The Stellar decomposition: A compact representation for simplicial complexes and beyond

We introduce the Stellar decomposition, a model for efficient topological data structures over broad range of simplicial and cell complexes. A decomposition complex is collection regions indexing complex's vertices cells such that each region has sufficient information to locally reconstruct star its vertices, i.e., incident in region's vertices. decompositions are general they can compactly represent efficiently traverse arbitrary complexes with manifold or non-manifold domain. They scalable high dimension large size, enable users easily construct tailored application-dependent using fraction memory required by corresponding global structure on complex. As concrete realization this spatially embedded complexes, we tree, which combines nested spatial tree simple tuning parameter control number region. trees exploit locality reordering vertex indices according compressing sequential ranges indices. competitive state-ofthe-art offer significant improvements conclude highlevel description several mesh processing analysis applications utilize process datasets.