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		FaceIter faces_begin() { return face_db.begin();	}
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		FaceIter faces_begin() { return face_db.begin();	}
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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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		/** HalfEdge collapse precondition.
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		/** \brief HalfEdge collapse precondition.
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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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				the halfedge given as second arg. The reason is that the collapse
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				the halfedge given as second arg. The reason is that the collapse
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				would violate the manifold property of the mesh. */
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				would violate the manifold property of the mesh.
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				The test is as follows.
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				1. For the two vertices adjacent to the edge, we generate
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				a list of all their neighbouring vertices. We then generate a
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				list of the vertices that occur in both these lists. That is,
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				we find all vertices connected by edges to both endpoints
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				of the edge and store these in a list.
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				2. For both faces incident on the edge, check whether they
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				are triangular. If this is the case, the face will be removed,
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				and it is ok that the the third vertex is connected to both
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				endpoints. Thus the third vertex in such a face is removed
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				from the list generated in 1.
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				3. If the list is now empty, all is well. Otherwise, there
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				would be a vertex in the new mesh with two edges connecting
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				it to the same vertex. Return false.
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				4. TETRAHEDRON TEST:
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				If the valency of both vertices is
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				three, and the incident faces are triangles, we also disallow
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				the operation. Reason: It introduces a vertex of valency two
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				and if the final two polygons incident on the vertices
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				that are adjacent to the edge being collapsed are triangles, then
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				the construction will collapse
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				5. VALENCY 4 TEST:
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				If a face adjacent to the edge being collapsed is a triangle,
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				it will disappear, and the valency of the final vertex beloning to
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				this edge will be reduced by one. Hence this valency should be at
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				least 4. A valency three vertex will be reduced to a valency two
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				vertex which is considered illegal.
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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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				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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				situation.	*/
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		bool collapse_precond(VertexIter, HalfEdgeIter);
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		bool collapse_precond(VertexIter, HalfEdgeIter);
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		/** Collapse the halfedge given as second argument. The first argument
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		/** Collapse the halfedge given as second argument.
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		The first argument
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				is the vertex that is being removed. This function is not guaranteed
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				is the vertex that is being removed. The second is a halfedge pointing
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				away from that vertex. This function is not guaranteed
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				to keep the mesh sane unless, collapse_precond has returned true. */
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				to keep the mesh sane unless, collapse_precond has returned true. */
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		void collapse_halfedge(VertexIter, HalfEdgeIter, bool=false);
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		void collapse_halfedge(VertexIter, HalfEdgeIter, bool=false);
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		/** Split a face (first argument) by connecting two vertices (the
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		/** Split a face (first argument) by connecting two vertices (the
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				next two arguments). */
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				next two arguments). */