On the computational geometry of ruled surfaces

Martin Peternell, Helmut Pottmann, Bahram Ravani

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


This article presents a brief introduction to the classical geometry of ruled surfaces with emphasis on the Klein image and studies aspects which arise in connection with a computational treatment of these surfaces. As ruled surfaces are one parameter families of lines, one can apply curve theory and algorithms to the Klein image, when handling these surfaces. We study representations of rational ruled surfaces and get efficient algorithms for computation of planar intersections and contour outlines. Further, low degree boundary curves, useful for tensor product representations, are studied and illustrated at hand of several examples. Finally, we show how to compute efficiently low degree rational G1 ruled surfaces.

Original languageEnglish (US)
Pages (from-to)17-32
Number of pages16
JournalCAD Computer Aided Design
Issue number1
StatePublished - Jan 1 1999

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering


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