A primer on splines and NURBS for isogeometric analysis. (English) Zbl 1325.65027

Jüttler, Bert

Beer, Gernot (ed.) et al., Isogeometric methods for numerical simulation. Papers based on the presentations at the course. Wien: Springer (ISBN 978-3-7091-1842-9/hbk; 978-3-7091-1843-6/ebook). CISM Courses and Lectures 561, 1-19 (2015).

Summary: This chapter collects fundamental facts concerning theory and algorithms for rational spline functions. In addition, it addresses fundamental techniques for creating domain parameterizations for isogeometric analysis. All presented facts are covered in more detail by the the rich literature on Computer Aided Geometric Design, e.g., [G. E. Farin, Curves and surfaces for computer aided geometric design: a practical guide. 5th ed. San Francisco: Morgan Kaufmann Publishers (2002); G. Farin (ed.) et al., Handbook of computer aided geometric design. Amsterdam: Elsevier (2002; Zbl 1003.68179); J. Hoschek and D. Lasser, Fundamentals of computer aided geometric design. Wellesley, MA: A. K. Peters (1996; doi:10.2307/2153462); L. Piegl and W. Tiller, The NURBS book. Berlin: Springer-Verlag (1995; Zbl 0828.68118); H. Prautzsch et al., Bézier and B-spline techniques. Berlin: Springer (2002; Zbl 1033.65008)].
For the entire collection see [Zbl 1317.74004].

MSC:

65D07	Numerical computation using splines
65D17	Computer-aided design (modeling of curves and surfaces)

Citations:

Zbl 1003.68179; Zbl 0828.68118; Zbl 1033.65008