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using namespace CGLA;
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using namespace CGLA;
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using namespace std;
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using namespace std;
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namespace HMesh
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namespace HMesh
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{
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{
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	FaceIter get_null_face_iter()
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	{
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		static FaceList l;
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		return l.end();
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	}
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		template<class R>
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	template<class R>
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		Face_template<R>::Face_template():
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	Face_template<R>::Face_template():
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				last(NULL_HALFEDGE_ITER),
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	last(NULL_HALFEDGE_ITER),
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				touched(0)
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	touched(0)
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		{}
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	{}
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		int no_edges(FaceIter f)
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	int no_edges(FaceIter f)
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	{
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		FaceCirculator fc(f);
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		while(!fc.end()) ++fc;
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		return fc.no_steps();
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	}
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- 
 
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	Vec3f normal(FaceIter f)
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	{
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		vector<Vec3f> v;
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		FaceCirculator fc(f);
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		int k;
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		for(k=0;!fc.end();++fc,++k)
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		{
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		{
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				FaceCirculator fc(f);
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				while(!fc.end()) ++fc;
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			Vec3f p = fc.get_vertex()->pos;
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				return fc.no_steps();
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			v.push_back(p);
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		}
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		}
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		Vec3f normal(FaceIter f)
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		Vec3f norm(0);
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		for(int i=0;i<k;++i)
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		{
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		{
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				vector<Vec3f> v;
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				FaceCirculator fc(f);
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				int k;
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				for(k=0;!fc.end();++fc,++k)
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				{
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						Vec3f p = fc.get_vertex()->pos;
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						v.push_back(p);
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				}
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				Vec3f norm(0);
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				for(int i=0;i<k;++i)
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				{
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						norm[0] += (v[i][1]-v[(i+1)%k][1])*(v[i][2]+v[(i+1)%k][2]);
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			norm[0] += (v[i][1]-v[(i+1)%k][1])*(v[i][2]+v[(i+1)%k][2]);
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						norm[1] += (v[i][2]-v[(i+1)%k][2])*(v[i][0]+v[(i+1)%k][0]);
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			norm[1] += (v[i][2]-v[(i+1)%k][2])*(v[i][0]+v[(i+1)%k][0]);
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						norm[2] += (v[i][0]-v[(i+1)%k][0])*(v[i][1]+v[(i+1)%k][1]);
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			norm[2] += (v[i][0]-v[(i+1)%k][0])*(v[i][1]+v[(i+1)%k][1]);
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				}
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				float l = norm.length();
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				if(l>0.0f)
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						norm /= l;
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				return norm;
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		}
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		}
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		float l = norm.length();
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		if(l>0.0f)
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			norm /= l;
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		return norm;
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	}
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		float area(FaceIter f)
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	float area(FaceIter f)
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	{
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		FaceCirculator fc(f);
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		int k;
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		// M is a matrix that projects a vector onto the orthogonal
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		// complement of the face normal
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		Vec3f n = normal(f);
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		Vec3f a,b;
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		orthogonal(n, a, b);
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		Mat3x3f M(a,b,n);
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		// Get all projected vertices
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		vector<Vec2f> v;
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		for(k=0;!fc.end();++fc,++k)
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		{
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		{
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				FaceCirculator fc(f);
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				int k;
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				// M is a matrix that projects a vector onto the orthogonal
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				// complement of the face normal
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				Vec3f n = normal(f);
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				Vec3f a,b;
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				orthogonal(n, a, b);
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				Mat3x3f M(a,b,n);
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				// Get all projected vertices
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				vector<Vec2f> v;
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				for(k=0;!fc.end();++fc,++k)
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				{
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						Vec3f p = M * fc.get_vertex()->pos;
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			Vec3f p = M * fc.get_vertex()->pos;
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						v.push_back(Vec2f(p[0], p[1]));
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			v.push_back(Vec2f(p[0], p[1]));
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				}
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				float area = 0;
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				for(int i=0;i<k;++i)
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				{
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						area += 0.5 * cross(v[i], v[(i+1)%k]);
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				}
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				return fabs(area);
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		}
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		}
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		float area = 0;
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		Vec3f centre(FaceIter f)
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		for(int i=0;i<k;++i)
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		{
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		{
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				Vec3f c(0);
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				FaceCirculator fc(f);
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				while(!fc.end())
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				{
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						c += fc.get_vertex()->pos;
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			area += 0.5 * cross(v[i], v[(i+1)%k]);
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						++fc;
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				}
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				c /= fc.no_steps();
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				return c;
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		}
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		}
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		return fabs(area);
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	}
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	Vec3f centre(FaceIter f)
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 83 
	{
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		Vec3f c(0);
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 85 
		FaceCirculator fc(f);
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 86 
		while(!fc.end())
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		{
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			c += fc.get_vertex()->pos;
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			++fc;
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		}
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		c /= fc.no_steps();
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		return c;
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	}
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		template struct Face_template<Iters>;
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	template struct Face_template<Iters>;
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}
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}