In this paper, the efficiency in mesh updating (r-adaptivity) of the Transfinite Mean value Interpolation (TMI) and its generalization (k-TMI) are compared on three standardized problems to the well-known Inverse Distance Weighted interpolation (IDW) and Radial Basis Function interpolation (RBF) for unstructured data points and the new k-Transfinite Barycentric Interpolation (k-TBI) for structured data points such as, for instance, curves or surfaces in 3D. This is achieved by introducing a dynamical version of these interpolations via an ordinary differential equation that can be solved by standard ODE methods that are more economical than, for instance, solving vector partial differential equations as in the pseudo-solid method.

A review of the very recent mathematical foundations of the k-TMI and k-TBI constructed from the function alone (standard) or from the function and its derivatives (enhanced) is provided in the first part of the paper.

在本文中，在三个标准化问题上，将超长平均值插值（TMI）的网格更新效率（r-适应性）及其泛化（k -TMI）与众所周知的反距离加权插值（IDW）和非结构化数据点的径向基函数插值（RBF）和新的k-超重心重心插值（k-TBI）用于结构化数据点，例如3D中的曲线或曲面。这是通过通过普通的微分方程引入这些插值的动态版本来实现的，该微分方程可以通过标准的ODE方法求解，比例如在伪固体方法中求解矢量偏微分方程更经济。

在本文的第一部分中，对仅由函数（标准）或由函数及其导数（增强）构造的k -TMI和k -TBI的最新数学基础进行了回顾。