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	/** \brief A Data structure representing an open or closed manifold.
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	/** \brief A Data structure representing an open or closed manifold.
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			Manifold keeps lists of the entities making up a halfedge mesh
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			Manifold keeps lists of the entities making up a halfedge mesh
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			and provides basic functions for creating new faces, halfedges
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			and provides basic functions for creating new faces, halfedges
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			and vertices. There are also primitive operations for editing
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			and vertices. There are also primitive operations for editing
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			such as edge collapse. */
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			such as edge collapse. */
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	struct Manifold
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	class Manifold
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	{
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	{
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		std::list<Vertex> vertex_db;
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		std::list<Vertex> vertex_db;
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		std::list<Face> face_db;
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		std::list<Face> face_db;
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		std::list<HalfEdge> halfedge_db;
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		std::list<HalfEdge> halfedge_db;
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		{
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		{
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			halfedge_db.push_back(HalfEdge());
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			halfedge_db.push_back(HalfEdge());
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			return --halfedge_db.end();
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			return --halfedge_db.end();
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		}
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		}
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		/** Erase halfedge h.
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				In general, you should never call this function but use the
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		/// Erase halfedge h. Assumes it is safe to do so. Use with care.
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				collapse_halfedge function instead since blindly erasing geometry
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				is most likely to invalidate the Mesh. Quite possibly this function
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				will be removed from the public interface. */
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		void erase_halfedge(HalfEdgeIter h)
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		void erase_halfedge(HalfEdgeIter h)
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		{
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		{
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			halfedge_db.erase(h);
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			halfedge_db.erase(h);
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		}
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		}
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		/** Erase vertex v.
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				In general, you should never call this function but use the
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		/// Erase vertex v. Assumes it is safe to do so. Use with care.
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				collapse_halfedge function to collapse the vertex away.
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				Blindly erasing is extremely likely to invalidate the
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				Mesh. Quite possibly this function will be removed from the
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				public interface. */
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		void erase_vertex(VertexIter v)
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		void erase_vertex(VertexIter v)
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		{
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		{
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			vertex_db.erase(v);
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			vertex_db.erase(v);
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		}
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		}
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		/** Erase face f.
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		/// Erase face f. Assumes it is safe to do so. Use with care.
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				In general, you should never call this function but use
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				collapse_halfedge in conjunction with other functions to
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				remove the face through (Euler) operations which preserve
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				the mesh in a valid state.
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				Blindly erasing is extremely likely to invalidate the
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				Mesh. Quite possibly this function will be removed from the
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				public interface. */
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		void erase_face(FaceIter f)
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		void erase_face(FaceIter f)
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		{
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		{
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			face_db.erase(f);
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			face_db.erase(f);
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		}
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		}
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		/// Return iterator pointing to beyond the last face.
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		/// Return iterator pointing to beyond the last face.
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		FaceIter faces_end() { return face_db.end(); }
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		FaceIter faces_end() { return face_db.end(); }
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		/** \brief HalfEdge collapse precondition.
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		/** \brief HalfEdge collapse precondition.
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				The first argument, v, is the vertex we want to remove. The
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		    The argument h is the halfedge we want to collapse.
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				second, h, is a halfedge pointing away from that vertex.
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				If this function does not return true, it is illegal to collapse
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				If this function does not return true, it is illegal to collapse
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				h. The reason is that the collapse would violate the manifold property
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				h. The reason is that the collapse would violate the manifold property
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				of the mesh.
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				of the mesh.
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				6. PREVENT MERGING HOLES:
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				6. PREVENT MERGING HOLES:
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				We do not want to collapse an edge if its end points are boundary
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				We do not want to collapse an edge if its end points are boundary
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				vertices, but its two adjacent faces are not NULL faces, because
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				vertices, but its two adjacent faces are not NULL faces, because
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				in that case we create a vertex where two holes meet. A non manifold
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				in that case we create a vertex where two holes meet. A non manifold
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				situation.	*/
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				situation.	*/
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		bool collapse_precond(VertexIter v, HalfEdgeIter h);
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		bool collapse_precond(HalfEdgeIter h);
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		/** Collapse the halfedge h.
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		/** Collapse the halfedge h.
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				The first argument, v, is the vertex that is being removed. The
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		    The argument h is the halfedge being removed. The vertex
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				second, h, is a halfedge pointing away from that vertex.
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				v=h->opp->vert is the one being removed while h->vert survives.
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				The final argument is a boolean indicating whether the vertex
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				The final argument is a boolean indicating whether the vertex
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				that survives the collapse should have a position which is the
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				that survives the collapse should have a position which is the
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				average of its own position and the vertex that is removed.
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				average of its own position and the vertex that is removed.
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				By default false meaning that the surviving vertex retains it
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				By default false.
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				position.
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				This function is not guaranteed to keep the mesh sane unless,
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				This function is not guaranteed to keep the mesh sane unless,
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				collapse_precond has returned true.
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				collapse_precond has returned true !!
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		*/
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		*/
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		void collapse_halfedge(VertexIter v, HalfEdgeIter h, bool=false);
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		void collapse_halfedge(HalfEdgeIter h, bool=false);
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		/** Split a face.
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		/** Split a face.
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		    The face, f, is split by connecting two
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		    The face, f, is split by connecting two
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				vertices v0 and v1 (the next two arguments). The vertices of
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				vertices v0 and v1 (the next two arguments). The vertices of
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				the old face between v0 and v1 (in counter clockwise order)
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				the old face between v0 and v1 (in counter clockwise order)