Reconstruction of 3D objects from their 2D cross-sections by subdivision schemes for sets

Abstract: 

This talk starts with a short introduction to subdivision schemes generating curves from a given sequence of points by repeated refinements. This notion is then extended to the refinement of 2D sets, for the generation of 3D objects from  2D cross-sections approximating or interpolating the given sequence of sets. Examples of such reconstructions by different subdivision schemes are shown and compared, and the approximation properties of these reconstructions are presented.

This is a joint work with Shay Kels.