Determine master point (key point) of 3D polygon, shape, surface

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I have 3D polygon: solid (first case) and plane (second case). How to determine master point (key point)? Ex.: master points of a cylinder are the centers of its caps.

I can't use convex hull algorithm because master point can be a part of a hull and I can't check it with the plain (2D) polygon algorithm because the surface can be arched.

I will enjoy any links to read about the question or straightforward answers.

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Micromega On

You can try alphashapes. Its a delaunay triangulation without edges exceeding alpha.