Locally C1 interpolation of functions on an arbitrary simplex mesh using a simple feed-forward perceptron

In this paper we present a solution to a C¹ interpolation problem for lower dimensional data in Euclidean space. The solution presented falls into two parts, the first being the formulation of an abstract simplex mesh that parametrizes the data while the second part presents an interpolation algorithm based on the structure of a simple feed-forward perceptron. To emphasise the connection between our approach and classical spline interpolation we choose cubic polynomial activation functions in the neural units of the perceptron