Approximation of Clock-like Point Sets

Abstract

This chapter has a theoretical character and can be studied by some medical staff researchers that seek methods of approximation of very irregular point sets. When the shape of an obtained polygon based on the point set is similar to a chain of bells, then it will be difficult to find a continuous standard curve that should approximate the polygon without making a large approximation error. The studies of some medical data give rise to the creation of polygons consisting of finite numbers of points tied together. Since the polygons are not formalized by some mathematical expressions, we suggest creating continuous functions that approximate them thoroughly in spite of their irregular shapes. To warrant a high accuracy of approximation, otherwise impossible to obtain when using standard curves, we test a continuous function composed of joined truncated π-functions or joined truncated s-functions. © 2007 Springer.