Shape space manipulation

Abstract

Shape spaces can be used to facilitate shape manipulation, such as synthesis, categorization, retrieval, and transformation of geometric shapes. However, the existing works in shape space manipulation have challenges in topology changes handling and efficiency.This thesis develops the space of shapes bounded by the skin, which is defined by Edelsbrunner et al. We concentrate on a subspace of such shape space, that is, the affine hull of a set of reference shapes. We find that the shapes in such affine hull share a finite number of Voronoi complexes. Furthermore, these common Voronoi complexes can be computed with the Voronoi complexes of the reference shapes. By reusing generated Voronoi complexes, we can compute arbitrary shapes in the affine hull efficiently.Moreover, we can deal with shapes with different topologies gracefully. We design an algorithm to compute the common Voronoi complexes, and an implementation is done in $\R^3$.