/****************************************************************************
* VCGLib                                                            o o     *
* Visual and Computer Graphics Library                            o     o   *
*                                                                _   O  _   *
* Copyright(C) 2014                                                \/)\/    *
* Visual Computing Lab                                            /\/|      *
* ISTI - Italian National Research Council                           |      *
*                                                                    \      *
* All rights reserved.                                                      *
*                                                                           *
* This program is free software; you can redistribute it and/or modify      *
* it under the terms of the GNU General Public License as published by      *
* the Free Software Foundation; either version 2 of the License, or         *
* (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.                                                         *
*                                                                           *
****************************************************************************/
#include <vcg/math/histogram.h>
#include <vcg/complex/algorithms/update/curvature.h>
#include <vcg/complex/algorithms/update/flag.h>
#include <algorithm>

#ifndef VCG_TANGENT_FIELD_OPERATORS
#define VCG_TANGENT_FIELD_OPERATORS

namespace vcg {
namespace tri{


template < typename ScalarType >
vcg::Point2<ScalarType> InterpolateNRosy2D(const std::vector<vcg::Point2<ScalarType> > &V,
                                           const std::vector<ScalarType>  &W,
                                           const int N)
{
    // check parameter
    assert(V.size() == W.size() && N > 0);

    // create a vector of angles
    std::vector<ScalarType> angles(V.size(), 0);

    // make angle mod 2pi/N by multiplying times N
    for (size_t i = 0; i < V.size(); i++)
        angles[i] = std::atan2(V[i].Y(), V[i].X() ) * N;

    // create vector of directions
    std::vector<vcg::Point2<ScalarType> > VV(V.size(), vcg::Point2<ScalarType>(0,0));

    // compute directions
    for (size_t i = 0; i < V.size(); i++) {
        VV[i].X() = std::cos(angles[i]);
        VV[i].Y() = std::sin(angles[i]);
    }

    // average vector
    vcg::Point2<ScalarType> Res(0,0);

    // compute average of the unit vectors
    ScalarType Sum=0;
    for (size_t i = 0; i < VV.size(); i++)
    {
        Res += VV[i] * W[i];
        Sum+=W[i];
    }
    Res /=Sum;

    //R /= VV.rows();

    // scale them back
    ScalarType a = std::atan2(Res.Y(), Res.X()) / N;
    Res.X() = std::cos(a);
    Res.Y() = std::sin(a);

    return Res;
}

template < typename ScalarType >
vcg::Point3<ScalarType> InterpolateNRosy3D(const std::vector<vcg::Point3<ScalarType> > &V,
                                           const std::vector<vcg::Point3<ScalarType> > &Norm,
                                           const std::vector<ScalarType>  &W,
                                           const int N,
                                           const vcg::Point3<ScalarType> &TargetN)
{
    typedef typename vcg::Point3<ScalarType> CoordType;
    ///create a reference frame along TargetN
    CoordType TargetZ=TargetN;
    TargetZ.Normalize();
    CoordType U=CoordType(1,0,0);
    if (fabs(TargetZ*U)>0.999)
        U=CoordType(0,1,0);

    CoordType TargetX=TargetZ^U;
    CoordType TargetY=TargetX^TargetZ;
    TargetX.Normalize();
    TargetY.Normalize();
    vcg::Matrix33<ScalarType> RotFrame=vcg::TransformationMatrix(TargetX,TargetY,TargetZ);
    vcg::Matrix33<ScalarType> RotFrameInv=vcg::Inverse(RotFrame);
    std::vector<vcg::Point2<ScalarType> > Cross2D;
    ///rotate each vector to transform to 2D
    for (size_t i=0;i<V.size();i++)
    {
        CoordType NF=Norm[i];
        NF.Normalize();
        CoordType Vect=V[i];
        Vect.Normalize();
        //ScalarType Dot=fabs(Vect*NF);

        ///rotate the vector to become tangent to the reference plane
        vcg::Matrix33<ScalarType> RotNorm=vcg::RotationMatrix(Norm[i],TargetN);
        CoordType rotV=RotNorm*V[i];
        //assert(fabs(rotV*TargetN)<0.000001);
        rotV.Normalize();
        ///trassform to the reference frame
        rotV=RotFrame*rotV;
        //it's 2D from now on
        Cross2D.push_back(vcg::Point2<ScalarType>(rotV.X(),rotV.Y()));
    }
    vcg::Point2<ScalarType> AvDir2D=InterpolateNRosy2D(Cross2D,W,N);
    CoordType AvDir3D=CoordType(AvDir2D.X(),AvDir2D.Y(),0);
    //transform back to 3D
    AvDir3D=RotFrameInv*AvDir3D;
    return AvDir3D;
}

template <class MeshType>
class CrossField
{
    typedef typename MeshType::FaceType FaceType;
    typedef typename MeshType::VertexType VertexType;
    typedef typename MeshType::CoordType CoordType;
    typedef typename MeshType::ScalarType ScalarType;

private:
    static ScalarType Sign(ScalarType a){return (ScalarType)((a>0)?+1:-1);}

public:

    static CoordType FollowDirection(const FaceType &f0,
                                     const  FaceType &f1,
                                     const  CoordType &dir0)
    {
        ///first it rotate dir to match with f1
        CoordType dirR=vcg::tri::CrossField<MeshType>::Rotate(f0,f1,dir0);
        ///then get the closest upf to K*PI/2 rotations
        CoordType dir1=f1.cPD1();
        CoordType ret=vcg::tri::CrossField<MeshType>::K_PI(dir1,dirR,f1.cN());
        return ret;
    }

    static int FollowDirection(const FaceType &f0,
                               const  FaceType &f1,
                               int dir0)
    {
        ///first it rotate dir to match with f1
        CoordType dirS=CrossVector(f0,dir0);
        CoordType dirR=vcg::tri::CrossField<MeshType>::Rotate(f0,f1,dirS);
        ///then get the closest upf to K*PI/2 rotations
        CoordType dir1=f1.cPD1();
        //int ret=I_K_PI(dir1,dirR,f1.cN());
        CoordType dir[4];
        CrossVector(f1,dir);
        ScalarType best=-1;
        int ret=-1;
        for (int i=0;i<4;i++)
        {
            ScalarType dot=dir[i]*dirR;
            if (dot>best)
            {
                best=dot;
                ret=i;
            }
        }
        assert(ret!=-1);

        return ret;
    }

    static int FollowLineDirection(const FaceType &f0,
                                   const FaceType &f1,
                                   int dir)
    {
        ///first it rotate dir to match with f1
        CoordType dir0=CrossVector(f0,dir);
        CoordType dir0R=vcg::tri::CrossField<MeshType>::Rotate(f0,f1,dir0);
        ///then get the closest upf to K*PI/2 rotations
        CoordType dir1_test=CrossVector(f1,dir);
        CoordType dir2_test=-dir1_test;
        if ((dir1_test*dir0R)>(dir2_test*dir0R))
            return dir;
        return ((dir+2)%4);

    }

    ///fird a tranformation matrix to transform
    ///the 3D space to 2D tangent space specified
    ///by the cross field (where Z=0)
    static vcg::Matrix33<ScalarType> TransformationMatrix(const FaceType &f)
    {
        typedef typename FaceType::CoordType CoordType;
        typedef typename FaceType::ScalarType ScalarType;

        ///transform to 3d
        CoordType axis0=f.cPD1();
        CoordType axis1=f.cPD2();//axis0^f.cN();
        CoordType axis2=f.cN();

        return (vcg::TransformationMatrix(axis0,axis1,axis2));
    }


    ///transform a given angle in tangent space wrt X axis of
    ///tangest space will return the corresponding 3D vector
    static CoordType TangentAngleToVect(const FaceType &f,const ScalarType &angle)
    {
        ///find 2D vector
        vcg::Point2<ScalarType> axis2D=vcg::Point2<ScalarType>(cos(angle),sin(angle));
        CoordType axis3D=CoordType(axis2D.X(),axis2D.Y(),0);
        vcg::Matrix33<ScalarType> Trans=TransformationMatrix(f);
        vcg::Matrix33<ScalarType> InvTrans=Inverse(Trans);
        ///then transform
        return (InvTrans*axis3D);
    }

    ///find an angle with respect to dirX on the plane perpendiculr to DirZ
    ///dirX and dirZ should be perpendicular
    static ScalarType TangentVectToAngle(const CoordType dirX,
                                         const CoordType dirZ,
                                         const CoordType &vect3D)
    {
        const CoordType dirY=dirX^dirZ;
        dirX.Normalize();
        dirY.Normalize();
        dirZ.Normalize();
        vcg::Matrix33<ScalarType> Trans=TransformationMatrix(dirX,dirY,dirZ);
        ///trensform the vector to the reference frame by rotating it
        CoordType vect_transf=Trans*vect3D;

        ///then put to zero to the Z coordinate
        vcg::Point2<ScalarType> axis2D=vcg::Point2<ScalarType>(vect_transf.X(),vect_transf.Y());
        axis2D.Normalize();

        ///then find the angle with respact to axis 0
        ScalarType alpha=atan2(axis2D.Y(),axis2D.X());	////to sum up M_PI?
        if (alpha<0)
            alpha=(2*M_PI+alpha);
        if (alpha<0)
            alpha=0;
        return alpha;
    }

    ///find an angle with respect to the tangent frame of given face
    static ScalarType VectToAngle(const FaceType &f,const CoordType &vect3D)
    {
        vcg::Matrix33<ScalarType> Trans=TransformationMatrix(f);

        ///trensform the vector to the reference frame by rotating it
        CoordType vect_transf=Trans*vect3D;

        ///then put to zero to the Z coordinate
        vcg::Point2<ScalarType> axis2D=vcg::Point2<ScalarType>(vect_transf.X(),vect_transf.Y());
        axis2D.Normalize();

        ///then find the angle with respact to axis 0
        ScalarType alpha=atan2(axis2D.Y(),axis2D.X());	////to sum up M_PI?
        if (alpha<0)
            alpha=(2*M_PI+alpha);
        if (alpha<0)
            alpha=0;
        return alpha;
    }

    ///return the 4 directiona of the cross field in 3D
    ///given a first direction as input
    static void CrossVector(const CoordType &dir0,
                            const CoordType &norm,
                            CoordType axis[4])
    {
        axis[0]=dir0;
        axis[1]=norm^axis[0];
        axis[2]=-axis[0];
        axis[3]=-axis[1];
    }

    ///return the 4 direction in 3D of
    ///the cross field of a given face
    static void CrossVector(const FaceType &f,
                            CoordType axis[4])
    {
        CoordType dir0=f.cPD1();
        CoordType dir1=f.cPD2();
        axis[0]=dir0;
        axis[1]=dir1;
        axis[2]=-dir0;
        axis[3]=-dir1;
    }

    ///return the 4 direction in 3D of
    ///the cross field of a given face
    static void CrossVector(const VertexType &v,
                            CoordType axis[4])
    {
        CoordType dir0=v.cPD1();
        CoordType dir1=v.cPD2();
        axis[0]=dir0;
        axis[1]=dir1;
        axis[2]=-dir0;
        axis[3]=-dir1;
    }

    ///return a specific direction given an integer 0..3
    ///considering the reference direction of the cross field
    static CoordType CrossVector(const FaceType &f,
                                 const int &index)
    {
        assert((index>=0)&&(index<4));
        CoordType axis[4];
        CrossVector(f,axis);
        return axis[index];
    }

    ///return a specific direction given an integer 0..3
    ///considering the reference direction of the cross field
    static CoordType CrossVector(const VertexType &v,
                                 const int &index)
    {
        assert((index>=0)&&(index<4));
        CoordType axis[4];
        CrossVector(v,axis);
        return axis[index];
    }

    ///set the cross field of a given face
    static void SetCrossVector(FaceType &f,
                               CoordType dir0,
                               CoordType dir1)
    {
        f.PD1()=dir0;
        f.PD2()=dir1;
    }

    ///set the face cross vector from vertex one
    static void SetFaceCrossVectorFromVert(FaceType &f)
    {
        const CoordType &t0=f.V(0)->PD1();
        const CoordType &t1=f.V(1)->PD1();
        const CoordType &t2=f.V(2)->PD1();
        const CoordType &N0=f.V(0)->N();
        const CoordType &N1=f.V(0)->N();
        const CoordType &N2=f.V(0)->N();
        const CoordType &NF=f.N();
        const CoordType bary=CoordType(0.33333,0.33333,0.33333);
        CoordType tF0,tF1;
        tF0=InterpolateCrossField(t0,t1,t2,N0,N1,N2,NF,bary);
        tF1=NF^tF0;
        tF0.Normalize();
        tF1.Normalize();
        SetCrossVector(f,tF0,tF1);
    }

    static void SetFaceCrossVectorFromVert(MeshType &mesh)
    {
        for (unsigned int i=0;i<mesh.face.size();i++)
        {
            FaceType *f=&mesh.face[i];
            if (f->IsD())continue;
            SetFaceCrossVectorFromVert(*f);
        }
    }

    ///set the face cross vector from vertex one
    static void SetVertCrossVectorFromFace(VertexType &v)
    {
        std::vector<FaceType *> faceVec;
        std::vector<int> index;
        vcg::face::VFStarVF(&v,faceVec,index);
        std::vector<CoordType> TangVect;
        std::vector<CoordType> Norms;
        for (unsigned int i=0;i<faceVec.size();i++)
        {
            TangVect.push_back(faceVec[i]->PD1());
            Norms.push_back(faceVec[i]->N());
        }
        std::vector<ScalarType> Weights(TangVect.size(),1.0/(ScalarType)TangVect.size());
        CoordType NRef=v.N();
        CoordType N0=faceVec[0]->N();
        CoordType DirRef=faceVec[0]->PD1();
        ///find the rotation matrix that maps between normals
        vcg::Matrix33<ScalarType> rotation=vcg::RotationMatrix(N0,NRef);
        DirRef=rotation*DirRef;


        CoordType tF1=vcg::tri::CrossField<MeshType>::InterpolateCrossField(TangVect,Weights,Norms,NRef);
        tF1.Normalize();
        CoordType tF2=NRef^tF1;
        tF2.Normalize();
        v.PD1()=tF1;
        v.PD2()=tF2;
    }

    static void SetVertCrossVectorFromFace(MeshType &mesh)
    {
        for (unsigned int i=0;i<mesh.vert.size();i++)
        {
            VertexType *v=&mesh.vert[i];
            if (v->IsD())continue;
            SetVertCrossVectorFromFace(*v);
        }
    }

    ///rotate a given vector from the tangent space
    ///of f0 to the tangent space of f1 by considering the difference of normals
    static CoordType Rotate(const FaceType &f0,const FaceType &f1,const CoordType &dir3D)
    {
        CoordType N0=f0.cN();
        CoordType N1=f1.cN();

        ///find the rotation matrix that maps between normals
        vcg::Matrix33<ScalarType> rotation=vcg::RotationMatrix(N0,N1);
        CoordType rotated=rotation*dir3D;
        return rotated;
    }

    // returns the 90 deg rotation of a (around n) most similar to target b
    /// a and b should be in the same plane orthogonal to N
    static CoordType K_PI(const CoordType &a, const CoordType &b, const CoordType &n)
    {
        CoordType c = (a^n).normalized();///POSSIBLE SOURCE OF BUG CHECK CROSS PRODUCT
        ScalarType scorea = a*b;
        ScalarType scorec = c*b;
        if (fabs(scorea)>=fabs(scorec)) return a*Sign(scorea); else return c*Sign(scorec);
    }

    // returns the 90 deg rotation of a (around n) most similar to target b
    /// a and b should be in the same plane orthogonal to N
    static int I_K_PI(const CoordType &a, const CoordType &b, const CoordType &n)
    {
        CoordType c = (n^a).normalized();
        ScalarType scorea = a*b;
        ScalarType scorec = c*b;
        if (fabs(scorea)>=fabs(scorec))///0 or 2
        {
            if (scorea>0)return 0;
            return 2;
        }else ///1 or 3
        {
            if (scorec>0)return 1;
            return 3;
        }
    }

    ///interpolate cross field with barycentric coordinates
    static CoordType InterpolateCrossField(const CoordType &t0,
                                           const CoordType &t1,
                                           const CoordType &t2,
                                           const CoordType &n0,
                                           const CoordType &n1,
                                           const CoordType &n2,
                                           const CoordType &target_n,
                                           const CoordType &bary)
    {
        std::vector<CoordType > V,Norm;
        std::vector<ScalarType > W;
        V.push_back(t0);
        V.push_back(t1);
        V.push_back(t2);
        Norm.push_back(n0);
        Norm.push_back(n1);
        Norm.push_back(n2);
        W.push_back(bary.X());
        W.push_back(bary.Y());
        W.push_back(bary.Z());

        CoordType sum=vcg::tri::InterpolateNRosy3D(V,Norm,W,4,target_n);
        return sum;
    }

    ///interpolate cross field with barycentric coordinates using normalized weights
    static  CoordType InterpolateCrossField(const std::vector<CoordType> &TangVect,
                                            const std::vector<ScalarType> &Weight,
                                            const std::vector<CoordType> &Norms,
                                            const CoordType &BaseNorm)
    {

        CoordType sum=InterpolateNRosy3D(TangVect,Norms,Weight,4,BaseNorm);
        return sum;
    }

    ///interpolate cross field with scalar weight
    static typename FaceType::CoordType InterpolateCrossFieldLine(const typename FaceType::CoordType &t0,
                                                                  const typename FaceType::CoordType &t1,
                                                                  const typename FaceType::CoordType &n0,
                                                                  const typename FaceType::CoordType &n1,
                                                                  const typename FaceType::CoordType &target_n,
                                                                  const typename FaceType::ScalarType &weight)
    {
        std::vector<CoordType > V,Norm;
        std::vector<ScalarType > W;
        V.push_back(t0);
        V.push_back(t1);
        Norm.push_back(n0);
        Norm.push_back(n1);
        W.push_back(weight);
        W.push_back(1-weight);
        InterpolateNRosy3D(V,Norm,&W,4,target_n);
    }


    ///return the difference of two cross field, values between [0,0.5]
    static typename FaceType::ScalarType DifferenceCrossField(const typename FaceType::CoordType &t0,
                                                              const typename FaceType::CoordType &t1,
                                                              const typename FaceType::CoordType &n)
    {
        CoordType trans0=t0;
        CoordType trans1=K_PI(t1,t0,n);
        ScalarType diff = 1-fabs(trans0*trans1);
        return diff;
    }

    ///return the difference of two cross field, values between [0,0.5]
    static typename FaceType::ScalarType DifferenceCrossField(const typename vcg::Point2<ScalarType> &t0,
                                                              const typename vcg::Point2<ScalarType> &t1)
    {
        CoordType t03D=CoordType(t0.X(),t0.Y(),0);
        CoordType t13D=CoordType(t1.X(),t1.Y(),0);
        CoordType trans0=t03D;
        CoordType n=CoordType(0,0,1);
        CoordType trans1=K_PI(t13D,t03D,n);
        ScalarType diff = 1-fabs(trans0*trans1);
        return diff;
    }

    ///compute the mismatch between 2 directions
    ///each one si perpendicular to its own normal
    static int MissMatchByCross(const CoordType &dir0,
                                const CoordType &dir1,
                                const CoordType &N0,
                                const CoordType &N1)
    {
        CoordType dir0Rot=Rotate(dir0,N0,N1);
        CoordType dir1Rot=dir1;

        dir0Rot.Normalize();
        dir1Rot.Normalize();

        ScalarType angle_diff=VectToAngle(dir0Rot,N0,dir1Rot);

        ScalarType step=M_PI/2.0;
        int i=(int)floor((angle_diff/step)+0.5);
        int k=0;
        if (i>=0)
            k=i%4;
        else
            k=(-(3*i))%4;
        return k;
    }

    ///compute the mismatch between 2 faces
    static int MissMatchByCross(const FaceType &f0,
                                const FaceType &f1)
    {
        CoordType dir0=CrossVector(f0,0);
        CoordType dir1=CrossVector(f1,0);

        CoordType dir1Rot=Rotate(f1,f0,dir1);
        dir1Rot.Normalize();

        ScalarType angle_diff=VectToAngle(f0,dir1Rot);

        ScalarType step=M_PI/2.0;
        int i=(int)floor((angle_diff/step)+0.5);
        int k=0;
        if (i>=0)
            k=i%4;
        else
            k=(-(3*i))%4;
        return k;
    }


    ///return true if a given vertex is singular,
    ///return also the missmatch
    static bool IsSingularByCross(const VertexType &v,int &missmatch)
    {
        typedef typename VertexType::FaceType FaceType;
        ///check that is on border..
        if (v.IsB())return false;

        std::vector<face::Pos<FaceType> > posVec;
        //SortedFaces(v,faces);
        face::Pos<FaceType> pos(v.cVFp(), v.cVFi());
        vcg::face::VFOrderedStarFF(pos, posVec);

        missmatch=0;
        for (unsigned int i=0;i<posVec.size();i++)
        {
            FaceType *curr_f=posVec[i].F();
            FaceType *next_f=posVec[(i+1)%posVec.size()].F();

            ///find the current missmatch
            missmatch+=MissMatchByCross(*curr_f,*next_f);

        }
        missmatch=missmatch%4;
        return(missmatch!=0);
    }

    ///select singular vertices
    static void SelectSingularByCross(MeshType &mesh)
    {
        for (unsigned int i=0;i<mesh.vert.size();i++)
        {
            if (mesh.vert[i].IsD())continue;
            if (mesh.vert[i].IsB())continue;

            int missmatch;
            if (IsSingularByCross(mesh.vert[i],missmatch))
                mesh.vert[i].SetS();
            else
                mesh.vert[i].ClearS();

        }
    }


    static void GradientToCross(const FaceType &f,
                                const vcg::Point2<ScalarType> &UV0,
                                const vcg::Point2<ScalarType> &UV1,
                                const vcg::Point2<ScalarType> &UV2,
                                CoordType &dirU,
                                CoordType &dirV)
    {
        ///compute non normalized normal
        CoordType n  =  f.cN();

        CoordType p0 =f.cP(1) - f.cP(0);
        CoordType p1 =f.cP(2) - f.cP(1);
        CoordType p2 =f.cP(0) - f.cP(2);

        CoordType t[3];
        t[0] =  -(p0 ^ n);
        t[1] =  -(p1 ^ n);
        t[2] =  -(p2 ^ n);

        dirU = t[1]*UV0.X() + t[2]*UV1.X() + t[0]*UV2.X();
        dirV = t[1]*UV0.Y() + t[2]*UV1.Y() + t[0]*UV2.Y();
    }

    static void MakeDirectionFaceCoherent(FaceType *f0,
                                          FaceType *f1)
    {
        CoordType dir0=f0->PD1();
        CoordType dir1=f1->PD1();

        CoordType dir0Rot=Rotate(*f0,*f1,dir0);
        dir0Rot.Normalize();

        CoordType targD=K_PI(dir1,dir0Rot,f1->N());

        f1->PD1()=targD;
        f1->PD2()=f1->N()^targD;
        f1->PD2().Normalize();
    }

    static void MakeDirectionFaceCoherent(MeshType &mesh,
                                          bool normal_diff=true)
    {
        vcg::tri::UpdateFlags<MeshType>::FaceClearV(mesh);
        vcg::tri::UpdateTopology<MeshType>::FaceFace(mesh);

        typedef typename std::pair<FaceType*,FaceType*> FacePair;
        std::vector<std::pair<ScalarType,FacePair> > heap;

        while (true)
        {
            bool found=false;
            for (int i=0; i<(int)mesh.face.size(); i++)
            {
                FaceType *f=&(mesh.face[i]);
                if (f->IsD())continue;
                if (f->IsV())continue;
                f->SetV();
                found=true;

                for (int i=0;i<f->VN();i++)
                {
                    FaceType *Fopp=f->FFp(i);
                    if (Fopp==f)continue;

                    FacePair entry(f,Fopp);

                    ScalarType val=0;
                    if (normal_diff)val=-(f->N()-Fopp->N()).Norm();

                    heap.push_back(std::pair<ScalarType,FacePair>(val,entry));
                }
                break;
            }

            if (!found)
            {

                vcg::tri::UpdateFlags<MeshType>::FaceClearV(mesh);
                return;///all faces has been visited
            }

            std::make_heap (heap.begin(),heap.end());

            while (!heap.empty())
            {
                std::pop_heap(heap.begin(), heap.end());
                FaceType *f0=heap.back().second.first;
                FaceType *f1=heap.back().second.second;
                assert(f0->IsV());
                heap.pop_back();

                MakeDirectionFaceCoherent(f0,f1);
                f1->SetV();
                for (int k=0; k<f1->VN(); k++)
                {
                    FaceType* f2 = f1->FFp(k);
                    if (f2->IsV())continue;
                    if (f2->IsD())continue;
                    if (f2==f1)continue;

                    FacePair entry(f1,f2);

                    ScalarType val=0;
                    if (normal_diff)val=-(f1->N()-f2->N()).Norm();

                    heap.push_back(std::pair<ScalarType,FacePair>(val,entry));
                    std::push_heap (heap.begin(),heap.end());
                }
            }
        }

    }

    ///transform curvature to UV space
    static vcg::Point2<ScalarType> CrossToUV(FaceType &f)
    {
        typedef typename FaceType::ScalarType ScalarType;
        typedef typename FaceType::CoordType CoordType;

        CoordType Curv=CrossVector(f,0);
        Curv.Normalize();

        CoordType bary3d=(f.P(0)+f.P(1)+f.P(2))/3.0;
        vcg::Point2<ScalarType> Uv0=f.V(0)->T().P();
        vcg::Point2<ScalarType> Uv1=f.V(1)->T().P();
        vcg::Point2<ScalarType> Uv2=f.V(2)->T().P();
        vcg::Point2<ScalarType> baryUV=(Uv0+Uv1+Uv2)/3.0;
        CoordType direct3d=bary3d+Curv;
        CoordType baryCoordsUV;
        vcg::InterpolationParameters<FaceType,ScalarType>(f,direct3d,baryCoordsUV);
        vcg::Point2<ScalarType> curvUV=baryCoordsUV.X()*Uv0+
                baryCoordsUV.Y()*Uv1+
                baryCoordsUV.Z()*Uv2-baryUV;
        curvUV.Normalize();
        return curvUV;
    }

};///end class
} //End Namespace Tri
} // End Namespace vcg
#endif