Filling polyhedral molds

Prosenjit Bose, Marc Van Kreveld, Godfried Toussaint

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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(n2) time. A reduction from a well-known problem indicates that improving the O(n2) 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 log2n log log(n/k)), where k is the number of local maxima. Finally, we relate fillability to certain known classes of polyhedral.

Original languageEnglish (US)
Title of host publicationAlgorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings
PublisherSpringer-Verlag
Pages210-221
Number of pages12
ISBN (Print)9783540571551
StatePublished - Jan 1 1993
Event3rd Workshop on Algorithms and Data Structures, WADS 1993 - Montreal, Canada
Duration: Aug 11 1993Aug 13 1993

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume709 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other3rd Workshop on Algorithms and Data Structures, WADS 1993
CountryCanada
CityMontreal
Period8/11/938/13/93

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Bose, P., Van Kreveld, M., & Toussaint, G. (1993). Filling polyhedral molds. In Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings (pp. 210-221). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 709 LNCS). Springer-Verlag.