The conversion of a dynamic B-spline curve into piecewise polynomials in power form

Abstract

The evaluation of points and the computations of inflection points or cusps on a curve are often necessary in CAGD applications. When a curve is represented in a B-spline form, such computations can be made easier once it is transformed into a set of piecewise polynomial curves in power form. The usual practice of the transformation of a B-spline curve into a set of piecewise polynomial curves in power form is done either by a knot refinement followed by basis conversions, or by applying a Taylor expansion on each knot span of a B-spline curve. Presented in this paper is a new algorithm to convert a B-spline curve into a set of piecewise polynomial curves in power form. Experiment shows that the proposed algorithm significantly outperforms the conventional approach when one or more control points of a B-spline curve are continuously moving.