**1. Introduction**

Radial basis functions can be used to construct trial spaces that have high precision in arbitrary dimensions with arbitrary smoothness. The applications of RBFs (or so-called meshfree methods) can be found in many different areas of science and engineering, including geometric modeling with surfaces [1].The globally supported radial basis functions such as Gaussians or generalized (inverse) multiquadrics have excellent approximation properties. However, they often produce dense discrete systems, which tend to have poor conditioning and lead to a high computational cost. The radial basis functions with compact supports can lead to a very well conditioned sparse system. The goal of this work is to design a truncated exponential function that has compact support and is strictly positive definite and radial on arbitrary *n*-dimensional space R*n* and to show the advantages of the truncated exponential radial function approximation for surface modeling.
