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On Computing All Immobilizing Grasps of a Simple Polygon with Few Contacts

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Algorithms and Computation (ISAAC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2906))

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Abstract

We study the output-sensitive computation of all combinations of edges and vertices of a simple polygon P that allow a form-closure grasp with less than four point contacts. We present an O(m 4/3log1/3 m + K)-time algorithm to compute all form-closure grasps using two frictionless point contacts, and an O(n 2logO(1) n + K)-time algorithm to compute all such grasps with three point contacts. Here, n is the number of edges and m is the number of concave vertices of P. We also present an O(n 2log4 n + K)-time algorithm that enumerates all edge triples with a second-order immobility grasp using Czyzowicz’s conditions.

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Authors and Affiliations

  1. Institute of Information and Computing Sciences, Utrecht University, P.O.Box 80.089, 3508 TB, Utrecht, The Netherlands

    Jae-Sook Cheong, Herman J. Haverkort & A. Frank van der Stappen

Authors
  1. Jae-Sook Cheong
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  2. Herman J. Haverkort
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  3. A. Frank van der Stappen
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Editor information

Editors and Affiliations

  1. School of Science and Technology, Kwansei Gakuin University, Sanda, Japan

    Toshihide Ibaraki

  2. Department of Architecture and Architectural Engineering, Kyoto University, 615-8540, Nishikyo-ku, Kyoto, Japan

    Naoki Katoh

  3. Department of Computer Science and Communication Engineering, Kyushu University, 812-8581, Fukuoka, Japan

    Hirotaka Ono

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© 2003 Springer-Verlag Berlin Heidelberg

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Cheong, JS., Haverkort, H.J., van der Stappen, A.F. (2003). On Computing All Immobilizing Grasps of a Simple Polygon with Few Contacts. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_28

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  • DOI: https://doi.org/10.1007/978-3-540-24587-2_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20695-8

  • Online ISBN: 978-3-540-24587-2

  • eBook Packages: Springer Book Archive

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