The eccentricity of conic sections formulated as rational Bézier quadratics

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• 作者：Chendong Xu ; Tae-wan Kim ; Gerald Farin
• 关键词：Conic sections ; Eccentricity ; Rational Bé ; zier curves ; CAGD
• 刊名：Computer Aided Geometric Design
• 出版年：2010
• 出版时间：August 2010
• 年：2010
• 卷：27
• 期：6
• 页码：458-460
• 全文大小：109 K

文摘

The eccentricity of rational quadratic Bézier curves is formulated directly in terms of their control-points and weights. Based on this expression, we analyze the range and extreme values of the eccentricity of conic sections expressed in this form. We also provide an explicit expression for the eccentricity of the osculating conic of a rational Bézier curve of high degree.