Abstract
In this paper, we present a new approach to solve approximate implicitization of parametric curves. The basic idea is to divide the normal parametric curve into several curve segments at three types of critical points and then use multiquadric quasi-interpolation to approximate each curve segment. Meanwhile, we interpolate two endpoints of each segment using compactly supported radial basis functions in order to maintain the continuity of the adjacent curve segments. The resulting implicit curves possess certain shape preserving and good approximation behaviors.
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