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2006•Journal of Hefei UniversityRequires access

A Class of Quadratic Trigonometric Bézier Curves with Two Shape Parameters

Jin Xie, Hongyi Wu

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Abstract

A quadratic trigonometric Bezier curve(named briefly QT-Bezier curve) with two shape parameters λ and μ is presented in this paper.The curve that interpolates start point and end point is(analogous) to Bezier curve,The curve possesses most of the properties of the quadratic Bezier curve.By taking the different values of λ and μ, the shape of the curve can be adjusted locally or totally,and two pieces of QT-Bezier curves can be connected with C~1 continuity flexibly.The ellipse and parabola arc can be represented exactly by QT-Bezier curve.

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What this paper is about

A quadratic trigonometric Bezier curve(named briefly QT-Bezier curve) with two shape parameters λ and μ is presented in this paper.The curve that interpolates start point and end point is(analogous) to Bezier curve,The curve possesses most of the properties of the quadratic Bezier curve.By taking the different values of λ and μ, the shape of the curve can be adjusted locally or totally,and two pieces of QT-Bezier curves can be connected with C~1 continuity flexibly.The ellipse and parabola arc can be represented exactly by QT-Bezier curve.

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Available abstract

A quadratic trigonometric Bezier curve(named briefly QT-Bezier curve) with two shape parameters λ and μ is presented in this paper.The curve that interpolates start point and end point is(analogous) to Bezier curve,The curve possesses most of the properties of the quadratic Bezier curve.By taking the different values of λ and μ, the shape of the curve can be adjusted locally or totally,and two pieces of QT-Bezier curves can be connected with C~1 continuity flexibly.The ellipse and parabola arc can be represented exactly by QT-Bezier curve.

Key concepts: Bézier curve, Mathematics, Ellipse, Parabola, Quadratic equation, Tripling-oriented Doche–Icart–Kohel curve, Hessian form of an elliptic curve, Family of curves

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