Analysis and applications of pipe surfaces

Takashi Maekawa*, Nicholas M. Patrikalakis, Takis Sakkalis, Guoxin Yu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

70 Citations (Scopus)


A pipe (or tubular) surface is the envelope of a one-parameter family of spheres with constant radii r and centers C(t). In this paper we investigate necessary and sufficient conditions for the nonsingularity of pipe surfaces. In addition, when C(t) is a rational function, we develop an algorithmic method for the rational parametrization of such a surface. The latter is based on finding two rational functions α(t) and β(t) such that |C′(t)|2 = α2(t) + β2(t) (Lü and Pottmann, 1996).

Original languageEnglish
Pages (from-to)437-458
Number of pages22
JournalComputer Aided Geometric Design
Issue number5
Publication statusPublished - 1998 May
Externally publishedYes


  • Global self-intersection
  • Local self-intersection
  • Pipe surface
  • Rational parametrization

ASJC Scopus subject areas

  • Modelling and Simulation
  • Automotive Engineering
  • Aerospace Engineering
  • Computer Graphics and Computer-Aided Design


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