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vcglib/vcg/complex/algorithms/parametrization/tangent_field_operators.h

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/****************************************************************************
* 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;
// }
//// missmatch=missmatch%4;
// return(missmatch!=0);
// }
///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);
int curr_dir=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);
curr_dir=FollowDirection(*curr_f,*next_f,curr_dir);
//missmatch=missmatch%4;
}
missmatch=curr_dir;
return(curr_dir!=0);
}
///select singular vertices
static void UpdateSingularByCross(MeshType &mesh)
{
bool hasSingular = vcg::tri::HasPerVertexAttribute(mesh,std::string("Singular"));
bool hasSingularIndex = vcg::tri::HasPerVertexAttribute(mesh,std::string("SingularIndex"));
typename MeshType::template PerVertexAttributeHandle<bool> Handle_Singular;
typename MeshType::template PerVertexAttributeHandle<int> Handle_SingularIndex;
if (hasSingular)
Handle_Singular=vcg::tri::Allocator<MeshType>::template GetPerVertexAttribute<bool>(mesh,std::string("Singular"));
else
Handle_Singular=vcg::tri::Allocator<MeshType>::template AddPerVertexAttribute<bool>(mesh,std::string("Singular"));
if (hasSingularIndex)
Handle_SingularIndex=vcg::tri::Allocator<MeshType>::template GetPerVertexAttribute<int>(mesh,std::string("SingularIndex"));
else
Handle_SingularIndex=vcg::tri::Allocator<MeshType>::template AddPerVertexAttribute<int>(mesh,std::string("SingularIndex"));
for (size_t 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))
{
Handle_Singular[i]=true;
Handle_SingularIndex[i]=missmatch;
}
else
{
Handle_Singular[i]=false;
Handle_SingularIndex[i]=0;
}
}
}
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 OrientDirectionFaceCoherently(MeshType &mesh)
{
for (size_t i=0;i<mesh.face.size();i++)
{
FaceType *f=&mesh.face[i];
if (f->IsD())continue;
CoordType Ntest=mesh.face[i].PD1()^mesh.face[i].PD2();
if ((Ntest*vcg::Normal(f->P(0),f->P(1),f->P(2)))<0)mesh.face[i].PD2()=-mesh.face[i].PD2();
}
}
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
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