Algorithms and Data Structures
Volume 1272 of the series Lecture Notes in Computer Science pp 136149
On some geometric optimization problems in layered manufacturing
 Jayanth MajhiAffiliated withDept. of Computer Science, Univ. of Minnesota
 , Ravi JanardanAffiliated withDept. of Computer Science, Univ. of Minnesota
 , Michiel SmidAffiliated withFakultät für Informatik, OttovonGuerickeUniversität Magdeburg
 , Prosenjit GuptaAffiliated withBell Laboratories
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 stairstepping on the surfaces of the manufactured object, minimizing the volume of the socalled support structures used, and minimizing the contact area between the supports and the manufactured objectall of which are factors that affect the speed and accuracy of the process. The stairstep 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 nonconvex, simple polygons. The techniques used include construction and searching of certain arrangements on the sphere, 3D convex hulls, halfplane range searching, rayshooting, visibility, and constrained optimization.
 Title
 On some geometric optimization problems in layered manufacturing
 Book Title
 Algorithms and Data Structures
 Book Subtitle
 5th International Workshop, WADS'97 Halifax, Nova Scotia, Canada August 6–8, 1997 Proceedings
 Pages
 pp 136149
 Copyright
 1997
 DOI
 10.1007/3540633073_54
 Print ISBN
 9783540633075
 Online ISBN
 9783540694229
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1272
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Jayanth Majhi ^{(1)}
 Ravi Janardan ^{(1)}
 Michiel Smid ^{(2)}
 Prosenjit Gupta ^{(3)}
 Author Affiliations

 1. Dept. of Computer Science, Univ. of Minnesota, 55455, Minneapolis, MN, USA
 2. Fakultät für Informatik, OttovonGuerickeUniversität Magdeburg, D39106, Magdeburg, Germany
 3. Bell Laboratories, 600 Mountain Avenue, 07974, Murray Hill, NJ, USA
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