The best G1 cubic and G2 quartic Bézier approximations of circular arcs

Authors:
Seok Hur;Tae-wan Kim
Affiliations:
Department of Mathematical Science, Seoul National University, Seoul 151-747, South Korea;Department of Naval Architecture and Ocean Engineering, and Research Institute of Marine Systems Engineering, Seoul National University, Seoul 151-744, South Korea
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

We obtain cubic and quartic Bezier approximations of circular arcs that respectively satisfy G^1 and G^2 end-point interpolation conditions. We identify the necessary and sufficient conditions for such approximations to be the best, in the sense that they have the minimum Hausdorff distance to the circular arc. We then establish the existence and uniqueness of these best approximations and present practical methods to calculate them, which are verified by examples.