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

Fellegara, Riccardo and Weiss, Kenneth and De Floriani, Leila (2021) The Stellar decomposition: A compact representation for simplicial complexes and beyond. Computers & Graphics, 98, pp. 322-343. Elsevier. doi: 10.1016/j.cag.2021.05.002. ISSN 0097-8493.

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Official URL: https://www.sciencedirect.com/science/article/abs/pii/S0097849321000819?via%3Dihub

Abstract

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

Item URL in elib:https://elib.dlr.de/146782/
Document Type:Article
Title:The Stellar decomposition: A compact representation for simplicial complexes and beyond
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Fellegara, RiccardoRiccardo.Fellegara (at) dlr.dehttps://orcid.org/0000-0002-8758-2802
Weiss, Kennethkweiss (at) llnl.govhttps://orcid.org/0000-0001-6649-8022
De Floriani, Leiladeflo (at) umiacs.umd.eduhttps://orcid.org/0000-0002-1361-2888
Date:August 2021
Journal or Publication Title:Computers & Graphics
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:98
DOI :10.1016/j.cag.2021.05.002
Page Range:pp. 322-343
Publisher:Elsevier
ISSN:0097-8493
Status:Published
Keywords:Mesh data structure Scalable representations Vietoris-Rips complex High dimensional simplicial complexes
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space System Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Space System Technology
DLR - Research theme (Project):R - Tasks SISTEC
Location: Braunschweig
Institutes and Institutions:Institute for Software Technology
Institute for Software Technology > Software for Space Systems and Interactive Visualisation
Deposited By: Fellegara, Dr Riccardo
Deposited On:08 Dec 2021 09:41
Last Modified:08 Dec 2021 09:41

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