Shape parameter deletion for Pólya curves

Phillip J. Barry, Ronald N. Goldman

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


We present a simple change of basis technique for transforming one type of Pólya curve to another closely related Pólya curve form. Repeated use of this method yields algorithms for transforming one arbitrary Pólya form to another, as well as algorithms for evaluating, subdividing, and differentiating Pólya curves. These procedures can be applied to almost all Pólya curves, including Bézier curves and Lagrange interpolating polynomials.

Original languageEnglish (US)
Pages (from-to)121-137
Number of pages17
JournalNumerical Algorithms
Issue number2
StatePublished - Jun 1 1991


  • Ball's basis
  • Bézier curve
  • Lagrange interpolating polynomial
  • Newton basis
  • Pólya curve
  • Subject classification AMS: 41A10
  • differentiation
  • divided difference
  • evaluation
  • knot insertion
  • monomial basis
  • subdivision
  • transformations
  • variation diminishing property


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