Computing the Minkowski sum of ruled surfaces

Heidrun Mühlthaler, Helmut Pottmann*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


The boundary of the Minkowski sum of two geometric objects is part of the so-called convolution surface of the boundary surfaces of the two input objects. In most cases, convolution surfaces can be computed only by numerical algorithms. The present paper studies convolution surfaces of ruled surfaces. There, explicit parameterizations for the convolution surface can be derived. Moreover, we study the rational convolution surface of two rational ruled surfaces and the connection to rational parameterizations of offsets of rational ruled surfaces.

Original languageEnglish (US)
Pages (from-to)369-384
Number of pages16
JournalGraphical Models
Issue number6
StatePublished - Nov 2003
Externally publishedYes


  • Convolution surface
  • General offset
  • Minkowski sum
  • Offset surface
  • Rational parameterization
  • Ruled surface

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Geometry and Topology
  • Computer Graphics and Computer-Aided Design


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