Title: Approximate implicitization of planar parametric curves by using quadratic algebraic splines
Abstract: Parametric curves/surfaces and implicit curves/surfaces are two important topics in Computer Aided Geometry Design and Geometric Modeling.The procedure of converting parametric form into implicit form is called exact implicitization.For a general parametric curve/surface,we usually cannot compute its exact implicit form.Even though its exact implicit form can be computed,the curve/surface implicitization involves relatively complicated computation and the degree is higher.Moreover,it may have unexpected components and self-intersections.All these unsatisfied properties limit the applications of the exact implicitization.So finding curve/surface approximate implicitization has become a practical problem.In this paper,we present an algorithm to solve the approximate implicitization of a given parametric curve by using a quadratic algebraic spline curve.The constructed algebraic spline curve not only possesses unwanted components and unexpected singular points but also satisfies C2 con-tinuity.The proposed algorithm is implemented and numerical results show its efficiency.
Publication Year: 2010
Publication Date: 2010-01-01
Language: en
Type: article
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