Filling polyhedral molds

Prosenjit Bose, Marc Van Kreveld, Godfried Toussaint

    Research output: Contribution to journalArticle

    Abstract

    In manufacturing industry, finding an orientation for a mold that eliminates surface defects and ensures a complete fill after termination of the gravity casting process is an important and difficult 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 pockets 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 pockets. 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. We relate fillability to some well known classes of polyhedra. For some of these classes of objects, an optimal direction of fillability can be determined in linear time. Finally, for molds that satisfy a local regularity condition, we give an improved algorithm that runs in time O(nklog2 nlog log(n/k)), where k is the number of venting holes needed to avoid air pockets in an optimal orientation.

    Original languageEnglish (US)
    Pages (from-to)245-254
    Number of pages10
    JournalCAD Computer Aided Design
    Volume30
    Issue number4
    DOIs
    StatePublished - Jan 1 1998

    Fingerprint

    Molds
    Surface defects
    Air
    Gravitation
    Casting
    Industry

    Keywords

    • Algorithms
    • Casting
    • Computational geometry
    • Filling
    • Polyhedral molds

    ASJC Scopus subject areas

    • Computer Science Applications
    • Computer Graphics and Computer-Aided Design
    • Industrial and Manufacturing Engineering

    Cite this

    Bose, P., Van Kreveld, M., & Toussaint, G. (1998). Filling polyhedral molds. CAD Computer Aided Design, 30(4), 245-254. https://doi.org/10.1016/S0010-4485(97)00075-4

    Filling polyhedral molds. / Bose, Prosenjit; Van Kreveld, Marc; Toussaint, Godfried.

    In: CAD Computer Aided Design, Vol. 30, No. 4, 01.01.1998, p. 245-254.

    Research output: Contribution to journalArticle

    Bose, P, Van Kreveld, M & Toussaint, G 1998, 'Filling polyhedral molds', CAD Computer Aided Design, vol. 30, no. 4, pp. 245-254. https://doi.org/10.1016/S0010-4485(97)00075-4
    Bose P, Van Kreveld M, Toussaint G. Filling polyhedral molds. CAD Computer Aided Design. 1998 Jan 1;30(4):245-254. https://doi.org/10.1016/S0010-4485(97)00075-4
    Bose, Prosenjit ; Van Kreveld, Marc ; Toussaint, Godfried. / Filling polyhedral molds. In: CAD Computer Aided Design. 1998 ; Vol. 30, No. 4. pp. 245-254.
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