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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. *
* *
****************************************************************************/
/****************************************************************************
History
$Log: not supported by cvs2svn $
Revision 1.14 2007/03/22 11:07:16 cignoni
Solved an issue related to different casting double-float between gcc 3 and gcc 4
Revision 1.13 2007/02/25 09:20:10 cignoni
Added Rad to the NormalThr Option and removed a bug in multiple exectuion of non optimal simplification (missing an isD check)
Revision 1.12 2007/01/19 09:13:14 cignoni
Added Finalize() method to the interface, corrected minor bugs on border preserving and postsimplification cleanup
Avoided double make_heap (it is done only in the local_optimization init)
Revision 1.11 2006/10/15 07:31:21 cignoni
typenames and qualifiers for gcc compliance
Revision 1.10 2006/10/09 20:12:55 cignoni
Heavyly restructured for meshlab inclusion. Now the access to the quadric elements are mediated by a static helper class.
Revision 1.9 2006/10/07 17:20:25 cignoni
Updated to the new style face->Normal() becomes Normal(face)
Revision 1.8 2005/10/02 23:19:36 cignoni
Changed the sign of the priority of a collapse. Now it is its the error as it should (and not -error)
Revision 1.7 2005/04/14 11:35:07 ponchio
*** empty log message ***
Revision 1.6 2005/01/19 10:35:28 cignoni
Better management of symmetric/asymmetric edge collapses
Revision 1.5 2004/12/10 01:07:15 cignoni
Moved param classes inside; added support for optimal placement and symmetric; added update heap also here (not only in the base class)
Revision 1.4 2004/11/23 10:34:23 cignoni
passed parameters by reference in many funcs and gcc cleaning
Revision 1.3 2004/10/25 07:07:56 ganovelli
A vcg.::Pos was used to implement the collapse type. CHanged
to vcg::Edge
Revision 1.2 2004/09/29 17:08:16 ganovelli
corrected error in -error (see localoptimization)
****************************************************************************/
#ifndef __VCG_TRIMESHCOLLAPSE_QUADRIC__
#define __VCG_TRIMESHCOLLAPSE_QUADRIC__
#include<vcg/math/quadric.h>
#include<vcg/simplex/face/pos.h>
#include<vcg/complex/trimesh/update/flag.h>
#include<vcg/complex/trimesh/update/bounding.h>
#include<vcg/complex/local_optimization/tri_edge_collapse.h>
#include<vcg/complex/local_optimization.h>
namespace vcg{
namespace tri{
/**
This class describe Quadric based collapse operation.
Requirements:
Vertex
must have:
incremental mark
VF topology
must have:
members
QuadricType Qd();
ScalarType W() const;
A per-vertex Weight that can be used in simplification
lower weight means that error is lowered,
standard: return W==1.0
void Merge(MESH_TYPE::vertex_type const & v);
Merges the attributes of the current vertex with the ones of v
(e.g. its weight with the one of the given vertex, the color ect).
Standard: void function;
OtherWise the class should be templated with a static helper class that helps to retrieve these functions.
If the vertex class exposes these functions a default static helper class is provided.
*/
//**Helper CLASSES**//
template <class VERTEX_TYPE>
class QInfoStandard
{
public:
QInfoStandard(){};
static void Init(){};
static math::Quadric<double> &Qd(VERTEX_TYPE &v) {return v.Qd();}
static math::Quadric<double> &Qd(VERTEX_TYPE *v) {return v->Qd();}
static typename VERTEX_TYPE::ScalarType W(VERTEX_TYPE *v) {return 1.0;};
static typename VERTEX_TYPE::ScalarType W(VERTEX_TYPE &v) {return 1.0;};
static void Merge(VERTEX_TYPE & v_dest, VERTEX_TYPE const & v_del){};
};
class TriEdgeCollapseQuadricParameter
{
public:
double QualityThr; // all
double BoundaryWeight;
double NormalThrRad;
double CosineThr;
double QuadricEpsilon;
double ScaleFactor;
bool UseArea;
bool UseVertexWeight;
bool NormalCheck;
bool QualityCheck;
bool OptimalPlacement;
bool MemoryLess;
bool ComplexCheck;
bool ScaleIndependent;
//***********************
bool QualityQuadric; // During the initialization manage all the edges as border edges adding a set of additional quadrics that are useful mostly for keeping face aspect ratio good.
bool PreserveTopology;
bool PreserveBoundary;
bool MarkComplex;
bool FastPreserveBoundary;
bool SafeHeapUpdate;
};
template<class TriMeshType,class MYTYPE, class HelperType = QInfoStandard<typename TriMeshType::VertexType> >
class TriEdgeCollapseQuadric: public TriEdgeCollapse< TriMeshType, MYTYPE>
{
public:
typedef typename vcg::tri::TriEdgeCollapse< TriMeshType, MYTYPE > TEC;
typedef typename TEC::EdgeType EdgeType;
typedef typename TriEdgeCollapse<TriMeshType, MYTYPE>::HeapType HeapType;
typedef typename TriEdgeCollapse<TriMeshType, MYTYPE>::HeapElem HeapElem;
typedef typename TriMeshType::CoordType CoordType;
typedef typename TriMeshType::ScalarType ScalarType;
typedef math::Quadric< double > QuadricType;
typedef typename TriMeshType::FaceType FaceType;
typedef typename TriMeshType::VertexType VertexType;
typedef TriEdgeCollapseQuadricParameter QParameter;
typedef HelperType QH;
static QParameter & Params(){
static QParameter p;
return p;
}
enum Hint {
HNHasFFTopology = 0x0001, // La mesh arriva con la topologia ff gia'fatta
HNHasVFTopology = 0x0002, // La mesh arriva con la topologia bf gia'fatta
HNHasBorderFlag = 0x0004 // La mesh arriva con i flag di bordo gia' settati
};
static int & Hnt(){static int hnt; return hnt;} // the current hints
static void SetHint(Hint hn) { Hnt() |= hn; }
static void ClearHint(Hint hn) { Hnt()&=(~hn);}
static bool IsSetHint(Hint hn) { return (Hnt()&hn)!=0; }
// puntatori ai vertici che sono stati messi non-w per preservare il boundary
static std::vector<typename TriMeshType::VertexPointer> & WV(){
static std::vector<typename TriMeshType::VertexPointer> _WV; return _WV;
};
inline TriEdgeCollapseQuadric(const EdgeType &p, int i)
//:TEC(p,i){}
{
this->localMark = i;
this->pos=p;
this->_priority = ComputePriority();
}
inline bool IsFeasible(){
bool res = ( !Params().PreserveTopology || LinkConditions(this->pos) );
if(!res) ++( TriEdgeCollapse< TriMeshType,MYTYPE>::FailStat::LinkConditionEdge() );
return res;
}
void Execute(TriMeshType &m)
{ CoordType newPos;
if(Params().OptimalPlacement) newPos= static_cast<MYTYPE*>(this)->ComputeMinimal();
else newPos=this->pos.V(1)->P();
//this->pos.V(1)->Qd()+=this->pos.V(0)->Qd();
QH::Qd(this->pos.V(1))+=QH::Qd(this->pos.V(0));
//int FaceDel=
DoCollapse(m, this->pos, newPos); // v0 is deleted and v1 take the new position
//m.fn-=FaceDel;
//--m.vn;
}
// Final Clean up after the end of the simplification process
static void Finalize(TriMeshType &m,HeapType&h_ret)
{
// if the mesh was prepared with precomputed borderflags
// correctly set them again.
if(IsSetHint(HNHasBorderFlag) )
vcg::tri::UpdateFlags<TriMeshType>::FaceBorderFromVF(m);
// If we had the boundary preservation we should clean up the writable flags
if(Params().FastPreserveBoundary)
{
typename TriMeshType::VertexIterator vi;
for(vi=m.vert.begin();vi!=m.vert.end();++vi)
if(!(*vi).IsD()) (*vi).SetW();
}
if(Params().PreserveBoundary)
{
typename std::vector<typename TriMeshType::VertexPointer>::iterator wvi;
for(wvi=WV().begin();wvi!=WV().end();++wvi)
if(!(*wvi)->IsD()) (*wvi)->SetW();
}
}
static void Init(TriMeshType &m,HeapType&h_ret){
typename TriMeshType::VertexIterator vi;
typename TriMeshType::FaceIterator pf;
EdgeType av0,av1,av01;
Params().CosineThr=cos(Params().NormalThrRad);
if(!IsSetHint(HNHasVFTopology) ) vcg::tri::UpdateTopology<TriMeshType>::VertexFace(m);
if(Params().MarkComplex) {
vcg::tri::UpdateTopology<TriMeshType>::FaceFace(m);
vcg::tri::UpdateFlags<TriMeshType>::FaceBorderFromFF(m);
vcg::tri::UpdateTopology<TriMeshType>::VertexFace(m);
} // e' un po' piu' lenta ma marca i vertici complex
else
if(!IsSetHint(HNHasBorderFlag) )
vcg::tri::UpdateFlags<TriMeshType>::FaceBorderFromVF(m);
if(Params().FastPreserveBoundary)
{
for(pf=m.face.begin();pf!=m.face.end();++pf)
if( !(*pf).IsD() && (*pf).IsW() )
for(int j=0;j<3;++j)
if((*pf).IsB(j))
{
(*pf).V(j)->ClearW();
(*pf).V1(j)->ClearW();
}
}
if(Params().PreserveBoundary)
{
WV().clear();
for(pf=m.face.begin();pf!=m.face.end();++pf)
if( !(*pf).IsD() && (*pf).IsW() )
for(int j=0;j<3;++j)
if((*pf).IsB(j))
{
if((*pf).V(j)->IsW()) {(*pf).V(j)->ClearW(); WV().push_back((*pf).V(j));}
if((*pf).V1(j)->IsW()) {(*pf).V1(j)->ClearW();WV().push_back((*pf).V1(j));}
}
}
InitQuadric(m);
// Initialize the heap with all the possible collapses
if(IsSymmetric())
{ // if the collapse is symmetric (e.g. u->v == v->u)
for(vi=m.vert.begin();vi!=m.vert.end();++vi)
if(!(*vi).IsD() && (*vi).IsRW())
{
vcg::face::VFIterator<FaceType> x;
for( x.F() = (*vi).VFp(), x.I() = (*vi).VFi(); x.F()!=0; ++ x){
x.V1()->ClearV();
x.V2()->ClearV();
}
for( x.F() = (*vi).VFp(), x.I() = (*vi).VFi(); x.F()!=0; ++x )
{
assert(x.F()->V(x.I())==&(*vi));
if((x.V0()<x.V1()) && x.V1()->IsRW() && !x.V1()->IsV()){
x.V1()->SetV();
h_ret.push_back(HeapElem(new MYTYPE(EdgeType(x.V0(),x.V1()),TriEdgeCollapse< TriMeshType,MYTYPE>::GlobalMark() )));
}
if((x.V0()<x.V2()) && x.V2()->IsRW()&& !x.V2()->IsV()){
x.V2()->SetV();
h_ret.push_back(HeapElem(new MYTYPE(EdgeType(x.V0(),x.V2()),TriEdgeCollapse< TriMeshType,MYTYPE>::GlobalMark() )));
}
}
}
}
else
{ // if the collapse is A-symmetric (e.g. u->v != v->u)
for(vi=m.vert.begin();vi!=m.vert.end();++vi)
if(!(*vi).IsD() && (*vi).IsRW())
{
vcg::face::VFIterator<FaceType> x;
m.UnMarkAll();
for( x.F() = (*vi).VFp(), x.I() = (*vi).VFi(); x.F()!=0; ++ x)
{
assert(x.F()->V(x.I())==&(*vi));
if(x.V()->IsRW() && x.V1()->IsRW() && !m.IsMarked(x.F()->V1(x.I()))){
h_ret.push_back( HeapElem( new MYTYPE( EdgeType (x.V(),x.V1()),TriEdgeCollapse< TriMeshType,MYTYPE>::GlobalMark())));
}
if(x.V()->IsRW() && x.V2()->IsRW() && !m.IsMarked(x.F()->V2(x.I()))){
h_ret.push_back( HeapElem( new MYTYPE( EdgeType (x.V(),x.V2()),TriEdgeCollapse< TriMeshType,MYTYPE>::GlobalMark())));
}
}
}
}
}
static float HeapSimplexRatio() {return IsSymmetric()?5.0f:9.0f;}
static bool IsSymmetric() {return Params().OptimalPlacement;}
static bool IsVertexStable() {return !Params().OptimalPlacement;}
static void SetDefaultParams(){
Params().UseArea=true;
Params().UseVertexWeight=false;
Params().NormalCheck=false;
Params().NormalThrRad=M_PI/2;
Params().QualityCheck=true;
Params().QualityThr=.1;
Params().BoundaryWeight=.5;
Params().QualityQuadric=false;
Params().OptimalPlacement=true;
Params().ScaleIndependent=true;
Params().ComplexCheck=false;
Params().QuadricEpsilon =1e-15;
Params().ScaleFactor=1.0;
Params().PreserveTopology = false;
}
///*
// Funzione principale di valutazione dell'errore del collasso.
// In pratica simula il collasso vero e proprio.
//
// Da ottimizzare il ciclo sulle normali (deve sparire on e si deve usare per face normals)
//*/
ScalarType ComputePriority() {
ScalarType error;
typename vcg::face::VFIterator<FaceType> x;
std::vector<CoordType> on; // original normals
typename TriMeshType::VertexType * v[2];
v[0] = this->pos.V(0);
v[1] = this->pos.V(1);
if(Params().NormalCheck){ // Compute maximal normal variation
// store the old normals for non-collapsed face in v0
for(x.F() = v[0]->VFp(), x.I() = v[0]->VFi(); x.F()!=0; ++x ) // for all faces in v0
if(x.F()->V(0)!=v[1] && x.F()->V(1)!=v[1] && x.F()->V(2)!=v[1] ) // skip faces with v1
on.push_back(NormalizedNormal(*x.F()));
// store the old normals for non-collapsed face in v1
for(x.F() = v[1]->VFp(), x.I() = v[1]->VFi(); x.F()!=0; ++x ) // for all faces in v1
if(x.F()->V(0)!=v[0] && x.F()->V(1)!=v[0] && x.F()->V(2)!=v[0] ) // skip faces with v0
on.push_back(NormalizedNormal(*x.F()));
}
//// Move the two vertexe into new position (storing the old ones)
CoordType OldPos0=v[0]->P();
CoordType OldPos1=v[1]->P();
if(Params().OptimalPlacement) { v[0]->P() = ComputeMinimal(); v[1]->P()=v[0]->P();}
else v[0]->P() = v[1]->P();
//// Rescan faces and compute quality and difference between normals
int i;
double ndiff,MinCos = 1e100; // minimo coseno di variazione di una normale della faccia
// (e.g. max angle) Mincos varia da 1 (normali coincidenti) a
// -1 (normali opposte);
double qt, MinQual = 1e100;
CoordType nn;
for(x.F() = v[0]->VFp(), x.I() = v[0]->VFi(),i=0; x.F()!=0; ++x ) // for all faces in v0
if(x.F()->V(0)!=v[1] && x.F()->V(1)!=v[1] && x.F()->V(2)!=v[1] ) // skip faces with v1
{
if(Params().NormalCheck){
nn=NormalizedNormal(*x.F());
ndiff=nn.dot(on[i++]);
if(ndiff<MinCos) MinCos=ndiff;
}
if(Params().QualityCheck){
qt= QualityFace(*x.F());
if(qt<MinQual) MinQual=qt;
}
}
for(x.F() = v[1]->VFp(), x.I() = v[1]->VFi(),i=0; x.F()!=0; ++x ) // for all faces in v1
if(x.F()->V(0)!=v[0] && x.F()->V(1)!=v[0] && x.F()->V(2)!=v[0] ) // skip faces with v0
{
if(Params().NormalCheck){
nn=NormalizedNormal(*x.F());
ndiff=nn.dot(on[i++]);
if(ndiff<MinCos) MinCos=ndiff;
}
if(Params().QualityCheck){
qt= QualityFace(*x.F());
if(qt<MinQual) MinQual=qt;
}
}
QuadricType qq=QH::Qd(v[0]);
qq+=QH::Qd(v[1]);
Point3d tpd=Point3d::Construct(v[1]->P());
double QuadErr = Params().ScaleFactor*qq.Apply(tpd);
// All collapses involving triangles with quality larger than <QualityThr> has no penalty;
if(MinQual>Params().QualityThr) MinQual=Params().QualityThr;
if(Params().NormalCheck){
// All collapses where the normal vary less than <NormalThr> (e.g. more than CosineThr)
// have no penalty
if(MinCos>Params().CosineThr) MinCos=Params().CosineThr;
MinCos=(MinCos+1)/2.0; // Now it is in the range 0..1 with 0 very dangerous!
}
if(QuadErr<Params().QuadricEpsilon) QuadErr=Params().QuadricEpsilon;
if( Params().UseVertexWeight ) QuadErr *= (QH::W(v[1])+QH::W(v[0]))/2;
if(!Params().QualityCheck && !Params().NormalCheck) error = (ScalarType)(QuadErr);
if( Params().QualityCheck && !Params().NormalCheck) error = (ScalarType)(QuadErr / MinQual);
if(!Params().QualityCheck && Params().NormalCheck) error = (ScalarType)(QuadErr / MinCos);
if( Params().QualityCheck && Params().NormalCheck) error = (ScalarType)(QuadErr / (MinQual*MinCos));
//Rrestore old position of v0 and v1
v[0]->P()=OldPos0;
v[1]->P()=OldPos1;
this->_priority = error;
return this->_priority;
}
//
//static double MaxError() {return 1e100;}
//
inline void UpdateHeap(HeapType & h_ret)
{
this->GlobalMark()++;
VertexType *v[2];
v[0]= this->pos.V(0);
v[1]= this->pos.V(1);
v[1]->IMark() = this->GlobalMark();
// First loop around the remaining vertex to unmark visited flags
vcg::face::VFIterator<FaceType> vfi(v[1]);
while (!vfi.End()){
vfi.V1()->ClearV();
vfi.V2()->ClearV();
++vfi;
}
// Second Loop
vfi = face::VFIterator<FaceType>(v[1]);
while (!vfi.End())
{
assert(!vfi.F()->IsD());
for (int j=0;j<3;j++)
{
if( !(vfi.V1()->IsV()) && vfi.V1()->IsRW())
{
vfi.V1()->SetV();
h_ret.push_back(HeapElem(new MYTYPE(EdgeType(vfi.V0(),vfi.V1()), this->GlobalMark())));
std::push_heap(h_ret.begin(),h_ret.end());
if(!IsSymmetric()){
h_ret.push_back(HeapElem(new MYTYPE(EdgeType(vfi.V1(),vfi.V0()), this->GlobalMark())));
std::push_heap(h_ret.begin(),h_ret.end());
}
}
if( !(vfi.V2()->IsV()) && vfi.V2()->IsRW())
{
vfi.V2()->SetV();
h_ret.push_back(HeapElem(new MYTYPE(EdgeType(vfi.V0(),vfi.V2()),this->GlobalMark())));
std::push_heap(h_ret.begin(),h_ret.end());
if(!IsSymmetric()){
h_ret.push_back(HeapElem(new MYTYPE(EdgeType(vfi.V2(),vfi.V0()), this->GlobalMark())));
std::push_heap(h_ret.begin(),h_ret.end());
}
}
if(Params().SafeHeapUpdate && vfi.V1()->IsRW() && vfi.V2()->IsRW() )
{
h_ret.push_back(HeapElem(new MYTYPE(EdgeType(vfi.V1(),vfi.V2()),this->GlobalMark())));
std::push_heap(h_ret.begin(),h_ret.end());
if(!IsSymmetric()){
h_ret.push_back(HeapElem(new MYTYPE(EdgeType(vfi.V2(),vfi.V1()), this->GlobalMark())));
std::push_heap(h_ret.begin(),h_ret.end());
}
}
}
++vfi;
}
}
static void InitQuadric(TriMeshType &m)
{
typename TriMeshType::FaceIterator pf;
typename TriMeshType::VertexIterator pv;
int j;
QH::Init();
// m.ClearFlags();
for(pv=m.vert.begin();pv!=m.vert.end();++pv) // Azzero le quadriche
if( ! (*pv).IsD() && (*pv).IsW())
QH::Qd(*pv).SetZero();
for(pf=m.face.begin();pf!=m.face.end();++pf)
if( !(*pf).IsD() && (*pf).IsR() )
if((*pf).V(0)->IsR() &&(*pf).V(1)->IsR() &&(*pf).V(2)->IsR())
{
QuadricType q;
Plane3<ScalarType,false> p;
// Calcolo piano
p.SetDirection( ( (*pf).V(1)->cP() - (*pf).V(0)->cP() ) ^ ( (*pf).V(2)->cP() - (*pf).V(0)->cP() ));
// Se normalizzo non dipende dall'area
if(!Params().UseArea)
p.Normalize();
p.SetOffset( p.Direction().dot((*pf).V(0)->cP()));
// Calcolo quadrica delle facce
q.ByPlane(p);
for(j=0;j<3;++j)
if( (*pf).V(j)->IsW() ) QH::Qd((*pf).V(j)) += q; // Sommo la quadrica ai vertici
for(j=0;j<3;++j)
if( (*pf).IsB(j) || Params().QualityQuadric ) // Bordo!
{
Plane3<ScalarType,false> pb; // Piano di bordo
// Calcolo la normale al piano di bordo e la sua distanza
// Nota che la lunghezza dell'edge DEVE essere Normalizzata
// poiche' la pesatura in funzione dell'area e'gia fatta in p.Direction()
// Senza la normalize il bordo e' pesato in funzione della grandezza della mesh (mesh grandi non decimano sul bordo)
pb.SetDirection(p.Direction() ^ ( (*pf).V1(j)->cP() - (*pf).V(j)->cP() ).normalized());
if( (*pf).IsB(j) ) pb.SetDirection(pb.Direction()* (ScalarType)Params().BoundaryWeight); // amplify border planes
else pb.SetDirection(pb.Direction()* (ScalarType)(Params().BoundaryWeight/100.0)); // and consider much less quadric for quality
pb.SetOffset(pb.Direction().dot((*pf).V(j)->cP()));
q.ByPlane(pb);
if( (*pf).V (j)->IsW() ) QH::Qd((*pf).V (j)) += q; // Sommo le quadriche
if( (*pf).V1(j)->IsW() ) QH::Qd((*pf).V1(j)) += q;
}
}
if(Params().ScaleIndependent)
{
vcg::tri::UpdateBounding<TriMeshType>::Box(m);
//Make all quadric independent from mesh size
Params().ScaleFactor = 1e8*pow(1.0/m.bbox.Diag(),6); // scaling factor
//Params().ScaleFactor *=Params().ScaleFactor ;
//Params().ScaleFactor *=Params().ScaleFactor ;
//printf("Scale factor =%f\n",Params().ScaleFactor );
//printf("bb (%5.2f %5.2f %5.2f)-(%5.2f %5.2f %5.2f) Diag %f\n",m.bbox.min[0],m.bbox.min[1],m.bbox.min[2],m.bbox.max[0],m.bbox.max[1],m.bbox.max[2],m.bbox.Diag());
}
if(Params().ComplexCheck)
{
// secondo loop per diminuire quadriche complex (se non c'erano i complex si poteva fare in un giro solo)
//for(pf=m.face.begin();pf!=m.face.end();++pf)
//if( !(*pf).IsD() && (*pf).IsR() )
// if((*pf).V(0)->IsR() &&(*pf).V(1)->IsR() &&(*pf).V(2)->IsR())
// {
// for(j=0;j<3;++j)
// if((*pf).IsCF(j)) // Complex!
// {
// if( (*pf).V (j)->IsW() ) (*pf).V (j)->q *= 0.01; // Scalo le quadriche
// if( (*pf).V1(j)->IsW() ) (*pf).V1(j)->q *= 0.01;
// }
// }
}
}
//
//
//
//
//
//
//static void InitMesh(MESH_TYPE &m){
// Params().CosineThr=cos(Params().NormalThr);
// InitQuadric(m);
// //m.Topology();
// //OldInitQuadric(m,UseArea);
// }
//
CoordType ComputeMinimal()
{
typename TriMeshType::VertexType * v[2];
v[0] = this->pos.V(0);
v[1] = this->pos.V(1);
QuadricType q=QH::Qd(v[0]);
q+=QH::Qd(v[1]);
Point3<QuadricType::ScalarType> x;
bool rt=q.Minimum(x);
if(!rt) { // if the computation of the minimum fails we choose between the two edge points and the middle one.
Point3<QuadricType::ScalarType> x0=Point3d::Construct(v[0]->P());
Point3<QuadricType::ScalarType> x1=Point3d::Construct(v[1]->P());
x.Import((v[0]->P()+v[1]->P())/2);
double qvx=q.Apply(x);
double qv0=q.Apply(x0);
double qv1=q.Apply(x1);
if(qv0<qvx) x=x0;
if(qv1<qvx && qv1<qv0) x=x1;
}
return CoordType::Construct(x);
}
//
//
};
} // namespace tri
} // namespace vcg
#endif
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