TY - GEN

T1 - Filling polyhedral molds

AU - Bose, Prosenjit

AU - Van Kreveld, Marc

AU - Toussaint, Godfried

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1993.

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

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U2 - 10.1007/3-540-57155-8_249

DO - 10.1007/3-540-57155-8_249

M3 - Conference contribution

AN - SCOPUS:84934376409

SN - 9783540571551

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 210

EP - 221

BT - Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings

A2 - Dehne, Frank

A2 - Sack, Jorg-Rudiger

A2 - Santoro, Nicola

A2 - Whitesides, Sue

PB - Springer Verlag

T2 - 3rd Workshop on Algorithms and Data Structures, WADS 1993

Y2 - 11 August 1993 through 13 August 1993

ER -