Extension of the Ball Basis

A new series of the generalized Ball basises of degree-n with parameter k ( 2 ≤ k ≤■n 2■ +1) are constructed as the transition from Wang-Ball basis (k=2) to Said-Ball basis (k= ■n 2 ■ +1), and some properties of them are given. Then, the new generalized Ball curves are based on these new basises and the algorithms for recursive evaluation, degree-elevation, and degree-reduction are introduced. Finally, the corresponding trigonal Ball basises are shown and the algorithms for the recursive evaluation and degree-elevation of trigonal Ball surfaces are given.