On the derivatives of rational B\'ezier curves
Abstract
By studying the existing higher order derivation formulas of rational B\'ezier curves, we find that they fail when the order of the derivative exceeds the degree of the curves. In this paper, we present a new derivation formula for rational B\'ezier curves that overcomes this drawback and show that the kth degree derivative of a nth degree rational B\'ezier curve can be written in terms of a (2kn)th degree rational B\'ezier curve.we also consider the properties of the endpoints and the bounds of the derivatives.
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