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Biquadratic TC-Bézier Curves with Shape Parameter

Xu Min Liu, Xian Peng Yang, Yan Wu

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Abstract

Shape controlling is a popular topic in curves and surfaces design with free form. In this paper, a new curve, to be called Biquadratic TC-Bézier curves with shape parameter , is constructed in the space . We show that such curves share the same properties as the traditional Bézier curves in polynomial spaces. The shape of new curves, representing circle and ellipse accurately, can be adjusted by changing the value of the parameter . Then we give the G1 continuity conditions of Biquadratic TC-Bézier curves with shape parameter and its application in surfaces modeling.

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What this paper is about

Shape controlling is a popular topic in curves and surfaces design with free form. In this paper, a new curve, to be called Biquadratic TC-Bézier curves with shape parameter , is constructed in the space . We show that such curves share the same properties as the traditional Bézier curves in polynomial spaces. The shape of new curves, representing circle and ellipse accurately, can be adjusted by changing the value of the parameter . Then we give the G1 continuity conditions of Biquadratic TC-Bézier curves with shape parameter and its application in surfaces modeling.

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Available abstract

Shape controlling is a popular topic in curves and surfaces design with free form. In this paper, a new curve, to be called Biquadratic TC-Bézier curves with shape parameter , is constructed in the space . We show that such curves share the same properties as the traditional Bézier curves in polynomial spaces. The shape of new curves, representing circle and ellipse accurately, can be adjusted by changing the value of the parameter . Then we give the G1 continuity conditions of Biquadratic TC-Bézier curves with shape parameter and its application in surfaces modeling.

Key concepts: Ellipse, Bézier curve, Shape parameter, Mathematics, Parameter space, Family of curves, Geometry, Mathematical analysis

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