Approximation and Modeling with B-Splines
Klaus Höllig and Jörg Hörner
The slides facilitate teaching courses on approximation and geometric modeling based on the SIAM book. For each subsection, a pdf file with a presentation of the main topics is provided. Moreover, a template explains how to generate additional presentations in the same style. This allows professors and instructors to adapt the material according to the content of their course.
The problem collection contains theoretical as well as programming exercises pertaining to the topics of the book. Moreover, an extended pdf document with solutions is available for professors on request (contact Klaus Höllig at [email protected]). For the majority of problems test values are suggested which provides a simple indication whether a problem has been solved correctly. With the appropriate software this allows to check answers automatically.
The small collection of MATLAB programs and demos illustrates the methods described in the book. Many algorithms have become standard tools in commercial software involving B-splines (see, e.g., the MATLAB Curve Fitting Toolbox) and are described in classical textbooks (see, e.g., A Practical Guide to Splines by Carl de Boor). In contrast to software meeting professional standards the program codes are kept as simple as possible to make the details easily accessible for students. MATLAB serves as an ideal programming language, especially because of the simple syntax of linear algebra operations, the graphic capabilities, and the flexible data structures.
The programs are intended for educational use only, and for illustrating the methods described in the SIAM book Approximation and Modeling with B-Splines. No permission is granted for any other application, in particular for any commercial use or applications of the programs which can result in material or physical damage. A possible lack of reliability of numerical algorithms is emphasized. As a consequence, no guarantees for the correctness of the computed results can be given. In addition to the above restrictions, the general terms of MathWorks for using MATLAB programs apply.
For programs and demos illustrating the use of B-splines in finite element methods see the supplementary material for the book Finite Element Methods with B-Splines (FR26).