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Mathematical Problems in Engineering
Volume 2009, Article ID 327457, 12 pages
Research Article

Approximate Implicitization of Parametric Curves Using Cubic Algebraic Splines

College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

Received 25 February 2009; Revised 13 June 2009; Accepted 10 September 2009

Academic Editor: Alexander P. Seyranian

Copyright © 2009 Xiaolei Zhang and Jinming Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents an algorithm to solve the approximate implicitization of planar parametric curves using cubic algebraic splines. It applies piecewise cubic algebraic curves to give a global continuity approximation to planar parametric curves. Approximation error on approximate implicitization of rational curves is given. Several examples are provided to prove that the proposed method is flexible and efficient.