Optimal one-sided approximants of circular arc 

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.