On some geometric optimization problems in layered manufacturing

  • Jayanth Majhi
  • Ravi Janardan
  • Michiel Smid
  • Prosenjit Gupta
Session 5A: Invited Lecture
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1272)


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.


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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Jayanth Majhi
    • 1
  • Ravi Janardan
    • 1
  • Michiel Smid
    • 2
  • Prosenjit Gupta
    • 3
  1. 1.Dept. of Computer ScienceUniv. of MinnesotaMinneapolisUSA
  2. 2.Fakultät für InformatikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany
  3. 3.Bell LaboratoriesMurray HillUSA

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