Swept Volumes

Martin Peternell, Helmut Pottmann, Tibor Steiner, Hongkai Zhao

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


Given a solid S ⊂ R3 with a piecewise smooth boundary, we compute an approximation of the boundary surface of the volume which is swept by S under a smooth one-parameter motion. Using knowledge from kinematical and elementary differential geometry, the algorithm computes a set of points plus surface normals from the envelope surface. A study of the evolution speed of the so called characteristic set along the envelope is used to achieve a prescribed sampling density. With a marching algorithm in a grid, the part of the envelope which lies on the boundary of the swept volume is extracted. The final boundary representation of the swept volume is either a triangle mesh, a B-spline surface or a point-set surface.

Original languageEnglish (US)
Pages (from-to)599-608
Number of pages10
JournalComputer-Aided Design and Applications
Issue number5
StatePublished - 2005
Externally publishedYes


  • Envelope
  • Marching algorithm
  • Motion
  • NC verification
  • Point-set surface
  • Swept volume

ASJC Scopus subject areas

  • Computational Mechanics
  • Computer Graphics and Computer-Aided Design
  • Computational Mathematics


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