Smooth polynomial approximation of spiral arcs

Robert Cripps, MZ Hussain, S Zhu

Research output: Contribution to journalArticle

10 Citations (Scopus)


Constructing fair curve segments using parametric polynomials is difficult due to the oscillatory nature of polynomials. Even NURBS curves can exhibit unsatisfactory curvature profiles. Curve segments with monotonic curvature profiles, for example spiral arcs, exist but are intrinsically non-polynomial in nature and thus difficult to integrate into existing CAD systems. A method of constructing an approximation to a generalised Cornu spiral (GCS) arc using non-rational quintic Bezier curves matching end points, end slopes and end curvatures is presented. By defining an objective function based on the relative error between the curvature profiles of the GCS and its Bezier approximation, a curve segment is constructed that has a monotonic curvature profile within a specified tolerance. (C) 2009 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)2227-2234
JournalJournal of Computational and Applied Mathematics
Issue number9
Publication statusPublished - 9 Oct 2009


  • Quintic Bezier
  • Generalised cornu spiral
  • Approximation
  • Curvature profile


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