Interpolating scattered data with \(C^ 2\) surfaces
The authors present a method for interpolating scattered data over a region in \(\mathbb{R}^2\), such that the resulting surface of interpolation is guaranteed to be \(C^2\)-continuous. The two main steps of the method are: Find a network of curves (over a given triangulation of the region), which minimizes a certain functional, explicitly given in the paper. The main result of the paper says that there is a unique solution of this minimization problem, and that this solution is given by a certain spline under tension network. In a second step, one extends this network into the interior of the triangles by means of side-vertex interpolants on triangles, which transfer the geometric properties from the network to the resulting surface. A number of colour plates illustrates the method.
scientific article; zbMATH DE number 777937