This article presents three simple algorithms for determining the distance between any point, and the domain of interpolation associated with a cluster of control points of a vectorial function. The first algorithm uses the convex hull polytope of the cluster in the support space to accurately estimate the domain. The second algorithm is a neuron-like good approximation of the first. When the number of vertices of the polytope is large, a more economical approach is to approximate the domain by its circumscribed sphere, which is what the third algorithm does. It is also shown that there is a significant relation between these three measures of the distance between any test point and a set of learning points, and the generalization errors made by an artificial neural network.