Determine if a point is interior or exterior to a 3D Alpha-shapes surface in CGAL

Question

I am using CGAL to create the concave hull of a set of 3D points using ex_alpha_shapes_3 example. Next, I would like to find out whether a point query in space is located within the surface created by the triangular concave hull faces (the output of ex_alpha_shapes_3 code) or not. A "point in polygon" technique should be useful for this purpose. I would appreciate it if anyone could help me with this problem.

Answer 1

You can use the locate function and depending on the simplex the point fall on and the output of the function classify of the simplex you'll directly know if you're inside, outside or on the boundary.

• whatever simplex type, EXTERIOR is exterior, INTERIOR is interior.
• If the point falls on an edge, REGULAR is on the boundary and SINGULAR depends whether what an isolated edge should be in your setting
• If the points fall on a vertex, REGULAR is on the boundary and SINGULAR is depends whether an isolated input point should be in your setting