Constrained shepard method for modeling and visualization of scattered data

Abstract

The problem of modelling and visualization of scattered data where there are inherit constraints on value of the data exist in many scientific and business research areas. For example, the value of mass concentration always has the lower bound of 0 and upper bound of 1. The modeling functions having gradient usually do not guarantee to preserve the bounds of data. In this paper we present the Constrained Shepard method for interpolation of scattered data satisfying the lower and upper bounds specified by the two constraint functions. The constrained interpolant is an extension of the Modified Quadratic Shepard method with comparable efficiency and accuracy. The proposed method is easy to implement and extend to higher dimensionality. The constrained interpolation function is Cd continuus.