Constructing an n-dimensional cell complex from a soup of (N − 1)-dimensional faces

Ken Arroyo Ohori, Guillaume Damiand, Hugo Ledoux

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

4 Citations (Scopus)

Abstract

There is substantial value in the use of higher-dimensional (>3D) digital objects in GIS that are built from complex real-world data. This use is however hampered by the difficulty of constructing such objects. In this paper, we present a dimension independent algorithm to build an n-dimensional cellular complex with linear geometries from its isolated (n − 1)-dimensional faces represented as combinatorial maps. It does so by efficiently finding the common (n − 2)-cells (ridges) along which they need to be linked. This process can then be iteratively applied in increasing dimension to construct objects of any dimension. We briefly describe combinatorial maps, present our algorithm using them as a base, and show an example using 2D, 3D and 4D objects which was verified to be correct, both manually and using automated methods.

Original languageEnglish
Title of host publicationApplied Algorithms
Subtitle of host publicationFirst International Conference, ICAA 2014, Kolkata, India, January 13-15, 2014. Proceedings
EditorsP. Gupta, C. Zaroliagis
Place of PublicationSwitzerland
PublisherSpringer
Pages37-48
Number of pages12
Volume8321
ISBN (Electronic)978-3-319-04126-1
ISBN (Print)978-3-319-04125-4
DOIs
Publication statusPublished - 2014
Event1st International Conference on Applied Algorithms, ICAA 2014 - Kolkata, India
Duration: 13 Jan 201415 Jan 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8321
ISSN (Print)03029743
ISSN (Electronic)16113349

Conference

Conference1st International Conference on Applied Algorithms, ICAA 2014
CountryIndia
CityKolkata
Period13/01/1415/01/14

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    Arroyo Ohori, K., Damiand, G., & Ledoux, H. (2014). Constructing an n-dimensional cell complex from a soup of (N − 1)-dimensional faces. In P. Gupta, & C. Zaroliagis (Eds.), Applied Algorithms: First International Conference, ICAA 2014, Kolkata, India, January 13-15, 2014. Proceedings (Vol. 8321, pp. 37-48). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8321). Springer. https://doi.org/10.1007/978-3-319-04126-1_4, https://doi.org/10.1007/978-3-319-04126-1_4