Article thumbnail

Smooth polynomial approximation of spiral arcs

By R.J. Cripps, M.Z. Hussain and S. Zhu


AbstractConstructing 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 Bézier 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 Bézier approximation, a curve segment is constructed that has a monotonic curvature profile within a specified tolerance

Publisher: Elsevier B.V.
Year: 2010
DOI identifier: 10.1016/
OAI identifier:

Suggested articles

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.