geometry.cpp 69.1 KB
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#include "inmost.h"
#if defined(USE_MESH)
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#include <deque>
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using namespace std;
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const std::string normal_name = "PROTECTED_GEOM_UTIL_NORMAL";
const std::string measure_name = "PROTECTED_GEOM_UTIL_MEASURE";
const std::string centroid_name = "PROTECTED_GEOM_UTIL_CENTROID";
const std::string barycenter_name = "PROTECTED_GEOM_UTIL_BARYCENTER";

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namespace INMOST
{
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	typedef struct orient_face_t
	{
		Edge bridge;
		Node first;
		Face face;
		orient_face_t(Edge _bridge, Node _first, Face _face)
		:bridge(_bridge),first(_first),face(_face)
		{
		}
	} orient_face;
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	__INLINE static void vec_diff(const Storage::real * vecin1, const Storage::real * vecin2, Storage::real * vecout, unsigned int size)
	{
		for(unsigned int i = 0; i < size; i++)
			vecout[i] = vecin1[i] - vecin2[i];
	}
	
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	__INLINE static void vec_diff(const Storage::real_array & vecin1, const Storage::real * vecin2, Storage::real * vecout, unsigned int size)
	{
		for(unsigned int i = 0; i < size; i++)
			vecout[i] = vecin1[i] - vecin2[i];
	}
	
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	__INLINE static void vec_diff(const Storage::real_array & vecin1,const Storage::real_array & vecin2, Storage::real * vecout, unsigned int size)
	{
		for(unsigned int i = 0; i < size; i++)
			vecout[i] = vecin1[i] - vecin2[i];
	}
	
	
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	__INLINE static void vec_cross_product(const Storage::real * vecin1, const Storage::real * vecin2, Storage::real * vecout)
	{
		Storage::real temp[3];
		temp[0] = vecin1[1]*vecin2[2] - vecin1[2]*vecin2[1];
		temp[1] = vecin1[2]*vecin2[0] - vecin1[0]*vecin2[2];
		temp[2] = vecin1[0]*vecin2[1] - vecin1[1]*vecin2[0];
		vecout[0] = temp[0];
		vecout[1] = temp[1];
		vecout[2] = temp[2];
	}
	
	__INLINE static Storage::real vec_dot_product(const Storage::real * vecin1,const Storage::real * vecin2, unsigned int size)
	{
		Storage::real ret = 0;
		for(unsigned int i = 0; i < size; i++)
			ret += vecin1[i]*vecin2[i];
		return ret;
	}
	
	__INLINE static Storage::real vec_len2(const Storage::real * vecin, unsigned int size)
	{
		return vec_dot_product(vecin,vecin,size);
	}
	
	__INLINE static Storage::real vec_len(const Storage::real * vecin, unsigned int size)
	{
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		return ::sqrt(vec_len2(vecin,size));
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	}
	
	__INLINE static Storage::real det3d(Storage::real a, Storage::real b, Storage::real c,
	                         Storage::real d, Storage::real e, Storage::real f,
	                         Storage::real g, Storage::real h, Storage::real i ) 
	{
		return a*e*i - c*e*g + b*f*g - a*f*h + c*d*h - b*d*i;
	}
	
	__INLINE static Storage::real det3v(const Storage::real * x,const Storage::real * y,const Storage::real * z) 
	{
		return det3d(x[0], x[1], x[2],  y[0], y[1], y[2],  z[0], z[1], z[2]);
	}
	
	__INLINE static Storage::real det4v(const Storage::real * w, const Storage::real * x, const Storage::real * y, const Storage::real * z) 
	{
		return det3d(x[0]-w[0], x[1]-w[1], x[2]-w[2],  y[0]-w[0], y[1]-w[1], y[2]-w[2],  z[0]-w[0], z[1]-w[1], z[2]-w[2]);
	}	
	
	
	__INLINE static Storage::real vec_normalize(Storage::real * vecin, unsigned int size)
	{
		Storage::real len = 0;
		for(unsigned int i = 0; i < size; i++)
			len += vecin[i]*vecin[i];
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		len = ::sqrt(len);
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		for(unsigned int i = 0; i < size; i++)
			vecin[i] /= len;
		return len;
	}
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	__INLINE static Storage::real triarea3d(const Storage::real p1[3], const Storage::real p2[3], const Storage::real p3[3])
	{
		Storage::real v12[3], v13[3], v23[3], l12, l13, l23, halfperim;
		vec_diff(p2,p1,v12,3);
		vec_diff(p3,p1,v13,3);
		vec_diff(p3,p2,v23,3);
		l12 = vec_len(v12,3);
		l13 = vec_len(v13,3);
		l23 = vec_len(v23,3);
		halfperim = 0.5*(l12+l13+l23);
		return sqrt(halfperim*(halfperim-l12)*(halfperim-l13)*(halfperim-l23));
	}
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	ElementArray<Cell> Cell::NeighbouringCells() const
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	{
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		ElementArray<Cell> ret(GetMeshLink());
		ElementArray<Face> faces = getFaces();
		for(ElementArray<Face>::iterator f = faces.begin(); f != faces.end(); f++)
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		{
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			Cell c = Neighbour(f->self());
			if( c.isValid() ) ret.push_back(c);
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		}
		return ret;
	}
	
	
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	Cell Cell::Neighbour(Face f) const
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	{
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		Cell b = f->BackCell();
		if( b == self() )
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			return f->FrontCell();
		return b;
	}
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	bool Face::Inside(const Storage::real * point) const
	{
		Mesh * mesh = GetMeshLink();
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		real eps = mesh->GetEpsilon();
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		integer dim = mesh->GetDimensions();
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		integer mdim = GetElementDimension();
		
		if(mdim < 2)
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		{
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			// check whether point lies on edge
			real v1[3], v2[3], v12[3], r1[3], r2[3], nrm[3], area, h, len;
			ElementArray<Node> nodes = getNodes();
			assert(nodes.size() == 2);// 
			nodes[0].Centroid(v1);
			nodes[1].Centroid(v2);
			vec_diff(point,v1,r1,dim);
			vec_diff(point,v2,r2,dim);
			vec_diff(v2,v1,v12,dim);
			len = vec_len(v12,dim);
			assert(len > 1e-20);
			vec_cross_product(r1,v12,nrm);
			area = vec_len(nrm,dim);
			h = area / len;
			if( h > eps )	return false; // point does not lie on line
			return vec_dot_product(r1,r2,dim) <= 0.0; // point is between edge nodes
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		}

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		real nrm[3], cnt[3], v[3];
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		UnitNormal(nrm);
		Centroid(cnt);
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		vec_diff(cnt,point,v,dim);
		real d = vec_dot_product(nrm,v,dim);
		if(fabs(d) > eps)	return false;	// point is too far from the face plane
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		// 2d algorithm from Cell::Inside 
		real data[9][3];
		for(int k = 0; k < 9; k++) for(int j = 0; j < 3; j++)	data[k][j] = 0;
		ElementArray<Node> nodes = getNodes();
		for(int i = 0; i < static_cast<int>(nodes.size()); i++)
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		{
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			int j = (i+1)%nodes.size();
			nodes[i].Centroid(data[1]);
			nodes[j].Centroid(data[2]);
			vec_diff(point,data[0],data[3],dim);
			vec_diff(point,data[1],data[4],dim);
			vec_diff(point,data[2],data[5],dim);
			vec_cross_product(data[3],data[4],data[6]);
			vec_cross_product(data[4],data[5],data[7]);
			vec_cross_product(data[5],data[3],data[8]);
			
			if( vec_dot_product(data[6],data[7],dim) >= 0 &&
				vec_dot_product(data[7],data[8],dim) >= 0 &&
				vec_dot_product(data[8],data[6],dim) >= 0 )
				return true; //inside one of the triangles
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		}
		return false;
	}
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	bool Cell::Inside(const Storage::real * point) const//check for 2d case
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	{
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		Mesh * mesh = GetMeshLink();
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		integer dim = GetElementDimension();
		if( dim == 3 )
		{
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			/*
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			std::map<HandleType,real,16> hits;
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			real ray[3];
			ray[0] = rand()/(real)RAND_MAX;
			ray[1] = rand()/(real)RAND_MAX;
			ray[2] = rand()/(real)RAND_MAX;
			CastRay(point,ray,hits);
			if( hits.size()%2 == 0 ) return false;
			return true;
			 */
			assert(mesh->GetDimensions() == 3);
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			integer vp = 0;
			integer vm = 0;
			integer vz = 0;
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			real eps = mesh->GetEpsilon();
			real c,d, fcnt[3];
			real_array v1,v2;
			ElementArray<Face> data = getFaces();
			Face cur = data[0];
			MarkerType mrk = mesh->CreatePrivateMarker();
			MarkerType rev = mesh->CreatePrivateMarker(); //reverse orientation
			data.SetPrivateMarker(mrk); //0-th face orientation is default
			cur->RemPrivateMarker(mrk);
			Node n1,n2; //to retrive edge
			bool reverse = false; //reverse orientation in considered face
			std::deque< orient_face > stack; //edge and first node and face for visiting
			//todo: can do faster by retriving edges and going over their nodes
			//should not use FindSharedAdjacency
			ElementArray<Edge> edges = cur->getEdges();
			do
			{
				//figure out starting node order
				if( edges[0]->getBeg() == edges[1]->getBeg() ||
				   edges[0]->getBeg() == edges[1]->getEnd() )
				{
					n1 = edges[0]->getEnd();
					n2 = edges[0]->getBeg();
				}
				else
				{
					n1 = edges[0]->getBeg();
					n2 = edges[0]->getEnd();
				}
				//schedule unvisited adjacent faces
				for(unsigned j = 0; j < edges.size(); j++)
				{
					//schedule face adjacent to considered edge
					ElementArray<Face> adjacent = edges[j]->getFaces(mrk);
					assert(adjacent.size() <= 1);
					if( !adjacent.empty() && adjacent[0].GetPrivateMarker(mrk))
					{
						adjacent.RemPrivateMarker(mrk);
						stack.push_back(orient_face(edges[j],reverse ? n2 : n1,adjacent[0]));
					}
					//update edge nodes
					n1 = n2; //current end is new begin
					//find new end
					if( n2 == edges[(j+1)%edges.size()]->getBeg() )
						n2 = edges[(j+1)%edges.size()]->getEnd();
					else
						n2 = edges[(j+1)%edges.size()]->getBeg();
				}
				if( stack.empty() ) break;
				//get entry from stack
				orient_face r = stack.front();
				//remove face from stack
				stack.pop_front();
				//retrive edges for new face
				edges = r.face->getEdges();
				reverse = false;
				//figure out starting node order
				if( edges[0]->getBeg() == edges[1]->getBeg() ||
				   edges[0]->getBeg() == edges[1]->getEnd() )
				{
					n1 = edges[0]->getEnd();
					n2 = edges[0]->getBeg();
				}
				else
				{
					n1 = edges[0]->getBeg();
					n2 = edges[0]->getEnd();
				}
				//find out common edge orientation
				for(unsigned j = 0; j < edges.size(); j++)
				{
					if( edges[j] == r.bridge ) //found the edge
					{
						//reverse ordering on this face
						if( r.first == n1 )
						{
							r.face->SetPrivateMarker(rev);
							reverse = true;
						}
						break;
					}
					//update edge nodes
					n1 = n2; //current end is new begin
					//find new end
					if( n2 == edges[(j+1)%edges.size()]->getBeg() )
						n2 = edges[(j+1)%edges.size()]->getEnd();
					else
						n2 = edges[(j+1)%edges.size()]->getBeg();
				}
			} while(true);
			data.RemPrivateMarker(mrk);
			mesh->ReleasePrivateMarker(mrk);
			for(ElementArray<Face>::size_type f = 0; f < data.size(); f++)
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			{
				d = 0.0;
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				data[f]->Centroid(fcnt);
				ElementArray<Node> nodes = data[f]->getNodes();
				v1 = nodes[0].Coords();
				for (ElementArray<Node>::size_type i=0; i<nodes.size(); i++)
				{
					v2 = nodes[(i+1)%nodes.size()].Coords();
					d += c = det4v(point, fcnt, v1.data(), v2.data());
					v1.swap(v2);
				}
				//if(!data[f]->FaceOrientedOutside(self()))
				if( data[f]->GetPrivateMarker(rev) )
					c = -1.0;
				else
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					c = 1.0;
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				if(c*d > eps)
					vp++;
				else if(c*d < -eps)
					vm++;
				else
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					vz++;
			}
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			data.RemPrivateMarker(rev);
			mesh->ReleasePrivateMarker(rev);
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			if(vp*vm > 0) return false;
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			else if( vz == 0 ) return true;
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			else return true;
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		}
		else
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		{
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			int mdim = mesh->GetDimensions();
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			assert(mdim <= 3);
			Storage::real data[9][3];
			if( mdim < 3 )
			{
				memset(data,0,sizeof(Storage::real)*9*3);
			}
			Centroid(data[0]);
			ElementArray<Node> nodes = getNodes();
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			for(int i = 0; i < static_cast<int>(nodes.size()); i++)
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			{
				int j = (i+1)%nodes.size();
				nodes[i].Centroid(data[1]);
				nodes[j].Centroid(data[2]);
				vec_diff(point,data[0],data[3],mdim);
				vec_diff(point,data[1],data[4],mdim);
				vec_diff(point,data[2],data[5],mdim);
				vec_cross_product(data[3],data[4],data[6]);
				vec_cross_product(data[4],data[5],data[7]);
				vec_cross_product(data[5],data[3],data[8]);
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				if( vec_dot_product(data[6],data[7],mdim) >= 0 &&
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				   vec_dot_product(data[7],data[8],mdim) >= 0 &&
				   vec_dot_product(data[6],data[8],mdim) >= 0 )
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					return true; //inside one of the triangles
			}
			return false;
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		}
	}
	
	
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	void Face::UnitNormal(real * nrm) const
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	{
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		Mesh * m = GetMeshLink();
		m->GetGeometricData(GetHandle(),NORMAL,nrm); 
		integer dim = m->GetDimensions();
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		real    l   = ::sqrt(vec_dot_product(nrm,nrm,dim)); 
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		if(::fabs(l) > m->GetEpsilon()) 
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		{
			for(integer i = 0; i < dim; i++) 
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				nrm[i] /= l; 
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		}
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	}
	
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	void Face::OrientedNormal(Cell c, Storage::real * nrm) const
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	{
		Normal(nrm); 
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		if( !FaceOrientedOutside(c) )
		{
			integer dim = GetMeshLink()->GetDimensions();
			for(integer i = 0; i < dim; i++) 
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				nrm[i] = -nrm[i];
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		}
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	}
	
	
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	void Face::OrientedUnitNormal(Cell c, Storage::real * nrm) const
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	{
		UnitNormal(nrm); 
		if( !FaceOrientedOutside(c) ) 
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		{
			integer dim = GetMeshLink()->GetDimensions();
			for(integer i = 0; i < dim; i++) 
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				nrm[i] = -nrm[i];
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		}
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	}
	
	
	
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	bool Mesh::TestClosure(const HandleType * elements, integer num) const
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	{
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		integer i;
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		std::map<HandleType,int> e_visit;
		std::map<HandleType,int>::iterator it;
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		if( !HideMarker() )
		{
			for(i = 0; i < num; i++)
			{
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				Element::adj_type const & lc = LowConn(elements[i]);
				for(Element::adj_type::size_type jt = 0; jt < lc.size(); jt++)
					e_visit[lc[jt]]++;
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			}
		}
		else
		{
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			for(i = 0; i < num; i++) if( !GetMarker(elements[i],HideMarker()) )
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			{
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				Element::adj_type const & lc = LowConn(elements[i]);
				for(Element::adj_type::size_type jt = 0; jt < lc.size(); jt++) 
				{
					if( !GetMarker(lc[jt],HideMarker()) ) 
						e_visit[lc[jt]]++;
				}
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			}
		}
		for(it = e_visit.begin(); it != e_visit.end(); it++)
			if( it->second != 2 ) return false;
		return true;
	}
	
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	Element::GeometricType Mesh::ComputeGeometricType(ElementType etype, const HandleType * lc, INMOST_DATA_ENUM_TYPE size)
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	{
		Element::GeometricType ret = Element::Unset;
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		INMOST_DATA_ENUM_TYPE s = 0;
		if( isMeshModified() )
			s = Mesh::Count(lc,size,HideMarker());
		else s = size;
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		int dmax = -1, dmin = 4;
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		if( s == 0 && etype != NODE) return ret;
		switch(etype)
		{
			case NODE: ret = Element::Vertex; break;
			case EDGE:
				if( s == 1 )
					ret = Element::Vertex;
				else if( s == 2 )
					ret = Element::Line;
				break;
			case FACE:
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				for (INMOST_DATA_ENUM_TYPE k = 0; k < size; ++k) if( !Hidden(lc[k]) )
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				{
					int d = Element::GetGeometricDimension(GetGeometricType(lc[k]));
					if (dmax < d) dmax = d;
					if (dmin > d) dmin = d;
				}
				if (dmax != dmin)
				{
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					ret = Element::MultiLine;
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				}
				else if( dmax == 0 )
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				{ 
					ret = Element::Line;
				}
				else
				{
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					if( !GetTopologyCheck(NEED_TEST_CLOSURE) || TestClosure(lc,size) )
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					{
						if( s == 3 )
							ret = Element::Tri;
						else if( s == 4 )
							ret = Element::Quad;
						else
							ret = Element::Polygon;
					}
					else ret = Element::MultiLine;
				}
				break;
			case CELL:
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				for (INMOST_DATA_ENUM_TYPE k = 0; k < size; ++k) if( !Hidden(lc[k]) )
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				{
					int d = Element::GetGeometricDimension(GetGeometricType(lc[k]));
					if (dmax < d) dmax = d;
					if (dmin > d) dmin = d;
				}
				if (dmax != dmin)
				{
					ret = Element::MultiPolygon;
				}
				else if(  dmax == 1 )
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				{
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					if( !GetTopologyCheck(NEED_TEST_CLOSURE) || TestClosure(lc,size) )
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					{
						if( s == 3 )
							ret = Element::Tri;
						else if( s == 4 )
							ret = Element::Quad;
						else
							ret = Element::Polygon;
					}
					else ret = Element::MultiLine;
				}
				else 
				{
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					if( !GetTopologyCheck(NEED_TEST_CLOSURE) ||  TestClosure(lc,size) )
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					{
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						// for simple cells there is no more then one common edge
						// otherwise the cell should be treated as polyhedron
						bool check = true;
						MarkerType common = CreatePrivateMarker();
						for(INMOST_DATA_ENUM_TYPE i = 0; i < s; ++i)
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						{
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							const Element::adj_type & ilc = LowConn(lc[i]); // access edges of the i-th face
							for(INMOST_DATA_ENUM_TYPE r = 0; r < ilc.size(); ++r ) SetPrivateMarker(ilc[r],common);
							for(INMOST_DATA_ENUM_TYPE j = i+1; j < s; ++j )
							{
								const Element::adj_type & jlc = LowConn(lc[j]); // access edges of the j-th face
								int cnt = 0;
								for(INMOST_DATA_ENUM_TYPE r = 0; r < jlc.size(); ++r )
									if( GetPrivateMarker(jlc[r],common) ) cnt++;
								if( cnt > 1 ) check = false;
							}
							for(INMOST_DATA_ENUM_TYPE r = 0; r < ilc.size(); ++r ) RemPrivateMarker(ilc[r],common);
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						}
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						ReleasePrivateMarker(common);
						if( check )
						{
							//test c_faces closure, if no closure, set as MultiPolygon
							INMOST_DATA_ENUM_TYPE quads = 0,tris = 0,i;
							for(i = 0; i < size; i++) if( !Hidden(lc[i]) )
							{
								if( GetGeometricType(lc[i]) == Element::Tri )
									tris++;
								else if( GetGeometricType(lc[i]) == Element::Quad )
									quads++;
							}
							if( tris == 4 && s == 4 )
								ret = Element::Tet;
							else if( quads == 6 && s == 6 )
								ret = Element::Hex;
							else if( tris == 4 && quads == 1 && s == tris+quads)
								ret = Element::Pyramid;
							else if( quads == 3 && tris == 2 && s == tris+quads)
								ret = Element::Prism;
							else
								ret = Element::Polyhedron;
						}
						else ret = Element::Polyhedron;
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					}
					else ret = Element::MultiPolygon;
				}
				break;
			case ESET: ret = Element::Set; break;
		}
		return ret;
	}

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	Storage::real Edge::Length() const 
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	{
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		Storage::real ret; 
		GetMeshLink()->GetGeometricData(GetHandle(),MEASURE,&ret); 
		return ret;
	}

	Storage::real Face::Area() const 
	{
		real ret; 
		GetMeshLink()->GetGeometricData(GetHandle(),MEASURE,&ret); 
		return ret;
	}
	void Face::Normal(real * nrm) const 
	{
		GetMeshLink()->GetGeometricData(GetHandle(),NORMAL,nrm);
	}

	Storage::real Cell::Volume() const 
	{
		real ret; 
		GetMeshLink()->GetGeometricData(GetHandle(),MEASURE,&ret); 
		return ret;
	}

	void Element::ComputeGeometricType() const
	{
		GetMeshLink()->ComputeGeometricType(GetHandle());
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	}
	
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	void Mesh::ComputeGeometricType(HandleType h) 
	{
		SetGeometricType(h,Element::Unset);
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		if( GetElementType() > NODE )
		{
			Element::adj_type const & lc = LowConn(h);
			if( !lc.empty() )
				SetGeometricType(h,ComputeGeometricType(GetHandleElementType(h),lc.data(),static_cast<integer>(lc.size())));
		}
		else SetGeometricType(h,Element::Vertex);
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	}
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	void Mesh::RecomputeGeometricData(HandleType e)
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	{
		//static std::map<Element *, int> numfixes;
		GeometricData d ;
		for(d = CENTROID; d <= NORMAL; d++) // first compute centroids and normals 
		{
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			if( HaveGeometricData(d,GetHandleElementType(e)) ) //compute centroid first
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			{
				Tag t = GetGeometricTag(d);
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				Storage::real * a = static_cast<Storage::real *>(MGetDenseLink(e,t));
				HideGeometricData(d,GetHandleElementType(e));
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				GetGeometricData(e,d,a);
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				ShowGeometricData(d,GetHandleElementType(e));
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			}
		}


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		if( HaveGeometricData(ORIENTATION,FACE) )
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		{
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			if( GetHandleElementType(e) == CELL ) //then correct the normal
			{
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				Element::adj_type & lc = LowConn(e); //faces
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				for(Element::adj_type::iterator it = lc.begin(); it != lc.end(); ++it)
					if( !GetMarker(*it,HideMarker()) )
					{
						//Element::adj_type & hc = HighConn(e);
						//if( Mesh::Count(&hc[0],hc.size(),HideMarker()) == 1 )
							Face(this,*it)->FixNormalOrientation();
					}
			}
			else if( GetHandleElementType(e) == FACE )
				Face(this,e)->FixNormalOrientation();
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		}
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		for(d = MEASURE; d <= BARYCENTER; d++) // compute the rest
		{
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			if( HaveGeometricData(d,GetHandleElementType(e)) )
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			{
				Tag t = GetGeometricTag(d);
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				Storage::real * a = static_cast<Storage::real *>(MGetDenseLink(e,t));
				HideGeometricData(d,GetHandleElementType(e));
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				GetGeometricData(e,d,a);
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				ShowGeometricData(d,GetHandleElementType(e));
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			}
		}
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		if( GetHandleElementType(e) == CELL ) //then correct the normal
		{
			
		}
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	}
	
	
	void Mesh::RemoveGeometricData(GeomParam table)
	{
		for(GeomParam::iterator it = table.begin(); it != table.end(); ++it)
		{
			if( it->first == MEASURE    ) 
			{
				if(measure_tag.isValid())    
					measure_tag    = DeleteTag(measure_tag   ,it->second);
				for(ElementType etype = EDGE; etype <= CELL; etype = etype << 1) if( etype & it->second) HideGeometricData(MEASURE,etype);
			}
			if( it->first == CENTROID   ) 
			{
				if(centroid_tag.isValid())   
					centroid_tag   = DeleteTag(centroid_tag  ,it->second);
				for(ElementType etype = EDGE; etype <= CELL; etype = etype << 1) if( etype & it->second) HideGeometricData(CENTROID,etype);
			}
			if( it->first == BARYCENTER ) 
			{
				if(barycenter_tag.isValid()) 
					barycenter_tag = DeleteTag(barycenter_tag,it->second);
				for(ElementType etype = EDGE; etype <= CELL; etype = etype << 1) if( etype & it->second) HideGeometricData(BARYCENTER,etype);
			}
			if( it->first == NORMAL     ) 
			{
				if(normal_tag.isValid())
					normal_tag     = DeleteTag(normal_tag    ,it->second);
				for(ElementType etype = FACE; etype <= CELL; etype = etype << 1) if( etype & it->second) HideGeometricData(NORMAL,etype);
			}
			if( it->first == ORIENTATION) 
				if( FACE & it->second) HideGeometricData(ORIENTATION,FACE);
		}
	}
	
	void Mesh::RestoreGeometricTags()
	{
		for(GeometricData gtype = MEASURE; gtype <= NORMAL; gtype++)
		{
			bool restore = false;
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			for(ElementType etype = EDGE; etype <= CELL && !restore; etype = NextElementType(etype))
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				if( HaveGeometricData(gtype,etype) )
					restore = true;
			if( restore )
			{
				switch(gtype)
				{
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				case MEASURE:       measure_tag = GetTag(measure_name);    break;
				case CENTROID:     centroid_tag = GetTag(centroid_name);   break;
				case BARYCENTER: barycenter_tag = GetTag(barycenter_name); break;
				case NORMAL:         normal_tag = GetTag(normal_name);     break;
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				}
			}
		}
	}
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	void Mesh::RepairGeometricTags()
	{
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		if( HaveTag(measure_name) )
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		{
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			measure_tag = GetTag(measure_name);
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			for(ElementType etype = EDGE; etype <= CELL; etype = NextElementType(etype))
				if( measure_tag.isDefined(etype) && !HaveGeometricData(MEASURE,etype) )
					ShowGeometricData(MEASURE,etype);
		}
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		if( HaveTag(centroid_name) )
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		{
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			centroid_tag = GetTag(centroid_name);
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			for(ElementType etype = EDGE; etype <= CELL; etype = NextElementType(etype))
				if( centroid_tag.isDefined(etype) && !HaveGeometricData(CENTROID,etype) )
					ShowGeometricData(CENTROID,etype);
		}
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		if( HaveTag(barycenter_name) )
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		{
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			barycenter_tag = GetTag(barycenter_name);
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			for(ElementType etype = EDGE; etype <= CELL; etype = NextElementType(etype))
				if( barycenter_tag.isDefined(etype) && !HaveGeometricData(BARYCENTER,etype) )
					ShowGeometricData(BARYCENTER,etype);
		}
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		if( HaveTag(normal_name) )
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		{
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			normal_tag = GetTag(normal_name);
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			for(ElementType etype = EDGE; etype <= CELL; etype = NextElementType(etype))
				if( normal_tag.isDefined(etype) && !HaveGeometricData(NORMAL,etype) )
					ShowGeometricData(NORMAL,etype);
		}
	}
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	void Mesh::PrepareGeometricData(GeomParam table)
	{
		for(GeomParam::iterator it = table.begin(); it != table.end(); ++it)
		{
			GeometricData types = it->first;
			ElementType mask = it->second;
			if( types == ORIENTATION )
			{
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				//std::cout << "ORIENTATION" << std::endl;
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				if( mask & FACE )
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				{
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					if( HideMarker() )
					{
						MarkerType hm = HideMarker();
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#if defined(USE_OMP)
#pragma omp parallel for
#endif
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						for(integer e = 0; e < FaceLastLocalID(); ++e) 
						{
							if( isValidElement(FACE,e) )
							{
								HandleType h = ComposeHandle(FACE,e);
								if( !GetMarker(h,hm) )
									Face(this,h)->FixNormalOrientation();
							}
						}
					}
					else
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					{
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						//std::cout << "Fix orientation" << std::endl;
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#if defined(USE_OMP)
#pragma omp parallel for
#endif
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						for(integer e = 0; e < FaceLastLocalID(); ++e) if( isValidElement(FACE,e) )
							Face(this,ComposeHandle(FACE,e))->FixNormalOrientation();
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					}
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				}
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				ShowGeometricData(ORIENTATION,FACE);
			}
			if( types == MEASURE )
			{
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				//std::cout << "MEASURE" << std::endl;
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				for(ElementType etype = EDGE; etype <= CELL; etype = NextElementType(etype))
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				{
					if( (mask & etype) && !HaveGeometricData(MEASURE,etype))
					{
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						measure_tag = CreateTag(measure_name,DATA_REAL,etype,NONE,1);
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						if( HideMarker() )
						{
							MarkerType hm = HideMarker();
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#if defined(USE_OMP)
#pragma omp parallel for
#endif
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							for(integer e = 0; e < LastLocalID(etype); ++e) if( isValidElement(etype,e) )
							{
								HandleType h = ComposeHandle(etype,e);
								if( !GetMarker(h,hm) ) GetGeometricData(h,MEASURE,static_cast<Storage::real *>(MGetDenseLink(h,measure_tag)));
							}
						}
						else
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						{
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#if defined(USE_OMP)
#pragma omp parallel for
#endif
							for(integer e = 0; e < LastLocalID(etype); ++e) if( isValidElement(etype,e) )
							{
								HandleType h = ComposeHandle(etype,e);
								GetGeometricData(h,MEASURE,static_cast<Storage::real *>(MGetDenseLink(h,measure_tag)));
							}
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						}
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						ShowGeometricData(MEASURE,etype);
					}
				}
			}
			if( types == CENTROID )
			{
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				//std::cout << "CENTROID" << std::endl;
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				for(ElementType etype = EDGE; etype <= CELL; etype = NextElementType(etype))
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				{
					if( (mask & etype) && !HaveGeometricData(CENTROID,etype))
					{
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						centroid_tag = CreateTag(centroid_name,DATA_REAL,etype,NONE,GetDimensions());
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						if( HideMarker() )
						{
							MarkerType hm = HideMarker();
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#if defined(USE_OMP)
#pragma omp parallel for
#endif
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							for(integer k = 0; k < LastLocalID(etype); ++k) if( isValidElement(etype,k) )
							{
								HandleType h = ComposeHandle(etype,k);
								if( !GetMarker(h,hm) ) GetGeometricData(h,CENTROID,static_cast<Storage::real *>(MGetDenseLink(h,centroid_tag)));
							}
						}
						else
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						{
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#if defined(USE_OMP)
#pragma omp parallel for
#endif
							for(integer k = 0; k < LastLocalID(etype); ++k) if( isValidElement(etype,k) )
							{
								HandleType h = ComposeHandle(etype,k);
								GetGeometricData(h,CENTROID,static_cast<Storage::real *>(MGetDenseLink(h,centroid_tag)));
							}
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						}
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						ShowGeometricData(CENTROID,etype);
					}
				}
			}
			if( types == BARYCENTER )
			{
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				//std::cout << "BARYCENTER" << std::endl;
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				for(ElementType etype = EDGE; etype <= CELL; etype = NextElementType(etype))
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				{
					if( (mask & etype) && !HaveGeometricData(BARYCENTER,etype))
					{
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						barycenter_tag = CreateTag(barycenter_name,DATA_REAL,etype,NONE,GetDimensions());
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						if( HideMarker() )
						{
							MarkerType hm = HideMarker();
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#if defined(USE_OMP)
#pragma omp parallel for
#endif
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							for(integer e = 0; e < LastLocalID(etype); ++e) if( isValidElement(etype,e) )
							{
								HandleType h = ComposeHandle(etype,e);
								if( !GetMarker(h,hm) ) GetGeometricData(h,BARYCENTER,static_cast<Storage::real *>(MGetDenseLink(h,barycenter_tag)));
							}
						}
						else
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						{
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#if defined(USE_OMP)
#pragma omp parallel for
#endif
							for(integer e = 0; e < LastLocalID(etype); ++e) if( isValidElement(etype,e) )
							{
								HandleType h = ComposeHandle(etype,e);
								GetGeometricData(h,BARYCENTER,static_cast<Storage::real *>(MGetDenseLink(h,barycenter_tag)));
							}
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						}
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						ShowGeometricData(BARYCENTER,etype);
					}
				}	
			}
			if( types == NORMAL )
			{
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				//std::cout << "NORMAL" << std::endl;
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				for(ElementType etype = FACE; etype <= CELL; etype = NextElementType(etype))
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				{
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					if( (mask & etype) && !HaveGeometricData(NORMAL,etype))
					{
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						normal_tag = CreateTag(normal_name,DATA_REAL,etype,NONE,GetDimensions());
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						if( HideMarker() )
						{
							MarkerType hm = HideMarker();
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#if defined(USE_OMP)
#pragma omp parallel for
#endif
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							for(integer e = 0; e < LastLocalID(etype); ++e) if( isValidElement(etype,e) )
							{
								HandleType h = ComposeHandle(etype,e);
								if( !GetMarker(h,hm) ) GetGeometricData(h,NORMAL,static_cast<Storage::real *>(MGetDenseLink(h,normal_tag)));
							}
						}
						else
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						{
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#if defined(USE_OMP)
#pragma omp parallel for
#endif
							for(integer e = 0; e < LastLocalID(etype); ++e) if( isValidElement(etype,e) )
							{
								HandleType h = ComposeHandle(etype,e);
								GetGeometricData(h,NORMAL,static_cast<Storage::real *>(MGetDenseLink(h,normal_tag)));
							}
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						}
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						ShowGeometricData(NORMAL,etype);
					}
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				}
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			}
		}
	}
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	bool Cell::CheckConvexity() const {return GetMeshLink()->CheckConvexity(getFaces());}

	bool Mesh::CheckConvexity(const ElementArray<Face> & faces) const
	{
		if( !faces.empty() )
		{
			std::vector<Storage::real> x(faces.size()*6,0.0);
			Storage::real * n = &x[faces.size()*3];
			Storage::real eps = GetEpsilon();
			//precompute data for all faces
#if defined(USE_OMP)
#pragma omp critical (reorder_edges)
#endif
			{ //collect data safely so that nobody changes it
				for(ElementArray<Face>::size_type j = 0; j != faces.size(); ++j)
				{
					faces[j].Centroid(&x[j*3]);
					faces[j].UnitNormal(&n[j*3]);
				}
			}
			//run comparison
			for(ElementArray<Face>::size_type j = 0; j != faces.size(); ++j)
			{
				Storage::real dota = 0, dots = 0, dotv, v[3] = {0.,0.,0.};
				for(ElementArray<Face>::size_type m = 0; m != faces.size(); ++m)
				{
					vec_diff(&x[m*3],&x[j*3],v,3);
					dotv = vec_dot_product(&n[j*3],v,3);
					dots += dotv;
					dota += fabs(dotv);
				}
				if( fabs(fabs(dots) - dota) > eps )
					return false;
			}
		}
		return true;
	}
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	void Mesh::FacesOrientation(ElementArray<Face> & faces, MarkerType rev)
	{
		//can copy orientation-independent algorithm from
		//incident_matrix.hpp: incident_matrix::compute_measure
		//assume mdim is of size 3 at most
		if( !faces.empty() )
		{
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			if( CheckConvexity(faces) ) //simpler algorithm
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			{
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				std::vector<Storage::real> x(faces.size()*6);
				Storage::real * n = &x[faces.size()*3];
				Storage::real xc[3] = {0.,0.,0.}, v[3] = {0.,0.,0.};
				for(ElementArray<Face>::size_type j = 0; j != faces.size(); ++j)
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				{
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					faces[j].Centroid(&x[j*3]);
					faces[j].UnitNormal(&n[j*3]);
					xc[0] += x[j*3+0];
					xc[1] += x[j*3+1];
					xc[2] += x[j*3+2];
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				}
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				xc[0] /= (Storage::real)faces.size();
				xc[1] /= (Storage::real)faces.size();
				xc[2] /= (Storage::real)faces.size();
				for(ElementArray<Face>::size_type j = 0; j != faces.size(); ++j)
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				{
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					vec_diff(&x[j*3],xc,v,3);
					if( vec_dot_product(&n[j*3],v,3) < 0 )
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					{
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						if( isPrivate(rev) )
							faces[j].SetPrivateMarker(rev);
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						else
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							faces[j].SetMarker(rev);
					}
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				}
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			}
			else
			{
				//real was = *ret/3.0;
				Face cur = faces[0];
				Mesh * mesh = faces.GetMeshLink();
				//firstly, have to figure out orientation of each face
				//mark all faces, so that we can perform adjacency retrival
				MarkerType mrk = mesh->CreatePrivateMarker();
				//MarkerType rev = mesh->CreatePrivateMarker(); //reverse orientation
				faces.SetPrivateMarker(mrk); //0-th face orientation is default
				cur->RemPrivateMarker(mrk);
				Node n1,n2; //to retrive edge
				bool reverse = false; //reverse orientation in considered face
				std::deque< orient_face > stack; //edge and first node and face for visiting
				ElementArray<Edge> edges = cur->getEdges();
				do
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				{
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					//figure out starting node order
					if( edges[0]->getBeg() == edges[1]->getBeg() ||
						edges[0]->getBeg() == edges[1]->getEnd() )
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					{
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						n1 = edges[0]->getEnd();
						n2 = edges[0]->getBeg();
					}
					else
					{
						n1 = edges[0]->getBeg();
						n2 = edges[0]->getEnd();
					}
					//schedule unvisited adjacent faces
					for(unsigned j = 0; j < edges.size(); j++)
					{
						//schedule face adjacent to considered edge
						ElementArray<Face> adjacent = edges[j]->getFaces(mrk);
						assert(adjacent.size() <= 1);
						if( !adjacent.empty() )
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						{
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							adjacent.RemPrivateMarker(mrk);
							stack.push_back(orient_face(edges[j],reverse ? n2 : n1,adjacent[0]));
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						}
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						//update edge nodes
						n1 = n2; //current end is new begin
						//find new end
						if( n2 == edges[(j+1)%edges.size()]->getBeg() )
							n2 = edges[(j+1)%edges.size()]->getEnd();
							else
								n2 = edges[(j+1)%edges.size()]->getBeg();
								}
					if( stack.empty() ) break;
					//get entry from stack
					orient_face r = stack.front();
					//remove face from stack
					stack.pop_front();
					//retrive edges for new face
					edges = r.face->getEdges();
					reverse = false;
					//figure out starting node order
					if( edges[0]->getBeg() == edges[1]->getBeg() ||
						edges[0]->getBeg() == edges[1]->getEnd() )
					{
						n1 = edges[0]->getEnd();
						n2 = edges[0]->getBeg();
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					}
					else
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					{
						n1 = edges[0]->getBeg();
						n2 = edges[0]->getEnd();
					}
					//find out common edge orientation
					for(unsigned j = 0; j < edges.size(); j++)
					{
						if( edges[j] == r.bridge ) //found the edge
						{
							//reverse ordering on this face
							if( r.first == n1 )
							{
								if( isPrivate(rev) )
									r.face->SetPrivateMarker(rev);
								else
									r.face->SetMarker(rev);
								reverse = true;
							}
							break;
						}
						//update edge nodes
						n1 = n2; //current end is new begin
						//find new end
						if( n2 == edges[(j+1)%edges.size()]->getBeg() )
							n2 = edges[(j+1)%edges.size()]->getEnd();
						else
							n2 = edges[(j+1)%edges.size()]->getBeg();
					}
				} while(true);
				faces.RemPrivateMarker(mrk);
				mesh->ReleasePrivateMarker(mrk);
				//faces.RemPrivateMarker(rev);
			}
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		}
	}
	
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	void Mesh::GetGeometricData(HandleType e, GeometricData type, Storage::real * ret)
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	{
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		assert(e != InvalidHandle());
		assert(ret != NULL);
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		assert(type == MEASURE ||
			   type == CENTROID ||
			   type == BARYCENTER ||
			   type == NORMAL);
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		ElementType etype = GetHandleElementType(e);
		integer edim = Element::GetGeometricDimension(GetGeometricType(e));
		integer mdim = GetDimensions();
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		switch(type)
		{
			case MEASURE:
			if( HaveGeometricData(MEASURE,etype) )
			{
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				*ret = static_cast<Storage::real *>(MGetDenseLink(e,measure_tag))[0];
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				//~ if( isnan(*ret) || fabs(*ret) < 1e-15  ) throw -1;
			}
			else
			{
				switch(edim)
				{
					case 0: *ret = 0; break;
					case 1: //length of edge
					{
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						ElementArray<Node> nodes = Element(this,e)->getNodes();
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						if( nodes.size() > 1 )
						{
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							real c[3] = {0,0,0};
							real_array v0 = nodes[0].Coords();
							real_array v1 = nodes[1].Coords();
							vec_diff(v0.data(),v1.data(),c,mdim);
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							*ret = vec_len(c,mdim);
						}
						else *ret = 0;
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						//~ if( isnan(*ret) || fabs(*ret) < 1e-15  ) throw -1;
						break;
					}
					case 2: //area of face
					{
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						ElementArray<Node> nodes = Element(this,e)->getNodes();
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						if( nodes.size() > 2 )
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						{
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							*ret = 0;
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							real nt[3] = { 0,0,0 }, l1[3] = { 0,0,0 }, l2[3] = { 0,0,0 }, n0[3] = { 0,0,0 };// , ss, at;
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							real_array v0, v1, v2;
							v0 = nodes[0].Coords();
							for(int i = 1; i < (int)nodes.size()-1; i++)
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							{
								v1 = nodes[i].Coords();
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								v2 = nodes[i+1].Coords();
								vec_diff(v1,v0,l1,mdim);
								vec_diff(v2,v0,l2,mdim);
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								vec_cross_product(l1,l2,nt);
								for(int q = 0; q < 3; ++q)
									n0[q] += nt[q]*0.5;
							}
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							*ret = vec_len(n0,3);
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							//code below is not really needed
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							/*
							for(int i = 1; i < (int)nodes.size()-1; i++)
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							{
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								v1 = nodes[i].Coords();
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								v2 = nodes[i+1].Coords();
								vec_diff(v1,v0,l1,mdim);
								vec_diff(v2,v0,l2,mdim);
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								vec_cross_product(l1,l2,nt);
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								for(int q = 0; q < 3; ++q) 
									nt[q] *= 0.5;
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								ss = vec_dot_product(n0,nt,3);
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								if( ss ) ss /= fabs(ss);
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								at = sqrt(vec_dot_product(nt,nt,3))*ss;
								*ret += at;
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							}
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							*/
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							if( *ret != *ret ) std::cout << "area is nan" << std::endl;
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							*ret = fabs(*ret);
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						} else *ret = 0;
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						//~ if( isnan(*ret) || fabs(*ret) < 1e-15  ) throw -1;
						break;
					}
					case 3: //volume of cell
					{
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						//bool print = false;
//redo:
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						Cell me = Cell(this,e);
						ElementArray<Face> faces = me->getFaces();
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						//bool ornt = true;//!HaveGeometricData(ORIENTATION,FACE);
						bool ornt = !HaveGeometricData(ORIENTATION,FACE);
						//bool ornt = !CheckConvexity(faces);
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						MarkerType rev = 0;
						if( ornt )
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						{
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							rev = CreatePrivateMarker();
							FacesOrientation(faces,rev);
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						}
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						real vol = 0, a, at, volp;
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						real x[3] = {0,0,0}, n0[3] = {0,0,0}, s, ss;
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						real l1[3] = {0,0,0}, l2[3] = {0,0,0};
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						real nt[3] = {0,0,0};
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						real vc[3] = {0,0,0};
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						//me.Centroid(cx);
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						//if( print ) std::cout << "cx: " << cx[0] << " " << cx[1] << " " << cx[2] << std::endl;
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						for(unsigned j = 0; j < faces.size(); j++)
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						{
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							//compute normal to face
							ElementArray<Node> nodes = faces[j].getNodes();
							if( ornt )
								s = faces[j].GetPrivateMarker(rev) ? -1.0 : 1.0;
							else
								s = faces[j].FaceOrientedOutside(me) ? 1.0 : -1.0;
							x[0] = x[1] = x[2] = 0;
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							n0[0] = n0[1] = n0[2] = 0;
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							vc[0] = vc[1] = vc[2] = 0;
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							a = 0;
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							real_array v0 = nodes[0].Coords(), v1, v2;
							for(int i = 1; i < (int)nodes.size()-1; i++)
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							{
								v1 = nodes[i].Coords();
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								v2 = nodes[i+1].Coords();
								vec_diff(v1,v0,l1,mdim);
								vec_diff(v2,v0,l2,mdim);
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								vec_cross_product(l1,l2,nt);
								for(int q = 0; q < 3; ++q)
									n0[q] += nt[q]*0.5;
							}
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							for(int i = 1; i < (int)nodes.size()-1; i++)
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							{
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								v1 = nodes[i].Coords();
								v2 = nodes[i+1].Coords();
								vec_diff(v1,v0,l1,mdim);
								vec_diff(v2,v0,l2,mdim);
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								vec_cross_product(l1,l2,nt);
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								for(int q = 0; q < 3; ++q) 
									nt[q] *= 0.5;
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								ss = vec_dot_product(n0,nt,3);
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								if( ss ) 
									ss /= fabs(ss);
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								at = sqrt(vec_dot_product(nt,nt,3))*ss;
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								//same as faces[j].Barycenter(x)
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								for(int q = 0; q < 3; ++q)
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									x[q] += at*(v0[q]+v1[q]+v2[q])/3.0;
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								a += at;
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							}
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							if( a )
							{
								for(int q = 0; q < 3; ++q) 
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									x[q] = x[q]/a;
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							}
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							else Element(this,e).Centroid(x);
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							volp = vec_dot_product(x,n0,3) / 3.0;
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							vol += s*volp;
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						}
						if( ornt )
						{
							if( vol < 0.0 ) vol = -vol;
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							faces.RemPrivateMarker(rev);
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							ReleasePrivateMarker(rev);
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						}
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						*ret = vol;
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