### 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 log^{2}n log log(n/k)), where k is the number of local maxima. Finally, we relate fillability to certain known classes of polyhedral.

Original language | English (US) |
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Title of host publication | Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings |

Editors | Frank Dehne, Jorg-Rudiger Sack, Nicola Santoro, Sue Whitesides |

Publisher | Springer Verlag |

Pages | 210-221 |

Number of pages | 12 |

ISBN (Print) | 9783540571551 |

DOIs | |

State | Published - 1993 |

Event | 3rd Workshop on Algorithms and Data Structures, WADS 1993 - Montreal, Canada Duration: Aug 11 1993 → Aug 13 1993 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 709 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd Workshop on Algorithms and Data Structures, WADS 1993 |
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Country | Canada |

City | Montreal |

Period | 8/11/93 → 8/13/93 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

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