Approximate Implicitization of Parametric Curves Using Cubic Algebraic Splines
نویسندگان
چکیده
منابع مشابه
Approximate Implicitization of Parametric Curves Using Cubic Algebraic Splines
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 G2 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...
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A quadratic Bézier spline with G-continuity is given to approximate a planar parametric curve. In its construction, the parametric curve is first divided into several segments. A rational quadratic Bézier curve is then applied to approximate each segment and recursive subdivision for the segment may be used if the approximation error is out of the given range. With this method, we not only keep...
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This paper presents an approach to nding an approximate implicit equation and an approximate inversion map of a planar rational parametric curve or a rational parametric surface. High accuracy of the approximation is achieved with a relatively small number of low-degree curve segments or surface patches. By using monoid curves and surfaces, the method eliminates the undesirable singularities an...
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In this paper we use Gröbner bases for the implicitization of rational parametric curves and surfaces in 3D-space. We prove that the implicit form of a curve or surface given by the rational parametrization x1 := p1 q1 x2 := p2 q2 x3 := p3 q3 , where the p’s and q’s are univariate polynomials in y1 or bivariate polynomials in y1, y2 over a field K, can always be found by computing GB({q1 · x1 −...
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ژورنال
عنوان ژورنال: Mathematical Problems in Engineering
سال: 2009
ISSN: 1024-123X,1563-5147
DOI: 10.1155/2009/327457