Free-Form Surfaces

Surfaces have been studied as an expanded form of curves for a long time. As the pioneers of studies on surface representations, Coons and Bezier can be referred. In 1964, Coons proposed the Coons surface[44] for surface representation. It is used to define surface shapes interactively in computers. Bezier proposed the Bezier surf ace [11,13] in 1966, also for representing surfaces and it is used in the design of automobile bodies. Both the Coons and the Bezier surfaces, used for surface representations, create rectangular patches. Since the Coons and Bezier surfaces, a lot of research has been done to expand and generalize representations by these surfaces.