# Calculating the volume of a triangular mesh?

I have an unorganized point cloud with a bunch of 3d points. I use a certain surface reconstruction method to obtain a triangle mesh of the underlying surface. The surface could be closed or not. Can somebody point me out to how I would go about estimating the volume enclosed by such a surface (if its closed). If its not closed, then what would a way to "close" it and get a volume? I would appreciate if somebody could even point out C++ libraries that would help me do this.

• This is maybe already answered on StackOverflow. Feb 15, 2013 at 14:43
• Thanks Libor, that was helpful. Could I keep this question alive to see if I get answers to the second part of my question? The thread mentioned before doesn't deal with surface that are not closed. What are my options in such a case ? Feb 15, 2013 at 17:42
• This is an interesting problem for geometry and graph theory. I am sure there is a simple iterative algorithm for closing the holes or maybe just improvement of your algorithm that does not introduce the holes. I have a feeling the problem can be defined in 2D as well. Posting such problems in simpler and well defined form on math.stackexchange.com helped me a lot several times. Feb 15, 2013 at 18:06
• If the first part of your question is answered by StackOverflow, link to SO and then remove that part from the question, so this is just about the second part. Apr 3, 2013 at 13:55