/****************************************************************************
* 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 <assert.h>
#include <vcg/math/base.h>
#include <vcg/container/simple_temporary_data.h>
#include <vcg/simplex/face/pos.h>
#include <vcg/simplex/face/topology.h>
#include <vcg/complex/algorithms/update/quality.h>
#include <deque>
#include <vector>
#include <list>
#include <functional>
/*
class for computing approximated geodesic distances on a mesh.
basic example: farthest vertex from a specified one
MyMesh m;
MyMesh::VertexPointer seed,far;
MyMesh::ScalarType dist;
vcg::Geo<MyMesh> g;
g.FarthestVertex(m,seed,far,d);
*/
namespace vcg{
namespace tri{
template <class MeshType>
struct EuclideanDistance{
typedef typename MeshType::VertexType VertexType;
typedef typename MeshType::ScalarType ScalarType;
EuclideanDistance(){}
ScalarType operator()(const VertexType * v0, const VertexType * v1) const
{return vcg::Distance(v0->cP(),v1->cP());}
};
template <class MeshType, class DistanceFunctor = EuclideanDistance<MeshType> >
class Geo{
public:
typedef typename MeshType::VertexType VertexType;
typedef typename MeshType::VertexIterator VertexIterator;
typedef typename MeshType::VertexPointer VertexPointer;
typedef typename MeshType::FaceType FaceType;
typedef typename MeshType::CoordType CoordType;
typedef typename MeshType::ScalarType ScalarType;
/* Auxiliary class for keeping the heap of vertices to visit and their estimated distance
*/
struct VertDist{
VertDist(){}
VertDist(VertexPointer _v, ScalarType _d):v(_v),d(_d){}
VertexPointer v;
ScalarType d;
};
/* Temporary data to associate to all the vertices: estimated distance and boolean flag
*/
struct TempData{
TempData(){}
TempData(const ScalarType & d_){d=d_;source = NULL;}
ScalarType d;
VertexPointer source;//closest source
};
typedef SimpleTempData<std::vector<VertexType>, TempData > TempDataType;
//TempDataType * TD;
struct pred: public std::binary_function<VertDist,VertDist,bool>{
pred(){};
bool operator()(const VertDist& v0, const VertDist& v1) const
{return (v0.d > v1.d);}
};
struct pred_addr: public std::binary_function<VertDist,VertDist,bool>{
pred_addr(){};
bool operator()(const VertDist& v0, const VertDist& v1) const
{return (v0.v > v1.v);}
};
//************** calcolo della distanza di pw in base alle distanze note di pw1 e curr
//************** sapendo che (curr,pw,pw1) e'una faccia della mesh
//************** (vedi figura in file distance.gif)
static ScalarType Distance(const VertexPointer &pw,
const VertexPointer &pw1,
const VertexPointer &curr,
const ScalarType &d_pw1,
const ScalarType &d_curr)
{
ScalarType curr_d=0;
ScalarType ew_c = DistanceFunctor()(pw,curr);
ScalarType ew_w1 = DistanceFunctor()(pw,pw1);
ScalarType ec_w1 = DistanceFunctor()(pw1,curr);
CoordType w_c = (pw->cP()-curr->cP()).Normalize() * ew_c;
CoordType w_w1 = (pw->cP() - pw1->cP()).Normalize() * ew_w1;
CoordType w1_c = (pw1->cP() - curr->cP()).Normalize() * ec_w1;
ScalarType alpha,alpha_, beta,beta_,theta,h,delta,s,a,b;
alpha = acos((w_c.dot(w1_c))/(ew_c*ec_w1));
s = (d_curr + d_pw1+ec_w1)/2;
a = s/ec_w1;
b = a*s;
alpha_ = 2*acos ( std::min<ScalarType>(1.0,sqrt( (b- a* d_pw1)/d_curr)));
if ( alpha+alpha_ > M_PI){
curr_d = d_curr + ew_c;
}else
{
beta_ = 2*acos ( std::min<ScalarType>(1.0,sqrt( (b- a* d_curr)/d_pw1)));
beta = acos((w_w1).dot(-w1_c)/(ew_w1*ec_w1));
if ( beta+beta_ > M_PI)
curr_d = d_pw1 + ew_w1;
else
{
theta = ScalarType(M_PI)-alpha-alpha_;
delta = cos(theta)* ew_c;
h = sin(theta)* ew_c;
curr_d = sqrt( pow(h,2)+ pow(d_curr + delta,2));
}
}
return (curr_d);
}
/*
starting from the seeds, it assign a distance value to each vertex. The distance of a vertex is its
approximated geodesic distance to the closest seeds.
This is function is not meant to be called (although is not prevented). Instead, it is invoked by
wrapping function.
*/
static VertexPointer Visit(
MeshType & m,
std::vector<VertDist> & seedVec,
ScalarType & max_distance,
bool farthestOnBorder = false,
ScalarType distance_threshold = std::numeric_limits<ScalarType>::max(),
typename MeshType::template PerVertexAttributeHandle<VertexPointer> * sources = NULL
)
{
bool isLeaf;
std::vector<VertDist> frontier;
VertexPointer curr,farthest=0,pw1;
ScalarType unreached = std::numeric_limits<ScalarType>::max();
VertexPointer pw;
//Requirements
assert(m.HasVFTopology());
assert(!seedVec.empty());
TempDataType TD(m.vert,unreached);
typename std::vector <VertDist >::iterator ifr;
for(ifr = seedVec.begin(); ifr != seedVec.end(); ++ifr){
TD[(*ifr).v].d = 0.0;
(*ifr).d = 0.0;
TD[(*ifr).v].source = (*ifr).v;
frontier.push_back(VertDist((*ifr).v,0.0));
}
// initialize Heap
make_heap(frontier.begin(),frontier.end(),pred());
ScalarType curr_d,d_curr = 0.0,d_heap;
VertexPointer curr_s = NULL;
max_distance=0.0;
typename std::vector<VertDist >:: iterator iv;
while(!frontier.empty() && max_distance < distance_threshold)
{
pop_heap(frontier.begin(),frontier.end(),pred());
curr = (frontier.back()).v;
curr_s = TD[curr].source;
if(sources!=NULL)
(*sources)[curr] = curr_s;
d_heap = (frontier.back()).d;
frontier.pop_back();
assert(TD[curr].d <= d_heap);
assert(curr_s != NULL);
if(TD[curr].d < d_heap )// a vertex whose distance has been improved after it was inserted in the queue
continue;
assert(TD[curr].d == d_heap);
d_curr = TD[curr].d;
isLeaf = (!farthestOnBorder || curr->IsB());
face::VFIterator<FaceType> x;int k;
for( x.f = curr->VFp(), x.z = curr->VFi(); x.f!=0; ++x )
for(k=0;k<2;++k)
{
if(k==0) {
pw = x.f->V1(x.z);
pw1=x.f->V2(x.z);
}
else {
pw = x.f->V2(x.z);
pw1=x.f->V1(x.z);
}
const ScalarType & d_pw1 = TD[pw1].d;
{
const ScalarType inter = DistanceFunctor()(curr,pw1);//(curr->P() - pw1->P()).Norm();
const ScalarType tol = (inter + d_curr + d_pw1)*.0001f;
if ( (TD[pw1].source != TD[curr].source)||// not the same source
(inter + d_curr < d_pw1 +tol ) ||
(inter + d_pw1 < d_curr +tol ) ||
(d_curr + d_pw1 < inter +tol ) // triangular inequality
)
curr_d = d_curr + DistanceFunctor()(pw,curr);//(pw->P()-curr->P()).Norm();
else
curr_d = Distance(pw,pw1,curr,d_pw1,d_curr);
}
if(TD[(pw)].d > curr_d){
TD[(pw)].d = curr_d;
TD[pw].source = curr_s;
frontier.push_back(VertDist(pw,curr_d));
push_heap(frontier.begin(),frontier.end(),pred());
}
if(isLeaf){
if(d_curr > max_distance){
max_distance = d_curr;
farthest = curr;
}
}
}
}// end while
// Copy found distance onto the Quality (\todo parametric!)
for(VertexIterator vi = m.vert.begin(); vi != m.vert.end(); ++vi) if(!(*vi).IsD())
(*vi).Q() = TD[&(*vi)].d;
return farthest;
}
public:
/*
Given a mesh and a vector of pointers to vertices (sources), assigns the approximated geodesic
distance from the cloasest source to all the mesh vertices and returns the pointer to the farthest.
Note: update the field Q() of the vertices
*/
static bool FarthestVertex( MeshType & m,
std::vector<VertexPointer> & fro,
VertexPointer & farthest,
ScalarType & distance,
ScalarType distance_thr = std::numeric_limits<ScalarType>::max(),
typename MeshType::template PerVertexAttributeHandle<VertexPointer> * sources = NULL){
typename std::vector<VertexPointer>::iterator fi;
std::vector<VertDist>fr;
if(fro.empty()) return false;
for( fi = fro.begin(); fi != fro.end() ; ++fi)
fr.push_back(VertDist(*fi,0.0));
farthest = Visit(m,fr,distance,false,distance_thr,sources);
return true;
}
/*
Given a mesh and a pointers to a vertex-source (source), assigns the approximated geodesic
distance from the vertex-source to all the mesh vertices and returns the pointer to the farthest
Note: update the field Q() of the vertices
*/
static void FarthestVertex( MeshType & m,
VertexPointer seed,
VertexPointer & farthest,
ScalarType & distance,
ScalarType distance_thr = std::numeric_limits<ScalarType>::max()){
std::vector<VertexPointer> seedVec;
seedVec.push_back( seed );
VertexPointer v0;
FarthestVertex(m,seedVec,v0,distance,distance_thr);
farthest = v0;
}
/*
Same as FarthestPoint but the returned pointer is to a border vertex
Note: update the field Q() of the vertices
*/
static void FarthestBVertex(MeshType & m,
std::vector<VertexPointer> & seedVec,
VertexPointer & farthest,
ScalarType & distance,
typename MeshType::template PerVertexAttributeHandle<VertexPointer> * sources = NULL
){
typename std::vector<VertexPointer>::iterator fi;
std::vector<VertDist>fr;
for( fi = seedVec.begin(); fi != seedVec.end() ; ++fi)
fr.push_back(VertDist(*fi,-1));
farthest = Visit(m,fr,distance,true,sources);
}
/*
Same as FarthestPoint but the returned pointer is to a border vertex
Note: update the field Q() of the vertices
*/
static void FarthestBVertex( MeshType & m,
VertexPointer seed,
VertexPointer & farthest,
ScalarType & distance,
typename MeshType::template PerVertexAttributeHandle<VertexPointer> * sources = NULL){
std::vector<VertexPointer> fro;
fro.push_back( seed );
VertexPointer v0;
FarthestBVertex(m,fro,v0,distance,sources);
farthest = v0;
}
/*
Assigns to each vertex of the mesh its distance to the closest vertex on the border
Note: update the field Q() of the vertices
*/
static bool DistanceFromBorder( MeshType & m,
ScalarType & distance,
typename MeshType::template PerVertexAttributeHandle<VertexPointer> * sources = NULL
){
std::vector<VertexPointer> fro;
VertexIterator vi;
VertexPointer farthest;
for(vi = m.vert.begin(); vi != m.vert.end(); ++vi)
if( (*vi).IsB())
fro.push_back(&(*vi));
if(fro.empty()) return false;
tri::UpdateQuality<MeshType>::VertexConstant(m,0);
return FarthestVertex(m,fro,farthest,distance,std::numeric_limits<ScalarType>::max(),sources);
}
};
};// end namespace tri
};// end namespace vcg