1.4 B-spline curves and surfaces

Early fundamental work on the B-spline basis functions was performed almost 50 years ago by Schoenberg [368], and this was followed by development of fundamental algorithms by Cox [67] and de Boor [72,73]. B-splines in the context of Computer Aided Geometric Design were proven to be a viable and attractive representation method by many pioneers of this field, such as Riesenfeld [345,130], Boehm [33], Schumaker [369] and many subsequent researchers.

In this section, we provide definitions and the basic properties and
algorithms of B-splines. However, we do not deal with fitting,
approximation and fairing methods using B-splines which are very
important in their own right. For these topics, there are specialized
books, monographs and proceedings and a large variety of papers
[365,175,92,314,45].

- 1.4.1 B-splines
- 1.4.2 B-spline curve
- 1.4.3 Algorithms for B-spline curves
- 1.4.4 B-spline surface