Radial Basis Functions for Shape Preserving Planar Interpolating Curves

摘要

The problem of scattered data interpolation is of great significance in various areas of scientific research. However, we often have some additional information that we wish to confine to interpolation such as positivity, convexity and monotonicity. In this paper, we present a new approach to construct shape preserving planar interpolating curves. It is primarily based on the use of a class of multiquadric quasi-interpolation operator and compactly supported radial basis functions. This approach possesses the advantages of shape preserving and good approximation behavior. The proposed algorithm is relatively easy to implement.