Computer Aided Geometric Design

Computer Aided Geometric Design(CAGD) is a branch of applied mathematics concerned with algorithms for the design of smooth curves and surfaces and for their efficient mathematical representation. The representation is used for the computation of the curves and surfaces, as well as geometrical quantities of importance such as curvatures, intersection curves between two surfaces and offset surfaces. The Bezier curves are basically and widely used in CAGD. The Bezier curves were independently developed by P. de Casteljau about 1959 and by P. Bezier about 1962. The underlying mathematical theory is based on the concept of Bernstein polynomials. De Casteljau directly exploited this relationship; but it was not before 1970 that R. Forrest discovered the connection between Bezier's work and Bernstein polynomials. Bezier and de Casteljau developed their theories as part of CAD systems that were being built up at two French car companies, Renault and Citroen. The Renault system UNISURF (by Bezier) was soon described in several publications; this is the reason that the underlying theory now bears Bezier's name. Bezier curves and surfaces are now established as the mathematical basis of many CAD systems, they have also become a major tool for the development of new methods for curve and surface descriptions. Farin summarize the basic theory of such curves and provide many relevant references.

Microsoft Computer Graphics Group Biomedical Imaging Group International Computer Graphics Group MRL Texture mapping Gerald E. Farin C.de Boor Larry L.Schumaker Tom Lyche Richard F. Riesenfeld Elaine Cohen Nira Dyn Michael Floater Rida T. Farouki Tony DeRose Robert Schaback Peter Schroder Denis Zorin Joe Warren Jarek Rossignac Greg Turk Hans-Peter Seidel John C. Hart Michael Garland Hugues Hoppe Rainbow Velho Leif Kobbelt Ron Fedkiw

[Last Update: 2003.12.15] `2003 byung-gook lee