/*************************************************************************
*  Copyright (C) 2006 by Bruno Chareyre                                *
*  bruno.chareyre@grenoble-inp.fr                                        *
*                                                                        *
*  This program is free software; it is licensed under the terms of the  *
*  GNU General Public License v2 or later. See file LICENSE for details. *
*************************************************************************/

//FIXME: handle that a better way
#define MAX_ID 200000

namespace yade { // Cannot have #include directive inside.

namespace CGT {

	// FIXME - remove these
	using std::cerr;
	using std::cout;
	using std::endl;

	template <class TT> _Tesselation<TT>::_Tesselation(void)
	{
		Tri = &tri;
		Tes = Tri;
		computed = false;
		maxId = -1;
		TotalFiniteVoronoiVolume = 0;
		area = 0;
		TotalInternalVoronoiPorosity = 0;
		TotalInternalVoronoiVolume = 0;
	}
	template <class TT>
	_Tesselation<TT>::_Tesselation(RTriangulation& T)
	        : Tri(&T)
	        , Tes(&T)
	        , computed(false)
	{
		std::cout << "Tesselation(RTriangulation &T)" << std::endl;
		compute();
	}

	template <class TT> _Tesselation<TT>::~_Tesselation(void) { }

	template <class TT> void _Tesselation<TT>::Clear(void)
	{
		if (Tri) Tri->clear();
		vertexHandles.clear();
		maxId = 0;
	}
	template <class TT> typename _Tesselation<TT>::VertexHandle _Tesselation<TT>::insert(Real x, Real y, Real z, Real rad, unsigned int id, bool isFictious)
	{
		VertexHandle Vh;
		Vh = Tri->insert(Sphere(Point(x, y, z), pow(rad, 2)));
		if (Vh != NULL) {
			Vh->info().setId(id);
			Vh->info().isFictious = isFictious;
			assert(vertexHandles.size() > id);
			vertexHandles[id] = Vh;
			/*if ( !isFictious ) */ maxId = math::max(maxId, (int)id);
		} else
			cout << "Failed to triangulate body with id=" << id << " Point=" << Point(x, y, z) << " rad=" << rad << endl;
		return Vh;
	}
	template <class TT> typename _Tesselation<TT>::VertexHandle _Tesselation<TT>::move(Real x, Real y, Real z, Real rad, unsigned int id)
	{
		bool         fictious = vertexHandles[id]->info().isFictious;
		VertexHandle Vh;
		Vh = Tri->move(vertexHandles[id], Sphere(Point(x, y, z), pow(rad, 2)));
		if (Vh != NULL) {
			vertexHandles[id] = Vh;
			Vh->info().setId(id);
			Vh->info().isFictious = fictious;
		} else
			cerr << "Vh==NULL"
			     << " id=" << id << " Point=" << Point(x, y, z) << " rad=" << rad << endl;
		return Vh;
	}

	template <class TT> void _Tesselation<TT>::voisins(VertexHandle v, VectorVertex& Output_vector)
	{
		Tri->incident_vertices(v, back_inserter(Output_vector));
	}

	template <class TT> typename _Tesselation<TT>::RTriangulation& _Tesselation<TT>::Triangulation(void) { return *Tri; }

	template <class TT> Real _Tesselation<TT>::Volume(FiniteCellsIterator cell)
	{
		return (Tetrahedron(
		                cell->vertex(0)->point().point(),
		                cell->vertex(1)->point().point(),
		                cell->vertex(2)->point().point(),
		                cell->vertex(3)->point().point()))
		        .volume();
	}

	template <class TT> Plane _Tesselation<TT>::Dual(VertexHandle S1, VertexHandle S2)
	{
		Segment seg(S1->point(), S2->point());
		Real    r = 0.5
		        * (1.0 + ((S1->point()).weight() * (S1->point()).weight() - (S2->point()).weight() * (S2->point()).weight()) / seg.squared_length());
		return Plan(S1->point() + seg.to_vector() * r, seg.to_vector());
	}

	template <class TT> Point _Tesselation<TT>::Dual(const CellHandle& cell) { return cell->info(); }

	template <class TT> void _Tesselation<TT>::compute()
	{
		FiniteCellsIterator cellEnd = Tri->finite_cells_end();
		for (FiniteCellsIterator cell = Tri->finite_cells_begin(); cell != cellEnd; cell++)
			cell->info().setPoint(circumCenter(cell));
		computed = true;
	}

	template <class TT> Point _Tesselation<TT>::circumCenter(const Sphere& S0, const Sphere& S1, const Sphere& S2, const Sphere& S3)
	{
		Real x, y, z;
		CGAL::weighted_circumcenterC3(
		        S0.point().x(),
		        S0.point().y(),
		        S0.point().z(),
		        S0.weight(),
		        S1.point().x(),
		        S1.point().y(),
		        S1.point().z(),
		        S1.weight(),
		        S2.point().x(),
		        S2.point().y(),
		        S2.point().z(),
		        S2.weight(),
		        S3.point().x(),
		        S3.point().y(),
		        S3.point().z(),
		        S3.weight(),
		        x,
		        y,
		        z);
		return Point(x, y, z);
	}

	//construct the circumCenter of a facet vs. an external sphere of weight wExt (wExt=alpha, typically)
	template <class TT>
	Point _Tesselation<TT>::circumCenter(const CellHandle& cell, const short facet, const Real wExt, bool& violate, Sphere& SAlpha, CVector& normal)
	{
		const Sphere& S0 = cell->vertex(facetVertices[facet][0])->point();
		const Sphere& S1 = cell->vertex(facetVertices[facet][1])->point();
		const Sphere& S2 = cell->vertex(facetVertices[facet][2])->point();
		const Sphere& Sin = cell->vertex(facet)->point();
		CVector       surface = 0.5 * cross_product(S0.point() - S1.point(), S0.point() - S2.point());
		//check if the surface vector is inward or outward
		Real dotP = surface * (S0.point() - Sin.point());
		if (dotP < 0) surface = -surface;
		Real area2 = sqrt(surface.squared_length());
		normal = surface / area2; //unit normal
		                          // 	p1 = setCircumCenter(cell1);//starting point of the polygon
		Point vv = setCircumCenter(cell);
		Real  h1 = (S0.point() - vv) * normal; //orthogonal distance from Voronoi vertex to the plane in which the spheres lie, call the intersection V
		Point p2 = vv + h1 * normal;
		Real  sqR = (p2 - S0.point()).squared_length(); //squared distance between V and the center of sphere 0
		Real  temp = wExt + S0.weight() - sqR;
		Point OAlpha = p2 + sqrt(temp) * normal; //center of the alpha sphere
		SAlpha = Sphere(OAlpha, wExt);
		p2 = circumCenter(SAlpha, S0, S1, S2);
		violate = ((p2 - vv) * normal < 0);
		// 	cerr<<"circumCenter(0) "<<OAlpha<<" "<<vv<<" "<< S0.point() <<" "<<S1.point()  <<" "<< S2.point() <<" "<< Sin.point() <<" "<< S0.point() << " "<<  S0.weight()<<" "<<normal<<" " <<violate<<endl;
		return p2;
	}

	template <class TT> Point _Tesselation<TT>::circumCenter(const CellHandle& cell, const short facet, const Sphere& sExt, bool& violate)
	{
		const Sphere& S0 = cell->vertex(facetVertices[facet][0])->point();
		const Sphere& S1 = cell->vertex(facetVertices[facet][1])->point();
		const Sphere& S2 = cell->vertex(facetVertices[facet][2])->point();
		const Sphere& Sin = cell->vertex(facet)->point();
		CVector       surface = 0.5 * cross_product(S0.point() - S1.point(), S0.point() - S2.point());
		//check if the surface vector is inward or outward
		Real dotP = surface * (S0.point() - Sin.point());
		if (dotP < 0) surface = -surface;
		//         Real area = sqrt ( surface.squared_length() );
		//         CVector normal = surface/area; //unit normal
		//      p1 = setCircumCenter(cell1);//starting point of the polygon
		Point vv = setCircumCenter(cell);
		Point p2 = circumCenter(S0, S1, S2, sExt);
		violate = ((p2 - vv) * (S0.point() - Sin.point()) < 0);
		return p2;
	}

	template <class TT> Point _Tesselation<TT>::circumCenter(const CellHandle& cell)
	{
		const Sphere& S0 = cell->vertex(0)->point();
		const Sphere& S1 = cell->vertex(1)->point();
		const Sphere& S2 = cell->vertex(2)->point();
		const Sphere& S3 = cell->vertex(3)->point();
		return circumCenter(S0, S1, S2, S3);
	}
	template <class TT> Point _Tesselation<TT>::setCircumCenter(const CellHandle& cell, bool force)
	{
		if (force or cell->info() == CGAL::ORIGIN) cell->info().setPoint(circumCenter(cell));
		return (Point)cell->info();
	}

	template <class TT> std::vector<int> _Tesselation<TT>::getAlphaVertices(Real alpha)
	{
		cerr << "Warning: this is extremely slow - only for experiments" << endl;
		RTriangulation temp(*Tri);
		AlphaShape     as(temp);
		if (!alpha) alpha = as.find_alpha_solid();
		as.set_alpha(alpha);
		std::list<VertexHandle> alphaVertices;
		as.get_alpha_shape_vertices(std::back_inserter(alphaVertices), AlphaShape::REGULAR);
		std::vector<int> res;
		for (auto v = alphaVertices.begin(); v != alphaVertices.end(); v++)
			res.push_back((*v)->info().id());
		return res;
	}

	template <class TT> void _Tesselation<TT>::testAlphaShape(Real alpha)
	{
		// 	if (not computed) compute();
		using math::max; // when used inside function it does not leak - it is safe.

		RTriangulation temp(*Tri);
		AlphaShape     as(temp);
		if (!alpha) alpha = as.find_alpha_solid();
		as.set_alpha(alpha);
		cerr << "Alpha shape computed. alpha_solid=" << alpha << endl;

		std::list<CellHandle>   cells, cells2, cells3, cells4;
		std::list<Facet>        facets, facets2, facets3;
		std::list<VertexHandle> alphaVertices;
		std::list<CVector>      normals;
		std::list<CVector>      normals2;
		std::list<Edge>         edges0, edges1, edges2, edges3;
		as.get_alpha_shape_cells(std::back_inserter(cells), AlphaShape::REGULAR);
		as.get_alpha_shape_cells(std::back_inserter(cells2), AlphaShape::EXTERIOR);
		as.get_alpha_shape_cells(std::back_inserter(cells3), AlphaShape::INTERIOR);
		as.get_alpha_shape_cells(std::back_inserter(cells4), AlphaShape::SINGULAR);
		as.get_alpha_shape_facets(std::back_inserter(facets), AlphaShape::REGULAR);
		as.get_alpha_shape_vertices(std::back_inserter(alphaVertices), AlphaShape::REGULAR);
		as.get_alpha_shape_edges(std::back_inserter(edges0), AlphaShape::INTERIOR);
		as.get_alpha_shape_edges(std::back_inserter(edges1), AlphaShape::REGULAR);
		as.get_alpha_shape_edges(std::back_inserter(edges2), AlphaShape::SINGULAR);
		as.get_alpha_shape_edges(std::back_inserter(edges3), AlphaShape::EXTERIOR);

		int finitEdges = 0;
		for (FiniteEdgesIterator ed_it = Tri->finite_edges_begin(); ed_it != Tri->finite_edges_end(); ed_it++)
			++finitEdges;

		std::cerr << "num regular cells " << cells.size() << " vs. " << cells2.size() << " vs. " << cells3.size() << " vs. " << cells4.size()
		          << std::endl;
		std::cerr << "num regular facets " << facets.size() << std::endl;
		std::cerr << "num edges " << edges0.size() << " " << edges1.size() << " " << edges2.size() << " " << edges3.size()
		          << "(finite ones:" << finitEdges << ")" << std::endl;
		// 	for (auto v=alphaVertices.begin(); v!=alphaVertices.end();v++){
		// 		std::cerr<< "alpha vertex:"<<(*v)->info().id()<<std::endl;
		// 	}
		for (auto e = edges1.begin(); e != edges1.end(); e++) {
			std::cerr << "alpha edge:" << e->first->vertex(e->second)->info().id() << " " << e->first->vertex(e->third)->info().id() << " "
			          << alphaVoronoiFaceArea(*e, as, *Tri) << std::endl;
		}
		// 	for (auto c=cells.begin(); c!=cells.end();c++){
		// 		(*c)->info().setPoint(circumCenter(*c));
		// 		std::cerr<< "alpha cell:"<<(Point) (*c)->info()<<std::endl;
		// 	}

		for (auto f = facets.begin(); f != facets.end(); f++) {
			const int& idx = f->second; //index of the facet within cell defined by f->first
			                            // 		std::cerr << f->first->vertex(facetVertices[idx][0])->info().id()
			                            // 			<<" "<< f->first->vertex(facetVertices[idx][1])->info().id()
			                            // 			<<" "<< f->first->vertex(facetVertices[idx][2])->info().id()  << std::endl;
			CVector surface
			        = 0.5
			        * cross_product(
			                  f->first->vertex(facetVertices[idx][0])->point().point() - f->first->vertex(facetVertices[idx][1])->point().point(),
			                  f->first->vertex(facetVertices[idx][0])->point().point() - f->first->vertex(facetVertices[idx][2])->point().point());
			//largest sphere
			Real maxWeight = math::max(
			        f->first->vertex(facetVertices[idx][0])->point().weight(),
			        max(f->first->vertex(facetVertices[idx][1])->point().weight(), f->first->vertex(facetVertices[idx][2])->point().weight()));
			Point pp;
			Point vv;
			if (as.classify(f->first) == AlphaShape::INTERIOR) {
				pp = f->first->vertex(f->second)->point().point();
				if (not computed) f->first->info().setPoint(circumCenter(f->first));
				// 			std::cerr<< "alpha cell:"<<(Point) f->first->info()<<std::endl;
				vv = f->first->info();
				// 			std::cerr << "vv="<<vv<<std::endl;
				// 			if (not computed) f->first->info().setPoint(Tri->dual(f->first));
				// 			std::cerr << "found as.classify(f->first)==Alpha_shape_3::INTERIOR"<<std::endl;
			} else {
				if (as.classify(f->first->neighbor(f->second)) != AlphaShape::INTERIOR)
					std::cerr << "_____________BIG PROB. HERE ___________" << std::endl;

				pp = f->first->neighbor(f->second)->vertex(Tri->mirror_index(f->first, f->second))->point().point();
				if (not computed) f->first->neighbor(f->second)->info().setPoint(circumCenter(f->first->neighbor(f->second)));
				// 			std::cerr<< "alpha cell:"<<(Point) f->first->neighbor(f->second)->info()<<std::endl;
				vv = f->first->neighbor(f->second)->info();
				// 			std::cerr << "vv="<<vv<<std::endl;
				// 			if (not computed) f->first->neighbor(f->second)->info().setPoint(Tri->dual(f->first->neighbor(f->second)));
				// 			std::cerr << "not an Alpha_shape_3::INTERIOR"<<std::endl;
			}
			//check if the surface vector is inward or outward
			Real dotP = surface * (f->first->vertex(facetVertices[f->second][0])->point().point() - pp);
			if (dotP < 0) surface = -surface;
			Real    area2 = sqrt(surface.squared_length());
			CVector normal = surface / area2; //unit normal
			                                  // 		std::cerr <<"dotP="<<dotP<<std::endl<<"surface: "<<surface<<std::endl;

			Real h1 = (f->first->vertex(facetVertices[idx][0])->point().point() - vv) * surface
			        / area2; //orthogonal distance from Voronoi vertex to the plane in which the spheres lie, call the intersection V
			Point V = vv + h1 * normal;
			Real  distLiu = sqrt((V - Point(0, 0, 0)).squared_length());
			Real  sqR = (V - f->first->vertex(facetVertices[idx][0])->point().point())
			                   .squared_length(); //squared distance between V and the center of sphere 0
			Real temp2 = alpha + f->first->vertex(facetVertices[idx][0])->point().weight() - sqR;
			if (temp2 < 0) {
				temp2 = 0;
				std::cerr << "NEGATIVE TEMP!" << std::endl;
			}
			if (temp2 > maxWeight) temp2 = maxWeight; //if alpha vertex is too far, crop
			Real h2 = sqrt(temp2);                    // this is now the distance from Voronoi vertex to "alpha" vertex (after cropping if needed)
			V = V + h2 * normal;
			std::cerr << "dist alpha center:" << sqrt((V - Point(0, 0, 0)).squared_length()) << "(vs. Liu:" << distLiu << ")" << std::endl;
		}
	}

	template <class TT> void _Tesselation<TT>::setAlphaFaces(std::vector<AlphaFace>& faces, Real alpha)
	{
		RTriangulation temp(*Tri);
		AlphaShape     as(temp);
		if (!alpha) {
			as.set_alpha(as.find_alpha_solid());
		/*cerr << "Alpha shape computed. alpha_solid=" <<as.find_alpha_solid() <<endl;*/}
	else
			as.set_alpha(alpha);

		std::list<Facet>   facets;
		std::list<CVector> normals;
		as.get_alpha_shape_facets(std::back_inserter(facets), AlphaShape::REGULAR); // get the list of "contour" facets
		faces.resize(facets.size());
		int k = 0;

		for (auto f = facets.begin(); f != facets.end(); f++) {
			int     idx = f->second; //index of the facet within cell defined by f->first
			CVector normal
			        = 0.5
			        * cross_product(
			                  f->first->vertex(facetVertices[idx][0])->point().point() - f->first->vertex(facetVertices[idx][1])->point().point(),
			                  f->first->vertex(facetVertices[idx][0])->point().point() - f->first->vertex(facetVertices[idx][2])->point().point());
			Point pp;
			if (as.classify(f->first) == AlphaShape::INTERIOR) pp = f->first->vertex(f->second)->point().point();
			else
				pp = f->first->neighbor(f->second)->vertex(Tri->mirror_index(f->first, f->second))->point().point();
			//check if the normal vector is inward or outward
			Real dotP = normal * (f->first->vertex(facetVertices[f->second][0])->point().point() - pp);
			if (dotP < 0) normal = -normal;
			// set the face in the global list
			for (int ii = 0; ii < 3; ii++)
				faces[k].ids[ii] = f->first->vertex(facetVertices[idx][ii])->info().id();
			faces[k++].normal = normal;
		}
	}

	template <class TT> std::vector<Vector3r> _Tesselation<TT>::getExtendedAlphaGraph(Real alpha, Real shrinkedAlpha, bool fixedAlpha)
	{
		std::vector<Vector3r> vSegments;
		RTriangulation        temp(*Tri);
		AlphaShape            as(temp);
		Real                  minAlpha = as.find_alpha_solid();
		if (!alpha) as.set_alpha(minAlpha);
		else {
			as.set_alpha(alpha);
			if (alpha < minAlpha) cerr << "TesselationWrapper: Using alpha<minAlpha will not work. Consider using default alpha (=0)" << endl;
		}
		if (fixedAlpha) { //insert one sphere per regular facet, with a fixed size shrinkedAlpha
			std::list<Facet> facets;
			as.get_alpha_shape_facets(std::back_inserter(facets), AlphaShape::REGULAR);
			for (auto fp = facets.begin(); fp != facets.end(); fp++) {
				Facet f = *fp;
				if (as.classify(f.first) != AlphaShape::INTERIOR) f = as.mirror_facet(f);
				Sphere  sph;
				bool    b;
				CVector n;
				//FIXME: suboptimal, we are calculating/returning a point for no good
				/*Point p =*/circumCenter(f.first, f.second, alpha, b, sph, n);
				VertexHandle Vh = Tri->insert(Sphere(sph.point(), shrinkedAlpha));
				if (Vh != NULL) Vh->info().isFictious = true;
				else
					cerr << " : __Vh==NULL__ :(" << endl;
			}


		} else { //insert one sphere per exterior/infinite cell, the radius is derived from the alpha value of the corresponding cell or 4*alpha for infinite cells

			Real             alphaRad = sqrt(alpha);
			Real             deltaAlpha = alphaRad - sqrt(shrinkedAlpha);
			std::list<Facet> facets; // the infinite ones
			as.get_alpha_shape_facets(std::back_inserter(facets), AlphaShape::REGULAR);
			for (auto fp = facets.begin(); fp != facets.end(); fp++) {
				Facet f = *fp;
				if (as.classify(f.first) != AlphaShape::INTERIOR) f = as.mirror_facet(f);
				const CellHandle& outerCell = f.first->neighbor(f.second);
				if (as.is_infinite(outerCell)) {
					Sphere  sph;
					bool    b;
					CVector n;
					/*Point p =*/circumCenter(f.first, f.second, alpha * 4, b, sph, n);
					VertexHandle Vh = Tri->insert(Sphere(sph.point(), pow(2 * alphaRad - deltaAlpha, 2)));
					if (Vh != NULL) Vh->info().isFictious = true;
					else
						cerr << " : __Vh==NULL__ :(" << endl;
				} else {
					if (!outerCell->info().isFictious) {
						outerCell->info().isFictious = true;
						Point p = setCircumCenter(outerCell);
						Real  weight
						        = (p - outerCell->vertex(0)->point().point()).squared_length() - outerCell->vertex(0)->point().weight();
						VertexHandle Vh = Tri->insert(Sphere(p, pow(sqrt(weight) - deltaAlpha, 2)));
						if (Vh != NULL) Vh->info().isFictious = true;
						else
							cerr << " : __Vh==NULL__ :(" << endl;
					}
				}
			}
		}


		for (auto e = Tri->finite_facets_begin(); e != Tri->finite_facets_end(); e++) {
			short countFictious = e->first->vertex(facetVertices[e->second][0])->info().isFictious
			        + e->first->vertex(facetVertices[e->second][1])->info().isFictious
			        + e->first->vertex(facetVertices[e->second][2])->info().isFictious;
			if (countFictious == 1) {
				vSegments.push_back(makeVector3r(setCircumCenter(e->first)));
				vSegments.push_back(makeVector3r(setCircumCenter(e->first->neighbor(e->second))));
			}
		}
		return vSegments;
	}


	template <class TT> void _Tesselation<TT>::setExtendedAlphaCaps(std::vector<AlphaCap>& caps, Real alpha, Real shrinkedAlpha, bool fixedAlpha)
	{
		std::vector<CVector> areas;
		std::vector<CVector> centroids;
		std::vector<CVector> areaMoments;
		std::vector<Real>    areaNormSums;
		//initialize area vectors in a list accessed via ids (hence the size), later refactored into a shorter list in "caps"
		areas.resize(maxId + 1, CVector(0, 0, 0));       // from 0 to maxId
		centroids.resize(maxId + 1, CVector(0, 0, 0));   // from 0 to maxId
		areaMoments.resize(maxId + 1, CVector(0, 0, 0)); // from 0 to maxId
		areaNormSums.resize(maxId + 1, 0.);              // from 0 to maxId

		RTriangulation temp(*Tri);
		AlphaShape     as(temp);
		Real           minAlpha = as.find_alpha_solid();
		if (!alpha) as.set_alpha(minAlpha);
		else {
			as.set_alpha(alpha);
			if (alpha < minAlpha) cerr << "TesselationWrapper: Using alpha<minAlpha will not work. Consider using default alpha (=0)" << endl;
		}
		std::list<Facet> facets;
		as.get_alpha_shape_facets(std::back_inserter(facets), AlphaShape::REGULAR);
		if (fixedAlpha) { //insert one sphere per regular facet, with a fixed size shrinkedAlpha
			for (auto fp = facets.begin(); fp != facets.end(); fp++) {
				Facet f = *fp;
				if (as.classify(f.first) != AlphaShape::INTERIOR) f = as.mirror_facet(f);
				Sphere  sph;
				bool    b;
				CVector n;
				circumCenter(f.first, f.second, alpha, b, sph, n);
				VertexHandle Vh = Tri->insert(Sphere(sph.point(), shrinkedAlpha));
				if (Vh != NULL) Vh->info().isFictious = true;
				else
					cerr << " : __Vh==NULL__ :(" << endl;
			}
		} else { //insert one sphere per exterior/infinite cell, the radius is derived from the alpha value of the corresponding cell or 4*alpha for infinite cells
			Real alphaRad = sqrt(alpha);
			Real deltaAlpha = alphaRad - sqrt(shrinkedAlpha);
			for (auto fp = facets.begin(); fp != facets.end(); fp++) {
				Facet f = *fp;
				if (as.classify(f.first) != AlphaShape::INTERIOR) f = as.mirror_facet(f);
				const CellHandle& outerCell = f.first->neighbor(f.second);
				if (as.is_infinite(outerCell)) {
					Sphere  sph;
					bool    b;
					CVector n;
					/*Point p =*/circumCenter(f.first, f.second, alpha * 4, b, sph, n);
					VertexHandle Vh = Tri->insert(Sphere(sph.point(), pow(2 * alphaRad - deltaAlpha, 2)));
					if (Vh != NULL) Vh->info().isFictious = true;
					else
						cerr << " : __Vh==NULL__ :(" << endl;
				} else if (!outerCell->info().isFictious) {
					outerCell->info().isFictious = true;
					Point p = setCircumCenter(outerCell);
					Real  weight = (p - outerCell->vertex(0)->point().point()).squared_length() - outerCell->vertex(0)->point().weight();
					VertexHandle Vh = Tri->insert(Sphere(p, pow(sqrt(weight) - deltaAlpha, 2)));
					if (Vh != NULL) Vh->info().isFictious = true;
					else
						cerr << " : __Vh==NULL__ :(" << endl;
				}
			}
		}
		for (auto e = Tri->finite_facets_begin(); e != Tri->finite_facets_end(); e++) {
			short countFictious = e->first->vertex(facetVertices[e->second][0])->info().isFictious
			        + e->first->vertex(facetVertices[e->second][1])->info().isFictious
			        + e->first->vertex(facetVertices[e->second][2])->info().isFictious;
			if (countFictious == 1) {
				short ftx = 0;
				while (!e->first->vertex(facetVertices[e->second][ftx])->info().isFictious)
					ftx++;
				const Point& fictV = e->first->vertex(facetVertices[e->second][ftx])->point().point();
				const int&   id1 = e->first->vertex(facetVertices[e->second][ftx > 0 ? ftx - 1 : 2])->info().id();
				const int&   id2 = e->first->vertex(facetVertices[e->second][ftx < 2 ? ftx + 1 : 0])->info().id();
				const Point& p1 = e->first->vertex(facetVertices[e->second][ftx > 0 ? ftx - 1 : 2])->point().point();
				const Point& p2 = e->first->vertex(facetVertices[e->second][ftx < 2 ? ftx + 1 : 0])->point().point();
				const Point& cc1 = setCircumCenter(e->first);
				const Point& cc2 = setCircumCenter(e->first->neighbor(e->second));
				CVector      u = cc1 - cc2;
				int          makeClockWise = u * cross_product(p2 - p1, fictV - p1) > 0 ? 1 : -1;
				CVector      area1 = (makeClockWise * 0.5) * cross_product(u, cc1 - p1);
				CVector      area2 = -(makeClockWise * 0.5) * cross_product(u, cc1 - p2);
				Real         area1Norm = sqrt(area1.squared_length());
				Real         area2Norm = sqrt(area2.squared_length());
				areas[id1] = areas[id1] + area1;
				areas[id2] = areas[id2] + area2;
				areaNormSums[id1] += area1Norm;
				areaNormSums[id2] += area2Norm;
				CVector cTri1 = CGAL::centroid(Triangle(cc1, cc2, p1)) - p1;
				CVector cTri2 = CGAL::centroid(Triangle(cc1, cc2, p2)) - p2;
				areaMoments[id1] = areaMoments[id1] + area1Norm * cTri1;
				areaMoments[id2] = areaMoments[id2] + area2Norm * cTri2;
				centroids[id1] = p1 - CGAL::ORIGIN;
				centroids[id2] = p2 - CGAL::ORIGIN;
			}
		}

		caps.clear();
		caps.reserve((long unsigned)(1.5 * 6 * pow(as.number_of_vertices(), 0.6666)));
		for (long id = 0; id <= maxId; id++) {
			if (areas[id] != CVector(0, 0, 0)) {
				centroids[id] = centroids[id] + 1.5 / areaNormSums[id] * areaMoments[id];
				AlphaCap cap;
				cap.id = id;
				cap.normal = areas[id];
				cap.centroid = centroids[id];
				// 			cerr << "cap: "<<cap.id<<" "<<cap.normal<<endl;
				caps.push_back(cap);
			}
		}
	}

	template <class TT> CVector _Tesselation<TT>::alphaVoronoiFaceArea(const Edge& ed_it, const AlphaShape& as, const RTriangulation& /*Tro*/)
	{
		//Overall, we calculate the area vector of the polygonal Voronoi face between two spheres, this is done by integrating x×dx
		using math::max; // when used inside function it does not leak - it is safe.

		Real           alpha = as.get_alpha();
		CellCirculator cell0, cell1, cell2;
		cell0 = as.incident_cells(ed_it);
		cell2 = cell0;
		while (as.classify(cell2) != AlphaShape::INTERIOR) {
			++cell2;
			if (cell2 == cell0) cerr << "infinite loop on an edge, probably singular" << endl;
		}
		cell1 = cell2;

		//pA,pB are the spheres of the edge, (p1,p2) are iterating over the vertices of the vornonoi face, p12 can be an intermediate point for EXTERIOR-EXTERIOR parts of the contour
		Point pA, pB, p1, p2, p12, vv0, vv;
		p1 = setCircumCenter(cell1); //starting point of the polygon
		CVector branch, normal;
		CVector branchArea(0, 0, 0);
		pA = (ed_it.first)->vertex(ed_it.second)->point().point(); //one sphere
		pB = (ed_it.first)->vertex(ed_it.third)->point().point();  //another sphere
		CVector AB = pB - pA;
		bool    interior1 = true; //keep track of last cell's status
		bool    interior2;
		do {
			++cell2;
			interior2 = (as.classify(cell2) == AlphaShape::INTERIOR);
			if (interior2) { //easy
				setCircumCenter(cell2);
				p2 = cell2->info();
				branch = p2 - p1;
				branchArea = branchArea + cross_product(branch, p1 - CGAL::ORIGIN);
				cerr << "branchArea(1) " << branch << " cross " << p1 << endl;
			} else { //tricky, we have to construct the face between INTERIOR-EXTERIOR, or even EXTERIOR-EXTERIOR
				CellCirculator baseCell = cell1;
				//handle EXTERIOR-EXTERIOR by checking the n+1 cell
				if (!interior1) {
					baseCell = cell2;
					baseCell++;
					vv0 = vv;
					if (as.classify(baseCell) != AlphaShape::INTERIOR) cerr << "3 consecutive EXTERIOR cells in a loop";
				}
				vv = setCircumCenter(baseCell);
				// finding the facet from baseCell to cell2 ...
				int idx = 0;
				while (baseCell->neighbor(idx) != cell2) {
					idx++;
					if (idx > 3) cerr << "HUUUUUUUH";
				}
				// ... then its surface vector
				CVector surface = 0.5
				        * cross_product(baseCell->vertex(facetVertices[idx][0])->point().point()
				                                - baseCell->vertex(facetVertices[idx][1])->point().point(),
				                        baseCell->vertex(facetVertices[idx][0])->point().point()
				                                - baseCell->vertex(facetVertices[idx][2])->point().point());
				//largest sphere
				Real maxWeight = math::max(
				        baseCell->vertex(facetVertices[idx][0])->point().weight(),
				        max(baseCell->vertex(facetVertices[idx][1])->point().weight(),
				            baseCell->vertex(facetVertices[idx][2])->point().weight()));
				//check if the surface vector is inward or outward
				Real dotP = surface * (baseCell->vertex(facetVertices[idx][0])->point().point() - baseCell->vertex(idx)->point().point());
				if (dotP < 0) surface = -surface;
				Real area2 = sqrt(surface.squared_length());
				normal = surface / area2; //unit normal
				Real h1 = (baseCell->vertex(facetVertices[idx][0])->point().point() - vv)
				        * normal; //orthogonal distance from Voronoi vertex to the plane in which the spheres lie, call the intersection V
				p2 = vv + h1 * normal;
				Real sqR = (p2 - baseCell->vertex(facetVertices[idx][0])->point().point())
				                   .squared_length(); //squared distance between V and the center of sphere 0
				Real temp2 = alpha + baseCell->vertex(facetVertices[idx][0])->point().weight() - sqR;
				if (temp2 < 0) {
					temp2 = 0;
					std::cerr << "NEGATIVE TEMP!" << std::endl;
				}
				if (temp2 > maxWeight) temp2 = maxWeight; //if alpha vertex is too far, crop
				Real h2 = sqrt(temp2); // this is now the distance from Voronoi vertex to "alpha" vertex (after cropping if needed)
				p2 = p2 + h2 * normal;

				bool coplanar = false;

				if (!(interior1 or interior2)) {
					//VERSION 1,intersection of orthogonal planes from two branches
					CVector tangent = cross_product(AB, p1 - vv0);
					tangent = tangent
					        / sqrt(tangent.squared_length()); //this is orthogonal to the _previous_ branch segment of the polygonal contour
					Real dotP2 = tangent * normal;
					coplanar = (math::abs(dotP2) < 1e-2);
					CVector p1mp2 = p1 - p2;
					if (!coplanar) {
						//make sure the construction is not singular (no intermediate vertex)
						if ((p1mp2 * (p1 - vv0) > 0) and (p1mp2 * normal < 0)) {
							p12 = p1 - (p1mp2)*normal / dotP2 * tangent;

							// 					if (((p12-p1)*p1mp2)*(p12-p2)*p1mp2)<0) {//make sure the construction is not singular (no intermediate vertex)
							cerr << "p12=" << p12 << " with p1=" << p1 << ", p2=" << p2 << " tangent=" << tangent << " " << AB
							     << " " << p1 - pA << endl;
							//VERSION 2... a different p12 (possibly parallelogram?)

							//Whatever the method:
							branchArea = branchArea + cross_product(p12 - p1, p1 - CGAL::ORIGIN);
							cerr << "branchArea(2) " << p12 - p1 << " cross " << p1 << endl;
							p1 = p12;
						}
					}
				}
				cerr << "branchArea(3) " << p2 - p1 << " cross " << p1 << endl;
				branchArea = branchArea + cross_product(p2 - p1, p1 - CGAL::ORIGIN);
			}
			cell1 = cell2;
			p1 = p2;
			interior1 = interior2;

		} while (cell2 != cell0);
		return 0.5 * branchArea; //0.5 because the above integral is twice the area
	}

	template <class TT> CVector _Tesselation<TT>::alphaVoronoiPartialCapArea(const Edge& ed_it, const AlphaShape& as, std::vector<Vector3r>& vSegments)
	{
		//Overall, a partial area vector based on only the outer part of a polygonal Voronoi face (see alphaVoronoiFaceArea), looping on REGULAR edges incident to a boundary sphere and using this function for each of them should give the contour integral of x×dx for the polygonal cap of the sphere.
		Real           alpha = as.get_alpha();
		CellCirculator cell0, cell1, cell2, cell3;
		cell0 = as.incident_cells(ed_it);
		cell1 = cell2 = cell0;
		bool violate1, violate2;
		++cell2;

		while (as.classify(cell1) != AlphaShape::INTERIOR
		       or as.classify(cell2) == AlphaShape::INTERIOR) { //we want interior->exterior starting sequence
			++cell1;
			if (cell0 == cell2++) cerr << "infinite loop on an edge, probably singular" << endl;
		}
		cell0 = cell1++; //keep the starting sequence as 0->1, cell1 is now equal to cell2
		cell3 = cell2;
		cell3++; //we have now cell0 < cell1=cell2 < cell3

		while (as.classify(cell3) != AlphaShape::INTERIOR) { //we want an exterior->interior end-point, could be that cell3=cell0 and that's ok
			++cell2;
			++cell3;
			if (cell2 == cell0) cerr << "infinite loop on an edge, probably singular(2)" << endl;
		}
		//now cell0 < cell1 < ... < cell2 < cell3

		const Sphere& sA = (ed_it.first)->vertex(ed_it.second)->point(); //one sphere
		const Sphere& sB = (ed_it.first)->vertex(ed_it.third)->point();  //another sphere
		const Point&  pA = sA.point();                                   //one sphere
		const Point&  pB = sB.point();                                   //another sphere

		//pA,pB are the spheres of the edge, (p1,p2) are iterating over the vertices of the vornonoi face, p12 is an intermediate point for convex parts
		Point p1, p2, p12, vv0, vv3;
		vv0 = setCircumCenter(cell0); //start point
		vv3 = setCircumCenter(cell3); //end point


		//   p1 = setCircumCenter ( cell1 ); //starting point of the polygon
		CVector branch, normal1, normal2;
		CVector branchArea(0, 0, 0);

		CVector AB = pB - pA;
		Sphere  SAlpha1, SAlpha2;

		Sphere SAlphaSmall1, SAlphaSmall2;
		Sphere sC1, sC2; //the 3rd spheres of each facet, not part of the edge
		bool   first = true;
		int    idx1, idx2;

		do { //this do-while will run twice and it should return the second time, we work with the "exit" and "enter" regions of a polyline wrt. the alpha contour
			CellCirculator baseCell = first ? cell0 : cell3;  //it plays the role of the internal cell
			CellCirculator outerCell = first ? cell1 : cell2; //it plays the role of the external cell

			// finding the facet from baseCell to outerCell ...
			int& idx = first ? idx1 : idx2;
			idx = 0;
			while (baseCell->neighbor(idx) != outerCell) {
				idx++;
				if (idx > 3) cerr << "HUUUUUUUH";
			}
			short thirdSphere = 0;
			while (baseCell->vertex(facetVertices[idx][thirdSphere]) == (ed_it.first)->vertex(ed_it.second)
			       or baseCell->vertex(facetVertices[idx][thirdSphere]) == (ed_it.first)->vertex(ed_it.third)) {
				thirdSphere++;
				if (thirdSphere > 3) cerr << "HUAAAUUH";
			}
			Sphere& sC = first ? sC1 : sC2;
			sC = baseCell->vertex(facetVertices[idx][thirdSphere])->point(); //forming the regular facet with sA and sB

			// ... then its surface vector
			//FIXME: for many cases this cross product is not needed if we set/use voronoi centers of alpha cells


			Sphere&  SAlpha = first ? SAlpha1 : SAlpha2;
			Point&   p = first ? p1 : p2;
			bool&    violate = first ? violate1 : violate2;
			Sphere&  SAlphaSmall = first ? SAlphaSmall1 : SAlphaSmall2;
			CVector& normal = first ? normal1 : normal2;

			p = circumCenter(baseCell, idx, alpha, violate, SAlpha, normal);

			SAlphaSmall = Sphere(SAlpha.point(), pow(sqrt(SAlpha.weight()) - 0.5, 2));
			p = circumCenter(baseCell, idx, SAlphaSmall, violate);
			first = !first;
		} while (!first);
		first = true;

		do {
			CellCirculator baseCell = first ? cell0 : cell3;  //it plays the role of the internal cell
			CellCirculator outerCell = first ? cell1 : cell2; //it plays the role of the external cell

			// finding the facet from baseCell to outerCell ...
			int&    idx = first ? idx1 : idx2;
			Sphere& sC = first ? sC1 : sC2;
			Sphere& SAlpha = first ? SAlpha1 : SAlpha2;
			Point&  p = first ? p1 : p2;
			bool&   violate = first ? violate1 : violate2;
			Sphere& SAlphaSmall = first ? SAlphaSmall1 : SAlphaSmall2;
			Sphere& SAlphaSmallInv = first ? SAlphaSmall2 : SAlphaSmall1;

			std::vector<Point> pi; /*pi.reserve(6);*/ //"interior" points
			                                          //                         cerr<<"violate "<<violate<<endl;
			bool  infCenter = false;
			Point pppInv = circumCenter(SAlphaSmall, sA, sB, SAlphaSmallInv);
			// 			if (!violate) {

			if ((p - pppInv) * (sA.point() - sC.point()) < 0) {
				infCenter = true;
				/////////////////

				p = pppInv;
			}
			// 			}
			if (violate) {
				Point ppp = circumCenter(baseCell->vertex(idx)->point(), sA, sB, SAlphaSmall);
				if ((ppp - pppInv) * (sA.point() - sC.point()) < 0) infCenter = true;


				p = ppp;
				if ((p - ppp) * (sA.point() - sC.point()) < 0) {
					Point ppp2 = circumCenter(baseCell->vertex(idx)->point(), sB, sC, SAlphaSmall);
					Point ppp3 = circumCenter(baseCell->vertex(idx)->point(), sA, sC, SAlphaSmall);
					if (infCenter) {
						Point    ppp2B = circumCenter(baseCell->vertex(idx)->point(), sB, SAlphaSmallInv, SAlphaSmall);
						Point    ppp3B = circumCenter(baseCell->vertex(idx)->point(), sA, SAlphaSmallInv, SAlphaSmall);
						Vector3r u = makeVector3r(ppp2) - makeVector3r(ppp2B);
						Vector3r v = makeVector3r(ppp3) - makeVector3r(ppp3B);
						Vector3r w = makeVector3r(ppp2) - makeVector3r(ppp3);
						for (int j = 0; j < 8; j++) {
							vSegments.push_back(makeVector3r(ppp2B) + j * (2 / 23.) * u);
							vSegments.push_back(makeVector3r(ppp2B) + (2. * j + 1) * (1 / 23.) * u);
							vSegments.push_back(makeVector3r(ppp3B) + j * (2 / 23.) * v);
							vSegments.push_back(makeVector3r(ppp3B) + (2. * j + 1) * (1 / 23.) * v);
							vSegments.push_back(makeVector3r(ppp3) + j * (2 / 23.) * w);
							vSegments.push_back(makeVector3r(ppp3) + (2. * j + 1) * (1 / 23.) * w);
						}

					} else {
						Vector3r u = makeVector3r(ppp2) - makeVector3r(ppp);
						Vector3r v = makeVector3r(ppp3) - makeVector3r(ppp);
						for (int j = 0; j < 3; j++) {
							vSegments.push_back(makeVector3r(ppp) + j * (2 / 5.) * u);
							vSegments.push_back(makeVector3r(ppp) + (2. * j + 1) * (1 / 5.) * u);
							vSegments.push_back(makeVector3r(ppp) + j * (2 / 5.) * v);
							vSegments.push_back(makeVector3r(ppp) + (2. * j + 1) * (1 / 5.) * v);
						}
					}

					//                                         vSegments.push_back(makeVector3r(ppp)); vSegments.push_back(makeVector3r(ppp2));

					//                                         vSegments.push_back(makeVector3r(ppp)); vSegments.push_back(makeVector3r(ppp3));
				} else {
				}
				//                                 p = circumCenter(sC,sA,sB,SAlpha);
				for (short k = 0; k < 3; k++) {
					const int         fct = facetVertices[idx][k];
					const int*        f = facetVertices[fct];
					const CellHandle& ncell = baseCell->neighbor(fct);
					short             nfacet = as.mirror_index(baseCell, fct);
					Point             pp;
					if (0 /*as.is_infinite(ncell)*/) {
						pp = circumCenter(
						        baseCell->vertex(f[0])->point(),
						        baseCell->vertex(f[1])->point(),
						        baseCell->vertex(f[2])->point(),
						        SAlpha);
						cerr << "INFINITE CELL" << endl;

					} else {
						//bool violate2;
						pp = circumCenter(ncell, nfacet, SAlpha, violate);
						cerr << "violate2 " << violate << endl;
					}


					/*if (!violate2)*/ pi.push_back(pp);
					//                                         else {
				}

			} else {
				//                          	pi.push_back(p2);
			}


			first = !first;
			// 		interior1=interior2;
		}
		// 	while ( as.classify ( cell3 ) !=AlphaShape::INTERIOR)
		while (!first);


		vSegments.push_back(makeVector3r(p1));
		vSegments.push_back(makeVector3r(p2));

		CVector tangent = cross_product(AB, p1 - vv0);
		CVector p1mp2 = p1 - p2;
		//                              bool clockWise = ( tangent*p1mp2>0 );//not sure it works
		bool clockWise = (cross_product(p1 - vv0, p2 - p1) * AB > 0);
		tangent = tangent / sqrt(tangent.squared_length()); //this is orthogonal to the _previous_ branch segment of the polygonal contour
		Real dotP = tangent * normal1;

		branchArea = branchArea + cross_product(p2 - p1, p1 - CGAL::ORIGIN);

		//check the orientation (we need to accumulate along the polyline with a given direction)
		if (clockWise) return 0.5 * branchArea;
		else
			return -0.5 * branchArea;
		//                         }


		cerr << "WE SHOULD NEVER REACH HERE" << endl;
		return CVector(0, 0, 0);
	}

	template <class TT>
	CVector _Tesselation<TT>::alphaVoronoiPartialCapArea(Facet facet, const AlphaShape& as, Real shrinkedAlpha, std::vector<Vector3r>& vSegments)
	{
		//Overall, a partial area vector based on only the outer part of a polygonal Voronoi face (see alphaVoronoiFaceArea), looping on REGULAR edges incident to a boundary sphere and using this function for each of them should give the contour integral of x×dx for the polygonal cap of the sphere.
		Real    alpha = as.get_alpha();
		Facet   adjactF[4];
		bool    violate[4];
		Point   circumC[4];
		Point   edgeC[3];
		Point   mirrorC[3];
		Sphere  alphaSph[4];
		Sphere  thirdSph[3];
		Sphere  mirrorSph[3];
		CVector norml[4];
		CVector dir[3];
		bool    internal = true;
		short   externalEdge;

		if (as.classify(facet.first) != AlphaShape::INTERIOR) facet = as.mirror_facet(facet);
		adjactF[0] = facet;

		Point p = circumCenter(facet.first, facet.second, alpha, violate[0], alphaSph[0], norml[0]);
		alphaSph[0] = Sphere(alphaSph[0].point(), shrinkedAlpha);
		circumC[0] = circumCenter(facet.first, facet.second, alphaSph[0], violate[0]);

		for (int k = 0; k < 3; k++) {
			FacetCirculator f;
			const short&    ii = facetVertices[facet.second][k];
			const Sphere&   sii = facet.first->vertex(ii)->point();
			const short&    jj = facetVertices[facet.second][k > 1 ? 0 : (k + 1)];
			const Sphere&   sjj = facet.first->vertex(jj)->point();
			const short&    kk = facetVertices[facet.second][k > 0 ? (k - 1) : 2];
			thirdSph[k] = facet.first->vertex(kk)->point();
			// 		const Sphere& skk = facet.first->vertex(kk)->point();
			f = as.incident_facets(
			        facet.first, //cell
			        ii,          //i
			        jj,          //j
			        facet);      //start
			FacetCirculator f0 = f;

			do {
				f++;
				if (f == f0) cerr << "PROB PROB1" << endl;
			} while (as.classify(*f) != AlphaShape::REGULAR);
			if (as.classify(f->first) == AlphaShape::INTERIOR) adjactF[k] = (*f);
			else
				adjactF[k] = as.mirror_facet(*f);
			const Facet& af = adjactF[k];

			Point p2 = circumCenter(af.first, af.second, alpha, violate[k + 1], alphaSph[k + 1], norml[k + 1]);
			short mirrorVtx = 0;
			while (af.first->vertex(facetVertices[af.second][mirrorVtx]) == facet.first->vertex(jj)
			       or af.first->vertex(facetVertices[af.second][mirrorVtx]) == facet.first->vertex(jj))
				mirrorVtx++;

			alphaSph[k + 1] = Sphere(alphaSph[k + 1].point(), shrinkedAlpha);
			circumC[k + 1] = circumCenter(af.first, af.second, alphaSph[k + 1], violate[k + 1]);
			edgeC[k] = circumCenter(alphaSph[0], sii, sjj, alphaSph[k + 1]);
			mirrorSph[k] = af.first->vertex(facetVertices[af.second][mirrorVtx])->point();
			mirrorC[k] = circumCenter(alphaSph[0], sii, sjj, mirrorSph[k]);

			dir[k] = cross_product(sii.point() - sjj.point(), sii.point() - alphaSph[0].point());
			dir[k] = ((sii.point() - thirdSph[k].point()) * dir[k]) * dir[k];
			if (((edgeC[k] - circumC[0]) * dir[k]) < 0) {
				internal = false;
				externalEdge = k;
			}
			// 		cerr<<"edge: "<<alphaSph[0]<<" "<< sii<<" "<<sjj <<" "<<alphaSph[k+1] <<endl;
		}
		if (internal) {
			for (int k = 0; k < 3; k++) {
				const short&  ii = facetVertices[facet.second][k];
				const Sphere& sii = facet.first->vertex(ii)->point();
				const short&  jj = facetVertices[facet.second][k > 1 ? 0 : (k + 1)];
				const Sphere& sjj = facet.first->vertex(jj)->point();
				const short&  kk = facetVertices[facet.second][k > 0 ? (k - 1) : 2];
				const Sphere& skk = facet.first->vertex(kk)->point();
				if (((mirrorSph[k].point() - skk.point()) * dir[k]) > 0 and ((mirrorC[k] - edgeC[k]) * dir[k]) < 0) {
					Point p1 = circumCenter(alphaSph[0], sjj, mirrorSph[k], alphaSph[k + 1]);
					Point p2 = circumCenter(alphaSph[0], mirrorSph[k], sii, alphaSph[k + 1]);
					if (((mirrorC[k] - circumC[0]) * dir[k]) > 0) {
						int     NN = 3;
						CVector u = mirrorC[k] - circumC[0];
						CVector v = mirrorC[k] - p1;
						CVector w = mirrorC[k] - p2;
						for (int j = 0; j < NN; j++) {
							vSegments.push_back(makeVector3r(circumC[0] + j * (2 / (2. * NN - 1.)) * u));
							vSegments.push_back(makeVector3r(circumC[0] + (2. * j + 1) * (1 / (2. * NN - 1.)) * u));
							vSegments.push_back(makeVector3r(p1 + j * (2 / (2. * NN - 1.)) * v));
							vSegments.push_back(makeVector3r(p1 + (2. * j + 1) * (1 / (2. * NN - 1.)) * v));
							vSegments.push_back(makeVector3r(p2 + j * (2 / (2. * NN - 1.)) * w));
							vSegments.push_back(makeVector3r(p2 + (2. * j + 1) * (1 / (2. * NN - 1.)) * w));
						}
					} else {
						Point   p1b = circumCenter(alphaSph[0], sjj, mirrorSph[k], skk);
						Point   p2b = circumCenter(alphaSph[0], mirrorSph[k], sii, skk);
						int     NN = 5;
						CVector u = p1b - p2b;
						CVector v = p1b - p1;
						CVector w = p2b - p2;
						for (int j = 0; j < NN; j++) {
							vSegments.push_back(makeVector3r(p2b + j * (2 / (2. * NN - 1.)) * u));
							vSegments.push_back(makeVector3r(p2b + (2. * j + 1) * (1 / (2. * NN - 1.)) * u));
							vSegments.push_back(makeVector3r(p1 + j * (2 / (2. * NN - 1.)) * v));
							vSegments.push_back(makeVector3r(p1 + (2. * j + 1) * (1 / (2. * NN - 1.)) * v));
							vSegments.push_back(makeVector3r(p2 + j * (2 / (2. * NN - 1.)) * w));
							vSegments.push_back(makeVector3r(p2 + (2. * j + 1) * (1 / (2. * NN - 1.)) * w));
						}
					}
				} else {
					if (((edgeC[k] - circumC[0]) * dir[k]) > 0) {
						// 				cerr<<"TEST1: "<<edgeC[k]<<" "<<circumC[0]<<" "<<dir[k]<<endl;

						int     NN = 11;
						CVector u = edgeC[k] - circumC[0];
						for (int j = 0; j < NN; j++) {
							vSegments.push_back(makeVector3r(circumC[0] + j * (2 / (2. * NN - 1.)) * u));
							vSegments.push_back(makeVector3r(circumC[0] + (2. * j + 1) * (1 / (2. * NN - 1.)) * u));
						}

					} else {
						Point p1 = circumCenter(alphaSph[0], sjj, skk, alphaSph[k + 1]);
						Point p2 = circumCenter(alphaSph[0], skk, sii, alphaSph[k + 1]);
						// 			vSegments.push_back(makeVector3r(edgeC[k])); vSegments.push_back(makeVector3r(p1));
						// 			vSegments.push_back(makeVector3r(edgeC[k])); vSegments.push_back(makeVector3r(p2));
						int     NN = 7;
						CVector u = edgeC[k > 1 ? 0 : (k + 1)] - p1;
						CVector v = edgeC[k > 0 ? (k - 1) : 2] - p2;
						for (int j = 0; j < NN; j++) {
							vSegments.push_back(makeVector3r(p1 + j * (2 / (2. * NN - 1.)) * u));
							vSegments.push_back(makeVector3r(p1 + (2. * j + 1) * (1 / (2. * NN - 1.)) * u));
							vSegments.push_back(makeVector3r(p2 + j * (2 / (2. * NN - 1.)) * v));
							vSegments.push_back(makeVector3r(p2 + (2. * j + 1) * (1 / (2. * NN - 1.)) * v));
						}
					}
				}
			}
		} else {
			const short&  k = externalEdge;
			const short&  ii = facetVertices[facet.second][k];
			const Sphere& sii = facet.first->vertex(ii)->point();
			const short&  jj = facetVertices[facet.second][k > 1 ? 0 : (k + 1)];
			const Sphere& sjj = facet.first->vertex(jj)->point();
			const short&  kk = facetVertices[facet.second][k > 0 ? (k - 1) : 2];
			const Sphere& skk = facet.first->vertex(kk)->point();
			Point         p1 = circumCenter(alphaSph[0], sjj, skk, alphaSph[k + 1]);
			Point         p2 = circumCenter(alphaSph[0], skk, sii, alphaSph[k + 1]);
			Point&        p1b = edgeC[k > 1 ? 0 : (k + 1)];
			Point&        p2b = edgeC[k > 0 ? (k - 1) : 2];

			Point mirror1 = circumCenter(alphaSph[0], sjj, skk, mirrorSph[k]);
			Point mirror2 = circumCenter(alphaSph[0], sii, skk, mirrorSph[k]);

			bool ext1 = ((mirror1 - p1) * dir[k] < 0);
			bool ext2 = ((mirror2 - p2) * dir[k] < 0);

			if (ext1 && ext2) {
				Point p1c = circumCenter(alphaSph[0], sjj, alphaSph[k + 1], mirrorSph[k]);
				vSegments.push_back(makeVector3r(p1c));
				vSegments.push_back(makeVector3r(mirror1));
				p1 = mirror1;
				Point p2c = circumCenter(alphaSph[0], sii, alphaSph[k + 1], mirrorSph[k]);
				vSegments.push_back(makeVector3r(p2c));
				vSegments.push_back(makeVector3r(mirror2));
				p2 = mirror2;
				vSegments.push_back(makeVector3r(p2));
				vSegments.push_back(makeVector3r(p1));
			} else if (ext2 && !ext1) {
				Point p2c = circumCenter(alphaSph[0], sii, alphaSph[k + 1], mirrorSph[k]);
				Point p2d = circumCenter(alphaSph[0], skk, sii, mirrorSph[k]);
				vSegments.push_back(makeVector3r(p2c));
				vSegments.push_back(makeVector3r(mirror2));
				p2 = mirror2;
				vSegments.push_back(makeVector3r(p2));
				vSegments.push_back(makeVector3r(p2d));
			} else if (ext1 && !ext2) {
				Point p1c = circumCenter(alphaSph[0], sjj, alphaSph[k + 1], mirrorSph[k]);
				Point p1d = circumCenter(alphaSph[0], skk, sjj, mirrorSph[k]);
				vSegments.push_back(makeVector3r(p1c));
				vSegments.push_back(makeVector3r(mirror1));
				p1 = mirror1;
				vSegments.push_back(makeVector3r(p1));
				vSegments.push_back(makeVector3r(p1d));
			}


			int     NN = 4;
			CVector u = p1b - p1;
			CVector v = p2b - p2;
			for (int j = 0; j < NN; j++) {
				vSegments.push_back(makeVector3r(p1 + j * (2 / (2. * NN - 1.)) * u));
				vSegments.push_back(makeVector3r(p1 + (2. * j + 1) * (1 / (2. * NN - 1.)) * u));
				vSegments.push_back(makeVector3r(p2 + j * (2 / (2. * NN - 1.)) * v));
				vSegments.push_back(makeVector3r(p2 + (2. * j + 1) * (1 / (2. * NN - 1.)) * v));
			}
		}
		if (0 /*internal*/) {
			CVector u = edgeC[0] - circumC[0];
			CVector v = edgeC[1] - circumC[0];
			CVector w = edgeC[2] - circumC[0];
			int     NN = 8;
			for (int j = 0; j < NN; j++) {
				if (internal) {
					vSegments.push_back(makeVector3r(circumC[0] + j * (2 / (2. * NN - 1.)) * u));
					vSegments.push_back(makeVector3r(circumC[0] + (2. * j + 1) * (1 / (2. * NN - 1.)) * u));
				}
				vSegments.push_back(makeVector3r(circumC[0] + j * (2 / (2. * NN - 1.)) * v));
				vSegments.push_back(makeVector3r(circumC[0] + (2. * j + 1) * (1 / (2. * NN - 1.)) * v));
				vSegments.push_back(makeVector3r(circumC[0] + j * (2 / (2. * NN - 1.)) * w));
				vSegments.push_back(makeVector3r(circumC[0] + (2. * j + 1) * (1 / (2. * NN - 1.)) * w));
			}
			cerr << "Segments(2):" << circumC[0] << " " << edgeC[0] << " " << edgeC[1] << " " << edgeC[2] << endl;
		}
		if (0 /*violate[0]*/) {
			Point              iCircumC[3];
			Point              iEdgeC[3];
			std::vector<Point> ll;
			// 		const Sphere& facet.first->vertex(facetVertices[facet.second][k])->point();
			for (short k = 0; k < 3; k++) {
				iCircumC[k] = circumCenter(
				        facet.first->vertex(facet.second)->point(),
				        facet.first->vertex(facetVertices[facet.second][k])->point(),
				        facet.first->vertex(facetVertices[facet.second][k > 1 ? 0 : (k + 1)])->point(),
				        alphaSph[0]);
				iEdgeC[k] = circumCenter(
				        alphaSph[0],
				        facet.first->vertex(facetVertices[facet.second][k])->point(),
				        facet.first->vertex(facetVertices[facet.second][k > 1 ? 0 : (k + 1)])->point(),
				        alphaSph[k + 1]);
			}

			for (short k = 0; k < 3; k++) {
				if ((iCircumC[k] - iEdgeC[k]) * (iEdgeC[k] - thirdSph[k].point()) > 0) {
					ll.push_back(circumCenter(
					        facet.first->vertex(facet.second)->point(),
					        facet.first->vertex(facetVertices[facet.second][k])->point(),
					        alphaSph[0],
					        alphaSph[k + 1]));
					ll.push_back(circumCenter(
					        facet.first->vertex(facet.second)->point(),
					        alphaSph[0],
					        facet.first->vertex(facetVertices[facet.second][k > 1 ? 0 : (k + 1)])->point(),
					        alphaSph[k + 1]));
				} else {
					ll.push_back(iCircumC[k]);
				}
			}
			if (ll.size() > 0) vSegments.push_back(makeVector3r(ll[0]));
			for (short n = 0; n < (ll.size() - 1); n++) {
				vSegments.push_back(makeVector3r(ll[n + 1]));
				vSegments.push_back(makeVector3r(ll[n + 1]));
			}
			if (ll.size() > 0) vSegments.push_back(makeVector3r(ll[0]));
		}
		return CVector(0, 0, 0);
	}

	template <class TT> Segment _Tesselation<TT>::Dual(FiniteFacetsIterator& f_it)
	{
		return Segment(f_it->first->info(), (f_it->first->neighbor(f_it->second))->info());
	}

	template <class TT> Real _Tesselation<TT>::computeVFacetArea(FiniteEdgesIterator ed_it)
	{
		CellCirculator cell0 = Tri->incident_cells(*ed_it);
		CellCirculator cell2 = cell0;

		if (Tri->is_infinite(cell2)) {
			++cell2;
			while (Tri->is_infinite(cell2) && cell2 != cell0)
				++cell2;
			if (cell2 == cell0) return 0;
		}
		cell0 = cell2++;
		CellCirculator cell1 = cell2++;
		Real           area2 = 0;

		while (cell2 != cell0) {
			area2 += sqrt(math::abs((Triangle(cell0->info(), cell1->info(), cell2->info())).squared_area()));
			++cell1;
			++cell2;
		}
		return area2;
	}

	template <class TT> void _Tesselation<TT>::AssignPartialVolume(FiniteEdgesIterator& ed_it)
	{
		//EdgeIterator ed_it
		CellCirculator cell0 = Tri->incident_cells(*ed_it);
		CellCirculator cell2 = cell0;
		if (Tri->is_infinite(cell2)) {
			++cell2;
			while (Tri->is_infinite(cell2) && cell2 != cell0)
				++cell2;
			if (cell2 == cell0) return;
		}
		cell0 = cell2++;
		CellCirculator cell1 = cell2++;
		bool           isFictious1 = (ed_it->first)->vertex(ed_it->second)->info().isFictious;
		bool           isFictious2 = (ed_it->first)->vertex(ed_it->third)->info().isFictious;
		Real           r;
		while (cell2 != cell0) {
			if (!Tri->is_infinite(cell1) && !Tri->is_infinite(cell2)) {
				if (!isFictious1) {
					r = math::abs(
					        (Tetrahedron(ed_it->first->vertex(ed_it->second)->point().point(), cell0->info(), cell1->info(), cell2->info()))
					                .volume());
					(ed_it->first)->vertex(ed_it->second)->info().v() += r;
					TotalFiniteVoronoiVolume += r;
				}
				if (!isFictious2) {
					r = math::abs(
					        (Tetrahedron(ed_it->first->vertex(ed_it->third)->point().point(), cell0->info(), cell1->info(), cell2->info()))
					                .volume());
					ed_it->first->vertex(ed_it->third)->info().v() += r;
					TotalFiniteVoronoiVolume += r;
				}
			}
			++cell1;
			++cell2;
		}
	}

	template <class TT> void _Tesselation<TT>::ResetVCellVolumes(void)
	{
		for (VertexIterator vIt = Tri->vertices_begin(); vIt != Tri->vertices_end(); vIt++)
			vIt->info().v() = 0;
		TotalFiniteVoronoiVolume = 0;
		TotalInternalVoronoiPorosity = 0;
	}

	template <class TT> void _Tesselation<TT>::computeVolumes(void)
	{
		if (!computed) compute();
		ResetVCellVolumes();
		for (FiniteEdgesIterator ed_it = Tri->finite_edges_begin(); ed_it != Tri->finite_edges_end(); ed_it++) {
			AssignPartialVolume(ed_it);
		}
		//FIXME: find a way to compute a volume correctly for spheres of the boarders.
	}

	template <class TT> void _Tesselation<TT>::computePorosity(void) //WARNING : This function will erase real volumes of cells
	{
		computeVolumes();
		FiniteVerticesIterator verticesEnd = Tri->finite_vertices_end();
		for (FiniteVerticesIterator vIt = Tri->finite_vertices_begin(); vIt != verticesEnd; vIt++) {
			if (vIt->info().v() && !vIt->info().isFictious) {
				Real r = 4.188790 * math::pow((vIt->point().weight()), 1.5); // 4/3*PI*R³ = 4.188...*R³
				TotalInternalVoronoiPorosity += r;
				TotalInternalVoronoiVolume += vIt->info().v();
				vIt->info().v() = (vIt->info().v() - r) / vIt->info().v();
			}
		}
		TotalInternalVoronoiPorosity = (TotalInternalVoronoiVolume - TotalInternalVoronoiPorosity) / TotalInternalVoronoiVolume;
	}


	template <class TT> bool _Tesselation<TT>::is_internal(FiniteFacetsIterator& facet)
	{
		return (!Tri->is_infinite(facet->first) && !Tri->is_infinite(facet->first->neighbor(facet->second)));
	}


	template <class Tesselation>
	typename Tesselation::VertexHandle
	PeriodicTesselation<Tesselation>::insert(Real x, Real y, Real z, Real rad, unsigned int id, bool isFictious, int duplicateOfId)
	{
		VertexHandle Vh;
		if (!Tri) cerr << "!Tri!" << endl;
		Vh = Tri->insert(Sphere(Point(x, y, z), pow(rad, 2)));
		if (Vh != NULL) {
			Vh->info() = id;
			Vh->info().isFictious = isFictious;
			if (duplicateOfId < 0) {
				assert(vertexHandles.size() > id);
				vertexHandles[id] = Vh;
				maxId = math::max(maxId, (int)id);
				Vh->info().isGhost = 0;
			} else
				Vh->info().isGhost = 1;
		} else
			cerr << " : Vh==NULL!!"
			     << " id=" << id << " Point=" << Point(x, y, z) << " rad=" << rad << " fictious=" << isFictious
			     << ", isGhost=" << bool(duplicateOfId >= 0) << endl;
		return Vh;
	}

} //namespace CGT

} // namespace yade
