The Taub Faculty of Computer Science Events and Talks

We introduce a new geometric definition of affine combinations of two compact subsets of R^n.

The 4-point interpolatory subdivision schemes for points is adapted to sets, by first expressing the insertion rule in terms of repeated binary averages, and then replacing these affine combinations of pairs of points by the new affine combinations of sets. This subdivision scheme is applied to the reconstruction of multidimensional objects from cross-sections.

We address the questions of convergence and approximation order of this new set-valued subdivision scheme and present several computational examples.