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An Algorithm for Polytope Overlapping Detection

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Computational Science and Its Applications – ICCSA 2021 (ICCSA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12949))

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Abstract

The intersection of polytopes is a basic problem of computational geometry with many engineering applications. Intersections of simplices or parallelotopes have been widely used in finite element grid generations. This paper is devoted to an algorithm for detecting overlapping polytopes. We present a new iterative algorithm, which is independent of the dimension of the Euclidean space. The main idea is triangulating the tested polytopes by simplicial finite elements and then investigating couples of potential simplices for an intersection. For that purpose, a method for overlapping detection of arbitrary simplices in \(\mathbf{R}^n\) is developed. A detailed description of the pseudocode of the original algorithm is presented. The advantages of the proposed method are demonstrated in the twelve-dimensional case.

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Author information

Authors and Affiliations

  1. Department of Technical Mechanics, Technical University, 5300, Gabrovo, Bulgaria

    Miroslav S. Petrov

  2. Department of Mathematics, Informatics and Natural Sciences, Technical University, 5300, Gabrovo, Bulgaria

    Todor D. Todorov

Authors
  1. Miroslav S. Petrov
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  2. Todor D. Todorov
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Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Cagliari, Cagliari, Italy

    Ivan Blečić

  6. Monash University, Clayton, VIC, Australia

    David Taniar

  7. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  8. University of Minho, Braga, Portugal

    Ana Maria A. C. Rocha

  9. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

  10. Polytechnic University of Bari, Bari, Italy

    Carmelo Maria Torre

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Petrov, M.S., Todorov, T.D. (2021). An Algorithm for Polytope Overlapping Detection. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science(), vol 12949. Springer, Cham. https://doi.org/10.1007/978-3-030-86653-2_2

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  • DOI: https://doi.org/10.1007/978-3-030-86653-2_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86652-5

  • Online ISBN: 978-3-030-86653-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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