Fitting Triangular B-Splines to Functional Scattered Data

Abstract

Scattered data is, by definition, irregularly spaced. Uniform surface schemes are not well adapted to the locally varying nature of such data. Conversely, Triangular B-Spline surfaces 2 are more flexible in that they can be built over arbitrary triangulations and thus can be adapted to the scattered data.This paper discusses the use of DMS spline surfaces for approximation of scattered data. A method is provided for automatically triangulating the domain containing the points and generating basis functions over this triangulation. A surface approximating the data is then found by a combination of least squares and bending energy minimization. This combination serves both to generate a smooth surface and to accommodate for gaps in the data. Examples are presented which demonstrate the eftectiveness of the technique for mathematical, geographical and other data sets.