Approximation and Modeling with B-Splines

B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this book provides a unified introduction to the basic components of B-spline theory: approximation methods, modeling techniques and geometric algorithms. Topics discussed include the Bezier form; approximation and interpolation; error estimates; spline representations of curves, surfaces and solids; hierarchical bases; and finite element simulation. This book is ideal as an advanced undergraduate or first-year graduate text for courses on splines or approximation and geometric modeling for students in mathematics, engineering and computer science. A supplementary web site provides a collection of problems with selected solutions, slides for use in lectures, and programs with demos. This book also represents a valuable resource for practitioners whose work involves B-splines in the context of numerical simulations, computer-aided design, or visualization.

Preface; Introduction; Notation and symbols; 1. Polynomials; 2. Bézier curves; 3. Rational Bézier curves; 4. B-splines; 5. Approximation; 6. Spline curves; 7. Multivariate splines; 8. Surfaces and solids; 9. Finite elements; Notes and comments; Appendix; Bibliography; Index.

Klaus Höllig is Chair for Numerical Analysis and Geometric Modeling at the University of Stuttgart. His research focuses on B-spline techniques for partial differential equations, approximation of curves and surfaces, and geometric algorithms. He is author of Finite Element Methods with B-Splines (2003) and coauthor of Box Splines (1993).
Jörg Hörner is a Research Associate in the Department of Mathematics at the University of Stuttgart. He develops finite element techniques for NURBS domains and is coauthor of the MATLAB® package FEMB. His interests also include educational projects; in particular he is technical director of Mathematik-Online.