// Remove small triangles with different semantics
void remove_singularSemantics(Polyhedron& exteriorPolyhe) {
	double SMALL_TRIANGLE_LIMIT = 0.1;
	Polyhedron::Facet_iterator exfIt;						// Iterate over exterior faces

	while (true) {
		bool newSemFound = false;
		for (exfIt = exteriorPolyhe.facets_begin(); exfIt != exteriorPolyhe.facets_end(); ++exfIt) {
			if (exfIt->area < SMALL_TRIANGLE_LIMIT) {
				std::map<std::string,double> semCountList;
				std::map<std::string,double>::iterator semCount;
				Polyhedron::Facet::Halfedge_around_facet_circulator itHDS = exfIt->facet_begin();

				double maxArea = 0;
				std::string newSem;
						
					do {
						if (is_coplanar(itHDS,false)) {
							std::string otherSem = itHDS->opposite()->facet()->semanticBLA;

							// Compute sum of area

							if (is_coplanar(itHDS->opposite()->next(),true) ||
								is_coplanar(itHDS->opposite()->prev(),true)) {
								semCount = semCountList.find(otherSem);
								if (semCount == semCountList.end())
									semCountList[otherSem] = 1; // Might not be needed
								else
									++(semCountList[otherSem]);
							}
						}
					} while (++itHDS != exfIt->facet_begin());
				
					for (semCount = semCountList.begin();semCount!=semCountList.end();++semCount) {
						if (semCount->second > maxArea) {
							maxArea = semCount->second;
							newSem = semCount->first;
						} else if (semCount->second == maxArea &&
							((exfIt->semanticBLA=="Anything"&&semCount->first!="Anything")||semCount->first==exfIt->semanticBLA))
							newSem = semCount->first;
					}
					
				if (maxArea > 0 && newSem!=exfIt->semanticBLA) {
					exfIt->semanticBLA = newSem;
					newSemFound = true;
					break;										// Dafuq? is this correct?
				}
			}
		}
		if (!newSemFound) break;								// Really?
	}
}
Example #2
0
 double lloyd_step (std::vector<Point> &points)
 {
   std::vector<Plane> planes;
   for (size_t i = 0; i < points.size(); ++i)
     planes.push_back(tangent_plane(points[i]));

   Polyhedron P;

   CGAL::internal::halfspaces_intersection(planes.begin(),
					   planes.end(), P, K());

   size_t N = points.size();
   points.clear();
   double totarea = 0.0;
   double vararea = 0.0;

   for (Polyhedron::Facet_iterator it = P.facets_begin();
	it != P.facets_end(); ++it)
     {
       Polyhedron::Halfedge_around_facet_circulator
	 h0 = it->facet_begin(), hf = h0--, hs = hf;
       hs ++;

       double farea = 0.0;
       Vector fcentroid (CGAL::NULL_VECTOR);
       while(1)
	 {
	   const Point &a  = h0->vertex()->point(),
	     &b = hf->vertex()->point(),
	     &c = hs->vertex()->point();
	   Vector v = 
	     CGAL::cross_product(b -a, c - a);
	   double tarea = .5 * sqrt(v.squared_length());
	   farea += tarea;
	   fcentroid = fcentroid +  (tarea/3.0) * ((a - CGAL::ORIGIN) + 
						   (b - CGAL::ORIGIN) + 
						   (c - CGAL::ORIGIN));
	   if (hs == h0)
	     break;
	   ++hs; ++hf;
	 }
       totarea += farea;
       vararea += pow(4.0 * M_PI / N - farea, 2.0);
       fcentroid = fcentroid/farea;
       points.push_back(project_back(CGAL::ORIGIN + fcentroid));
     }
   std::cerr << "area = " << totarea << ", "
	     << "vararea = " << vararea << "\n";
   return vararea/totarea;
 }
Example #3
0
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, &centroid);
	//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;
}