Link between Bézier and Lagrange curve and surface schemes

Gerald Farin, Phillip J. Barry

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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
Issue number10
StatePublished - Dec 1986

Bibliographical note

Funding Information:
This research was supportedi n part by Departmento f Energy Contract No. DE-AC02-85ER12046,b y NSF Grant DCR-8502858, and by the CDC Sponsored Research Project 85U101 to The Universityo f Utah. The authors thank D Hansford for creating Figures 4 and 5, N Sapididis for providing the data for Figure 4, and R E Barnhill for many useful comments.


  • Bézier curves
  • Lagrange interpolation
  • geometry
  • mathematics


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