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	double CurvatureEnergy::abs_mean_curv(const Vec3d& v, const vector<Vec3d>& ring) const
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	double CurvatureEnergy::abs_mean_curv(const Vec3d& v, const vector<Vec3d>& ring) const
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	{
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	{
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		const size_t N = ring.size();
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		const size_t N = ring.size();
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		double H = 0;
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		double H = 0;
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		for(int i = 0; i < N; ++i){
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		for(size_t i = 0; i < N; ++i){
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			Vec3d vnim1 = ring[(i+N-1)%N] - v;
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			Vec3d vnim1 = ring[(i+N-1)%N] - v;
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			Vec3d vni   = ring[i] - v;
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			Vec3d vni   = ring[i] - v;
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			Vec3d vnip1 = ring[(i+1)%N] - v;
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			Vec3d vnip1 = ring[(i+1)%N] - v;
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			Vec3d Nm = normalize(cross(vni, vnim1));
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			Vec3d Nm = normalize(cross(vni, vnim1));
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		double gauss_curv(const Vec3d& v, const vector<Vec3d>& ring) const
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		double gauss_curv(const Vec3d& v, const vector<Vec3d>& ring) const
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		{
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		{
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			const size_t N = ring.size();
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			const size_t N = ring.size();
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			double asum=0.0f;
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			double asum=0.0f;
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			double area_sum=0;
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			double area_sum=0;
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			for(int i = 0; i < N; ++i){
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			for(size_t i = 0; i < N; ++i){
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				const Vec3d& v1 = ring[i];
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				const Vec3d& v1 = ring[i];
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				const Vec3d& v2 = ring[(i+1)%N];
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				const Vec3d& v2 = ring[(i+1)%N];
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				Vec3d a = v1-v;
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				Vec3d a = v1-v;
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				Vec3d b = v2-v;
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				Vec3d b = v2-v;
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				asum += acos(max(-1.0, min(1.0, dot(a,b)/(length(a)*length(b)))));
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				asum += acos(max(-1.0, min(1.0, dot(a,b)/(length(a)*length(b)))));