In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a certain discrete sense. This way the H\"ollig-Koch conjecture on the existence and the approximation order is confirmed in the planar case for parametric polynomial curves of any degree.

翻译：在论文中,对数据点的平面多元几何内插法进行了重新审视,一般地得出了表明存在内插的简单充分的几何条件,要求数据点在某种离散的意义上具有共性。这样,关于存在和近似顺序的H\"ollig-Koch猜想在任何程度的对等多元曲线的平面案中就得到了确认。