Abstract
In geometric design, it is often required to improve the parametrization of a curve to an optimal one. In this paper, we develop a set of functions, called representation set, that represent a given B ezier curve. Then, the optimal-parametrization curve can be selected in the representation set. For a polynomial B ezier curve, its representation set is deduced by polynomial and rational reparameterization, respectively. For a rational B ezier curve, the representation set is calculated by a general degree elevation. Some important cases are presented to demonstrate the generation of the representation set geometrically. Moreover, we illustrate some examples which seek the optimal-parametrization curve from its representation set.
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