论文标题
根据Hausdorff距离的圆弧的最佳多项式几何插值
On optimal polynomial geometric interpolation of circular arcs according to the Hausdorff distance
论文作者
论文摘要
考虑了通过参数多项式曲线对圆弧最佳近似的问题。最佳性与Hausdorff距离有关，并且在文献中尚未研究。使用低度的参数多项式曲线，并在圆形弧的边界点处开出几何连续性。关于最佳近似值的存在和唯一性的一般理论，并为某些特殊情况进行了严格的分析，在某些特殊情况下，多项式曲线的程度和几何平滑度的顺序不同。这实际上包括抛物线$ g^0 $，立方$ g^1 $，四分之一$ g^2 $和QUINTIC $ G^3 $插值的案例。提出了几个数值示例，这些示例证实了理论结果。
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.
