
//				m_approxindex_FB = approxindex ;
//				m_attrindex_FB = attrindex ;
				m_frameB = m.template getAttribute<typename PFP::VEC3, VERTEX>("frameB") ;
				assert(m_frameB.isValid() || !"HalfEdgeSelector_LightfieldExp: frameB attribute is not valid") ;
				if (!saved)
				{
					m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
					saved = true ;
				}
			}
			else if(ok == 3 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == "frameN")
			{
				++ok ;
				m_approxindex_FN = approxindex ;
				m_attrindex_FN = attrindex ;
				m_frameN = m.template getAttribute<typename PFP::VEC3, VERTEX>("frameN") ;
				assert(m_frameN.isValid() || !"HalfEdgeSelector_LightfieldExp: frameN attribute is not valid") ;
				if (!saved)
				{
					m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
					saved = true ;
				}
			}
			else
			{
				std::stringstream s ;
				s << "PBcoefs" << k ;
				if(ok > 3 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == s.str().c_str())
				{
					++ok ;
					m_HF.push_back(m.template getAttribute<typename PFP::VEC3, VERTEX>(s.str().c_str())) ;
					if (m_HF[k++].isValid())
					{
						m_approxindex_HF.push_back(approxindex) ;
						m_attrindex_HF.push_back(attrindex) ;
						if (!saved)
						{
							m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
							saved = true ;
						}
					}
				}
			}
		}
	}
	m_K = k ;

	if(ok < 6)
		return false ;

	TraversorV<MAP> travV(m);
	for(Dart dit = travV.begin() ; dit != travV.end() ; dit = travV.next())
	{
		Utils::Quadric<REAL> q ;		// create one quadric
		m_quadricGeom[dit] = q ;		// per vertex
	}

	// Compute quadric per vertex
	TraversorF<MAP> travF(m) ;
	for(Dart dit = travF.begin() ; dit != travF.end() ; dit = travF.next()) // init QEM quadrics
	{
		Dart d1 = m.phi1(dit) ;					// for each triangle,
		Dart d_1 = m.phi_1(dit) ;					// initialize the quadric of the triangle

		Utils::Quadric<REAL> q(this->m_position[dit], this->m_position[d1], this->m_position[d_1]) ;
		m_quadricGeom[dit] += q ;						// and add the contribution of
		m_quadricGeom[d1] += q ;						// this quadric to the ones
		m_quadricGeom[d_1] += q ;						// of the 3 incident vertices
	}

	// Init multimap for each Half-edge
	halfEdges.clear() ;

	for(Dart d = m.begin() ; d != m.end() ; m.next(d))
	{
		initHalfEdgeInfo(d) ; // init the edges with their optimal position
	}						// and insert them in the multimap according to their error

	cur = halfEdges.begin() ; 	// init the current edge to the first one

	return true ;
}

template <typename PFP>
bool HalfEdgeSelector_LightfieldExp<PFP>::nextEdge(Dart& d)
{
	if(cur == halfEdges.end() || halfEdges.empty())
		return false ;
	d = (*cur).second ;
	return true ;
}

template <typename PFP>
void HalfEdgeSelector_LightfieldExp<PFP>::updateBeforeCollapse(Dart d)
{
	MAP& m = this->m_map ;

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	HalfEdgeInfo* edgeE = &(halfEdgeInfo[d]) ;
	if(edgeE->valid)
		halfEdges.erase(edgeE->it) ;
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	edgeE = &(halfEdgeInfo[m.phi1(d)]) ;
	if(edgeE->valid)						// remove all
		halfEdges.erase(edgeE->it) ;
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	edgeE = &(halfEdgeInfo[m.phi_1(d)]) ;	// the halfedges that will disappear
	if(edgeE->valid)
		halfEdges.erase(edgeE->it) ;
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										// from the multimap
	Dart dd = m.phi2(d) ;
	assert(dd != d) ;
	if(dd != d)
	{
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		edgeE = &(halfEdgeInfo[dd]) ;
		if(edgeE->valid)
			halfEdges.erase(edgeE->it) ;
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		edgeE = &(halfEdgeInfo[m.phi1(dd)]) ;
		if(edgeE->valid)
			halfEdges.erase(edgeE->it) ;
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		edgeE = &(halfEdgeInfo[m.phi_1(dd)]) ;
		if(edgeE->valid)
			halfEdges.erase(edgeE->it) ;
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	}
}

/**
 * Update quadric of a vertex
 * Discards quadrics of d and assigns freshly calculated
 * quadrics depending on the actual planes surrounding d
 * @param dart d
 */
template <typename PFP>
void HalfEdgeSelector_LightfieldExp<PFP>::recomputeQuadric(const Dart d, const bool recomputeNeighbors)
{
	Dart dFront,dBack ;
	Dart dInit = d ;

	// Init Front
	dFront = dInit ;

	m_quadricGeom[d].zero() ;

   	do {
   		// Make step
   		dBack = this->m_map.phi2(dFront) ;
   		dFront = this->m_map.phi2_1(dFront) ;

   		if (dBack != dFront)
   		{ // if dFront is no border
   			m_quadricGeom[d] += Utils::Quadric<REAL>(m_pos[d],m_pos[this->m_map.phi1(dFront)],m_pos[dBack]) ;
   		}
   		if (recomputeNeighbors)
   			recomputeQuadric(dBack, false) ;

    } while(dFront != dInit) ;
}

template <typename PFP>
void HalfEdgeSelector_LightfieldExp<PFP>::updateAfterCollapse(Dart d2, Dart dd2)
{
	MAP& m = this->m_map ;

	recomputeQuadric(d2, true) ;

	Dart vit = d2 ;
	do
	{
		updateHalfEdgeInfo(vit, true) ;
		Dart d = m.phi2(vit) ;
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		if (d != vit)
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			updateHalfEdgeInfo(d, true) ;

		updateHalfEdgeInfo(m.phi1(vit), true) ;
		d = m.phi2(m.phi1(vit)) ;
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		if (d != m.phi1(vit))
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			updateHalfEdgeInfo(d, true) ;

		Dart stop = m.phi2(vit) ;
		assert (stop != vit) ;
		Dart vit2 = m.phi12(m.phi1(vit)) ;
		do {
			updateHalfEdgeInfo(vit2, true) ;
			d = m.phi2(vit2) ;
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			if (d != vit2)
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				updateHalfEdgeInfo(d, true) ;

			updateHalfEdgeInfo(m.phi1(vit2), false) ;
			d = m.phi2(m.phi1(vit2)) ;
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			if (d != m.phi1(vit2))
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				updateHalfEdgeInfo(d, false) ;

			vit2 = m.phi12(vit2) ;
		} while (stop != vit2) ;
		vit = m.phi2_1(vit) ;
	} while(vit != d2) ;

	cur = halfEdges.begin() ; // set the current edge to the first one
}

template <typename PFP>
void HalfEdgeSelector_LightfieldExp<PFP>::initHalfEdgeInfo(Dart d)
{
	MAP& m = this->m_map ;
	HalfEdgeInfo heinfo ;
	if(m.edgeCanCollapse(d))
		computeHalfEdgeInfo(d, heinfo) ;
	else
		heinfo.valid = false ;

	halfEdgeInfo[d] = heinfo ;
}

template <typename PFP>
void HalfEdgeSelector_LightfieldExp<PFP>::updateHalfEdgeInfo(Dart d, bool recompute)
{
	MAP& m = this->m_map ;
	HalfEdgeInfo& heinfo = halfEdgeInfo[d] ;
	if(recompute)
	{
		if(heinfo.valid)
			halfEdges.erase(heinfo.it) ;			// remove the edge from the multimap
		if(m.edgeCanCollapse(d))
			computeHalfEdgeInfo(d, heinfo) ;
		else
			heinfo.valid = false ;
	}
	else
	{
		if(m.edgeCanCollapse(d))
		{								 	// if the edge can be collapsed now
			if(!heinfo.valid)				 // but it was not before
				computeHalfEdgeInfo(d, heinfo) ;
		}
		else
		{								 // if the edge cannot be collapsed now
			if(heinfo.valid)				 // and it was before
			{
				halfEdges.erase(heinfo.it) ;
				heinfo.valid = false ;
			}
		}
	}
}

template <typename PFP>
void HalfEdgeSelector_LightfieldExp<PFP>::computeHalfEdgeInfo(Dart d, HalfEdgeInfo& heinfo)
{
	MAP& m = this->m_map ;
	Dart dd = m.phi1(d) ;

	// New position
	Utils::Quadric<REAL> quad ;
	quad += m_quadricGeom[d] ;	// compute the sum of the
	quad += m_quadricGeom[dd] ;	// two vertices quadrics

	// compute all approximated attributes
	for(typename std::vector<ApproximatorGen<PFP>*>::iterator it = this->m_approximators.begin() ;
			it != this->m_approximators.end() ;
			++it)
	{
		(*it)->approximate(d) ;
	}

	// Get all approximated attributes
	// New position
	const VEC3& newPos = this->m_approx[m_approxindex_pos]->getApprox(d,m_attrindex_pos) ; // get newPos
	// New normal
	const VEC3& newFN = this->m_approx[m_approxindex_FN]->getApprox(d,m_attrindex_FN) ; // get new frameN

	// New function
	std::vector<VEC3> newHF ;
	newHF.resize(m_K) ;
	for (unsigned int k = 0 ; k < m_K ; ++k)
		newHF[k] = this->m_approx[m_approxindex_HF[k]]->getApprox(d,m_attrindex_HF[k]) ; // get newHFcoefsK

	// Compute errors
	// Position
	Utils::Quadric<REAL> quadGeom ;
	quadGeom += m_quadricGeom[d] ;	// compute the sum of the
	quadGeom += m_quadricGeom[dd] ;	// two vertices quadrics

	// hemisphere difference error
	double scal1 = double(m_frameN[d] * newFN) ;
	double alpha1 = acos(std::max(std::min(scal1, double(1)),double(-1))) ; // for epsilon normalization of newFN errors
	// angle 2
	double scal2 = double(m_frameN[dd] * newFN) ;
	double alpha2 = acos(std::max(std::min(scal2, double(1)),double(-1))) ; // for epsilon normalization of newFN errors

	assert(m_avgColor.isValid()) ;
	double alpha = alpha1 + alpha2 ;
	VEC3 avgColDiff = m_avgColor[d] ;
	avgColDiff -= m_avgColor[dd] ;
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	assert(m_quadricHF.isValid() | !"EdgeSelector_LightfieldExp<PFP>::computeEdgeInfo: quadricHF is not valid") ;
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	Utils::QuadricHF<REAL> quadHF = m_quadricHF[d] ;

	//std::cout << quadGeom(newPos) / (alpha/M_PI + quadHF(newHF)) << std::endl ;
	// sum of QEM metric and frame orientation difference
	const REAL& err =
			quadGeom(newPos) + // geom
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			(alpha / M_PI) * avgColDiff.norm2() / 3. + // average color times covering area
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			//alpha / M_PI + // frame
			quadHF(newHF) // function coefficients
			 ;

	// Check if errated values appear
	if (err < -1e-6)
		heinfo.valid = false ;
	else
	{
		heinfo.it = this->halfEdges.insert(std::make_pair(std::max(err,REAL(0)), d)) ;
		heinfo.valid = true ;
	}
}

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/************************************************************************************
 *              HALF EDGE LIGHTFIELD SELECTOR (using QEMml half-edge) KCL-like      *
 ************************************************************************************/

template <typename PFP>
bool HalfEdgeSelector_LightfieldKCL<PFP>::init()
{
	MAP& m = this->m_map ;

	// Verify availability of required approximators
	unsigned int ok = 0 ;
	unsigned int k = 0 ;
	for (unsigned int approxindex = 0 ; approxindex < this->m_approximators.size() ; ++approxindex)
	{
		if (this->m_approximators[approxindex]->getType() != A_hHalfCollapse)
		{
			std::cerr << "Approximator for selector (HalfEdgeSelector_LightfieldKCL) must be of A_hHalfCollapse" << std::endl ;
			return false ;
		}
		assert(this->m_approximators[approxindex]->getType() == A_hHalfCollapse
				|| !"Approximator for selector (HalfEdgeSelector_Lightfield) must be of A_hHalfCollapse") ;

		bool saved = false ;
		for (unsigned int attrindex = 0 ; attrindex < this->m_approximators[approxindex]->getNbApproximated() ; ++ attrindex)
		{
			// constraint : 2 approximators in specific order
			if(ok == 0 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == "position")
			{
				++ok ;
				m_approxindex_pos = approxindex ;
				m_attrindex_pos = attrindex ;
				if (!saved)
				{
					m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
					saved = true ;
				}
			}
			else if(ok == 1 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == "frameT")
			{
				++ok ;
				m_approxindex_FT = approxindex ;
				m_attrindex_FT = attrindex ;
				if (!saved)
				{
					m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
					assert(this->m_approx[approxindex]->getAttr(attrindex).isValid() || !"HalfEdgeSelector_LightfieldExp: frameT attribute is not valid") ;
					saved = true ;
				}
			}
			else if(ok == 2 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == "frameB")
			{
				++ok ;
				m_approxindex_FB = approxindex ;
				m_attrindex_FB = attrindex ;
				assert(this->m_approx[approxindex]->getAttr(attrindex).isValid() || !"HalfEdgeSelector_LightfieldExp: frameB attribute is not valid") ;
				if (!saved)
				{
					m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
					saved = true ;
				}
			}
			else if(ok == 3 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == "frameN")
			{
				++ok ;
				m_approxindex_FN = approxindex ;
				m_attrindex_FN = attrindex ;
				assert(this->m_approx[approxindex]->getAttr(attrindex).isValid() || !"HalfEdgeSelector_LightfieldExp: frameN attribute is not valid") ;
				if (!saved)
				{
					m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
					saved = true ;
				}
			}
			else
			{
				std::stringstream s ;
				s << "PBcoefs" << k ;
				if(ok > 3 && this->m_approximators[approxindex]->getApproximatedAttributeName(attrindex) == s.str().c_str())
				{
					++ok ;
					if (this->m_approx[approxindex]->getAttr(attrindex).isValid())
					{
						++k ;
						m_approxindex_HF.push_back(approxindex) ;
						m_attrindex_HF.push_back(attrindex) ;
						if (!saved)
						{
							m_approx.push_back(reinterpret_cast<Approximator<PFP, VEC3, DART>* >(this->m_approximators[approxindex])) ;
							saved = true ;
						}
					}
				}
			}
		}
	}
	m_K = k ;

	if(ok < 6)
		return false ;

	TraversorV<MAP> travV(m);
	for(Dart dit = travV.begin() ; dit != travV.end() ; dit = travV.next())
	{
		Utils::Quadric<REAL> q ;		// create one quadric
		m_quadricGeom[dit] = q ;		// per vertex
	}

	// Compute quadric per vertex
	TraversorF<MAP> travF(m) ;
	for(Dart dit = travF.begin() ; dit != travF.end() ; dit = travF.next()) // init QEM quadrics
	{
		Dart d1 = m.phi1(dit) ;					// for each triangle,
		Dart d_1 = m.phi_1(dit) ;					// initialize the quadric of the triangle

		Utils::Quadric<REAL> q(this->m_position[dit], this->m_position[d1], this->m_position[d_1]) ;
		m_quadricGeom[dit] += q ;						// and add the contribution of
		m_quadricGeom[d1] += q ;						// this quadric to the ones
		m_quadricGeom[d_1] += q ;						// of the 3 incident vertices
	}

	// compute vertex importance
	for(Dart v0 = travV.begin() ; v0 != travV.end() ; v0 = travV.next())
	{
		m_visualImportance[v0] = 0 ;
		REAL max = 0 ;
		Traversor2VVaE<MAP> tv(m,v0) ;
		unsigned int t = 0 ;
		for(Dart vi = tv.begin() ; vi != tv.end() ; vi = tv.next())
		{
			const REAL& err = sqrt(computeSquaredLightfieldDifference(v0,vi)) ;
			m_visualImportance[v0] += err ;
			++t ;
			if (err > max)
				max = err ;
		}
		if (max == 0)
			m_visualImportance[v0] = 0 ;
		else
			m_visualImportance[v0] /= (max*t) ;
	}

	// Init multimap for each Half-edge
	halfEdges.clear() ;

	for(Dart d = m.begin() ; d != m.end() ; m.next(d))
	{
		initHalfEdgeInfo(d) ; // init the edges with their optimal position
	}						// and insert them in the multimap according to their error

	cur = halfEdges.begin() ; 	// init the current edge to the first one

	return true ;
}

template <typename PFP>
bool HalfEdgeSelector_LightfieldKCL<PFP>::nextEdge(Dart& d)
{
	if(cur == halfEdges.end() || halfEdges.empty())
		return false ;
	d = (*cur).second ;
	return true ;
}

template <typename PFP>
void HalfEdgeSelector_LightfieldKCL<PFP>::updateBeforeCollapse(Dart d)
{
	MAP& m = this->m_map ;

	HalfEdgeInfo* edgeE = &(halfEdgeInfo[d]) ;
	if(edgeE->valid)
		halfEdges.erase(edgeE->it) ;

	edgeE = &(halfEdgeInfo[m.phi1(d)]) ;
	if(edgeE->valid)						// remove all
		halfEdges.erase(edgeE->it) ;

	edgeE = &(halfEdgeInfo[m.phi_1(d)]) ;	// the halfedges that will disappear
	if(edgeE->valid)
		halfEdges.erase(edgeE->it) ;
										// from the multimap
	Dart dd = m.phi2(d) ;
	assert(dd != d) ;
	if(dd != d)
	{
		edgeE = &(halfEdgeInfo[dd]) ;
		if(edgeE->valid)
			halfEdges.erase(edgeE->it) ;

		edgeE = &(halfEdgeInfo[m.phi1(dd)]) ;
		if(edgeE->valid)
			halfEdges.erase(edgeE->it) ;

		edgeE = &(halfEdgeInfo[m.phi_1(dd)]) ;
		if(edgeE->valid)
			halfEdges.erase(edgeE->it) ;
	}

	tmpVisualImportance = m_visualImportance[d] + m_visualImportance[dd] ;
}

/**
 * Update quadric of a vertex
 * Discards quadrics of d and assigns freshly calculated
 * quadrics depending on the actual planes surrounding d
 * @param dart d
 */
template <typename PFP>
void HalfEdgeSelector_LightfieldKCL<PFP>::recomputeQuadric(const Dart d, const bool recomputeNeighbors)
{
	Dart dFront,dBack ;
	Dart dInit = d ;

	// Init Front
	dFront = dInit ;

	m_quadricGeom[d].zero() ;
	const VertexAttribute<VEC3>& m_pos = this->m_approx[m_approxindex_pos]->getAttr(m_attrindex_pos) ;

   	do {
   		// Make step
   		dBack = this->m_map.phi2(dFront) ;
   		dFront = this->m_map.phi2_1(dFront) ;

   		if (dBack != dFront)
   		{ // if dFront is no border
   			m_quadricGeom[d] += Utils::Quadric<REAL>(m_pos[d],m_pos[this->m_map.phi1(dFront)],m_pos[dBack]) ;
   		}
   		if (recomputeNeighbors)
   			recomputeQuadric(dBack, false) ;

    } while(dFront != dInit) ;
}

template <typename PFP>
void HalfEdgeSelector_LightfieldKCL<PFP>::updateAfterCollapse(Dart d2, Dart dd2)
{
	MAP& m = this->m_map ;

	recomputeQuadric(d2, true) ;

	m_visualImportance[d2] = tmpVisualImportance ;

	Dart vit = d2 ;
	do
	{
		updateHalfEdgeInfo(vit, true) ;
		Dart d = m.phi2(vit) ;
		if (d != vit)
			updateHalfEdgeInfo(d, true) ;

		updateHalfEdgeInfo(m.phi1(vit), true) ;
		d = m.phi2(m.phi1(vit)) ;
		if (d != m.phi1(vit))
			updateHalfEdgeInfo(d, true) ;

		Dart stop = m.phi2(vit) ;
		assert (stop != vit) ;
		Dart vit2 = m.phi12(m.phi1(vit)) ;
		do {
			updateHalfEdgeInfo(vit2, true) ;
			d = m.phi2(vit2) ;
			if (d != vit2)
				updateHalfEdgeInfo(d, true) ;

			updateHalfEdgeInfo(m.phi1(vit2), false) ;
			d = m.phi2(m.phi1(vit2)) ;
			if (d != m.phi1(vit2))
				updateHalfEdgeInfo(d, false) ;

			vit2 = m.phi12(vit2) ;
		} while (stop != vit2) ;
		vit = m.phi2_1(vit) ;
	} while(vit != d2) ;

	cur = halfEdges.begin() ; // set the current edge to the first one
}

template <typename PFP>
void HalfEdgeSelector_LightfieldKCL<PFP>::initHalfEdgeInfo(Dart d)
{
	MAP& m = this->m_map ;
	HalfEdgeInfo heinfo ;
	if(m.edgeCanCollapse(d))
		computeHalfEdgeInfo(d, heinfo) ;
	else
		heinfo.valid = false ;

	halfEdgeInfo[d] = heinfo ;
}

template <typename PFP>
void HalfEdgeSelector_LightfieldKCL<PFP>::updateHalfEdgeInfo(Dart d, bool recompute)
{
	MAP& m = this->m_map ;
	HalfEdgeInfo& heinfo = halfEdgeInfo[d] ;
	if(recompute)
	{
		if(heinfo.valid)
			halfEdges.erase(heinfo.it) ;			// remove the edge from the multimap
		if(m.edgeCanCollapse(d))
			computeHalfEdgeInfo(d, heinfo) ;
		else
			heinfo.valid = false ;
	}
	else
	{
		if(m.edgeCanCollapse(d))
		{								 	// if the edge can be collapsed now
			if(!heinfo.valid)				 // but it was not before
				computeHalfEdgeInfo(d, heinfo) ;
		}
		else
		{								 // if the edge cannot be collapsed now
			if(heinfo.valid)				 // and it was before
			{
				halfEdges.erase(heinfo.it) ;
				heinfo.valid = false ;
			}
		}
	}
}

template <typename PFP>
void HalfEdgeSelector_LightfieldKCL<PFP>::computeHalfEdgeInfo(Dart d, HalfEdgeInfo& heinfo)
{
	MAP& m = this->m_map ;
	Dart dd = m.phi1(d) ;

	// compute all approximated attributes
	for(typename std::vector<ApproximatorGen<PFP>*>::iterator it = this->m_approximators.begin() ;
			it != this->m_approximators.end() ;
			++it)
	{
		(*it)->approximate(d) ;
	}

	// Compute errors
	// Position
	Utils::Quadric<REAL> quadGeom ;
	quadGeom += m_quadricGeom[d] ;	// compute the sum of the
	quadGeom += m_quadricGeom[dd] ;	// two vertices quadrics
	// New position
	const VEC3& newPos = (this->m_approx[m_approxindex_pos]->getAttr(m_attrindex_pos))[d] ; // get newPos

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	const REAL& geomErr = quadGeom(newPos) ;
	const REAL& visualI = m_visualImportance[dd] ;
	const REAL& lferr = computeLightfieldError(d) ;
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	//std::cout << lferr/geomErr << std::endl ;
	const REAL& err =
			geomErr + // geom
			//visualI + // visual importance of vertex that will disappear
			lferr / 10.
			 ;

	// Check if errated values appear
	if (lferr < 0 || err < -1e-6 || isnan(err))
	{
		std::cerr << "HalfEdgeSelector_LightfieldKCL<PFP>::computeHalfEdgeInfo: " << err << std::endl ;
		heinfo.valid = false ;
	}
	else
	{
		heinfo.it = this->halfEdges.insert(std::make_pair(std::max(err,REAL(0)), d)) ;
		heinfo.valid = true ;
	}
}

template <typename PFP>
typename PFP::REAL HalfEdgeSelector_LightfieldKCL<PFP>::computeLightfieldError(Dart v0)
{
	Dart v1 = this->m_map.phi1(v0) ;

	REAL err = 0 ;
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	/*Traversor2VVaE<MAP> tv0(this->m_map,v0) ; // all vertices surrounding vertex v0
	for (Dart vi = tv0.begin() ; vi != tv0.end() ; vi = tv0.next())
	{
		if (vi != v1)
		{
			err += computeSquaredLightfieldDifference(v1,vi) ;
		}
	}
	return err ;
*/

	// return computeSquaredLightfieldDifference(v0,v1) ;
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	Traversor2VVaE<MAP> tv(this->m_map,v1) ; // all vertices surrounding vertex v0
	for (Dart vi = tv.begin() ; vi != tv.end() ; vi = tv.next())
	{
		VEC3 edgeL = this->m_position[v1] - this->m_position[vi] ;
		err += sqrt(computeSquaredLightfieldDifference(v1,vi)) ;//* edgeL.norm() ;
		//std::cout << "1 : " <<  edgeL.norm() << std::endl ;
		edgeL = this->m_position[v0] - this->m_position[vi] ;
		//std::cout << "2 : " << edgeL.norm() << std::endl ;
		err -= sqrt(computeSquaredLightfieldDifference(v0,vi)) ;//* edgeL.norm() ;
	}
	return fabs(err) ;
}

template <typename PFP>
typename PFP::REAL HalfEdgeSelector_LightfieldKCL<PFP>::computeSquaredLightfieldDifference(Dart d1, Dart d2)
{
	// get two frames
	const VEC3& T1 = this->m_approx[m_approxindex_FT]->getAttr(m_attrindex_FT)[d1] ;
	const VEC3& T2 = this->m_approx[m_approxindex_FT]->getAttr(m_attrindex_FT)[d2] ;
	const VEC3& B1 = this->m_approx[m_approxindex_FB]->getAttr(m_attrindex_FB)[d1] ;
	const VEC3& B2 = this->m_approx[m_approxindex_FB]->getAttr(m_attrindex_FB)[d2] ;
	const VEC3& N1 = this->m_approx[m_approxindex_FN]->getAttr(m_attrindex_FN)[d1] ;
	const VEC3& N2 = this->m_approx[m_approxindex_FN]->getAttr(m_attrindex_FN)[d2] ;

	// compute new frame
	const VEC3& N = N1 ;
	VEC3 T ;
	if (N2 != N1)
		T = N2 ^ N1 ; // i is perpendicular to newNormal
	else
		T = N1 ^ VEC3(1,2,3) ; // second random vector
	T.normalize() ;

	// Compute D1' and D2'
	VEC3 B1prime = N1 ^ T ;
	B1prime.normalize() ;
	VEC3 B2prime = N2 ^ T ;
	B2prime.normalize() ;

	// Rotation dans sens trigo dans le plan tangent autour de N (T1 --> T)
	const REAL gamma1 = ((B1 * T) > 0 ? 1 : -1) * acos( std::max(std::min(1.0f, T1 * T ), -1.0f)) ; // angle positif ssi
	const REAL gamma2 = ((B2 * T) > 0 ? 1 : -1) * acos( std::max(std::min(1.0f, T2 * T ), -1.0f)) ; // -PI/2 < angle(i,j1) < PI/2  ssi i*j1 > 0
	// Rotation dans le sens trigo autour de l'axe T (N1 --> N)
	const REAL alpha1 = ((N * B1prime) > 0 ? -1 : 1) * acos( std::max(std::min(1.0f, N * N1), -1.0f) ) ; // angle positif ssi
	const REAL alpha2 = ((N * B2prime) > 0 ? -1 : 1) * acos( std::max(std::min(1.0f, N * N2), -1.0f) ) ; // PI/2 < angle(j1',n) < -PI/2 ssi j1'*n < 0

	double alpha = fabs(alpha1 + alpha2) ;

	// get coefs of v1 and v2
	std::vector<VEC3> coefs1, coefs2, coefs ;
	coefs1.resize(m_K) ; coefs2.resize(m_K) ;
	for (unsigned int i = 0 ; i < m_K ; ++i)
	{
		coefs1[i] = this->m_approx[m_approxindex_HF[i]]->getAttr(m_attrindex_HF[i])[d1] ;
		coefs2[i] = this->m_approx[m_approxindex_HF[i]]->getAttr(m_attrindex_HF[i])[d2] ;
	}

	Utils::QuadricHF<REAL> q(coefs1, gamma1, alpha1) ;
	bool opt = q.findOptimizedCoefs(coefs) ; // coefs of d1's lightfield rotated around new local axis
	q += Utils::QuadricHF<REAL>(coefs2, gamma2, alpha2) ;

	if (!opt)
	{
		std::cerr << "HalfEdgeSelector_LightfieldKCL::Optimization failed (should never happen since no optim is done)" << std::endl ;
		std::cout << alpha1 << std::endl ;
	}

	const VEC3 avgColDiff = m_avgColor[d1] - m_avgColor[d2] ;

	REAL err = q(coefs) ;
	if (fabs(err) < 1e-6)
		err = 0 ;

	return (alpha / M_PI) * avgColDiff.norm2()/3. + err ;

}



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} // namespace Decimation

} // namespace Algo

} // namespace CGoGN