Prescribing the length of rational Bézier curves

  • Roulier J
  • Piper B
  • 2


    Mendeley users who have this article in their library.
  • 7


    Citations of this article.


Theorems and corresponding algorithms are presented which produce a rational Bézier curve of a specified arc length subject to certain constraints. Extraneous inflection points are avoided. The problem is reduced to expressing the arc length as a function of a single variable. A general theorem from a previous paper of the authors is used which gives conditions under which the arc length function is convex or strictly convex. An algorithm to automatically choose the initial parameters for the secant method will produce a solution to this problem with performance comparable to the Newton-Raphson method. Theory and algorithms for rational parametric curves are presented. It is shown that in certain cases rational parametric curves of degree three can be used while polynomials of bounded degree cannot.

Author-supplied keywords

  • Arc length
  • Convex curve
  • Rational Bézier curve
  • Rational parametric curve

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


  • John A. Roulier

  • Bruce Piper

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free