Subdivision Algorithms For Generalized Ball Curves And Its Applications

The thesis is composed of five 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 the transformation formula from Bezier curves to Said-Ball curves is presented, and the subdivision algorithms for the Said-Ball curves is also described.Chapter two is focused on the Wang-Ball curves, including definition, properties and recursive algorithms. Using the dual functional of the Wang-Ball basis, the author derives the subdivision algorithms for the Wang-Ball curves for the first time and then obtains some identical equations of calculation combination.The emphasis of Chapter three is laid upon the Said- Bezier type generalized Ball (SBGB) curves which includes Said-Ball curve, Bezier curve and some intermediate curves between them. The contents involve the recursion algorithms, the dual functional of SBGB basis and the transformation formula between SBGB basis and Bernstein basis. The envelopes of SBGB curves and subdivision algorithms are also discussed.In Chapter four as the main part of this thesis, the Wang-Said type generalized Ball (WSGB) curves are introduced. It is pointed out that Wang-Ball curves, Said-Ball curves and some other intermediate curves are all members of the WSGB curves. Using the dual basis of WSGB curves, the author acquires the subdivision algorithms for the WSGB curves.Last but not least, subdivision transformations are introduced in Chapter five, the resemblance of subdivision transformations are also proved.