On optimal polynomial geometric interpolation of circular arcs according to the Hausdorff distance
14 Mar 2020
•
Vavpetič Aleš
•
Žagar Emil
The problem of the optimal approximation of circular arcs by parametric
polynomial curves is considered. The optimality relates to the Hausdorff
distance and have not been studied yet in the literature...Parametric polynomial
curves of low degree are used and a geometric continuity is prescribed at the
boundary points of the circular arc. A general theory about the existence and
the uniqueness of the optimal approximant is presented and a rigorous analysis
is done for some special cases for which the degree of the polynomial curve and
the order of the geometric smoothness differ by two. This includes practically
interesting cases of parabolic $G^0$, cubic $G^1$, quartic $G^2$ and quintic
$G^3$ interpolation. Several numerical examples are presented which confirm
theoretical results.(read more)