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vcglib/vcg/complex/algorithms/smooth.h

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/****************************************************************************
* 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 <cmath>
#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<>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 bsased 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)
{
int i;
FaceIterator fi;
for(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(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(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,0.0001f,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(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::Pos<FaceType> ep;
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;
}
}
static void VertexCoordPasoDoble(MeshType &m, int step, typename MeshType::ScalarType Sigma=0, int FitStep=10, typename MeshType::ScalarType FitLambda=0.05)
{
SimpleTempData< typename MeshType::VertContainer, PDVertInfo> TDV(m.vert);
SimpleTempData< typename MeshType::FaceContainer, PDFaceInfo> TDF(m.face);
PDVertInfo lpzv;
lpzv.np=CoordType(0,0,0);
PDFaceInfo lpzf(CoordType(0,0,0));
assert(m.HasVFTopology());
m.HasVFTopology();
TDV.Start(lpzv);
TDF.Start(lpzf);
for(int j=0;j<step;++j)
{
vcg::tri::UpdateNormal<MeshType>::PerFace(m);
FaceNormalAngleThreshold(m,TDF,Sigma);
for(int k=0;k<FitStep;k++)
FitMesh(m,TDV,TDF,FitLambda);
}
TDF.Stop();
TDV.Stop();
}
// The sigma parameter affect the normal smoothing step
static void VertexCoordPasoDobleFast(MeshType &m, int NormalSmoothStep, typename MeshType::ScalarType Sigma=0, int FitStep=50, bool SmoothSelected =false)
{
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<float> *tp=0)
{
SimpleTempData<typename MeshType::VertContainer,Point3f > TD(m.vert,Point3f(0,0,0));
VertexConstDataWrapper<MeshType> ww(m);
KdTree<float> *tree=0;
if(tp==0) tree = new KdTree<float>(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]=Point3f(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)
{
typename MeshType::VertexIterator vi;
for(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
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