The dual bases for the Bézier–Said–Wang type generalized Ball polynomial bases and their applications

A unifying representation for the existing generalized Ball bases and the Bernstein bases are given. Then the dual bases for the Bézier–Said–Wang type generalized bases (BSWGB for short) are presented. The Marsden identity and the mutual transformation formulas between Bézier curve and Bézier–Said–Wang type generalized curve (BSWGB curve) are also given. These results are very useful for the applications of BSWGB curves and their popularization in CAGD. Numerical examples are also given to show the effectiveness of our methods.