void ComputeGaussCurvature(Polyhedron::Vertex_iterator v1)
{
double theta(0.0);
Point3d p1 = v1->point();
Point3d p2,p3;
Vector3d v12, v13;
Polyhedron::Halfedge_around_vertex_circulator first, curr, next;
first = curr = v1->vertex_begin();
do
{
next = curr;
next++;
p2 = curr->opposite()->vertex()->point();
p3 = next->opposite()->vertex()->point();
v12 = p2-p1;
v13 = p3-p1;
theta += std::acos( dot(v12,v13) / (norm(v12)*norm(v13)) );
}
while(++curr!=first);
v1->set_gauss_curvature(2.0*M_PI - theta);
}
//**********************************************************************************
//returns min coordinates
Vector3r MinCoord(const shared_ptr<Shape>& cm1,const State& state1){
const Se3r& se3=state1.se3;
Polyhedra* A = static_cast<Polyhedra*>(cm1.get());
//move and rotate CGAL structure Polyhedron
Matrix3r rot_mat = (se3.orientation).toRotationMatrix();
Vector3r trans_vec = se3.position;
Transformation t_rot_trans(rot_mat(0,0),rot_mat(0,1),rot_mat(0,2), trans_vec[0],rot_mat(1,0),rot_mat(1,1),rot_mat(1,2),trans_vec[1],rot_mat(2,0),rot_mat(2,1),rot_mat(2,2),trans_vec[2],1.);
Polyhedron PA = A->GetPolyhedron();
std::transform( PA.points_begin(), PA.points_end(), PA.points_begin(), t_rot_trans);
Vector3r minccord = trans_vec;
for(Polyhedron::Vertex_iterator vi = PA.vertices_begin(); vi != PA.vertices_end(); ++vi){
if (vi->point()[0]<minccord[0]) minccord[0]=vi->point()[0];
if (vi->point()[1]<minccord[1]) minccord[1]=vi->point()[1];
if (vi->point()[2]<minccord[2]) minccord[2]=vi->point()[2];
}
return minccord;
}
void Polyhedron_demo_jet_fitting_plugin::on_actionEstimateCurvature_triggered()
{
// get active polyhedron
const Scene_interface::Item_id index = scene->mainSelectionIndex();
Scene_polyhedron_item* poly_item =
qobject_cast<Scene_polyhedron_item*>(scene->item(index));
if(!poly_item)
return;
// wait cursor
QApplication::setOverrideCursor(Qt::WaitCursor);
Polyhedron* pMesh = poly_item->polyhedron();
// types
typedef CGAL::Monge_via_jet_fitting<Kernel> Fitting;
typedef Fitting::Monge_form Monge_form;
typedef Kernel::Point_3 Point;
Scene_polylines_item* max_curv = new Scene_polylines_item;
max_curv->setColor(Qt::red);
max_curv->setName(tr("%1 (max curvatures)").arg(poly_item->name()));
Scene_polylines_item* min_curv = new Scene_polylines_item;
min_curv->setColor(Qt::green);
min_curv->setName(tr("%1 (min curvatures)").arg(poly_item->name()));
Polyhedron::Vertex_iterator v;
for(v = pMesh->vertices_begin();
v != pMesh->vertices_end();
v++)
{
std::vector<Point> points;
// pick central point
const Point& central_point = v->point();
points.push_back(central_point);
// compute min edge len around central vertex
// to scale the ribbons used to display the directions
typedef Kernel::FT FT;
FT min_edge_len = std::numeric_limits<FT>::infinity();
Polyhedron::Halfedge_around_vertex_circulator he = v->vertex_begin();
Polyhedron::Halfedge_around_vertex_circulator end = he;
CGAL_For_all(he,end)
{
const Point& p = he->opposite()->vertex()->point();
points.push_back(p);
FT edge_len = std::sqrt(CGAL::squared_distance(central_point,p));
min_edge_len = edge_len < min_edge_len ? edge_len : min_edge_len; // avoids #undef min
}
if(points.size() > 5)
{
// estimate curvature by fitting
Fitting monge_fit;
const int dim_monge = 2;
const int dim_fitting = 2;
Monge_form monge_form = monge_fit(points.begin(),points.end(),dim_fitting,dim_monge);
// make monge form comply with vertex normal (to get correct
// orientation)
typedef Kernel::Vector_3 Vector;
Vector n = CGAL::Polygon_mesh_processing::compute_vertex_normal(v, *pMesh);
monge_form.comply_wrt_given_normal(n);
Vector umin = min_edge_len * monge_form.minimal_principal_direction();
Vector umax = min_edge_len * monge_form.maximal_principal_direction();
Scene_polylines_item::Polyline max_segment(2), min_segment(2);
const double du = 0.2;
max_segment[0] = central_point + du * umax;
max_segment[1] = central_point - du * umax;
min_segment[0] = central_point + du * umin;
min_segment[1] = central_point - du * umin;
max_curv->polylines.push_back(max_segment);
min_curv->polylines.push_back(min_segment);
}
}
scene->addItem(max_curv);
scene->addItem(min_curv);
max_curv->changed();
min_curv->changed();
// default cursor
QApplication::restoreOverrideCursor();
}
// a helper method for running different iterators
void running_iterators( Polyhedron& P) {
if ( P.size_of_facets() == 0)
return;
std::size_t nv = P.size_of_vertices();
std::cout << "The number of vertices in the Polyhedron: " << nv << std::endl;
std::cout << "The number of facets in the Polyhedron: " << P.size_of_facets() << std::endl;
std::cout << "The number of half edges in the Polyhedron: " << P.size_of_halfedges() << std::endl;
std::cout << std:: endl;
Polyhedron::Vertex_iterator last_v = P.vertices_end();
-- last_v; // the last of the old vertices
Polyhedron::Edge_iterator last_e = P.edges_end();
-- last_e; // the last of the old edges
Polyhedron::Facet_iterator last_f = P.facets_end();
-- last_f; // the last of the old facets
int k = 0;
Polyhedron::Facet_iterator f = P.facets_begin();
do {
std::cout << "Printing a facet index: " << k++ << std::endl;
f->halfedge();
} while ( f++ != last_f);
std::cout << std::endl;
// -------------------------------------------------
// traverse the vertices
// -------------------------------------------------
std::cout << "Printing the vertex indices: " << std::endl;
int n=0;
for (Polyhedron::Vertex_iterator vi = P.vertices_begin(); vi != P.vertices_end(); ++vi)
{
Kernel::Point_3 p;
p = vi->point();
std::cout << "Vertex index: " << n++ << std::endl;
std::cout << "p.x() = " << p.x() << std::endl;
std::cout << "p.y() = " << p.y() << std::endl;
std::cout << "p.z() = " << p.z() << std::endl;
}
std::cout << std::endl;
// -------------------------------------------------
// traverse the edges
// -------------------------------------------------
std::cout << "Iterating over the edges.... " << std::endl;
n=0;
for (Polyhedron::Edge_iterator ei = P.edges_begin(); ei != P.edges_end(); ++ei)
{
ei->next();
Kernel::Point_3 p;
p = ei->vertex()->point();
std::cout << "For edge index: " << n++ << std::endl;
std::cout << "p.x() = " << p.x() << std::endl;
std::cout << "p.y() = " << p.y() << std::endl;
std::cout << "p.z() = " << p.z() << std::endl;
}
std::cout << std::endl;
// -----------------------------------------------
// Do something else with the edge iterators
// -----------------------------------------------
Polyhedron::Edge_iterator e = P.edges_begin();
++ last_e; // make it the past-the-end position again
while ( e != last_e) {
Polyhedron::Halfedge_handle h = e;
++e;
};
CGAL_postcondition( P.is_valid());
}
void Polyhedra::Initialize(){
if (init) return;
bool isRandom = false;
//get vertices
int N = (int) v.size();
if (N==0) {
//generate randomly
while ((int) v.size()<4) GenerateRandomGeometry();
N = (int) v.size();
isRandom = true;
}
//compute convex hull of vertices
std::vector<CGALpoint> points;
points.resize(v.size());
for(int i=0;i<N;i++) {
points[i] = CGALpoint(v[i][0],v[i][1],v[i][2]);
}
CGAL::convex_hull_3(points.begin(), points.end(), P);
//connect triagular facets if possible
std::transform(P.facets_begin(), P.facets_end(), P.planes_begin(),Plane_equation());
P = Simplify(P, 1E-9);
//modify order of v according to CGAl polyhedron
int i = 0;
v.clear();
for (Polyhedron::Vertex_iterator vIter = P.vertices_begin(); vIter != P.vertices_end(); ++vIter, i++){
v.push_back(Vector3r(vIter->point().x(),vIter->point().y(),vIter->point().z()));
}
//list surface triangles for plotting
faceTri.clear();
std::transform(P.facets_begin(), P.facets_end(), P.planes_begin(),Plane_equation());
for (Polyhedron::Facet_iterator fIter = P.facets_begin(); fIter != P.facets_end(); fIter++){
Polyhedron::Halfedge_around_facet_circulator hfc0;
int n = fIter->facet_degree();
hfc0 = fIter->facet_begin();
int a = std::distance(P.vertices_begin(), hfc0->vertex());
for (int i=2; i<n; i++){
++hfc0;
faceTri.push_back(a);
faceTri.push_back(std::distance(P.vertices_begin(), hfc0->vertex()));
faceTri.push_back(std::distance(P.vertices_begin(), hfc0->next()->vertex()));
}
}
//compute centroid and volume
P_volume_centroid(P, &volume, ¢roid);
//check vierd behavior of CGAL in tessalation
if(isRandom && volume*1.75<4./3.*3.14*size[0]/2.*size[1]/2.*size[2]/2.) {
v.clear();
seed = rand();
Initialize();
}
Vector3r translation((-1)*centroid);
//set centroid to be [0,0,0]
for(int i=0;i<N;i++) {
v[i] = v[i]-centroid;
}
if(isRandom) centroid = Vector3r::Zero();
Vector3r origin(0,0,0);
//move and rotate also the CGAL structure Polyhedron
Transformation t_trans(1.,0.,0.,translation[0],0.,1.,0.,translation[1],0.,0.,1.,translation[2],1.);
std::transform( P.points_begin(), P.points_end(), P.points_begin(), t_trans);
//compute inertia
Real vtet;
Vector3r ctet;
Matrix3r Itet1, Itet2;
Matrix3r inertia_tensor(Matrix3r::Zero());
for(int i=0; i<(int) faceTri.size(); i+=3){
vtet = std::abs((origin-v[faceTri[i+2]]).dot((v[faceTri[i]]-v[faceTri[i+2]]).cross(v[faceTri[i+1]]-v[faceTri[i+2]]))/6.);
ctet = (origin+v[faceTri[i]]+v[faceTri[i+1]]+v[faceTri[i+2]]) / 4.;
Itet1 = TetraInertiaTensor(origin-ctet, v[faceTri[i]]-ctet, v[faceTri[i+1]]-ctet, v[faceTri[i+2]]-ctet);
ctet = ctet-origin;
Itet2<<
ctet[1]*ctet[1]+ctet[2]*ctet[2], -ctet[0]*ctet[1], -ctet[0]*ctet[2],
-ctet[0]*ctet[1], ctet[0]*ctet[0]+ctet[2]*ctet[2], -ctet[2]*ctet[1],
-ctet[0]*ctet[2], -ctet[2]*ctet[1], ctet[1]*ctet[1]+ctet[0]*ctet[0];
inertia_tensor = inertia_tensor + Itet1 + Itet2*vtet;
}
if(std::abs(inertia_tensor(0,1))+std::abs(inertia_tensor(0,2))+std::abs(inertia_tensor(1,2)) < 1E-13){
// no need to rotate, inertia already diagonal
orientation = Quaternionr::Identity();
inertia = Vector3r(inertia_tensor(0,0),inertia_tensor(1,1),inertia_tensor(2,2));
}else{
// calculate eigenvectors of I
Vector3r rot;
Matrix3r I_rot(Matrix3r::Zero()), I_new(Matrix3r::Zero());
matrixEigenDecomposition(inertia_tensor,I_rot,I_new);
// I_rot = eigenvectors of inertia_tensors in columns
// I_new = eigenvalues on diagonal
// set positove direction of vectors - otherwise reloading does not work
Matrix3r sign(Matrix3r::Zero());
Real max_v_signed = I_rot(0,0);
Real max_v = std::abs(I_rot(0,0));
if (max_v < std::abs(I_rot(1,0))) {max_v_signed = I_rot(1,0); max_v = std::abs(I_rot(1,0));}
if (max_v < std::abs(I_rot(2,0))) {max_v_signed = I_rot(2,0); max_v = std::abs(I_rot(2,0));}
sign(0,0) = max_v_signed/max_v;
max_v_signed = I_rot(0,1);
max_v = std::abs(I_rot(0,1));
if (max_v < std::abs(I_rot(1,1))) {max_v_signed = I_rot(1,1); max_v = std::abs(I_rot(1,1));}
if (max_v < std::abs(I_rot(2,1))) {max_v_signed = I_rot(2,1); max_v = std::abs(I_rot(2,1));}
sign(1,1) = max_v_signed/max_v;
sign(2,2) = 1.;
I_rot = I_rot*sign;
// force the eigenvectors to be right-hand oriented
Vector3r third = (I_rot.col(0)).cross(I_rot.col(1));
I_rot(0,2) = third[0];
I_rot(1,2) = third[1];
I_rot(2,2) = third[2];
inertia = Vector3r(I_new(0,0),I_new(1,1),I_new(2,2));
orientation = Quaternionr(I_rot);
//rotate the voronoi cell so that x - is maximal inertia axis and z - is minimal inertia axis
//orientation.normalize(); //not needed
for(int i=0; i< (int) v.size();i++) {
v[i] = orientation.conjugate()*v[i];
}
//rotate also the CGAL structure Polyhedron
Matrix3r rot_mat = (orientation.conjugate()).toRotationMatrix();
Transformation t_rot(rot_mat(0,0),rot_mat(0,1),rot_mat(0,2),rot_mat(1,0),rot_mat(1,1),rot_mat(1,2),rot_mat(2,0),rot_mat(2,1),rot_mat(2,2),1.);
std::transform( P.points_begin(), P.points_end(), P.points_begin(), t_rot);
}
//initialization done
init = 1;
}
//**********************************************************************************
//generate "packing" of non-overlapping balls
vector<Vector3r> fillBoxByBalls_cpp(Vector3r minCoord, Vector3r maxCoord, Vector3r sizemin, Vector3r sizemax, Vector3r ratio, int seed, shared_ptr<Material> mat, int NumPoints){
vector<Vector3r> v;
Polyhedra trialP;
Polyhedron trial, trial_moved;
srand(seed);
int it = 0;
vector<Polyhedron> polyhedrons;
vector<vector<Vector3r> > vv;
Vector3r position;
bool intersection;
int count = 0;
Vector3r radii;
bool fixed_ratio = 0;
if (ratio[0] > 0 && ratio[1] > 0 && ratio[2]>0){
fixed_ratio = 1;
sizemax[0] = min(min(sizemax[0]/ratio[0], sizemax[1]/ratio[1]), sizemax[2]/ratio[2]);
sizemin[0] = max(max(sizemin[0]/ratio[0], sizemin[1]/ratio[1]), sizemin[2]/ratio[2]);
}
fixed_ratio = 1; //force spherical
//it - number of trials to make packing possibly more/less dense
Vector3r random_size;
while (it<1000){
it = it+1;
if (it == 1){
if (fixed_ratio) {
double rrr = (rand()*(sizemax[0]-sizemin[0])/RAND_MAX + sizemin[0])/2.;
radii = Vector3r(rrr,rrr,rrr);
}else {
radii = Vector3r(rand()*(sizemax[0]-sizemin[0])/2.,rand()*(sizemax[1]-sizemin[1])/2.,rand()*(sizemax[2]-sizemin[2])/2.)/RAND_MAX + sizemin/2.;
}
trialP.v = BallPoints(radii,NumPoints,rand());
trialP.Initialize();
trial = trialP.GetPolyhedron();
Matrix3r rot_mat = (trialP.GetOri()).toRotationMatrix();
Transformation t_rot(rot_mat(0,0),rot_mat(0,1),rot_mat(0,2),rot_mat(1,0),rot_mat(1,1),rot_mat(1,2),rot_mat(2,0),rot_mat(2,1),rot_mat(2,2),1.);
std::transform( trial.points_begin(), trial.points_end(), trial.points_begin(), t_rot);
}
position = Vector3r(rand()*(maxCoord[0]-minCoord[0]),rand()*(maxCoord[1]-minCoord[1]),rand()*(maxCoord[2]-minCoord[2]))/RAND_MAX + minCoord;
//move CGAL structure Polyhedron
Transformation transl(CGAL::TRANSLATION, ToCGALVector(position));
trial_moved = trial;
std::transform( trial_moved.points_begin(), trial_moved.points_end(), trial_moved.points_begin(), transl);
//calculate plane equations
std::transform( trial_moved.facets_begin(), trial_moved.facets_end(), trial_moved.planes_begin(),Plane_equation());
intersection = false;
//call test with boundary
for(Polyhedron::Vertex_iterator vi = trial_moved.vertices_begin(); (vi != trial_moved.vertices_end()) && (!intersection); vi++){
intersection = (vi->point().x()<minCoord[0]) || (vi->point().x()>maxCoord[0]) || (vi->point().y()<minCoord[1]) || (vi->point().y()>maxCoord[1]) || (vi->point().z()<minCoord[2]) || (vi->point().z()>maxCoord[2]);
}
//call test with other polyhedrons
for(vector<Polyhedron>::iterator a = polyhedrons.begin(); (a != polyhedrons.end()) && (!intersection); a++){
intersection = do_intersect(*a,trial_moved);
if (intersection) break;
}
if (!intersection){
polyhedrons.push_back(trial_moved);
v.clear();
for(Polyhedron::Vertex_iterator vi = trial_moved.vertices_begin(); vi != trial_moved.vertices_end(); vi++){
v.push_back(FromCGALPoint(vi->point()));
}
vv.push_back(v);
it = 0;
count ++;
}
}
cout << "generated " << count << " polyhedrons"<< endl;
//can't be used - no information about material
Scene* scene=Omega::instance().getScene().get();
for(vector<vector<Vector3r> >::iterator p=vv.begin(); p!=vv.end(); ++p){
shared_ptr<Body> BP = NewPolyhedra(*p, mat);
BP->shape->color = Vector3r(double(rand())/RAND_MAX,double(rand())/RAND_MAX,double(rand())/RAND_MAX);
scene->bodies->insert(BP);
}
return v;
}