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Computing 3D Periodic Triangulations

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Algorithms - ESA 2009 (ESA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5757))

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Abstract

This work is motivated by the need for software computing 3D periodic triangulations in numerous domains including astronomy, material engineering, biomedical computing, fluid dynamics etc. We design an algorithmic test to check whether a partition of the 3D flat torus into tetrahedra forms a triangulation (which subsumes that it is a simplicial complex). We propose an incremental algorithm that computes the Delaunay triangulation of a set of points in the 3D flat torus without duplicating any point, whenever possible; our algorithmic test detects when such a duplication can be avoided, which is usually possible in practical situations. Even in cases where point duplication is necessary, our algorithm always computes a triangulation that is homeomorpic to the flat torus. To the best of our knowledge, this is the first algorithm of this kind whose output is provably correct. The implementation will be released in Cgal[7].

This work was partially supported by the ANR (Agence Nationale de la Recherche) under the “Triangles” project of the Programme blanc (No BLAN07-2_194137) http://www-sop.inria.fr/geometrica/collaborations/triangles/ .

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Author information

Authors and Affiliations

  1. INRIA Sophia Antipolis – Méditerranée, France

    Manuel Caroli & Monique Teillaud

Authors
  1. Manuel Caroli
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  2. Monique Teillaud
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Editor information

Editors and Affiliations

  1. School of Computer Science, Tel Aviv University, Tel Aviv, Israel

    Amos Fiat

  2. Fakultät für Informatik, Universität Karlsruhe (TH), Am Fasanengarten 5, 76131, Karlsruhe, Germany

    Peter Sanders

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Caroli, M., Teillaud, M. (2009). Computing 3D Periodic Triangulations. In: Fiat, A., Sanders, P. (eds) Algorithms - ESA 2009. ESA 2009. Lecture Notes in Computer Science, vol 5757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04128-0_6

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  • DOI: https://doi.org/10.1007/978-3-642-04128-0_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04127-3

  • Online ISBN: 978-3-642-04128-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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