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. This book describes the algorithms and mathematical fundamentals of a widely used software package for data fitting with (tensor product) splines. As such it gives a survey of possibilities and benefits but also of the problems to cope with when approximating with this popular type of function. In particular it is demonstrated in detail how the properties of B-splines can be fully exploited for improving the computational efficiency and for incorporating different boundary or shape preserving constraints. Special attention is also paid to strategies for an automatic and adaptive knot selection with intent to obtain serious data reductions. The practical use of the smoothing software is illustrated with many examples, academic as well as taken from real life.
'Scientists and engineers with curve and surface fitting problems and practitioners of computer graphics and CAGD should all find the monograph useful. It is essentially self-contained, giving a brief introduction to the mathematics required as the need arises.'
'A distinguished feature of this book is its lucid presentation. Dierckx's choice of examples is excellent. The discussion is clear and complete enough to serve as an introduction for those beginning a study of spline fitting algorithms. The work is self-contained.'
E. Neuman, Zentralblatt für Mathematik, Band 782/94
`From the cloth edition:
the book is invaluable ... The book is clearly laid out ... contains a comprehensive set of references.'
Tim Thornton, Computing Reviews, June 1994
List of figures
List of tables
Part I: Spline Functions
1: Univariate Splines
2: Bivariate Splines
Part II: Curve Fitting
3: Curve Fitting: An Introduction
4: Least-Squares Spline Curve Fitting
5: Smoothing Spline Curve Fitting
6: More Smoothing Spline Curves
7: Fitting with Convexity Constraints
Part III: Surface Fitting
8: Surface Fitting: An Introduction
9: Scattered Data Surface Fitting
10: Mesh Data Surface Fitting
11: More Scattered Data Smoothing
12: More Mesh Data Smoothing
Part IV: FITPACK
13: Available Software