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2005•Journal of Hefei University of TechnologyRequires access

Cubic trigonometric Bézier curves with shape parameters

Lianqiang Yang, Hongyi Wu

Open publisher page 1 citations

Abstract

A cubic trigonometric Bezier curve,which is called the CT-Bezier curve,with two shape parameters λ_1 and λ_2 is presented in this paper.The curve possesses most of the properties of the cubic Bezier cuve.By taking the different values of λ_1 and λ_2,the shape of the curve can be adjusted locally or totally,and two pieces of CT-Bezier curves can be connected with C~1 or C~2 continuity flexibly.The elliptic and parabolic arcs can be represented exactly by the CT-Bezier curve.

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What this paper is about

A cubic trigonometric Bezier curve,which is called the CT-Bezier curve,with two shape parameters λ_1 and λ_2 is presented in this paper.The curve possesses most of the properties of the cubic Bezier cuve.By taking the different values of λ_1 and λ_2,the shape of the curve can be adjusted locally or totally,and two pieces of CT-Bezier curves can be connected with C~1 or C~2 continuity flexibly.The elliptic and parabolic arcs can be represented exactly by the CT-Bezier curve.

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Available abstract

A cubic trigonometric Bezier curve,which is called the CT-Bezier curve,with two shape parameters λ_1 and λ_2 is presented in this paper.The curve possesses most of the properties of the cubic Bezier cuve.By taking the different values of λ_1 and λ_2,the shape of the curve can be adjusted locally or totally,and two pieces of CT-Bezier curves can be connected with C~1 or C~2 continuity flexibly.The elliptic and parabolic arcs can be represented exactly by the CT-Bezier curve.

Key concepts: Bézier curve, Mathematics, Trigonometry, Tripling-oriented Doche–Icart–Kohel curve, Mathematical analysis, Geometry, Hessian form of an elliptic curve, Family of curves

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