2014•Journal of Hefei University of TechnologyRequires access
An extension of Bézier curve and its application
Guo Qing-we
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Abstract
A class of blending function of degree n+1(n≥2)with shape parameterλis presented in this paper.Based on the blending function,a method of generating piecewise polynomial curves with a shape parameter is given.The properties of the curves and the blending functions are analyzed,and the condition of G2 continuity of extension curve is discussed.It is found that with the control polygon of the constructed curve unchanged,the shape of curve can be adjusted by changing the shape parameter value.With the increase of the shape parameter value,the Bezier curves with shape parameter approximate to the control polygon.With the elevation of the degree of curve,the feasible range of the shape parameter value will be extended.Examples illustrate that this method of constructing curves and surfaces is useful in CAGD.