Manipulating Topological Decompositions of Non-Manifold Shapes

Abstract

Decomposing a non-manifold shape into its almost manifold components is a powerful tool for analyzing its complex structure. Many techniques for decomposing a non-manifold shape are available in the current literature, and provide a structural model, which exposes its non-manifold singularities, as well as the connectivity of its relevant subcomponents, connected through the singularities. However, the majority of the decompositions are static, and are not automatically updated, if the corresponding non-manifold shape is modified by an editing operator. In many cases, the resulting decomposition is recomputed from scratch without reusing the unchanged portions of the existing decomposition. In this paper, we describe how updating automatically a specific decomposition of a non-manifold shape. Here, we show that our approach may be useful for adapting many geometry processing techniques also to non-manifold shapes, where several problems may arise. One of the most promising applications consists of defining a multiresolution version for the specific structural model of interest, due to its good topological properties.