A dimension-independent data structure for simplicial complexes

Leila De Floriani, Annie Hui, Daniele Panozzo, David Canino

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider here the problem of representing non-manifold shapes discretized as d-dimensional simplicial Euclidean complexes. To this aim, we propose a dimension-independent data structure for simplicial complexes, called the Incidence Simplicial (IS) data structure, which is scalable to manifold complexes, and supports efficient navigation and topological modifications. The IS data structure has the same expressive power and exibits performances in query and update operations as the incidence graph, a widely-used representation for general cell complexes, but it is much more compact. Here, we describe the IS data structure and we evaluate its storage cost. Moreover, we present efficient algorithms for navigating and for generating a simplicial complex described as an IS data structure. We compare the IS data structure with the incidence graph and with dimension-specific representations for simplicial complexes.

Original languageEnglish (US)
Title of host publicationProceedings of the 19th International Meshing Roundtable, IMR 2010
Pages403-420
Number of pages18
DOIs
StatePublished - 2010
Event19th International Meshing Roundtable, IMR 2010 - Chattanooga, TN, United States
Duration: Oct 3 2010Oct 6 2010

Other

Other19th International Meshing Roundtable, IMR 2010
CountryUnited States
CityChattanooga, TN
Period10/3/1010/6/10

Fingerprint

Simplicial Complex
Data structures
Incidence
Data Structures
Cell Complex
Complex Manifolds
Expressive Power
Graph in graph theory
Navigation
Euclidean
Efficient Algorithms
Update
Query
Evaluate
Costs

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Modeling and Simulation

Cite this

De Floriani, L., Hui, A., Panozzo, D., & Canino, D. (2010). A dimension-independent data structure for simplicial complexes. In Proceedings of the 19th International Meshing Roundtable, IMR 2010 (pp. 403-420) https://doi.org/10.1007/978-3-642-15414-0_24

A dimension-independent data structure for simplicial complexes. / De Floriani, Leila; Hui, Annie; Panozzo, Daniele; Canino, David.

Proceedings of the 19th International Meshing Roundtable, IMR 2010. 2010. p. 403-420.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

De Floriani, L, Hui, A, Panozzo, D & Canino, D 2010, A dimension-independent data structure for simplicial complexes. in Proceedings of the 19th International Meshing Roundtable, IMR 2010. pp. 403-420, 19th International Meshing Roundtable, IMR 2010, Chattanooga, TN, United States, 10/3/10. https://doi.org/10.1007/978-3-642-15414-0_24
De Floriani L, Hui A, Panozzo D, Canino D. A dimension-independent data structure for simplicial complexes. In Proceedings of the 19th International Meshing Roundtable, IMR 2010. 2010. p. 403-420 https://doi.org/10.1007/978-3-642-15414-0_24
De Floriani, Leila ; Hui, Annie ; Panozzo, Daniele ; Canino, David. / A dimension-independent data structure for simplicial complexes. Proceedings of the 19th International Meshing Roundtable, IMR 2010. 2010. pp. 403-420
@inproceedings{e483a152f68142fdbf72c233e77c2c54,
title = "A dimension-independent data structure for simplicial complexes",
abstract = "We consider here the problem of representing non-manifold shapes discretized as d-dimensional simplicial Euclidean complexes. To this aim, we propose a dimension-independent data structure for simplicial complexes, called the Incidence Simplicial (IS) data structure, which is scalable to manifold complexes, and supports efficient navigation and topological modifications. The IS data structure has the same expressive power and exibits performances in query and update operations as the incidence graph, a widely-used representation for general cell complexes, but it is much more compact. Here, we describe the IS data structure and we evaluate its storage cost. Moreover, we present efficient algorithms for navigating and for generating a simplicial complex described as an IS data structure. We compare the IS data structure with the incidence graph and with dimension-specific representations for simplicial complexes.",
author = "{De Floriani}, Leila and Annie Hui and Daniele Panozzo and David Canino",
year = "2010",
doi = "10.1007/978-3-642-15414-0_24",
language = "English (US)",
isbn = "9783642154133",
pages = "403--420",
booktitle = "Proceedings of the 19th International Meshing Roundtable, IMR 2010",

}

TY - GEN

T1 - A dimension-independent data structure for simplicial complexes

AU - De Floriani, Leila

AU - Hui, Annie

AU - Panozzo, Daniele

AU - Canino, David

PY - 2010

Y1 - 2010

N2 - We consider here the problem of representing non-manifold shapes discretized as d-dimensional simplicial Euclidean complexes. To this aim, we propose a dimension-independent data structure for simplicial complexes, called the Incidence Simplicial (IS) data structure, which is scalable to manifold complexes, and supports efficient navigation and topological modifications. The IS data structure has the same expressive power and exibits performances in query and update operations as the incidence graph, a widely-used representation for general cell complexes, but it is much more compact. Here, we describe the IS data structure and we evaluate its storage cost. Moreover, we present efficient algorithms for navigating and for generating a simplicial complex described as an IS data structure. We compare the IS data structure with the incidence graph and with dimension-specific representations for simplicial complexes.

AB - We consider here the problem of representing non-manifold shapes discretized as d-dimensional simplicial Euclidean complexes. To this aim, we propose a dimension-independent data structure for simplicial complexes, called the Incidence Simplicial (IS) data structure, which is scalable to manifold complexes, and supports efficient navigation and topological modifications. The IS data structure has the same expressive power and exibits performances in query and update operations as the incidence graph, a widely-used representation for general cell complexes, but it is much more compact. Here, we describe the IS data structure and we evaluate its storage cost. Moreover, we present efficient algorithms for navigating and for generating a simplicial complex described as an IS data structure. We compare the IS data structure with the incidence graph and with dimension-specific representations for simplicial complexes.

UR - http://www.scopus.com/inward/record.url?scp=79957790316&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79957790316&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-15414-0_24

DO - 10.1007/978-3-642-15414-0_24

M3 - Conference contribution

AN - SCOPUS:79957790316

SN - 9783642154133

SP - 403

EP - 420

BT - Proceedings of the 19th International Meshing Roundtable, IMR 2010

ER -