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2006•Unpublished venueRequires access

A Method for Rational Approximation of Offset Curves

Qingwei Guo

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Abstract

The rational approximation of offset curve of Bezier curve is obtained when a polynomial is used to approximate the norm of parametric speed of Bezier curve.The obtained rational curve and the offset curve of Bezier curve have the same higher derivates at the endpoints.If the method is combined with the subdivision method of curve,the rational spline curve with higher-order continuity is presented which is the approximation of offset curve.Numerical examples are given to show effectiveness of the method.The results are compared with other methods,and conclusions are made based on the numerical examples.

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What this paper is about

The rational approximation of offset curve of Bezier curve is obtained when a polynomial is used to approximate the norm of parametric speed of Bezier curve.The obtained rational curve and the offset curve of Bezier curve have the same higher derivates at the endpoints.If the method is combined with the subdivision method of curve,the rational spline curve with higher-order continuity is presented which is the approximation of offset curve.Numerical examples are given to show effectiveness of the method.The results are compared with other methods,and conclusions are made based on the numerical examples.

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Available abstract

The rational approximation of offset curve of Bezier curve is obtained when a polynomial is used to approximate the norm of parametric speed of Bezier curve.The obtained rational curve and the offset curve of Bezier curve have the same higher derivates at the endpoints.If the method is combined with the subdivision method of curve,the rational spline curve with higher-order continuity is presented which is the approximation of offset curve.Numerical examples are given to show effectiveness of the method.The results are compared with other methods,and conclusions are made based on the numerical examples.

Key concepts: Bézier curve, Mathematics, Parametric equation, Curve fitting, Offset (computer science), Polynomial and rational function modeling, Applied mathematics, Stable curve

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