Curve and surface fitting

Researchers

• P. Dierckx

Description

Before fairing	After fairing

This research has been discontinued.

The fitting of a curve or surface through a set of observational data is a very frequent problem in different disciplines (mathematics, engineering, medicine, ...) with many interesting applications. At the Department, algorithms were developed for smoothing data using splines and tensor product splines under various boundary and shape-preserving constraints. Strategies were incorporated for an automatic and adaptive knot selection with intent to obtain serious data reductions. This research resulted in a software package, called FITPACK. It is available via netlib and a number of the Fitpack routines are also incorporated in the NAG library.

Tensor product splines also have disadvantages. As an alternative therefore splines on triangulations and Powell-Sabin splines in particular have been considered. Algorithms have been developed for smoothing scattered data with a convexity, nonnegativity or monotonicity preserving PS-surface on arbitrary approximation domains with a polygonal boundary.

There is a continuing research interest in the development of new spline fitting algorithms and the adaptation of existing ones to problems in higher dimensions or specific industrial problems such as the automatic reconstruction of aircraft trajectories from noisy radar data.