Analysis and applications of pipe surfaces

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

Research output: Contribution to journalArticle

51 Citations (Scopus)

Abstract

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
Volume15
Issue number5
DOIs
Publication statusPublished - 1998 Jan 1
Externally publishedYes

Fingerprint

Rational functions
Pipe
Rational function
Nonsingularity
Parametrization
Envelope
Radius
Necessary Conditions
Sufficient Conditions
Family

Keywords

  • 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

Cite this

Analysis and applications of pipe surfaces. / Maekawa, Takashi; Patrikalakis, Nicholas M.; Sakkalis, Takis; Yu, Guoxin.

In: Computer Aided Geometric Design, Vol. 15, No. 5, 01.01.1998, p. 437-458.

Research output: Contribution to journalArticle

Maekawa, Takashi ; Patrikalakis, Nicholas M. ; Sakkalis, Takis ; Yu, Guoxin. / Analysis and applications of pipe surfaces. In: Computer Aided Geometric Design. 1998 ; Vol. 15, No. 5. pp. 437-458.
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