Link between Bézier and Lagrange curve and surface schemes

Gerald Farin, Phillip J. Barry

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

A class of curves that vary continuously between polynomial Lagrange interpolants and polynomial Bézier curves is discussed. An element in this class is specified by a real number which could be used as a shape parameter for Bézier curves. A geometric derivation of this scheme is given, and the connection to Pólya curves is pointed out. A generalization to the case of tensor product and triangular surface patches is also described.

Original languageEnglish (US)
Pages (from-to)525-528
Number of pages4
JournalComputer-Aided Design
Volume18
Issue number10
DOIs
StatePublished - 1986
Externally publishedYes

Fingerprint

Curves and Surfaces
Lagrange
Polynomials
Curve
Tensors
Lagrange's polynomial
Shape Parameter
Interpolants
Tensor Product
Patch
Triangular
Vary
Polynomial
Class

Keywords

  • Bézier curves
  • geometry
  • Lagrange interpolation
  • mathematics

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering
  • Geometry and Topology

Cite this

Link between Bézier and Lagrange curve and surface schemes. / Farin, Gerald; Barry, Phillip J.

In: Computer-Aided Design, Vol. 18, No. 10, 1986, p. 525-528.

Research output: Contribution to journalArticle

Farin, Gerald ; Barry, Phillip J. / Link between Bézier and Lagrange curve and surface schemes. In: Computer-Aided Design. 1986 ; Vol. 18, No. 10. pp. 525-528.
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