Easy-to-implement multidimensional spline interpolation with application to ship design optimisation

Among the different techniques for interpolation/approximation of sparse data, Spline interpolation represents one of the most popular alternatives. It is largely used for one dimensional and two-dimensional problems, but the use in case of multi-dimensional datasets, where the space dimension is larger than 2, is not common. The necessity of a topology for the sample data, so that the proximal points are clearly identified, put some difficulties even in R2. Furthermore, the classical Spline algorithms are not straightforward to implement, so that for this reason probably they are not widely applied in ship design optimization, and other interpolation techniques are much more popular. In this paper, some elements of Spline interpolation theory are presented in order to produce a simple and efficient multi-dimensional interpolation method, easy to implement.