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On the complexity of the union of geometric objects

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Discrete and Computational Geometry (JCDCG 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2098))

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Abstract

Giben a family C of regions bounded by simple closed curves in the plane, the complexity of their union is defined as the number of points along the boundary ∪C, which belong to more than one curve. Similarly, one can define the complexity of the union of 3-dimensional bodies, as the number of points on the boundary of the union, belonging to the surfaces of at least three distinct members of the family. We survey some upper bounds on the complexity of the union of n geometric objects satisfying various natural conditions. These problems play a central role in the design and analysis of many geometric algorithms arising in motion planning and computer graphics.

Supported by the National Science Foundation (USA) and the National Fund for Scientific Research (Hungary).

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Author information

Authors and Affiliations

  1. Courant Institute, New York University and Hungarian Academy of Sciences, USA

    János Pach

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  1. János Pach
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Editors and Affiliations

  1. Research Institute of Educational Development, Tokai University, 2-28-4 Tomigaya, Shibuya-ku, Tokyo, 151-0063, Japan

    Jin Akiyama

  2. Department of Computer and Information Sciences, Ibaraki University, Hitachi, 316-8511, Japan

    Mikio Kano

  3. Department of Mathematics, Tokai University, 3-20-1 Orido Shimizu-shi, Shizuoka, 424-8610, Japan

    Masatsugu Urabe

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© 2001 Springer-Verlag Berlin Heidelberg

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Pach, J. (2001). On the complexity of the union of geometric objects. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol 2098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47738-1_28

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  • DOI: https://doi.org/10.1007/3-540-47738-1_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42306-5

  • Online ISBN: 978-3-540-47738-9

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