Urn models, recursive curve schemes, and computer aided geometric design

Urn models are used to generate curve and surface schemes which are generalizations of Bezier curves and surfaces. Properties of these schemes are investigated, mostly from the viewpoint of computer aided geometric design. One property such schemes will always possess is a de Casteljau-type evaluation algorithm, which may lead to extremely rapid evaluation if one employs specially designed hardware. Curves which can be generated in this manner include not only Bezier curves, but also such curves as B-splines and Lagrange polynomials. Surfaces arising from urn models are also discussed.