Approximation of conic section by quartic Bézier curve with endpoints continuity condition
A new method for approximation of conic section by quartic Bézier curve is presented, based on the quartic Bézier approximation of circular arcs. Here we give an upper bound of the Hausdorff distance between the conic section and the approximation curve, and show that the error bounds have the approximation order of eight. Furthermore, our method yields quartic G 2 continuous spline approximation of conic section when using the subdivision scheme, and the effectiveness of this method is demonstrated by some numerical examples.
Keywordsquartic Bézier curve conic section approximation Hausdorff distance
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- L Fang. G3 approximation of conic sections by quintic polynomial curves, Comput Aided Geom Design, 1999, 16(8): 755–766.Google Scholar
- E T Y Lee. The rational Bézier representation for conics, In: Geometric Modeling: Algorithms and New Trends, G E Farin, Ed, SIAM, Academic Press, 1987, 3–19.Google Scholar