Dual Basis Functions For Generalized Ball Basis And Its Application

The thesis is composed of four chapters.In Chapter one the author gives the definition of the Said-Ball curves and their properties. By means of the dual (functional) of Said-Ball basis, the Marsden identity is got in terms of Said-Ball basis, and a degree reduction algorithm for Said-Ball curves is presented through the transform from Bezier curves to Said-Ball curves.Chapter two is focused on the Wang-Ball curves, including definition, properties and recursion algorithms. The author derives the dual functional of the Wang-Ball basis for the first time and then obtains the explicit expression of Wang-Ball basis in terms of the Bernstein basis.The emphasis of Chapter three is laid upon the generalized Ball curves of Said-Bezier type (SBGB curves) which includes Said-Ball curves, Bezier curves and some of their intermediate curves as special cases. The contents involve the recursion algorithms, the dual functional of SBGB basis and the transformation formula between SBGB basis and Bernstein basis. The convex hull of SBGB and subdivision algorithms are also discussed.Last but not least, generalized Ball curves of the Wang-Said type (WSGB curves) are introduced in Chapter four. It is pointed out that Wang-Ball curves, Said-Ball curves and some other intermediate curves are all members of the WSGB family. By making a thorough study of WSGB curves, the author acquires two main results, i.e., the transformation formula from Bernstein basis to WSGB basis and the construction of the dual functionals for WSGB basis functions.