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Workshop on Algorithms and Data Structures

WADS 1993: Algorithms and Data Structures pp 210–221Cite as

Filling polyhedral molds

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 709))

Abstract

In the manufacturing industry, finding an orientation for a mold that eliminates surface defects and insures a complete fill after termination of the injection process is an important problem. We study the problem of determining a favorable position of a mold (modeled as a polyhedron), such that when it is filled, no air bubbles and ensuing surface defects arise. Given a polyhedron in a fixed orientation, we present a linear time algorithm that determines whether the mold can be filled from that orientation without forming air bubbles. We also present an algorithm that determines the most favorable orientation for a polyhedral mold in O(n 2) time. A reduction from a well-known problem indicates that improving the O(n 2) bound is unlikely for general polyhedral molds. But we give an improved algorithm for molds that satisfy a local regularity condition that runs in time O(nk log2 n log log(n/k)), where k is the number of local maxima. Finally, we relate fillability to certain known classes of polyhedra.

Research supported in part by NSERC PGSB scholarship, an NSERC international fellowship, and NSERC-OGP0009293 and FCAR-93ER0291.

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Author information

Authors and Affiliations

  1. School of Computer Science, McGill University, 3480 University St., H3A 2A7, Montréal, Québec, Canada

    Prosenjit Bose, Marc van Kreveld & Godfried Toussaint

Authors
  1. Prosenjit Bose
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  2. Marc van Kreveld
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  3. Godfried Toussaint
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Editor information

Frank Dehne Jörg-Rüdiger Sack Nicola Santoro Sue Whitesides

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© 1993 Springer-Verlag Berlin Heidelberg

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Bose, P., van Kreveld, M., Toussaint, G. (1993). Filling polyhedral molds. In: Dehne, F., Sack, JR., Santoro, N., Whitesides, S. (eds) Algorithms and Data Structures. WADS 1993. Lecture Notes in Computer Science, vol 709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57155-8_249

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  • DOI: https://doi.org/10.1007/3-540-57155-8_249

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57155-1

  • Online ISBN: 978-3-540-47918-5

  • eBook Packages: Springer Book Archive

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