On some geometric optimization problems in layered manufacturing

Jayanth Majhi, Ravi Janardan, Michiel Smid, Prosenjit Gupta

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

14 Scopus citations

Abstract

Efficient geometric algorithms are given for optimization problems arising in layered manufacturing, where a 3D object is built by slicing its CAD model into layers and manufacturing the layers successively. The problems considered include minimizing the degree of stair-stepping on the surfaces of the manufactured object, minimizing the volume of the so-called support structures used, and minimizing the contact area between the supports and the manufactured object-all of which are factors that affect the speed and accuracy of the process. The stair-step minimization algorithm is valid for any polyhedron, while the support minimization algorithms are applicable to convex polyhedra only. Algorithms are also given for optimizing supports for non-convex, simple polygons. The techniques used include construction and searching of certain arrangements on the sphere, 3D convex hulls, halfplane range searching, ray-shooting, visibility, and constrained optimization.

Original languageEnglish (US)
Title of host publicationAlgorithms and Data Structures - 5th International Workshop, WADS 1997, Proceedings
EditorsFrank Dehne, Jorg-Rudiger Sack, Andrew Rau-Chaplin, Roberto Tamassia
PublisherSpringer Verlag
Pages136-149
Number of pages14
ISBN (Print)3540633073, 9783540633075
DOIs
StatePublished - 1997
Event5th International Workshop on Algorithms and Data Structures, WADS 1997 - Halifax, Canada
Duration: Aug 6 1997Aug 8 1997

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1272
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other5th International Workshop on Algorithms and Data Structures, WADS 1997
Country/TerritoryCanada
CityHalifax
Period8/6/978/8/97

Bibliographical note

Funding Information:
I Portions of this work appear in preliminary form in [17]. The results in this paper, and in a companion paper [18], extend upon and improve the results in [17]. ∗Corresponding author. E-mail: michiel@isg.cs.uni-magdeburg.de 1E-mail: jayanth_majhi@mentorg.com. This work was done while the author was at the Department of Computer Science & Engineering at the University of Minnesota. Research supported in part by a Grant-in-Aid of Research from the Graduate School of the University of Minnesota and by NSF grant CCR-9712226. 2 E-mail: janardan@cs.umn.edu. Research supported in part by a Grant-in-Aid of Research from the Graduate School of the University of Minnesota and by NSF grant CCR-9712226. 3Part of this work was done while the author was at the Department of Computer Science, King’s College, London, UK. 4E-mail: pgupta@delsoft.com. Part of this work was done while the author was at the Max-Planck-Institut für Informatik, Saarbrücken, Germany, and at the Department of Computer Science & Engineering at the University of Minnesota.

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1997.

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