The eccentricity of conic sections formulated as rational Bézier quadratics

Authors:
Chendong Xu;Tae-wan Kim;Gerald Farin
Affiliations:
Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-744, Republic of Korea;Department of Naval Architecture and Ocean Engineering, and Research Institute of Marine Systems Engineering, Seoul National University, Seoul 151-744, Republic of Korea;School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, AZ 85287-8809, United States
Venue:
Computer Aided Geometric Design
Year:
2010

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Abstract

The eccentricity of rational quadratic Bezier 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 Bezier curve of high degree.