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2009•Jisuanji gongcheng yu shejiRequires access

Study on a class of quadratic TC-Bézier curve

Huang You-du

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Abstract

A class of trigonometric basis functions with two shape control parameters is presented,and the corresponding trigonometric curve with two shape parameters is defined,the property of basis functions and TC-Bezier curve is also analyzed.When-1≤ λ1,λ2≤1,the shape of curve can be controlled easily by changing with parameters.The straight line segment,ellipse(circular) and parabola arc can be represented exactly by TC-Bezier curve.At last,the C1 continuous joint of curve pieces is discussed and the example illustrates the TC-Bezier curve is useful in curve design.

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What this paper is about

A class of trigonometric basis functions with two shape control parameters is presented,and the corresponding trigonometric curve with two shape parameters is defined,the property of basis functions and TC-Bezier curve is also analyzed.When-1≤ λ1,λ2≤1,the shape of curve can be controlled easily by changing with parameters.The straight line segment,ellipse(circular) and parabola arc can be represented exactly by TC-Bezier curve.At last,the C1 continuous joint of curve pieces is discussed and the example illustrates the TC-Bezier curve is useful in curve design.

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Available abstract

A class of trigonometric basis functions with two shape control parameters is presented,and the corresponding trigonometric curve with two shape parameters is defined,the property of basis functions and TC-Bezier curve is also analyzed.When-1≤ λ1,λ2≤1,the shape of curve can be controlled easily by changing with parameters.The straight line segment,ellipse(circular) and parabola arc can be represented exactly by TC-Bezier curve.At last,the C1 continuous joint of curve pieces is discussed and the example illustrates the TC-Bezier curve is useful in curve design.

Key concepts: Bézier curve, Tripling-oriented Doche–Icart–Kohel curve, Ellipse, Parabola, Quadratic equation, Basis (linear algebra), Hessian form of an elliptic curve, Mathematics

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