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2005•Journal of Hefei University of TechnologyRequires access

Fairing of cubic Bézier curves

Jieqing Tan

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Abstract

Cubic Bezier curves are very important curves in the field of Computer Aided Geometric Design and widely used in practical applications. In this paper,the least bending energy is adopted in estimating the fairing of curves, and based on the improved Kjellander's method,the fairing of cubic Bezier curves is carried out through modifying control points and data points. Two formulae according to which the control points are moved so that the energy decreases are obtained,and the error analysis of the two formulae is also given. The better fairing effect of the two formulae is illustrated through examples.

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What this paper is about

Cubic Bezier curves are very important curves in the field of Computer Aided Geometric Design and widely used in practical applications. In this paper,the least bending energy is adopted in estimating the fairing of curves, and based on the improved Kjellander's method,the fairing of cubic Bezier curves is carried out through modifying control points and data points. Two formulae according to which the control points are moved so that the energy decreases are obtained,and the error analysis of the two formulae is also given. The better fairing effect of the two formulae is illustrated through examples.

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Available abstract

Cubic Bezier curves are very important curves in the field of Computer Aided Geometric Design and widely used in practical applications. In this paper,the least bending energy is adopted in estimating the fairing of curves, and based on the improved Kjellander's method,the fairing of cubic Bezier curves is carried out through modifying control points and data points. Two formulae according to which the control points are moved so that the energy decreases are obtained,and the error analysis of the two formulae is also given. The better fairing effect of the two formulae is illustrated through examples.

Key concepts: Bézier curve, Geometric design, Mathematics, Field (mathematics), Bézier surface, Geometry, Energy (signal processing), Data point

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