Developable rational Bézier and B-spline surfaces

Helmut Pottmann, Gerald Farin

Research output: Contribution to journalArticle

86 Citations (Scopus)

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 - 1995

Fingerprint

Rational Spline
B-spline Surface
Splines
Developable Surface
NURBS Surface
NURBS
Projective geometry
Geometric Approach
B-spline
Tensor Product
Duality
Curve
Tensors
Geometry
Context
Design
Form

Keywords

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

ASJC Scopus subject areas

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

Cite this

Developable rational Bézier and B-spline surfaces. / Pottmann, Helmut; Farin, Gerald.

In: Computer Aided Geometric Design, Vol. 12, No. 5, 1995, p. 513-531.

Research output: Contribution to journalArticle

Pottmann, Helmut ; Farin, Gerald. / Developable rational Bézier and B-spline surfaces. In: Computer Aided Geometric Design. 1995 ; Vol. 12, No. 5. pp. 513-531.
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