Optimal one-sided approximants of circular arc
CoRR(2024)
摘要
The optimal one-sided parametric polynomial approximants of a circular arc
are considered. More precisely, the approximant must be entirely in or out of
the underlying circle of an arc. The natural restriction to an arc's
approximants interpolating boundary points is assumed. However, the study of
approximants, which additionally interpolate corresponding tangent directions
and curvatures at the boundary of an arc, is also considered. Several
low-degree polynomial approximants are studied in detail. When several
solutions fulfilling the interpolation conditions exist, the optimal one is
characterized, and a numerical algorithm for its construction is suggested.
Theoretical results are demonstrated with several numerical examples and a
comparison with general (i.e. non-one-sided) approximants are provided.
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