Reduced-order shape optimization using offset surfaces

Przemyslaw Musialski, Thomas Auzinger, Michael Birsak, Michael Wimmer, Leif Kobbelty

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

63 Scopus citations

Abstract

Given the 2-manifold surface of a 3d object, we propose a novel method for the computation of an offset surface with varying thickness such that the solid volume between the surface and its offset satisfies a set of prescribed constraints and at the same time minimizes a given objective functional. Since the constraints as well as the objective functional can easily be adjusted to specific application requirements, our method provides a flexible and powerful tool for shape optimization. We use manifold harmonics to derive a reduced-order formulation of the optimization problem, which guarantees a smooth offset surface and speeds up the computation independently from the input mesh resolution without affecting the quality of the result. The constrained optimization problem can be solved in a numerically robust manner with commodity solvers. Furthermore, the method allows simultaneously optimizing an inner and an outer offset in order to increase the degrees of freedom. We demonstrate our method in a number of examples where we control the physical mass properties of rigid objects for the purpose of 3d printing. Copyright is held by the owner/author(s).

Original languageEnglish (US)
Title of host publicationProceedings of ACM SIGGRAPH 2015
PublisherAssociation for Computing Machinery
Volume34
Edition4
ISBN (Electronic)9781450333313
DOIs
StatePublished - Jul 27 2015
Externally publishedYes
EventACM Special Interest Group on Computer Graphics and Interactive Techniques Conference, SIGGRAPH 2015 - Los Angeles, United States
Duration: Aug 9 2015Aug 13 2015

Conference

ConferenceACM Special Interest Group on Computer Graphics and Interactive Techniques Conference, SIGGRAPH 2015
Country/TerritoryUnited States
CityLos Angeles
Period8/9/158/13/15

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design

Keywords

  • Digital fabrication
  • Geometric design optimization
  • Geometry processing
  • Physical mass properties
  • Reduced-order models
  • Shape optimization

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