{"title":"Arc Length of Rational Bezier Curves and Use for CAD Reparametrization","authors":"Maharavo Randrianarivony","country":null,"institution":"","volume":20,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":608,"pagesEnd":614,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/15282","abstract":"The length \u0003 of a given rational B'ezier curve is\r\nefficiently estimated. Since a rational B'ezier function is nonlinear,\r\nit is usually impossible to evaluate its length exactly. The\r\nlength is approximated by using subdivision and the accuracy\r\nof the approximation \u0003n is investigated. In order to improve\r\nthe efficiency, adaptivity is used with some length estimator.\r\nA rigorous theoretical analysis of the rate of convergence of\r\n\u0003n to \u0003 is given. The required number of subdivisions to\r\nattain a prescribed accuracy is also analyzed. An application\r\nto CAD parametrization is briefly described. Numerical results\r\nare reported to supplement the theory.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 20, 2008"}