# How to calculate the area and volume of a random 3d shape knowing only its coordinates?

Given a set of 3d points which make up an vector object of any shape (with any number of points), without the edges being known, how can the object's edges be found/detected so that the object's surface 3d area and internal 3d volume can be calculated?

Note: there may be points inside the object which do not form part of the outside edges.

• It might not be obvious which points are in the ‘inside’ – T. Fo Jan 13 at 2:59
• The term of art here is "convex hull". – Blue Jan 13 at 3:00
• A best cost or worst cost edge finding function would be fine – Aalawlx Jan 13 at 3:01
• @Blue thanks for that magic keyword! once the convex hull is calculated, then would it be easy to know the surface area and internal volume? Is there any special magic words for that too? – Aalawlx Jan 13 at 3:12
• @Aalawlx: I don't really have anything more specific to add. Just search for "volume of convex polyhedron". So far as I know, there's no good formula, but there appear to be algorithms. See, for instance, "Algorithm for finding the volume of a convex polytope" on MathOverflow. – Blue Jan 13 at 3:31