Since the 60s, the Bézier and B-spline representations of polynomials have become an important tool for constructing and editing curves and surfaces in computer-aided industrial applications.  These representations are intuitive, have geometric meaning, and allow for numerically robust algorithms.

In this lecture, we introduce the basics of Bézier and B-spline techniques.  In particular, we focus on algorithms for constructing curves and surfaces and impart an elementary understanding of various related geometric concepts.  For the most part, the lecture orients itself around the book "Bézier and B-Spline Techniques" listed below in the literature.

This lecture is part of the Bachelor's degree program with 4+2 SWS as well as a part of the Master's degree program in which the lab is not required.

Literature

• Prautzsch, Boehm, Paluszny: Bézier and B-Spline Techniques, Springer 2002.
• Farin: Curves and Surfaces for CAGD, Fifth Edition, 2002.
• de Boor: A practical guide to splines, 2001.
• Hoschek, Lasser: Grundlagen der geometrischen Datenverarbeitung, 1992.
• Boehm, Prautzsch: Numerical Methods, Vieweg, Braunschweig 1993
• De Casteljau: Shape mathematics and CAD, 1986.
• Lancaster, Salkauskas: Curve and Surface fitting, Acad. Press 1987.
• Cohen, Riesenfeld, Elber: Geometric Modelling with splines, 2001.
• Farouki:The Bernstein polynomial basis: a centennial retrospective.
  Computer Aided Geometric Design, Available online 30 March 2012.
  http://www.sciencedirect.com/science/article/pii/S0167839612000192?v=s5

Learning Tools

• CAGD-Applets
• Interactive B-Spline

Other

• Questions regarding "Curves and Surfaces in CAD II"
• Historical Survey