Developable rational Bézier and B-spline surfaces

Helmut Pottmann, Gerald Farin

Research output: Contribution to journalArticle

92 Scopus citations

Abstract

A constructive geometric approach to developable rational Bézier and B-spline surfaces is presented. It is based on the dual representation in the sense of projective geometry. By the principle of duality, projective algorithms for NURBS curves can be transferred to constructions for developable NURBS surfaces in dual rational B-spline form. We discuss the conversion to the usual tensor product representation of the obtained surfaces and develop algorithms for basic design problems arising in this context.

Original languageEnglish (US)
Pages (from-to)513-531
Number of pages19
JournalComputer Aided Geometric Design
Volume12
Issue number5
DOIs
StatePublished - Aug 1995

Keywords

  • Developable surface
  • Dual Bézier curve
  • NURBS
  • Principle of duality
  • Rational Bézier representation
  • projective geometry

ASJC Scopus subject areas

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

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