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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) 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. *
* *
****************************************************************************/
#include <vcg/math/matrix33.h>
#include <vcg/math/histogram.h>
#include <vcg/complex/algorithms/update/curvature.h>
#include <vcg/complex/algorithms/update/flag.h>
#include <vcg/simplex/face/topology.h>
#include <vcg/complex/algorithms/update/bounding.h>
#ifndef VCG_TANGENT_FIELD_OPERATORS
#define VCG_TANGENT_FIELD_OPERATORS
namespace vcg {
namespace tri{
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 void SetVertCrossFromCurvature(MeshType &mesh)
{
vcg::tri::UpdateTopology<MeshType>::FaceFace(mesh);
vcg::tri::UpdateTopology<MeshType>::VertexFace(mesh);
vcg::tri::UpdateBounding<MeshType>::Box(mesh);
//set as selected high curvature value
vcg::tri::UpdateCurvature<MeshType>::PrincipalDirectionsNormalCycles(mesh);
NormalizePerVertImportanceVal(mesh);
///save the curvature value
std::vector<ScalarType> K1,K2;
K1.resize(mesh.vert.size());
K2.resize(mesh.vert.size());
for (int j=0;j<mesh.vert.size();j++)
{
VertexType *v=&mesh.vert[j];
if(v->IsD())continue;
K1[j]=v->K1();
K2[j]=v->K2();
}
///then find multiscale curvature directions
vcg::tri::UpdateCurvature<MeshType>::PrincipalDirectionsPCA(mesh,mesh.bbox.Diag()/200.0);
///and save back importance val
for (int j=0;j<mesh.vert.size();j++)
{
VertexType *v=&mesh.vert[j];
if(v->IsD())continue;
v->K1()=K1[j];
v->K2()=K2[j];
}
///set normal according to curvature
for (int j=0;j<mesh.vert.size();j++)
{
VertexType *v=&mesh.vert[j];
if(v->IsD())continue;
CoordType N0=v->N();
v->N()=v->PD1()^v->PD2();
v->N().Normalize();
if (N0*v->N()<0)
v->N()=-v->N();
}
}
///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;
vcg::face::VFStarVF(&v,faceVec);
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=InterpolateCrossField(TangVect,Weights,Norms,NRef,DirRef);
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();
ScalarType scorea = a*b;
ScalarType scorec = c*b;
if (fabs(scorea)>=fabs(scorec)) return a*Sign(scorea); else return c*Sign(scorec);
}
///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)
{
vcg::Matrix33<ScalarType> R0=vcg::RotationMatrix(n0,target_n);
vcg::Matrix33<ScalarType> R1=vcg::RotationMatrix(n1,target_n);
vcg::Matrix33<ScalarType> R2=vcg::RotationMatrix(n2,target_n);
///rotate
CoordType trans0=R0*t0;
CoordType trans1=R1*t1;
CoordType trans2=R2*t2;
///normalize it
trans0.Normalize();
trans1.Normalize();
trans2.Normalize();
///k_PI/2 rotation
trans1=K_PI(trans1,trans0,target_n);
trans2=K_PI(trans2,trans0,target_n);
trans1.Normalize();
trans2.Normalize();
CoordType sum = trans0*bary.X() + trans1 * bary.Y() + trans2 * bary.Z();
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,
const CoordType &BaseDir)
{
CoordType sum = CoordType(0,0,0);
for (unsigned int i=0;i<TangVect.size();i++)
{
CoordType N1=Norms[i];
///find the rotation matrix that maps between normals
vcg::Matrix33<ScalarType> rotation=vcg::RotationMatrix(N1,BaseNorm);
CoordType rotated=rotation*TangVect[i];
CoordType Tdir=K_PI(rotated,BaseDir,BaseNorm);
Tdir.Normalize();
sum+=(Tdir*Weight[i]);
}
sum.Normalize();
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)
{
vcg::Matrix33<ScalarType> R0=vcg::RotationMatrix(n0,target_n);
vcg::Matrix33<ScalarType> R1=vcg::RotationMatrix(n1,target_n);
CoordType trans0=R0*t0;
CoordType trans1=R1*t1;
//CoordType trans0=t0;//R0*t0;
//CoordType trans1=t1;//R1*t1;
trans0.Normalize();
trans1.Normalize();
trans1=K_PI(trans1,trans0,target_n);
trans1.Normalize();
CoordType sum = trans0*weight + trans1 * (1.0-weight);
return sum;
}
///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<FaceType*> faces;
//SortedFaces(v,faces);
vcg::face::VFOrderedStarVF_FF(v,faces);
missmatch=0;
for (unsigned int i=0;i<faces.size();i++)
{
FaceType *curr_f=faces[i];
FaceType *next_f=faces[(i+1)%faces.size()];
///find the current missmatch
missmatch+=MissMatchByCross(*curr_f,*next_f);
}
missmatch=missmatch%4;
return(missmatch!=0);
}
///select singular vertices
static void SelectSingularByCross(MeshType &mesh)
{
for (unsigned int i=0;i<mesh.vert.size();i++)
{
if (mesh.vert[i].IsD())continue;
if (mesh.vert[i].IsB())continue;
int missmatch;
if (IsSingularByCross(mesh.vert[i],missmatch))
mesh.vert[i].SetS();
else
mesh.vert[i].ClearS();
}
}
static void GradientToCross(const FaceType &f,
const vcg::Point2<ScalarType> &UV0,
const vcg::Point2<ScalarType> &UV1,
const vcg::Point2<ScalarType> &UV2,
CoordType &dirU,
CoordType &dirV)
{
///compute non normalized normal
CoordType n = f.cN();
CoordType p0 =f.cP(1) - f.cP(0);
CoordType p1 =f.cP(2) - f.cP(1);
CoordType p2 =f.cP(0) - f.cP(2);
CoordType t[3];
t[0] = -(p0 ^ n);
t[1] = -(p1 ^ n);
t[2] = -(p2 ^ n);
dirU = t[1]*UV0.X() + t[2]*UV1.X() + t[0]*UV2.X();
dirV = t[1]*UV0.Y() + t[2]*UV1.Y() + t[0]*UV2.Y();
}
static void MakeDirectionFaceCoherent(MeshType &mesh)
{
vcg::tri::UpdateFlags<MeshType>::FaceClearS(mesh);
std::deque<FaceType*> d;
//std::vector<bool> done(mesh.face.size(), false);
//for (int i=0; i<(int)mesh.face.size(); i++)
// mesh.face[i].ClearS();
for (int i=0; i<(int)mesh.face.size(); i++)
{
if (mesh.face[i].IsD())continue;
if (mesh.face[i].IsS())continue;
mesh.face[i].SetS();
d.push_back(&mesh.face[i]);
break;
}
while (!d.empty())
{
while (!d.empty())
{
FaceType* f0 = d.at(0);
d.pop_front();
for (int k=0; k<3; k++)
{
FaceType* f1 = f0->FFp(k);
if (f1->IsS())continue;
if (f1->IsD())continue;
if (f1==f0)continue;
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()=f1->N()^targD;
f1->PD2().Normalize();
f1->SetS();
d.push_back(f1);
}
}
// d is empty: now put first non done element in it
for (int i=0; i<(int)mesh.face.size(); i++)
{
if (mesh.face[i].IsD())continue;
if (mesh.face[i].IsS())continue;
mesh.face[i].SetS();
assert(0);
d.push_back(&mesh.face[i]);
break;
}
}
vcg::tri::UpdateFlags<MeshType>::FaceClearS(mesh);
}
///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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