Variation Diminution and Blossoming for Curves and Surfaces G. Schmel tz

Here, I is an index set, <j>j are linear independent scalar functions on a domain D and Pj are points in the image space ]Rd. The <f>j are called the basis

functions or simply the basis; the P j axe referred to as control points. For curves, I = {0,. . . , n} for some n E IN and D = [a, b] with a, 6 E IR, while for surfaces, I = {(i, j, k) E INq : i + j + A; = n} and I? = A UVW is a triangle with vertices U ,V,W E IR2. In any case n will be called the order of the curve or surface, respectively.