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2008•Unpublished venueRequires access

H-Bézier Curves Based on Algebraic and Hyperbola Polynomials

Anfeng Zhu

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Abstract

An original basis is constructed on the space in this paper.This basis has the similar properties to Bezier basis of the endpoint and interpolation.Then H-Bezier basis is defined based on the space,also the formula of recursion is given when.Next the properties are discussed.Meanwhile H-Bezier curve and H-Bezier surface are defined,the properties of the curve is discussed.Last it is demonstrated that many valuable curves,such as algebraic curves and transcendental curves,can be expressed by H-Bezier curves.

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What this paper is about

An original basis is constructed on the space in this paper.This basis has the similar properties to Bezier basis of the endpoint and interpolation.Then H-Bezier basis is defined based on the space,also the formula of recursion is given when.Next the properties are discussed.Meanwhile H-Bezier curve and H-Bezier surface are defined,the properties of the curve is discussed.Last it is demonstrated that many valuable curves,such as algebraic curves and transcendental curves,can be expressed by H-Bezier curves.

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Available abstract

An original basis is constructed on the space in this paper.This basis has the similar properties to Bezier basis of the endpoint and interpolation.Then H-Bezier basis is defined based on the space,also the formula of recursion is given when.Next the properties are discussed.Meanwhile H-Bezier curve and H-Bezier surface are defined,the properties of the curve is discussed.Last it is demonstrated that many valuable curves,such as algebraic curves and transcendental curves,can be expressed by H-Bezier curves.

Key concepts: Bézier curve, Mathematics, Hyperbola, Basis (linear algebra), Interpolation (computer graphics), Algebraic curve, Basis function, Algebraic number

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