Arc Length of Rational Bézier Curves and Use for CAD Reparametrization
نویسنده
چکیده
The length Λ of a given rational Bézier curve is efficiently estimated. Since a rational Bézier function is nonlinear, it is usually impossible to evaluate its length exactly. The length is approximated by using subdivision and the accuracy of the approximation Λn is investigated. In order to improve the efficiency, adaptivity is used with some length estimator. A rigorous theoretical analysis of the rate of convergence of Λn to Λ is given. The required number of subdivisions to attain a prescribed accuracy is also analyzed. An application to CAD parametrization is briefly described. Numerical results are reported to supplement the theory. Keywords—Adaptivity, Length, Parametrization, Rational Bézier.
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