Mean distance from a curve to its control polygon

Authors:
Jesús Carnicer;Jorge Delgado
Affiliations:
Dept. Applied Mathematics/IUMA, University of Zaragoza, Zaragoza, Spain;Dept. Applied Mathematics, Escuela Politécnica Universitaria de Teruel, University of Zaragoza, Teruel, Spain
Venue:
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Year:
2008

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Abstract

The mean distance between a curve and its control polygon is bounded in terms of the norm of second order differences of the control points. We also analyze the distance of a rational curve to its control polygon and suggest a choice of the weight for obtaining rational curves much closer to its control polygon than Bézier curves.