vcglib/vcg/complex/algorithms/smooth.h

/****************************************************************************
* VCGLib                                                            o o     *
* Visual and Computer Graphics Library                            o     o   *
*                                                                _   O  _   *
* Copyright(C) 2004                                                \/)\/    *
* 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.                                                         *
*                                                                           *
****************************************************************************/


#ifndef __VCGLIB__SMOOTH
#define __VCGLIB__SMOOTH

#include <vcg/space/ray3.h>
#include <vcg/complex/algorithms/update/normal.h>
#include <vcg/complex/algorithms/update/halfedge_topology.h>
#include <vcg/complex/algorithms/closest.h>
#include <vcg/space/index/kdtree/kdtree.h>


namespace vcg
{
namespace tri
{
///
/** \addtogroup trimesh */
/*@{*/
/// Class of static functions to smooth and fair meshes and their attributes.

template <class SmoothMeshType>
class Smooth
{

public:
            typedef SmoothMeshType MeshType;
            typedef typename MeshType::VertexType     VertexType;
            typedef typename MeshType::VertexType::CoordType     CoordType;
            typedef typename MeshType::VertexPointer  VertexPointer;
            typedef typename MeshType::VertexIterator VertexIterator;
            typedef	typename MeshType::ScalarType			ScalarType;
            typedef typename MeshType::FaceType       FaceType;
            typedef typename MeshType::FacePointer    FacePointer;
            typedef typename MeshType::FaceIterator   FaceIterator;
            typedef typename MeshType::FaceContainer  FaceContainer;
      typedef typename vcg::Box3<ScalarType>  Box3Type;
        typedef typename vcg::face::VFIterator<FaceType> VFLocalIterator;

class ScaleLaplacianInfo
{
public:
    CoordType PntSum;
    ScalarType LenSum;
};

// This is precisely what curvature flow does.
// Curvature flow smoothes the surface by moving along the surface
// normal n with a speed equal to the mean curvature
void VertexCoordLaplacianCurvatureFlow(MeshType &/*m*/, int /*step*/, ScalarType /*delta*/)
{

}

// Another Laplacian smoothing variant,
// here we sum the baricenter of the faces incidents on each vertex weighting them with the angle

static void VertexCoordLaplacianAngleWeighted(MeshType &m, int step, ScalarType delta)
{
    ScaleLaplacianInfo lpz;
    lpz.PntSum=CoordType(0,0,0);
    lpz.LenSum=0;
    SimpleTempData<typename MeshType::VertContainer, ScaleLaplacianInfo > TD(m.vert,lpz);
    FaceIterator fi;
    for(int i=0;i<step;++i)
    {
        VertexIterator vi;
        for(vi=m.vert.begin();vi!=m.vert.end();++vi)
             TD[*vi]=lpz;
        ScalarType a[3];
        for(fi=m.face.begin();fi!=m.face.end();++fi)if(!(*fi).IsD())
        {
            CoordType  mp=((*fi).V(0)->P() + (*fi).V(1)->P() + (*fi).V(2)->P())/3.0;
            CoordType  e0=((*fi).V(0)->P() - (*fi).V(1)->P()).Normalize();
            CoordType  e1=((*fi).V(1)->P() - (*fi).V(2)->P()).Normalize();
            CoordType  e2=((*fi).V(2)->P() - (*fi).V(0)->P()).Normalize();

            a[0]=AngleN(-e0,e2);
            a[1]=AngleN(-e1,e0);
            a[2]=AngleN(-e2,e1);
            //assert(fabs(M_PI -a[0] -a[1] -a[2])<0.0000001);

            for(int j=0;j<3;++j){
                        CoordType dir= (mp-(*fi).V(j)->P()).Normalize();
                        TD[(*fi).V(j)].PntSum+=dir*a[j];
                        TD[(*fi).V(j)].LenSum+=a[j]; // well, it should be named angleSum
            }
        }
        for(vi=m.vert.begin();vi!=m.vert.end();++vi)
                if(!(*vi).IsD() && TD[*vi].LenSum>0 )
                 (*vi).P() = (*vi).P() +  (TD[*vi].PntSum/TD[*vi].LenSum ) * delta;

    }
};

// Scale dependent laplacian smoothing [Fujiwara 95]
// as described in
// Implicit Fairing of Irregular Meshes using Diffusion and Curvature Flow
// Mathieu Desbrun, Mark Meyer, Peter Schroeder, Alan H. Barr
// SIGGRAPH 99
// REQUIREMENTS: Border Flags.
//
// Note the delta parameter is in a absolute unit
// to get stability it should be a small percentage of the shortest edge.

static void VertexCoordScaleDependentLaplacian_Fujiwara(MeshType &m, int step, ScalarType delta)
{
    SimpleTempData<typename MeshType::VertContainer, ScaleLaplacianInfo > TD(m.vert);
    ScaleLaplacianInfo lpz;
    lpz.PntSum=CoordType(0,0,0);
    lpz.LenSum=0;
    FaceIterator fi;
    for(int i=0;i<step;++i)
    {
            VertexIterator vi;
            for(vi=m.vert.begin();vi!=m.vert.end();++vi)
                 TD[*vi]=lpz;

            for(fi=m.face.begin();fi!=m.face.end();++fi)if(!(*fi).IsD())
                for(int j=0;j<3;++j)
                    if(!(*fi).IsB(j)) {
                        CoordType edge= (*fi).V1(j)->P() -(*fi).V(j)->P();
                        ScalarType len=Norm(edge);
                        edge/=len;
                        TD[(*fi).V(j)].PntSum+=edge;
                        TD[(*fi).V1(j)].PntSum-=edge;
                        TD[(*fi).V(j)].LenSum+=len;
                        TD[(*fi).V1(j)].LenSum+=len;
                    }

            for(fi=m.face.begin();fi!=m.face.end();++fi)if(!(*fi).IsD())
                for(int j=0;j<3;++j)
                    // se l'edge j e' di bordo si riazzera tutto e si riparte
                    if((*fi).IsB(j)) {
                            TD[(*fi).V(j)].PntSum=CoordType(0,0,0);
                            TD[(*fi).V1(j)].PntSum=CoordType(0,0,0);
                            TD[(*fi).V(j)].LenSum=0;
                            TD[(*fi).V1(j)].LenSum=0;
                    }


            for(fi=m.face.begin();fi!=m.face.end();++fi) if(!(*fi).IsD())
                    for(int j=0;j<3;++j)
                        if((*fi).IsB(j))
                        {
                            CoordType edge= (*fi).V1(j)->P() -(*fi).V(j)->P();
                            ScalarType len=Norm(edge);
                            edge/=len;
                            TD[(*fi).V(j)].PntSum+=edge;
                            TD[(*fi).V1(j)].PntSum-=edge;
                            TD[(*fi).V(j)].LenSum+=len;
                            TD[(*fi).V1(j)].LenSum+=len;
                        }
  // The fundamental part:
    // We move the new point of a quantity
    //
    //  L(M) = 1/Sum(edgelen) * Sum(Normalized edges)
    //

            for(vi=m.vert.begin();vi!=m.vert.end();++vi)
                if(!(*vi).IsD() && TD[*vi].LenSum>0 )
                 (*vi).P() = (*vi).P() + (TD[*vi].PntSum/TD[*vi].LenSum)*delta;
    }
};


class LaplacianInfo
{
public:
    LaplacianInfo(const CoordType &_p, const int _n):sum(_p),cnt(_n) {}
    LaplacianInfo() {}
    CoordType sum;
    ScalarType cnt;
};

// Classical Laplacian Smoothing. Each vertex can be moved onto the average of the adjacent vertices.
// Can smooth only the selected vertices and weight the smoothing according to the quality
// In the latter case 0 means that the vertex is not moved and 1 means that the vertex is moved onto the computed position.
//
// From the Taubin definition "A signal proc approach to fair surface design"
// We define the discrete Laplacian of a discrete surface signal by weighted averages over the neighborhoods
//          \delta xi  = \Sum wij (xj - xi) ;
// where xj are the adjacent vertices of xi and wij is usually 1/n_adj
//
// This function simply accumulate over a TempData all the positions of the ajacent vertices
//
static void AccumulateLaplacianInfo(MeshType &m, SimpleTempData<typename MeshType::VertContainer,LaplacianInfo > &TD, bool cotangentFlag=false)
{
  float weight =1.0f;
            FaceIterator fi;
            for(fi=m.face.begin();fi!=m.face.end();++fi)
            {
                if(!(*fi).IsD())
                    for(int j=0;j<3;++j)
                        if(!(*fi).IsB(j))
                        {
                          if(cotangentFlag) {
                            float angle = Angle(fi->P1(j)-fi->P2(j),fi->P0(j)-fi->P2(j));
                            weight = tan((M_PI*0.5) - angle);
                          }

                            TD[(*fi).V0(j)].sum+=(*fi).P1(j)*weight;
                            TD[(*fi).V1(j)].sum+=(*fi).P0(j)*weight;
                            TD[(*fi).V0(j)].cnt+=weight;
                            TD[(*fi).V1(j)].cnt+=weight;
                        }
            }
            // si azzaera i dati per i vertici di bordo
            for(fi=m.face.begin();fi!=m.face.end();++fi)
            {
                if(!(*fi).IsD())
                    for(int j=0;j<3;++j)
                        if((*fi).IsB(j))
                        {
                            TD[(*fi).V0(j)].sum=(*fi).P0(j);
                            TD[(*fi).V1(j)].sum=(*fi).P1(j);
                            TD[(*fi).V0(j)].cnt=1;
                            TD[(*fi).V1(j)].cnt=1;
                        }
            }

            // se l'edge j e' di bordo si deve mediare solo con gli adiacenti
            for(fi=m.face.begin();fi!=m.face.end();++fi)
            {
                if(!(*fi).IsD())
                    for(int j=0;j<3;++j)
                        if((*fi).IsB(j))
                        {
                            TD[(*fi).V(j)].sum+=(*fi).V1(j)->P();
                            TD[(*fi).V1(j)].sum+=(*fi).V(j)->P();
                            ++TD[(*fi).V(j)].cnt;
                            ++TD[(*fi).V1(j)].cnt;
                        }
            }
}

static void VertexCoordLaplacian(MeshType &m, int step, bool SmoothSelected=false, bool cotangentWeight=false, vcg::CallBackPos * cb=0)
{
  VertexIterator vi;
    LaplacianInfo lpz(CoordType(0,0,0),0);
    SimpleTempData<typename MeshType::VertContainer,LaplacianInfo > TD(m.vert,lpz);
    for(int i=0;i<step;++i)
        {
            if(cb)cb(100*i/step, "Classic Laplacian Smoothing");
            TD.Init(lpz);
            AccumulateLaplacianInfo(m,TD,cotangentWeight);
            for(vi=m.vert.begin();vi!=m.vert.end();++vi)
                if(!(*vi).IsD() && TD[*vi].cnt>0 )
                {
                            if(!SmoothSelected || (*vi).IsS())
                                    (*vi).P() = ( (*vi).P() + TD[*vi].sum)/(TD[*vi].cnt+1);
                }
        }
}

// Same of above but moves only the vertices that do not change FaceOrientation more that the given threshold
static void VertexCoordPlanarLaplacian(MeshType &m, int step, float AngleThrRad = math::ToRad(1.0), bool SmoothSelected=false, vcg::CallBackPos * cb=0)
{
  VertexIterator vi;
    FaceIterator fi;
    LaplacianInfo lpz(CoordType(0,0,0),0);
    SimpleTempData<typename MeshType::VertContainer,LaplacianInfo > TD(m.vert,lpz);
    for(int i=0;i<step;++i)
        {
        if(cb)cb(100*i/step, "Planar Laplacian Smoothing");
        TD.Init(lpz);
        AccumulateLaplacianInfo(m,TD);
        for(vi=m.vert.begin();vi!=m.vert.end();++vi)
            if(!(*vi).IsD() && TD[*vi].cnt>0 )
            {
                if(!SmoothSelected || (*vi).IsS())
                    TD[*vi].sum = ( (*vi).P() + TD[*vi].sum)/(TD[*vi].cnt+1);
            }

        for(fi=m.face.begin();fi!=m.face.end();++fi){
                if(!(*fi).IsD()){
                    for (int j = 0; j < 3; ++j) {
                        if(Angle( NormalizedNormal(TD[(*fi).V0(j)].sum, (*fi).P1(j), (*fi).P2(j) ),
                                            NormalizedNormal(   (*fi).P0(j)     , (*fi).P1(j), (*fi).P2(j) ) ) > AngleThrRad )
                            TD[(*fi).V0(j)].sum = (*fi).P0(j);
                    }
                }
            }
            for(fi=m.face.begin();fi!=m.face.end();++fi){
                if(!(*fi).IsD()){
                    for (int j = 0; j < 3; ++j) {
                        if(Angle( NormalizedNormal(TD[(*fi).V0(j)].sum, TD[(*fi).V1(j)].sum, (*fi).P2(j) ),
                                            NormalizedNormal(   (*fi).P0(j)     ,    (*fi).P1(j),      (*fi).P2(j) ) ) > AngleThrRad )
                        {
                            TD[(*fi).V0(j)].sum = (*fi).P0(j);
                            TD[(*fi).V1(j)].sum = (*fi).P1(j);
                        }
                    }
                }
            }

            for(vi=m.vert.begin();vi!=m.vert.end();++vi)
                if(!(*vi).IsD() && TD[*vi].cnt>0 )
                        (*vi).P()= TD[*vi].sum;



        }// end step


}

static void VertexCoordLaplacianBlend(MeshType &m, int step, float alpha, bool SmoothSelected=false)
{
    VertexIterator vi;
    LaplacianInfo lpz(CoordType(0,0,0),0);
    assert (alpha<= 1.0);
    SimpleTempData<typename MeshType::VertContainer,LaplacianInfo > TD(m.vert);

    for(int i=0;i<step;++i)
        {
        TD.Init(lpz);
        AccumulateLaplacianInfo(m,TD);
        for(vi=m.vert.begin();vi!=m.vert.end();++vi)
            if(!(*vi).IsD() && TD[*vi].cnt>0 )
            {
                if(!SmoothSelected || (*vi).IsS())
                {
                    CoordType Delta = TD[*vi].sum/TD[*vi].cnt - (*vi).P();
                    (*vi).P() = (*vi).P() + Delta*alpha;
                }
            }
        }
}

/* a couple of notes about the lambda mu values
We assume that 0 < lambda , and mu  is a negative scale factor such that mu < - lambda.
Holds mu+lambda < 0 (e.g in absolute value mu is greater)

let kpb be the pass-band frequency, taubin says that:
            kpb = 1/lambda + 1/mu >0

Values of kpb from 0.01 to 0.1 produce good results according to the original paper.

kpb * mu - mu/lambda = 1
mu = 1/(kpb-1/lambda )

So if
* lambda == 0.5, kpb==0.1  -> mu = 1/(0.1 - 2)  = -0.526
* lambda == 0.5, kpb==0.01 -> mu = 1/(0.01 - 2) = -0.502
*/


static void VertexCoordTaubin(MeshType &m, int step, float lambda, float mu, bool SmoothSelected=false, vcg::CallBackPos * cb=0)
{
    LaplacianInfo lpz(CoordType(0,0,0),0);
    SimpleTempData<typename MeshType::VertContainer,LaplacianInfo > TD(m.vert,lpz);
    VertexIterator vi;
    for(int i=0;i<step;++i)
        {
          if(cb) cb(100*i/step, "Taubin Smoothing");
            TD.Init(lpz);
            AccumulateLaplacianInfo(m,TD);
            for(vi=m.vert.begin();vi!=m.vert.end();++vi)
                if(!(*vi).IsD() && TD[*vi].cnt>0 )
                {
                    if(!SmoothSelected || (*vi).IsS())
                    {
                        CoordType Delta = TD[*vi].sum/TD[*vi].cnt - (*vi).P();
                        (*vi).P() = (*vi).P() + Delta*lambda ;
                    }
                }
            TD.Init(lpz);
            AccumulateLaplacianInfo(m,TD);
            for(vi=m.vert.begin();vi!=m.vert.end();++vi)
                    if(!(*vi).IsD() && TD[*vi].cnt>0 )
                    {
                        if(!SmoothSelected || (*vi).IsS())
                        {
                            CoordType Delta = TD[*vi].sum/TD[*vi].cnt - (*vi).P();
                            (*vi).P() = (*vi).P() + Delta*mu ;
                        }
                    }
            } // end for step
}


static void VertexCoordLaplacianQuality(MeshType &m, int step, bool SmoothSelected=false)
{
  LaplacianInfo lpz;
    lpz.sum=CoordType(0,0,0);
    lpz.cnt=1;
    SimpleTempData<typename MeshType::VertContainer,LaplacianInfo > TD(m.vert,lpz);
    for(int i=0;i<step;++i)
        {
            for(VertexIterator vi=m.vert.begin();vi!=m.vert.end();++vi)
                    if(!(*vi).IsD() && TD[*vi].cnt>0 )
                        if(!SmoothSelected || (*vi).IsS())
                        {
                            float q=(*vi).Q();
                            (*vi).P()=(*vi).P()*q + (TD[*vi].sum/TD[*vi].cnt)*(1.0-q);
                        }
        } // end for
};

/*
  Improved Laplacian Smoothing of Noisy Surface Meshes
  J. Vollmer, R. Mencl, and H. M<EFBFBD>ller
  EUROGRAPHICS Volume 18 (1999), Number 3
*/

class HCSmoothInfo
{
public:
    CoordType dif;
    CoordType sum;
    int cnt;
};

static void VertexCoordLaplacianHC(MeshType &m, int step, bool SmoothSelected=false )
{
    ScalarType beta=0.5;
  HCSmoothInfo lpz;
    lpz.sum=CoordType(0,0,0);
    lpz.dif=CoordType(0,0,0);
    lpz.cnt=0;
        for(int i=0;i<step;++i)
        {
            SimpleTempData<typename MeshType::VertContainer,HCSmoothInfo > TD(m.vert,lpz);
            // First Loop compute the laplacian
            FaceIterator fi;
            for(fi=m.face.begin();fi!=m.face.end();++fi)if(!(*fi).IsD())
                {
                    for(int j=0;j<3;++j)
                    {
                        TD[(*fi).V(j)].sum+=(*fi).V1(j)->P();
                        TD[(*fi).V1(j)].sum+=(*fi).V(j)->P();
                        ++TD[(*fi).V(j)].cnt;
                        ++TD[(*fi).V1(j)].cnt;
                        // se l'edge j e' di bordo si deve sommare due volte
                        if((*fi).IsB(j))
                        {
                            TD[(*fi).V(j)].sum+=(*fi).V1(j)->P();
                            TD[(*fi).V1(j)].sum+=(*fi).V(j)->P();
                            ++TD[(*fi).V(j)].cnt;
                            ++TD[(*fi).V1(j)].cnt;
                        }
                    }
                }
            VertexIterator vi;
            for(vi=m.vert.begin();vi!=m.vert.end();++vi) if(!(*vi).IsD())
                 TD[*vi].sum/=(float)TD[*vi].cnt;

            // Second Loop compute average difference
            for(fi=m.face.begin();fi!=m.face.end();++fi) if(!(*fi).IsD())
                {
                    for(int j=0;j<3;++j)
                    {
                        TD[(*fi).V(j)].dif +=TD[(*fi).V1(j)].sum-(*fi).V1(j)->P();
                        TD[(*fi).V1(j)].dif+=TD[(*fi).V(j)].sum-(*fi).V(j)->P();
                        // se l'edge j e' di bordo si deve sommare due volte
                        if((*fi).IsB(j))
                        {
                            TD[(*fi).V(j)].dif +=TD[(*fi).V1(j)].sum-(*fi).V1(j)->P();
                            TD[(*fi).V1(j)].dif+=TD[(*fi).V(j)].sum-(*fi).V(j)->P();
                        }
                    }
                }

            for(vi=m.vert.begin();vi!=m.vert.end();++vi)
                {
                 TD[*vi].dif/=(float)TD[*vi].cnt;
                 if(!SmoothSelected || (*vi).IsS())
                        (*vi).P()= TD[*vi].sum - (TD[*vi].sum - (*vi).P())*beta  + (TD[*vi].dif)*(1.f-beta);
                }
        } // end for step
};

// Laplacian smooth of the quality.


class ColorSmoothInfo
{
public:
    unsigned int r;
    unsigned int g;
    unsigned int b;
    unsigned int a;
    int cnt;
};

static void VertexColorLaplacian(MeshType &m, int step, bool SmoothSelected=false, vcg::CallBackPos * cb=0)
{
    ColorSmoothInfo csi;
    csi.r=0; csi.g=0; csi.b=0; csi.cnt=0;
    SimpleTempData<typename MeshType::VertContainer, ColorSmoothInfo> TD(m.vert,csi);

    for(int i=0;i<step;++i)
    {
        if(cb) cb(100*i/step, "Vertex Color Laplacian Smoothing");
        VertexIterator vi;
        for(vi=m.vert.begin();vi!=m.vert.end();++vi)
            TD[*vi]=csi;

        FaceIterator fi;
        for(fi=m.face.begin();fi!=m.face.end();++fi)
            if(!(*fi).IsD())
                for(int j=0;j<3;++j)
                    if(!(*fi).IsB(j))
                    {
                        TD[(*fi).V(j)].r+=(*fi).V1(j)->C()[0];
                        TD[(*fi).V(j)].g+=(*fi).V1(j)->C()[1];
                        TD[(*fi).V(j)].b+=(*fi).V1(j)->C()[2];
                        TD[(*fi).V(j)].a+=(*fi).V1(j)->C()[3];

                        TD[(*fi).V1(j)].r+=(*fi).V(j)->C()[0];
                        TD[(*fi).V1(j)].g+=(*fi).V(j)->C()[1];
                        TD[(*fi).V1(j)].b+=(*fi).V(j)->C()[2];
                        TD[(*fi).V1(j)].a+=(*fi).V(j)->C()[3];

                        ++TD[(*fi).V(j)].cnt;
                        ++TD[(*fi).V1(j)].cnt;
                    }

        // si azzaera i dati per i vertici di bordo
        for(fi=m.face.begin();fi!=m.face.end();++fi)
            if(!(*fi).IsD())
                for(int j=0;j<3;++j)
                    if((*fi).IsB(j))
                    {
                        TD[(*fi).V(j)]=csi;
                        TD[(*fi).V1(j)]=csi;
                    }

        // se l'edge j e' di bordo si deve mediare solo con gli adiacenti
        for(fi=m.face.begin();fi!=m.face.end();++fi)
            if(!(*fi).IsD())
                for(int j=0;j<3;++j)
                    if((*fi).IsB(j))
                    {
                        TD[(*fi).V(j)].r+=(*fi).V1(j)->C()[0];
                        TD[(*fi).V(j)].g+=(*fi).V1(j)->C()[1];
                        TD[(*fi).V(j)].b+=(*fi).V1(j)->C()[2];
                        TD[(*fi).V(j)].a+=(*fi).V1(j)->C()[3];

                        TD[(*fi).V1(j)].r+=(*fi).V(j)->C()[0];
                        TD[(*fi).V1(j)].g+=(*fi).V(j)->C()[1];
                        TD[(*fi).V1(j)].b+=(*fi).V(j)->C()[2];
                        TD[(*fi).V1(j)].a+=(*fi).V(j)->C()[3];

                        ++TD[(*fi).V(j)].cnt;
                        ++TD[(*fi).V1(j)].cnt;
                    }

        for(vi=m.vert.begin();vi!=m.vert.end();++vi)
            if(!(*vi).IsD() && TD[*vi].cnt>0 )
                if(!SmoothSelected || (*vi).IsS())
                {
                    (*vi).C()[0] = (unsigned int) ceil((double) (TD[*vi].r / TD[*vi].cnt));
                    (*vi).C()[1] = (unsigned int) ceil((double) (TD[*vi].g / TD[*vi].cnt));
                    (*vi).C()[2] = (unsigned int) ceil((double) (TD[*vi].b / TD[*vi].cnt));
                    (*vi).C()[3] = (unsigned int) ceil((double) (TD[*vi].a / TD[*vi].cnt));
                }
    } // end for step
};

static void FaceColorLaplacian(MeshType &m, int step, bool SmoothSelected=false, vcg::CallBackPos * cb=0)
{
    ColorSmoothInfo csi;
    csi.r=0; csi.g=0; csi.b=0; csi.cnt=0;
    SimpleTempData<typename MeshType::FaceContainer, ColorSmoothInfo> TD(m.face,csi);

    for(int i=0;i<step;++i)
    {
        if(cb) cb(100*i/step, "Face Color Laplacian Smoothing");
        FaceIterator fi;
        for(fi=m.face.begin();fi!=m.face.end();++fi)
            TD[*fi]=csi;

        for(fi=m.face.begin();fi!=m.face.end();++fi)
        {
            if(!(*fi).IsD())
                for(int j=0;j<3;++j)
                    if(!(*fi).IsB(j))
                    {
                        TD[*fi].r+=(*fi).FFp(j)->C()[0];
                        TD[*fi].g+=(*fi).FFp(j)->C()[1];
                        TD[*fi].b+=(*fi).FFp(j)->C()[2];
                        TD[*fi].a+=(*fi).FFp(j)->C()[3];
                        ++TD[*fi].cnt;
                    }
        }
        for(fi=m.face.begin();fi!=m.face.end();++fi)
            if(!(*fi).IsD() && TD[*fi].cnt>0 )
                if(!SmoothSelected || (*fi).IsS())
                {
                    (*fi).C()[0] = (unsigned int) ceil((float) (TD[*fi].r / TD[*fi].cnt));
                    (*fi).C()[1] = (unsigned int) ceil((float) (TD[*fi].g / TD[*fi].cnt));
                    (*fi).C()[2] = (unsigned int) ceil((float) (TD[*fi].b / TD[*fi].cnt));
                    (*fi).C()[3] = (unsigned int) ceil((float) (TD[*fi].a / TD[*fi].cnt));
                }
    } // end for step
};

// Laplacian smooth of the quality.

class QualitySmoothInfo
{
public:
    ScalarType sum;
    int cnt;
};


static void VertexQualityLaplacian(MeshType &m, int step=1, bool SmoothSelected=false)
{
  QualitySmoothInfo lpz;
    lpz.sum=0;
    lpz.cnt=0;
    SimpleTempData<typename MeshType::VertContainer,QualitySmoothInfo> TD(m.vert,lpz);
    //TD.Start(lpz);
    for(int i=0;i<step;++i)
    {
        VertexIterator vi;
        for(vi=m.vert.begin();vi!=m.vert.end();++vi)
             TD[*vi]=lpz;

        FaceIterator fi;
        for(fi=m.face.begin();fi!=m.face.end();++fi)
            if(!(*fi).IsD())
                for(int j=0;j<3;++j)
                    if(!(*fi).IsB(j))
                        {
                            TD[(*fi).V(j)].sum+=(*fi).V1(j)->Q();
                            TD[(*fi).V1(j)].sum+=(*fi).V(j)->Q();
                            ++TD[(*fi).V(j)].cnt;
                            ++TD[(*fi).V1(j)].cnt;
                    }

            // si azzaera i dati per i vertici di bordo
            for(fi=m.face.begin();fi!=m.face.end();++fi)
                if(!(*fi).IsD())
                    for(int j=0;j<3;++j)
                        if((*fi).IsB(j))
                            {
                                TD[(*fi).V(j)]=lpz;
                                TD[(*fi).V1(j)]=lpz;
                            }

            // se l'edge j e' di bordo si deve mediare solo con gli adiacenti
            for(fi=m.face.begin();fi!=m.face.end();++fi)
                if(!(*fi).IsD())
                    for(int j=0;j<3;++j)
                        if((*fi).IsB(j))
                            {
                                TD[(*fi).V(j)].sum+=(*fi).V1(j)->Q();
                                TD[(*fi).V1(j)].sum+=(*fi).V(j)->Q();
                                ++TD[(*fi).V(j)].cnt;
                                ++TD[(*fi).V1(j)].cnt;
                        }

    //VertexIterator vi;
    for(vi=m.vert.begin();vi!=m.vert.end();++vi)
        if(!(*vi).IsD() && TD[*vi].cnt>0 )
            if(!SmoothSelected || (*vi).IsS())
                    (*vi).Q()=TD[*vi].sum/TD[*vi].cnt;
    }

    //TD.Stop();
};

static void VertexNormalLaplacian(MeshType &m, int step,bool SmoothSelected=false)
{
    LaplacianInfo lpz;
      lpz.sum=CoordType(0,0,0);
      lpz.cnt=0;
    SimpleTempData<typename MeshType::VertContainer,LaplacianInfo > TD(m.vert,lpz);
    for(int i=0;i<step;++i)
    {
        VertexIterator vi;
        for(vi=m.vert.begin();vi!=m.vert.end();++vi)
             TD[*vi]=lpz;

        FaceIterator fi;
        for(fi=m.face.begin();fi!=m.face.end();++fi)
            if(!(*fi).IsD())
                for(int j=0;j<3;++j)
                    if(!(*fi).IsB(j))
                        {
                            TD[(*fi).V(j)].sum+=(*fi).V1(j)->N();
                            TD[(*fi).V1(j)].sum+=(*fi).V(j)->N();
                            ++TD[(*fi).V(j)].cnt;
                            ++TD[(*fi).V1(j)].cnt;
                    }

            // si azzaera i dati per i vertici di bordo
            for(fi=m.face.begin();fi!=m.face.end();++fi)
                if(!(*fi).IsD())
                    for(int j=0;j<3;++j)
                        if((*fi).IsB(j))
                            {
                                TD[(*fi).V(j)]=lpz;
                                TD[(*fi).V1(j)]=lpz;
                            }

            // se l'edge j e' di bordo si deve mediare solo con gli adiacenti
            for(fi=m.face.begin();fi!=m.face.end();++fi)
                if(!(*fi).IsD())
                    for(int j=0;j<3;++j)
                        if((*fi).IsB(j))
                            {
                                TD[(*fi).V(j)].sum+=(*fi).V1(j)->N();
                                TD[(*fi).V1(j)].sum+=(*fi).V(j)->N();
                                ++TD[(*fi).V(j)].cnt;
                                ++TD[(*fi).V1(j)].cnt;
                        }

    //VertexIterator vi;
    for(vi=m.vert.begin();vi!=m.vert.end();++vi)
        if(!(*vi).IsD() && TD[*vi].cnt>0 )
            if(!SmoothSelected || (*vi).IsS())
                    (*vi).N()=TD[*vi].sum/TD[*vi].cnt;
    }

};

// Smooth solo lungo la direzione di vista
    // alpha e' compreso fra 0(no smoot) e 1 (tutto smoot)
  // Nota che se smootare il bordo puo far fare bandierine.
static void VertexCoordViewDepth(MeshType &m,
                 const CoordType & viewpoint,
                 const ScalarType alpha,
                 int step, bool SmoothBorder=false )
{
    LaplacianInfo lpz;
    lpz.sum=CoordType(0,0,0);
    lpz.cnt=0;
    SimpleTempData<typename MeshType::VertContainer,LaplacianInfo > TD(m.vert,lpz);
    for(int i=0;i<step;++i)
    {
        VertexIterator vi;
        for(vi=m.vert.begin();vi!=m.vert.end();++vi)
             TD[*vi]=lpz;

        FaceIterator fi;
        for(fi=m.face.begin();fi!=m.face.end();++fi)
            if(!(*fi).IsD())
                for(int j=0;j<3;++j)
                    if(!(*fi).IsB(j))
                        {
                            TD[(*fi).V(j)].sum+=(*fi).V1(j)->cP();
                            TD[(*fi).V1(j)].sum+=(*fi).V(j)->cP();
                            ++TD[(*fi).V(j)].cnt;
                            ++TD[(*fi).V1(j)].cnt;
                    }

            // si azzaera i dati per i vertici di bordo
            for(fi=m.face.begin();fi!=m.face.end();++fi)
                if(!(*fi).IsD())
                    for(int j=0;j<3;++j)
                        if((*fi).IsB(j))
                            {
                                TD[(*fi).V(j)]=lpz;
                                TD[(*fi).V1(j)]=lpz;
                            }

            // se l'edge j e' di bordo si deve mediare solo con gli adiacenti
     if(SmoothBorder)
            for(fi=m.face.begin();fi!=m.face.end();++fi)
                if(!(*fi).IsD())
                    for(int j=0;j<3;++j)
                        if((*fi).IsB(j))
                            {
                                TD[(*fi).V(j)].sum+=(*fi).V1(j)->cP();
                                TD[(*fi).V1(j)].sum+=(*fi).V(j)->cP();
                                ++TD[(*fi).V(j)].cnt;
                                ++TD[(*fi).V1(j)].cnt;
                        }

    for(vi=m.vert.begin();vi!=m.vert.end();++vi)
        if(!(*vi).IsD() && TD[*vi].cnt>0 )
            {
                CoordType np = TD[*vi].sum/TD[*vi].cnt;
                CoordType d = (*vi).cP() - viewpoint; d.Normalize();
                ScalarType s = d .dot ( np - (*vi).cP() );
                (*vi).P() += d * (s*alpha);
            }
    }
}



/****************************************************************************************************************/
/****************************************************************************************************************/
// Paso Double Smoothing
//  The proposed
// approach is a two step method where  in the first step the face normals
// are adjusted and then, in a second phase, the vertex positions are updated.
// Ref:
// A. Belyaev and Y. Ohtake, A Comparison of Mesh Smoothing Methods, Proc. Israel-Korea Bi-Nat"l Conf. Geometric Modeling and Computer Graphics, pp. 83-87, 2003.

/****************************************************************************************************************/
/****************************************************************************************************************/
// Classi di info

class PDVertInfo
{
public:
    CoordType np;
};


class PDFaceInfo
{
public:
  PDFaceInfo(){}
  PDFaceInfo(const CoordType &_m):m(_m){}
  CoordType m;
};
/***************************************************************************/
// Paso Doble Step 1 compute the smoothed normals
/***************************************************************************/
// Requirements:
// VF Topology
// Normalized Face Normals
//
// This is the Normal Smoothing approach of Shen and Berner
// Fuzzy Vector Median-Based Surface Smoothing TVCG 2004


void FaceNormalFuzzyVectorSB(MeshType &m,
                  SimpleTempData<typename MeshType::FaceContainer,PDFaceInfo > &TD,
                  ScalarType sigma)
{
    int i;

    FaceIterator fi;

    for(fi=m.face.begin();fi!=m.face.end();++fi)
    {
        CoordType bc=(*fi).Barycenter();
    // 1) Clear all the visited flag of faces that are vertex-adjacent to fi
        for(i=0;i<3;++i)
        {
        vcg::face::VFIterator<FaceType> ep(&*fi,i);
          while (!ep.End())
            {
                ep.f->ClearV();
                ++ep;
            }
        }

    // 1) Effectively average the normals weighting them with
    (*fi).SetV();
        CoordType mm=CoordType(0,0,0);
        for(i=0;i<3;++i)
        {
          vcg::face::VFIterator<FaceType> ep(&*fi,i);
          while (!ep.End())
            {
                if(! (*ep.f).IsV() )
                {
                    if(sigma>0)
                    {
                        ScalarType dd=SquaredDistance(ep.f->Barycenter(),bc);
                        ScalarType ang=AngleN(ep.f->N(),(*fi).N());
                        mm+=ep.f->N()*exp((-sigma)*ang*ang/dd);
                    }
                    else mm+=ep.f->N();
                    (*ep.f).SetV();
                }
                ++ep;
            }
        }
        mm.Normalize();
        TD[*fi].m=mm;
    }
}

// Replace the normal of the face with the average of normals of the vertex adijacent faces.
// Normals are weighted with face area.
// It assumes that:
// VF adjacency is present.

static void FaceNormalLaplacianVF(MeshType &m)
{
  tri::RequireVFAdjacency(m);
  PDFaceInfo lpzf(CoordType(0,0,0));
  SimpleTempData<typename MeshType::FaceContainer, PDFaceInfo> TDF(m.face,lpzf);

  tri::UpdateNormal<MeshType>::NormalizePerFaceByArea(m);

  for(FaceIterator fi=m.face.begin();fi!=m.face.end();++fi) if(!(*fi).IsD())
  {
    CoordType bc=Barycenter<FaceType>(*fi);
    // 1) Clear all the visited flag of faces that are vertex-adjacent to fi
    for(int i=0;i<3;++i)
    {
      VFLocalIterator ep(&*fi,i);
      for (;!ep.End();++ep)
        ep.f->ClearV();
    }

    // 2) Effectively average the normals
    CoordType normalSum=(*fi).N();

    for(int i=0;i<3;++i)
    {
      VFLocalIterator ep(&*fi,i);
      for (;!ep.End();++ep)
      {
        if(! (*ep.f).IsV() )
        {
          normalSum += ep.f->N();
          (*ep.f).SetV();
        }
      }
    }
    normalSum.Normalize();
    TDF[*fi].m=normalSum;
  }
  for(FaceIterator fi=m.face.begin();fi!=m.face.end();++fi)
    (*fi).N()=TDF[*fi].m;

  tri::UpdateNormal<MeshType>::NormalizePerFace(m);
}

// Replace the normal of the face with the average of normals of the face adijacent faces.
// Normals are weighted with face area.
// It assumes that:
// Normals are normalized:
// FF adjacency is present.


static void FaceNormalLaplacianFF(MeshType &m, int step=1, bool SmoothSelected=false )
{
  PDFaceInfo lpzf(CoordType(0,0,0));
  SimpleTempData<typename MeshType::FaceContainer, PDFaceInfo> TDF(m.face,lpzf);
  tri::RequireFFAdjacency(m);

  FaceIterator fi;
  tri::UpdateNormal<MeshType>::NormalizePerFaceByArea(m);
  for(int iStep=0;iStep<step;++iStep)
  {
    for(fi=m.face.begin();fi!=m.face.end();++fi) if(!(*fi).IsD())
    {
      CoordType normalSum=(*fi).N();

      for(int i=0;i<3;++i)
        normalSum+=(*fi).FFp(i)->N();

      TDF[*fi].m=normalSum;
    }
    for(fi=m.face.begin();fi!=m.face.end();++fi)
      if(!SmoothSelected || (*fi).IsS())
        (*fi).N()=TDF[*fi].m;

    tri::UpdateNormal<MeshType>::NormalizePerFace(m);
  }
}


/***************************************************************************/
// Paso Doble Step 1 compute the smoothed normals
/***************************************************************************/
// Requirements:
// VF Topology
// Normalized Face Normals
//
// This is the Normal Smoothing approach based on a angle thresholded weighting
// sigma is in the 0 .. 1 range, it represent the cosine of a threshold angle.
// sigma == 0 All the normals are averaged
// sigma == 1 Nothing is averaged.
// Only within the specified range are averaged toghether. The averagin is weighted with the


static void FaceNormalAngleThreshold(MeshType &m,
                                     SimpleTempData<typename MeshType::FaceContainer,PDFaceInfo> &TD,
                                     ScalarType sigma)
{
  for(FaceIterator fi=m.face.begin();fi!=m.face.end();++fi)
  {
    // 1) Clear all the visited flag of faces that are vertex-adjacent to fi
    for(int i=0;i<3;++i)
    {
      VFLocalIterator ep(&*fi,i);
      for (;!ep.End();++ep)
        ep.f->ClearV();
    }

    // 1) Effectively average the normals weighting them with the squared difference of the angle similarity
    // sigma is the cosine of a threshold angle. sigma \in 0..1
    // sigma == 0 All the normals are averaged
    // sigma == 1 Nothing is averaged.
    // The averaging is weighted with the difference between normals. more similar the normal more important they are.

    CoordType normalSum=CoordType(0,0,0);
    for(int i=0;i<3;++i)
    {
      VFLocalIterator ep(&*fi,i);
      for (;!ep.End();++ep)
      {
        if(! (*ep.f).IsV() )
        {
          ScalarType cosang=ep.f->N().dot((*fi).N());
          // Note that if two faces form an angle larger than 90 deg, their contribution should be very very small.
          // Without this clamping
          cosang = math::Clamp(cosang,ScalarType(0.0001),ScalarType(1.f));
          if(cosang >= sigma)
          {
            ScalarType w = cosang-sigma;
            normalSum += ep.f->N()*(w*w);   // similar normals have a cosang very close to 1 so cosang - sigma is maximized
          }
          (*ep.f).SetV();
        }
      }
    }
    normalSum.Normalize();
    TD[*fi].m=normalSum;
  }

  for(FaceIterator fi=m.face.begin();fi!=m.face.end();++fi)
    (*fi).N()=TD[*fi].m;
}

/****************************************************************************************************************/
// Restituisce il gradiente dell'area del triangolo nel punto p.
// Nota che dovrebbe essere sempre un vettore che giace nel piano del triangolo e perpendicolare al lato opposto al vertice p.
// Ottimizzato con Maple e poi pesantemente a mano.

static CoordType TriAreaGradient(CoordType &p,CoordType &p0,CoordType &p1)
{
    CoordType dd = p1-p0;
    CoordType d0 = p-p0;
    CoordType d1 = p-p1;
    CoordType grad;

    ScalarType t16 =  d0[1]* d1[2] - d0[2]* d1[1];
    ScalarType t5  = -d0[2]* d1[0] + d0[0]* d1[2];
    ScalarType t4  = -d0[0]* d1[1] + d0[1]* d1[0];

    ScalarType delta= sqrtf(t4*t4 + t5*t5 +t16*t16);

    grad[0]= (t5  * (-dd[2]) + t4 * ( dd[1]))/delta;
    grad[1]= (t16 * (-dd[2]) + t4 * (-dd[0]))/delta;
    grad[2]= (t16 * ( dd[1]) + t5 * ( dd[0]))/delta;

    return grad;
}

template <class ScalarType>
static CoordType CrossProdGradient(CoordType &p, CoordType &p0, CoordType &p1, CoordType &m)
{
    CoordType grad;
    CoordType p00=p0-p;
    CoordType p01=p1-p;
    grad[0] = (-p00[2] + p01[2])*m[1] + (-p01[1] + p00[1])*m[2];
    grad[1] = (-p01[2] + p00[2])*m[0] + (-p00[0] + p01[0])*m[2];
    grad[2] = (-p00[1] + p01[1])*m[0] + (-p01[0] + p00[0])*m[1];

    return grad;
}

/*
Deve Calcolare il gradiente di
E(p) = A(p,p0,p1) (n - m)^2 =
A(...) (2-2nm)   =
(p0-p)^(p1-p)
2A - 2A * ------------- m  =
2A

2A  -  2 (p0-p)^(p1-p) * m
*/

static CoordType FaceErrorGrad(CoordType &p,CoordType &p0,CoordType &p1, CoordType &m)
{
    return     TriAreaGradient(p,p0,p1) *2.0f
        - CrossProdGradient(p,p0,p1,m) *2.0f ;
}
/***************************************************************************/
// Paso Doble Step 2 Fitta la mesh a un dato insieme di normali
/***************************************************************************/


static void FitMesh(MeshType &m,
             SimpleTempData<typename MeshType::VertContainer, PDVertInfo> &TDV,
             SimpleTempData<typename MeshType::FaceContainer, PDFaceInfo> &TDF,
             float lambda)
{
    vcg::face::VFIterator<FaceType> ep;
    VertexIterator vi;
    for(vi=m.vert.begin();vi!=m.vert.end();++vi)
    {
        CoordType ErrGrad=CoordType(0,0,0);

        ep.f=(*vi).VFp();
        ep.z=(*vi).VFi();
        while (!ep.End())
        {
            ErrGrad+=FaceErrorGrad(ep.f->V(ep.z)->P(),ep.f->V1(ep.z)->P(),ep.f->V2(ep.z)->P(),TDF[ep.f].m);
            ++ep;
        }
        TDV[*vi].np=(*vi).P()-ErrGrad*(ScalarType)lambda;
    }

    for(vi=m.vert.begin();vi!=m.vert.end();++vi)
        (*vi).P()=TDV[*vi].np;

}
/****************************************************************************************************************/



static void FastFitMesh(MeshType &m,
             SimpleTempData<typename MeshType::VertContainer, PDVertInfo> &TDV,
       //SimpleTempData<typename MeshType::FaceContainer, PDFaceInfo> &TDF,
             bool OnlySelected=false)
{
    //vcg::face::Pos<FaceType> ep;
    vcg::face::VFIterator<FaceType> ep;
    VertexIterator vi;

    for(vi=m.vert.begin();vi!=m.vert.end();++vi)
    {
   CoordType Sum(0,0,0);
   ScalarType cnt=0;
   VFLocalIterator ep(&*vi);
     for (;!ep.End();++ep)
        {
      CoordType bc=Barycenter<FaceType>(*ep.F());
      Sum += ep.F()->N()*(ep.F()->N().dot(bc - (*vi).P()));
      ++cnt;
        }
        TDV[*vi].np=(*vi).P()+ Sum*(1.0/cnt);
    }

    if(OnlySelected)
    {
        for(vi=m.vert.begin();vi!=m.vert.end();++vi)
                if((*vi).IsS()) (*vi).P()=TDV[*vi].np;
    }
    else
    {
        for(vi=m.vert.begin();vi!=m.vert.end();++vi)
        (*vi).P()=TDV[*vi].np;
    }
}



// The sigma parameter affect the normal smoothing step

static void VertexCoordPasoDoble(MeshType &m, int NormalSmoothStep, typename MeshType::ScalarType Sigma=0, int FitStep=50, bool SmoothSelected =false)
{
  tri::RequireCompactness(m);
  tri::RequireVFAdjacency(m);
  PDVertInfo lpzv;
  lpzv.np=CoordType(0,0,0);
  PDFaceInfo lpzf(CoordType(0,0,0));

  assert(HasPerVertexVFAdjacency(m) && HasPerFaceVFAdjacency(m));
  SimpleTempData< typename MeshType::VertContainer, PDVertInfo> TDV(m.vert,lpzv);
  SimpleTempData< typename MeshType::FaceContainer, PDFaceInfo> TDF(m.face,lpzf);

  for(int j=0;j<NormalSmoothStep;++j)
    FaceNormalAngleThreshold(m,TDF,Sigma);

  for(int j=0;j<FitStep;++j)
    FastFitMesh(m,TDV,SmoothSelected);
}


static void VertexNormalPointCloud(MeshType &m, int neighborNum, int iterNum, KdTree<ScalarType> *tp=0)
{
  SimpleTempData<typename MeshType::VertContainer,CoordType > TD(m.vert,CoordType(0,0,0));
  VertexConstDataWrapper<MeshType> ww(m);
  KdTree<ScalarType> *tree=0;
  if(tp==0) tree = new KdTree<ScalarType>(ww);
  else tree=tp;

  tree->setMaxNofNeighbors(neighborNum);
  for(int ii=0;ii<iterNum;++ii)
  {
    for (VertexIterator vi = m.vert.begin();vi!=m.vert.end();++vi)
    {
      tree->doQueryK(vi->cP());
      int neighbours = tree->getNofFoundNeighbors();
      for (int i = 0; i < neighbours; i++)
      {
        int neightId = tree->getNeighborId(i);
        if(m.vert[neightId].cN()*vi->cN()>0)
          TD[vi]+= m.vert[neightId].cN();
        else
          TD[vi]-= m.vert[neightId].cN();
      }
    }
    for (VertexIterator vi = m.vert.begin();vi!=m.vert.end();++vi)
    {
      vi->N()=TD[vi];
      TD[vi]=CoordType(0,0,0);
    }
    tri::UpdateNormal<MeshType>::NormalizePerVertex(m);
  }

  if(tp==0) delete tree;
}

//! Laplacian smoothing with a reprojection on a target surface.
// grid must be a spatial index that contains all triangular faces of the target mesh gridmesh
template<class GRID, class MeshTypeTri>
static void VertexCoordLaplacianReproject(MeshType& m, GRID& grid, MeshTypeTri& gridmesh)
{
    for(VertexIterator vi=m.vert.begin();vi!=m.vert.end();++vi)
    {
        if(! (*vi).IsD())
            VertexCoordLaplacianReproject(m,grid,gridmesh,&*vi);
    }
}


template<class GRID, class MeshTypeTri>
static void VertexCoordLaplacianReproject(MeshType& m, GRID& grid, MeshTypeTri& gridmesh, typename MeshType::VertexType* vp)
{
    assert(MeshType::HEdgeType::HasHVAdjacency());

    // compute barycenter
    typedef std::vector<VertexPointer> VertexSet;
    VertexSet verts;
    verts = HalfEdgeTopology<MeshType>::getVertices(vp);

    typename MeshType::CoordType ct(0,0,0);
    for(typename VertexSet::iterator it = verts.begin(); it != verts.end(); ++it)
    {
        ct += (*it)->P();
    }
    ct /= verts.size();

    // move vertex
    vp->P() = ct;


    vector<FacePointer> faces2 = HalfEdgeTopology<MeshType>::get_incident_faces(vp);

    // estimate normal
    typename MeshType::CoordType avgn(0,0,0);

    for(unsigned int i = 0;i< faces2.size();i++)
        if(faces2[i])
        {
            vector<VertexPointer> vertices = HalfEdgeTopology<MeshType>::getVertices(faces2[i]);

            assert(vertices.size() == 4);

            avgn += vcg::Normal<typename MeshType::CoordType>(vertices[0]->cP(), vertices[1]->cP(), vertices[2]->cP());
            avgn += vcg::Normal<typename MeshType::CoordType>(vertices[2]->cP(), vertices[3]->cP(), vertices[0]->cP());

        }
    avgn.Normalize();

    // reproject
    ScalarType diag = m.bbox.Diag();
    typename MeshType::CoordType raydir = avgn;
    Ray3<typename MeshType::ScalarType> ray;

    ray.SetOrigin(vp->P());
    ScalarType t;
    typename MeshTypeTri::FaceType* f = 0;
    typename MeshTypeTri::FaceType* fr = 0;

    vector<typename MeshTypeTri::CoordType> closests;
    vector<typename MeshTypeTri::ScalarType> minDists;
    vector<typename MeshTypeTri::FaceType*> faces;
    ray.SetDirection(-raydir);
    f = vcg::tri::DoRay<MeshTypeTri,GRID>(gridmesh, grid, ray, diag/4.0, t);

    if (f)
    {
      closests.push_back(ray.Origin() + ray.Direction()*t);
      minDists.push_back(fabs(t));
      faces.push_back(f);
    }
    ray.SetDirection(raydir);
    fr = vcg::tri::DoRay<MeshTypeTri,GRID>(gridmesh, grid, ray, diag/4.0, t);
    if (fr)
    {
      closests.push_back(ray.Origin() + ray.Direction()*t);
      minDists.push_back(fabs(t));
      faces.push_back(fr);
    }

    if (fr) if (fr->N()*raydir<0) fr=0; // discard: inverse normal;
    typename MeshType::CoordType newPos;
    if (minDists.size() == 0)
    {
        newPos = vp->P();
        f = 0;
    }
    else
    {
        int minI = std::min_element(minDists.begin(),minDists.end()) - minDists.begin();
        newPos = closests[minI];
        f = faces[minI];
    }

    if (f)
        vp->P() = newPos;
}

}; //end Smooth class

}		// End namespace tri
}		// End namespace vcg

#endif //  VCG_SMOOTH