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2008•Journal of Hefei University of TechnologyRequires access

Extension of the quartic Bèzier curve with parameters

Zhu Gong-qin

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Abstract

A class of 5-degree polynomial basis functions containing three shape control parameters λ,μ and ν is presented.It is the extension of quartic Bernstein basis functions.Properties of this new basis are analyzed and a polynomial curve with the three shape parameters λ、μ and ν is defined based on it.The curve not only inherits the outstanding properties of the quartic curve,but it is also adjustable in shape and fits close to the control polygon.The parameters have obvious geometric meaning.The classical quartic Bezier curve and the two classes of curves in related literature are especial examples of this paper.Some examples illustrate that the curve defined in this paper provides an effective method for designing curves and surfaces.

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What this paper is about

A class of 5-degree polynomial basis functions containing three shape control parameters λ,μ and ν is presented.It is the extension of quartic Bernstein basis functions.Properties of this new basis are analyzed and a polynomial curve with the three shape parameters λ、μ and ν is defined based on it.The curve not only inherits the outstanding properties of the quartic curve,but it is also adjustable in shape and fits close to the control polygon.The parameters have obvious geometric meaning.The classical quartic Bezier curve and the two classes of curves in related literature are especial examples of this paper.Some examples illustrate that the curve defined in this paper provides an effective method for designing curves and surfaces.

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Available abstract

A class of 5-degree polynomial basis functions containing three shape control parameters λ,μ and ν is presented.It is the extension of quartic Bernstein basis functions.Properties of this new basis are analyzed and a polynomial curve with the three shape parameters λ、μ and ν is defined based on it.The curve not only inherits the outstanding properties of the quartic curve,but it is also adjustable in shape and fits close to the control polygon.The parameters have obvious geometric meaning.The classical quartic Bezier curve and the two classes of curves in related literature are especial examples of this paper.Some examples illustrate that the curve defined in this paper provides an effective method for designing curves and surfaces.

Key concepts: Quartic function, Bézier curve, Quartic surface, Mathematics, Extension (predicate logic), Quartic plane curve, Basis (linear algebra), Polygon (computer graphics)

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