vcglib/vcg/complex/algorithms/hole.h

/****************************************************************************
* VCGLib                                                            o o     *
* Visual and Computer Graphics Library                            o     o   *
*                                                                _   O  _   *
* Copyright(C) 2004                                                \/)\/    *
* Visual Computing Lab                                            /\/|      *
* ISTI - Italian National Research Council                           |      *
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* (at your option) any later version.                                       *
*                                                                           *
* This program 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 General Public License (http://www.gnu.org/licenses/gpl.txt)          *
* for more details.                                                         *
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****************************************************************************/
#ifndef __VCG_TRI_UPDATE_HOLE
#define __VCG_TRI_UPDATE_HOLE

#include <wrap/callback.h>
#include <vcg/math/base.h>
#include <vcg/complex/algorithms/clean.h>
#include <float.h>

// This file contains three Ear Classes
// - TrivialEar
// - MinimumWeightEar
// - SelfIntersectionEar
// and a static class Hole for filling holes that is templated on the ear class



namespace vcg {
	namespace tri {

	/*
	An ear is identified by TWO pos.
	The Three vertexes of an Ear are:
	e0.VFlip().v
	e0.v
	e1.v
	Invariants:
	  e1 == e0.NextB();
	  e1.FlipV() == e0;

	Situazioni ear non manifold, e degeneri (buco triangolare)

	T  XXXXXXXXXXXXX    A        /XXXXX        B      en/XXXXX
	/XXXXXXXXXXXXXXX            /XXXXXX                /XXXXXX
	XXXXXXep==en XXX     ep\   /en XXXX               /e1 XXXX
	XXXXXX ----/| XX   ------ ----/| XX       ------ ----/|XXX
	XXXXXX|   /e1 XX   XXXXXX|   /e1 XX       XXXXXX|  o/e0 XX
	XXXXXX|  /XXXXXX   XXXXXX|  /XXXXXX       XXXXXX|  /XXXXXX
	XXX e0|o/XXXXXXX   XXX e0|o/XXXXXXX       XXX ep| /XXXXXXX
	XXX  \|/XXXXXXXX   XXX  \|/XXXXXXXX       XXX  \|/XXXXXXXX
	XXXXXXXXXXXXXXXX   XXXXXXXXXXXXXXXX       XXXXXXXXXXXXXXXX
	*/
template<class MESH> class TrivialEar
{
public:
  typedef typename MESH::FaceType FaceType;
  typedef typename MESH::FacePointer FacePointer;
  typedef typename MESH::VertexPointer VertexPointer;
  typedef typename face::Pos<FaceType>    PosType;
  typedef typename MESH::ScalarType ScalarType;
  typedef typename MESH::CoordType CoordType;

  PosType e0;
  PosType e1;
  CoordType n; // the normal of the face defined by the ear
  const char * Dump() {return 0;}
  // The following members are useful to consider the Ear as a generic <triangle>
  // with p0 the 'center' of the ear.
  const CoordType &cP(int i) const {return P(i);}
  const CoordType &P(int i) const {
    switch(i) {
    case 0 : return e0.v->P();
    case 1 : return e1.v->P();
    case 2 : return e0.VFlip()->P();
    default: assert(0);
    }
    return e0.v->P();
  }

  ScalarType quality;
  ScalarType angleRad;
  TrivialEar(){}
  TrivialEar(const PosType & ep)
  {
    e0=ep;
    assert(e0.IsBorder());
    e1=e0;
    e1.NextB();
    n=vcg::Normal<TrivialEar>(*this);
    ComputeQuality();
    ComputeAngle();
  }

  /// Compute the angle of the two edges of the ear.
  // it tries to make the computation in a precision safe way.
  // the angle computation takes into account the case of reversed ears
  void ComputeAngle()
  {
    angleRad=Angle(cP(2)-cP(0), cP(1)-cP(0));
    ScalarType flipAngle = n.dot(e0.v->N());
    if(flipAngle<0)		angleRad = (2.0 *(ScalarType)M_PI) - angleRad;
  }

  virtual inline bool operator < ( const TrivialEar & c ) const { return quality <  c.quality; }

  bool IsNull(){return e0.IsNull() || e1.IsNull();}
  void SetNull(){e0.SetNull();e1.SetNull();}
  virtual	void ComputeQuality() {	quality = QualityFace(*this) ; }
  bool IsUpToDate()	{return ( e0.IsBorder() && e1.IsBorder());}
  // An ear is degenerated if both of its two endpoints are non manifold.
  bool IsDegen(const int nonManifoldBit)
  {
    if(e0.VFlip()->IsUserBit(nonManifoldBit) && e1.V()->IsUserBit(nonManifoldBit))
      return true;
    else return false;
  }
  bool IsConcave() const {return(angleRad > (float)M_PI);}

  // When you close an ear you have to check that the newly added triangle does not create non manifold situations
  // This can happen if the new edge already exists in the mesh.
  // We test that looping around one extreme of the ear we do not find the other vertex
  bool CheckManifoldAfterEarClose()
  {
    PosType pp = e1;
    VertexPointer otherV =  e0.VFlip();
    assert(pp.IsBorder());
    do
    {
      pp.FlipE();
      pp.FlipF();
      if(pp.VFlip()==otherV) return false;
    }
    while(!pp.IsBorder());
    return true;
  }

  virtual bool Close(PosType &np0, PosType &np1, FaceType * f)
  {
    // simple topological check
    if(e0.f==e1.f) {
      //printf("Avoided bad ear");
      return false;
    }

    //usato per generare una delle due nuove orecchie.
    PosType	ep=e0; ep.FlipV(); ep.NextB(); ep.FlipV(); // he precedente a e0
    PosType	en=e1; en.NextB();												 // he successivo a e1
    if(ep!=en)
      if(!CheckManifoldAfterEarClose()) return false;

    (*f).V(0) = e0.VFlip();
    (*f).V(1) = e0.v;
    (*f).V(2) = e1.v;
    face::ComputeNormalizedNormal(*f);

    face::FFAttachManifold(f,0,e0.f,e0.z);
    face::FFAttachManifold(f,1,e1.f,e1.z);
    face::FFSetBorder(f,2);

    // caso ear degenere per buco triangolare
    if(ep==en)
    {
      //printf("Closing the last triangle");
      face::FFAttachManifold(f,2,en.f,en.z);
      np0.SetNull();
      np1.SetNull();
    }
    // Caso ear non manifold a
    else if(ep.v==en.v)
    {
      //printf("Ear Non manif A\n");
      PosType	enold=en;
      en.NextB();
      face::FFAttachManifold(f,2,enold.f,enold.z);
      np0=ep;
      np1=en;
    }
    // Caso ear non manifold b
    else if(ep.VFlip()==e1.v)
    {
      //printf("Ear Non manif B\n");
      PosType	epold=ep;
      ep.FlipV(); ep.NextB(); ep.FlipV();
      face::FFAttachManifold(f,2,epold.f,epold.z);
      np0=ep;  // assign the two new
      np1=en;  // pos that denote the ears
    }
    else // caso standard // Now compute the new ears;
    {
      np0=ep;
      np1=PosType(f,2,e1.v);
    }

    return true;
  }

};  // end TrivialEar Class

//Ear with FillHoleMinimumWeight's quality policy
template<class MESH> class MinimumWeightEar : public TrivialEar<MESH>
{
public:
  static float &DiedralWeight() { static float _dw=0.1; return _dw;}
  typedef TrivialEar<MESH> TE;
  typename MESH::ScalarType dihedralRad;
  typename MESH::ScalarType aspectRatio;
  const char * Dump() {
    static char buf[200];
    if(this->IsConcave()) sprintf(buf,"Dihedral -(deg) %6.2f Quality %6.2f\n",math::ToDeg(dihedralRad),aspectRatio);
    else sprintf(buf,"Dihedral  (deg) %6.2f Quality %6.2f\n",math::ToDeg(dihedralRad),aspectRatio);
    return buf;
  }

  MinimumWeightEar(){}
  MinimumWeightEar(const typename face::Pos<typename MESH::FaceType>& ep) : TrivialEar<MESH>(ep)
  {
    ComputeQuality();
  }

  // In the heap, by default, we retrieve the LARGEST value,
  // so if we need the ear with minimal dihedral angle, we must reverse the sign of the comparison.
  // The concave elements must be all in the end of the heap, sorted accordingly,
  // So if only one of the two ear is Concave that one is always the minimum one.
  // the pow function is here just to give a way to play with different weighting schemas, balancing in a different way

  virtual inline bool operator <  ( const MinimumWeightEar & c ) const
  {
    if(TE::IsConcave()  && ! c.IsConcave() ) return true;
    if(!TE::IsConcave()  &&  c.IsConcave() ) return false;

    return aspectRatio - (dihedralRad/M_PI)*DiedralWeight() < c.aspectRatio -(c.dihedralRad/M_PI)*DiedralWeight();

//      return (pow((float)dihedralRad,(float)DiedralWeight())/aspectRatio) > (pow((float)c.dihedralRad,(float)DiedralWeight())/c.aspectRatio);
  }

  // the real core of the whole hole filling strategy.
  virtual void ComputeQuality()
  {
    //compute quality by (dihedral ancgle, area/sum(edge^2) )
    typename MESH::CoordType  n1=TE::e0.FFlip()->cN();
    typename MESH::CoordType n2=TE::e1.FFlip()->cN();

    dihedralRad = std::max(Angle(TE::n,n1),Angle(TE::n,n2));
    aspectRatio = QualityFace(*this);
  }

};  // end class MinimumWeightEar


//Ear for selfintersection algorithm
template<class MESH> class SelfIntersectionEar : public MinimumWeightEar<MESH>
{
public:
  typedef typename MESH::FaceType FaceType;
  typedef typename MESH::FacePointer FacePointer;
  typedef typename face::Pos<FaceType>    PosType;
  typedef typename MESH::ScalarType ScalarType;
  typedef typename MESH::CoordType CoordType;

  static std::vector<FacePointer> &AdjacencyRing()
  {
    static std::vector<FacePointer> ar;
    return ar;
  }

  SelfIntersectionEar(){}
  SelfIntersectionEar(const PosType & ep):MinimumWeightEar<MESH>(ep){}

  virtual bool Close(PosType &np0, PosType &np1, FacePointer f)
  {
    PosType	ep=this->e0; ep.FlipV(); ep.NextB(); ep.FlipV(); // he precedente a e0
    PosType	en=this->e1; en.NextB();	// he successivo a e1
//    bool triangularHole = false;
//    if(en==ep || en-) triangularHole=true;


    //costruisco la faccia e poi testo, o copio o butto via.
    (*f).V(0) = this->e0.VFlip();
    (*f).V(1) = this->e0.v;
    (*f).V(2) = this->e1.v;
    face::FFSetBorder(f,0);
    face::FFSetBorder(f,1);
    face::FFSetBorder(f,2);

    typename std::vector< FacePointer >::iterator it;
    for(it = this->AdjacencyRing().begin();it!= this->AdjacencyRing().end();++it)
    {
      if(!(*it)->IsD())
      {
        if(	tri::Clean<MESH>::TestFaceFaceIntersection(f,*it))
          return false;
        // We must also check that the newly created face does not have any edge in common with other existing surrounding faces
        // Only the two faces of the ear can share an edge with the new face
        if(face::CountSharedVertex(f,*it)==2)
        {
          int e0,e1;
          bool ret=face::FindSharedEdge(f,*it,e0,e1);
          assert(ret);
          if(!face::IsBorder(**it,e1))
            return false;
        }
      }
    }
    bool ret=TrivialEar<MESH>::Close(np0,np1,f);
    if(ret) AdjacencyRing().push_back(f);
    return ret;
  }
}; // end class SelfIntersectionEar

// Funzione principale per chiudier un buco in maniera topologicamente corretta.
// Gestisce situazioni non manifold ragionevoli
// (tutte eccetto quelle piu' di 2 facce per 1 edge).
// Controlla che non si generino nuove situazioni non manifold chiudendo orecchie
// che sottendono un edge che gia'esiste.

template <class MESH>
class Hole
{
public:
			typedef typename MESH::VertexType				VertexType;
			typedef typename MESH::VertexPointer		VertexPointer;
			typedef	typename MESH::ScalarType				ScalarType;
			typedef typename MESH::FaceType					FaceType;
			typedef typename MESH::FacePointer			FacePointer;
			typedef typename MESH::FaceIterator			FaceIterator;
			typedef typename MESH::CoordType				CoordType;
      typedef typename vcg::Box3<ScalarType>  Box3Type;
			typedef typename face::Pos<FaceType>    PosType;

public:

		class Info
		{
		public: 
			Info(){}
			Info(PosType const &pHole, int  const pHoleSize, Box3<ScalarType> &pHoleBB)
			{
				p=pHole;	
				size=pHoleSize;
				bb=pHoleBB;
			}

			PosType p;
			int size;
			Box3Type  bb;
			
			bool operator <  (const  Info & hh) const {return size <  hh.size;}

			ScalarType Perimeter()
			{
				ScalarType sum=0;
				PosType ip = p;
				do
				{
					sum+=Distance(ip.v->cP(),ip.VFlip()->cP());
					ip.NextB();
				}
				while (ip != p);
				return sum;				
			}

      // Support function to test the validity of a single hole loop
      // for now it test only that all the edges are border;
      // The real test should check if all non manifold vertices 
      // are touched only by edges belonging to this hole loop.
      bool CheckValidity()
      {
       if(!p.IsBorder()) 
         return false;
       PosType ip=p;ip.NextB();
       for(;ip!=p;ip.NextB())
       {
          if(!ip.IsBorder()) 
            return false;
       }       
       return true;
      }
		};


		class EdgeToBeAvoided
		{
		  VertexPointer v0,v1;
		  EdgeToBeAvoided(VertexPointer _v0, VertexPointer _v1):v0(_v0),v1(_v1)
		  {
			if(v0>v1) swap(v0,v1);
		  }
		  bool operator < (const EdgeToBeAvoided &e)
		  {
			if(this->v0!=e.v0) return this->v0<e.v0;
			return this->v1<e.v1;
		  }
		};
/// Main Single Hole Filling Function
/// Given a specific hole (identified by the Info h) it fills it
/// It also update a vector of face pointers
/// It uses an heap to choose the best ear to be closed

template<class EAR>
	static void FillHoleEar(MESH &m, // The mesh to be filled
							Info &h, // the particular hole to be filled
							std::vector<FacePointer *> &facePointersToBeUpdated)
	{
	  //Aggiungo le facce e aggiorno il puntatore alla faccia!
	  FaceIterator f = tri::Allocator<MESH>::AddFaces(m, h.size-2, facePointersToBeUpdated);

	  assert(h.p.f >= &*m.face.begin());
	  assert(h.p.f <= &m.face.back());
	  assert(h.p.IsBorder());

	  std::vector< EAR > EarHeap;
	  EarHeap.reserve(h.size);
	  int nmBit= VertexType::NewBitFlag(); // non manifoldness bit

	  //First loops around the hole to mark non manifold vertices.
	  PosType ip = h.p;   // Pos iterator
	  do{
		ip.V()->ClearUserBit(nmBit);
		ip.V()->ClearV();
		ip.NextB();
	  } while(ip!=h.p);

	  ip = h.p;   // Re init the pos iterator for another loop (useless if everithing is ok!!)
	  do{
		if(!ip.V()->IsV())
		  ip.V()->SetV();   // All the vertexes that are visited more than once are non manifold
		else ip.V()->SetUserBit(nmBit);
		ip.NextB();
	  } while(ip!=h.p);

	  PosType fp = h.p;
	  do{
		EAR appEar = EAR(fp);
		EarHeap.push_back( appEar );
		//printf("Adding ear %s ",app.Dump());
		fp.NextB();
		assert(fp.IsBorder());
	  }while(fp!=h.p);

	  int cnt=h.size;

	  make_heap(EarHeap.begin(), EarHeap.end());

	  //finche' il buco non e' chiuso o non ci sono piu' orecchie da analizzare.
	  while( cnt > 2 && !EarHeap.empty() )
	  {
		//printf("Front of the heap is %s", H.front().Dump());
		pop_heap(EarHeap.begin(), EarHeap.end());	 // retrieve the MAXIMUM value and put in the back;
		EAR BestEar=EarHeap.back();
		EarHeap.pop_back();

		if(BestEar.IsUpToDate() && !BestEar.IsDegen(nmBit))
		{
		  if((*f).HasPolyInfo()) (*f).Alloc(3);
		  PosType ep0,ep1;
		  if(BestEar.Close(ep0,ep1,&*f))
		  {
			if(!ep0.IsNull()){
			  EarHeap.push_back(EAR(ep0));
			  push_heap( EarHeap.begin(), EarHeap.end());
			}
			if(!ep1.IsNull()){
			  EarHeap.push_back(EAR(ep1));
			  push_heap( EarHeap.begin(), EarHeap.end());
			}
			--cnt;
			++f;
		  }
		}//is update()
	  }//fine del while principale.

	  while(f!=m.face.end()){
		tri::Allocator<MESH>::DeleteFace(m,*f);
		f++;
	  }

	  VertexType::DeleteBitFlag(nmBit); // non manifoldness bit
	}

	template<class EAR>
	static int EarCuttingFill(MESH &m, int sizeHole, bool Selected = false, CallBackPos *cb=0)
	{
	  std::vector< Info > vinfo;
	  GetInfo(m, Selected,vinfo);

	  typename std::vector<Info >::iterator ith;
	  int indCb=0;
	  int holeCnt=0;
	  std::vector<FacePointer *> facePtrToBeUpdated;
	  for(ith = vinfo.begin(); ith!= vinfo.end(); ++ith)
		facePtrToBeUpdated.push_back( &(*ith).p.f );

	  for(ith = vinfo.begin(); ith!= vinfo.end(); ++ith)
	  {
		indCb++;
		if(cb) (*cb)(indCb*10/vinfo.size(),"Closing Holes");
		if((*ith).size < sizeHole){
		  holeCnt++;
		  FillHoleEar< EAR >(m, *ith,facePtrToBeUpdated);
		}
	  }
	  return holeCnt;
	}

/// Main Hole Filling function.
/// Given a mesh search for all the holes smaller than a given size and fill them
/// It returns the number of filled holes.

template<class EAR>
	static int EarCuttingIntersectionFill(MESH &m, const int maxSizeHole, bool Selected, CallBackPos *cb=0)
	{
	  std::vector<Info > vinfo;
	  GetInfo(m, Selected,vinfo);
	  typename std::vector<Info>::iterator ith;

	  // collect the face pointer that has to be updated by the various addfaces
	  std::vector<FacePointer *> vfpOrig;
	  for(ith = vinfo.begin(); ith!= vinfo.end(); ++ith)
		vfpOrig.push_back( &(*ith).p.f );

	  int indCb=0;
	  int holeCnt=0;
	  for(ith = vinfo.begin(); ith!= vinfo.end(); ++ith)
	  {
		indCb++;
		if(cb) (*cb)(indCb*10/vinfo.size(),"Closing Holes");
		if((*ith).size < maxSizeHole){
		  std::vector<FacePointer *> facePtrToBeUpdated;
		  holeCnt++;
		  facePtrToBeUpdated=vfpOrig;
		  EAR::AdjacencyRing().clear();
		  //Loops around the hole to collect the faces that have to be tested for intersection.
		  PosType ip = (*ith).p;
		  do
		  {
			PosType inp = ip;
			do
			{
			  inp.FlipE();
			  inp.FlipF();
			  EAR::AdjacencyRing().push_back(inp.f);
			} while(!inp.IsBorder());
			ip.NextB();
		  }while(ip != (*ith).p);

		  typename std::vector<FacePointer>::iterator fpi;
		  for(fpi=EAR::AdjacencyRing().begin();fpi!=EAR::AdjacencyRing().end();++fpi)
			facePtrToBeUpdated.push_back( &*fpi );

		  FillHoleEar<EAR >(m, *ith,facePtrToBeUpdated);
		  EAR::AdjacencyRing().clear();
		}
	  }
	  return holeCnt;
	}



	static void GetInfo(MESH &m, bool Selected ,std::vector<Info >& VHI)
		{
	  tri::UpdateFlags<MESH>::FaceClearV(m);
			for(FaceIterator fi = m.face.begin(); fi!=m.face.end(); ++fi)
			{
				if(!(*fi).IsD())
				{
					if(Selected && !(*fi).IsS())
					{
						//se devo considerare solo i triangoli selezionati e 
						//quello che sto considerando non lo e' lo marchio e vado avanti
					  (*fi).SetV();
					}
					else
					{
							for(int j =0; j<3 ; ++j)
							{
							  if( face::IsBorder(*fi,j) && !(*fi).IsV() )
								{//Trovato una faccia di bordo non ancora visitata.
									(*fi).SetV();
							    PosType sp(&*fi, j, (*fi).V(j));
									PosType fp=sp;
									int holesize=0;

									Box3Type hbox;
									hbox.Add(sp.v->cP());
                  //printf("Looping %i : (face %i edge %i) \n", VHI.size(),sp.f-&*m.face.begin(),sp.z);
                                    sp.f->SetV();
									do
									{
										sp.f->SetV();
										hbox.Add(sp.v->cP());
										++holesize;
										sp.NextB();
										sp.f->SetV();
										assert(sp.IsBorder());
									}while(sp != fp);

									//ho recuperato l'inofrmazione su tutto il buco
									VHI.push_back( Info(sp,holesize,hbox) );
								}
							}//for sugli edge del triangolo
					}//S & !S
				}//!IsD()
			}//for principale!!!
		}

		//Minimum Weight Algorithm
		class Weight
		{
		public:

			Weight() { ang = 180; ar = FLT_MAX ;}
			Weight( float An, float Ar ) { ang=An ; ar= Ar;}
			~Weight() {}

			float angle() const { return ang; }
			float area()  const { return ar; }

			Weight operator+( const Weight & other ) const {return Weight( std::max( angle(), other.angle() ), area() + other.area());}
			bool operator<( const Weight & rhs ) const {return ( angle() < rhs.angle() ||(angle() == rhs.angle() && area() < rhs.area()));	}

		private:
			float ang;
			float ar;
		};

		/*     
    \ /        \/ 
   v1*---------*v4 
    / \       /
   /   \     /
  / 	  \   /
 /ear	   \ /
*---------*-
| v3      v2\
*/
		
	static float ComputeDihedralAngle(CoordType  p1,CoordType  p2,CoordType  p3,CoordType  p4)
		{
			CoordType  n1 = NormalizedNormal(p1,p3,p2);
			CoordType	 n2 = NormalizedNormal(p1,p2,p4);
			return  math::ToDeg(AngleN(n1,n2));
		}

  static bool existEdge(PosType pi,PosType pf)
		{
			PosType app = pi;
			PosType appF = pi;
			PosType tmp;
			assert(pi.IsBorder());
			appF.NextB();
			appF.FlipV();
			do
			{
				tmp = app;
				tmp.FlipV();
				if(tmp.v == pf.v)
					return true;
				app.FlipE();
				app.FlipF();

				if(app == pi)return false;
			}while(app != appF);
			return false;
		}

	static Weight computeWeight( int i, int j, int k,
			std::vector<PosType > pv,
			std::vector< std::vector< int > >  v)
		{
			PosType pi = pv[i];
			PosType pj = pv[j];
			PosType pk = pv[k];

			//test complex edge
			if(existEdge(pi,pj) || existEdge(pj,pk)|| existEdge(pk,pi)	)	
			{
				return Weight();
			}
			// Return an infinite weight, if one of the neighboring patches
			// could not be created.
			if(v[i][j] == -1){return Weight();}
			if(v[j][k] == -1){return Weight();}

			//calcolo il massimo angolo diedrale, se esiste.
			float angle = 0.0f;
			PosType px;
			if(i + 1 == j)
			{
				px = pj; 
				px.FlipE(); px.FlipV();
				angle = std::max<float>(angle , ComputeDihedralAngle(pi.v->P(), pj.v->P(), pk.v->P(), px.v->P())	);
			}
			else
			{
				angle = std::max<float>( angle, ComputeDihedralAngle(pi.v->P(),pj.v->P(), pk.v->P(), pv[ v[i][j] ].v->P()));
			}

			if(j + 1 == k)
			{
				px = pk; 
				px.FlipE(); px.FlipV();
				angle = std::max<float>(angle , ComputeDihedralAngle(pj.v->P(), pk.v->P(), pi.v->P(), px.v->P())	);
			}
			else
			{
				angle = std::max<float>( angle, ComputeDihedralAngle(pj.v->P(),pk.v->P(), pi.v->P(), pv[ v[j][k] ].v->P()));
			}

			if( i == 0 && k == (int)v.size() - 1)
			{
				px = pi; 
				px.FlipE(); px.FlipV();
				angle = std::max<float>(angle , ComputeDihedralAngle(pk.v->P(), pi.v->P(),  pj.v->P(),px.v->P() )	);
			}

			ScalarType area = ( (pj.v->P() - pi.v->P()) ^ (pk.v->P() - pi.v->P()) ).Norm() * 0.5;

			return Weight(angle, area);
		}

	static void calculateMinimumWeightTriangulation(MESH &m, FaceIterator f,std::vector<PosType > vv )
		{
			std::vector< std::vector< Weight > > w; //matrice dei pesi minimali di ogni orecchio preso in conzideraione
			std::vector< std::vector< int    > > vi;//memorizza l'indice del terzo vertice del triangolo

			//hole size
			int nv = vv.size();
			
			w.clear();
			w.resize( nv, std::vector<Weight>( nv, Weight() ) );

			vi.resize( nv, std::vector<int>( nv, 0 ) );

			//inizializzo tutti i pesi possibili del buco
			for ( int i = 0; i < nv-1; ++i )
				w[i][i+1] = Weight( 0, 0 );

			//doppio ciclo for per calcolare di tutti i possibili triangoli i loro pesi.
			for ( int j = 2; j < nv; ++j )
			{
				for ( int i = 0; i + j < nv; ++i )
				{
					//per ogni triangolazione mi mantengo il minimo valore del peso tra i triangoli possibili
					Weight minval;

					//indice del vertice che da il peso minimo nella triangolazione corrente
					int minIndex = -1;

					//ciclo tra i vertici in mezzo a i due prefissati
					for ( int m = i + 1; m < i + j; ++m )
					{
						Weight a = w[i][m];
						Weight b = w[m][i+j];
						Weight newval =  a + b + computeWeight( i, m, i+j, vv, vi);
						if ( newval < minval )
						{
							minval = newval;
							minIndex = m;
						}
					}
					w[i][i+j] = minval;
					vi[i][i+j] = minIndex;
				}
			}

			//Triangulate
			int i, j;
			i=0; j=nv-1;
			
			triangulate(m,f, i, j, vi, vv);

			while(f!=m.face.end())
			{
				(*f).SetD();
				++f;
				m.fn--;
			}
		}


	static void triangulate(MESH &m, FaceIterator &f,int i, int j,
                          std::vector< std::vector<int> > vi, std::vector<PosType > vv)
		{
			if(i + 1 == j){return;}
			if(i==j)return;

			int k = vi[i][j];

			if(k == -1)	return;

			//Setto i vertici
			f->V(0) = vv[i].v;
			f->V(1) = vv[k].v;
			f->V(2) = vv[j].v;
			
			f++;
			triangulate(m,f,i,k,vi,vv);
			triangulate(m,f,k,j,vi,vv);
		}

  static void MinimumWeightFill(MESH &m, int holeSize, bool Selected)
		{
			std::vector<PosType > vvi;
			std::vector<FacePointer * > vfp;

			std::vector<Info > vinfo;
			typename std::vector<Info >::iterator VIT;
			GetInfo(m, Selected,vinfo);

			for(VIT = vinfo.begin(); VIT != vinfo.end();++VIT)
			{
				vvi.push_back(VIT->p);
			}

			typename std::vector<PosType >::iterator ith;
			typename std::vector<PosType >::iterator ithn;
			typename std::vector<VertexPointer >::iterator itf;

			std::vector<PosType > app;
			PosType ps;
			std::vector<FaceType > tr;
			std::vector<VertexPointer > vf;

			for(ith = vvi.begin(); ith!= vvi.end(); ++ith)
			{
				tr.clear();
				vf.clear();
				app.clear();
				vfp.clear();

				ps = *ith;
				getBoundHole(ps,app);

        if(app.size() <= size_t(holeSize) )
				{
					typename std::vector<PosType >::iterator itP;
					std::vector<FacePointer *> vfp;

					for(ithn = vvi.begin(); ithn!= vvi.end(); ++ithn)
						vfp.push_back(&(ithn->f));

					for(itP = app.begin (); itP != app.end ();++itP)
						vfp.push_back( &(*itP).f );

					//aggiungo le facce
					FaceIterator f = tri::Allocator<MESH>::AddFaces(m, (app.size()-2) , vfp);

					calculateMinimumWeightTriangulation(m,f, app);
				}
			}		

		}

	static void getBoundHole (PosType sp,std::vector<PosType >&ret)
		{
			PosType fp = sp;
			//take vertex around the hole
			do
			{
				assert(fp.IsBorder());
				ret.push_back(fp);
				fp.NextB();
			}while(sp != fp);
		}

};//close class Hole

} // end namespace tri
} // end namespace vcg
#endif