Session 5A: Invited Lecture

Algorithms and Data Structures

Volume 1272 of the series Lecture Notes in Computer Science pp 136-149


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, Otto-von-Guericke-Universität Magdeburg
  • , Prosenjit GuptaAffiliated withBell Laboratories

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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.