The eccentricity of conic sections formulated as rational Bézier quadratics

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Abstract

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.

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    Citation Excerpt :

    In [6], complex arithmetic is used to calculate some geometric characteristics of conic sections. Most recently, in [7], the eccentricity of conics in Bézier form is formulated and this result is used for deriving the range and extreme values of this parameter. As a different approach, we resort to projective and affine geometry to calculate geometric characteristics of conic sections in Bézier form.

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At present Dr. Chendong Xu is associated with Faculty of Science, Ningbo University, Ningbo, Zhejiang 315211, PR China.

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