@inproceedings{8715cba2d5e843918db44a10e96e32fb,

title = "Filling polyhedral molds",

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.",

author = "Prosenjit Bose and {Van Kreveld}, Marc and Godfried Toussaint",

year = "1993",

doi = "10.1007/3-540-57155-8_249",

language = "English (US)",

isbn = "9783540571551",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "210--221",

editor = "Frank Dehne and Jorg-Rudiger Sack and Nicola Santoro and Sue Whitesides",

booktitle = "Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings",

note = "3rd Workshop on Algorithms and Data Structures, WADS 1993 ; Conference date: 11-08-1993 Through 13-08-1993",

}