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2008•Journal of Hefei University of TechnologyRequires access

Extensions of cubic Bézier Expansion curve with C~2 constraint

Bao-Hua Xing

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Abstract

A class of polynomial basis functions of 4th degree with two shape control parameters is presented.It is an extension of cubic Bernstein basis functions.Properties of the basis functions are analyzed and the corresponding polynomial curve with two shape parameters is defined.And the influence of the parameters on the end curvatures is discussed.The curve not only inherits the outstanding properties of the cubic Bezier curve,but it is also adjustable in shape parameters.The problem of curve extension with least energy is discussed based on C2 continuity.Some examples illustrate the algorithm is useful for the curve design.

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A class of polynomial basis functions of 4th degree with two shape control parameters is presented.It is an extension of cubic Bernstein basis functions.Properties of the basis functions are analyzed and the corresponding polynomial curve with two shape parameters is defined.And the influence of the parameters on the end curvatures is discussed.The curve not only inherits the outstanding properties of the cubic Bezier curve,but it is also adjustable in shape parameters.The problem of curve extension with least energy is discussed based on C2 continuity.Some examples illustrate the algorithm is useful for the curve design.

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Available abstract

A class of polynomial basis functions of 4th degree with two shape control parameters is presented.It is an extension of cubic Bernstein basis functions.Properties of the basis functions are analyzed and the corresponding polynomial curve with two shape parameters is defined.And the influence of the parameters on the end curvatures is discussed.The curve not only inherits the outstanding properties of the cubic Bezier curve,but it is also adjustable in shape parameters.The problem of curve extension with least energy is discussed based on C2 continuity.Some examples illustrate the algorithm is useful for the curve design.

Key concepts: Bézier curve, Mathematics, Basis function, Extension (predicate logic), Basis (linear algebra), Tripling-oriented Doche–Icart–Kohel curve, Constraint (computer-aided design), Cubic function

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