2005•Journal of Engineering GraphicsRequires access

Extension of Cubic Bézier Curve

Xuli Han

Abstract

A class of polynomial weight function of containing an adjustable constant parameter λ is presented to convert classical cubic Bernstein basis function into a quartic one.Properties of this new basis are analyzed and a polynomial curve with a shape parameter is defined based on it.The curve inherits the most properties of cubic Bezier curve,and its shape can be adjusted through changing the value of λ when λ=0 the quartic curve degenerates to cubic curve.The G 2-continuity condition of two-piece of curves is also discussed.

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Key concepts: Quartic function, Cubic function, Mathematics, Bézier curve, Cubic form, Shape parameter, Function (biology), Extension (predicate logic)