Recursive polynomial curve schemes and computer-aided geometric design

Phillip Barry, Ronald N. Goldman

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


A class of polynomial curve schemes is introduced that may have widespread application to CAGD (computer-aided geometric design), and which contains many well-known curve schemes, including Bézier curves, Lagrange polynomials, B-spline curve (segments), and Catmull-Rom spline (segments). The curves in this class can be characterized by a simple recursion formula. They are also shown to have many properties desirable for CAGD; in particular they are affine invariant, have the convex hull property, and possess a recursive evaluation algorithm. Further, these curves have shape parameters which may be used as a design tool for introducing such geometric effects as tautness, bias, or interpolation. The link between probability theory and this class of curves is also discussed.

Original languageEnglish (US)
Pages (from-to)65-96
Number of pages32
JournalConstructive Approximation
Issue number1
StatePublished - Mar 1 1990


  • AMS classification: 41A10
  • B-spline
  • Bézier curve
  • Computer-aided geometric design
  • Lagrange polynomial
  • Probability distribution
  • Recursion
  • Recursive evaluation algorithm
  • Urn model


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