Generalized ball curves | |
| Author | Kyaw Moe Lay |
| Call Number | AIT Thesis no.CS-98-10 |
| Subject(s) | Curves, Cubic Computer-aided design |
| Note | A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science, School of Advanced Technologies |
| Publisher | Asian Institute of Technology |
| Abstract | Based on two generalizations of the cubic Ball curve, one can readily extend them to the rational form to obtain the rational Said-Ball curves and rational Wang-Ball curves. This study provides the relevant theoretical background concerning the non-rational Said-Ball curves and non-rational Wang-Ball curves for use in developing the corresponding rational curves. However, due to the fact that many results have been obtained for the non-rational and rational Said-Ball curves, this study focuses on the derivation of similar results for the Wang-Ball curves, using the polar form approach, particularly their relationships with the Bezier curves of the same degree. From these relationships, the study derives the corresponding relationships between the rational Said-Ball curves and rational Wang-Ball curves expressed in terms of their weights and control points. Moreover, two new algorithms are devised, one for the rational Said-Ball curves, and the other for the rational Wang-Ball curves. Their complexity is also analyzed. Finally, the research establishes the conditions of two (non-rational and rational) Wang-Ball curves to have C1 -, C2 -, GC1 - and GC2 -continuity at their join points. |
| Year | 1998 |
| Type | Thesis |
| School | School of Advanced Technologies (SAT) |
| Department | Department of Information and Communications Technologies (DICT) |
| Academic Program/FoS | Computer Science (CS) |
| Chairperson(s) | Huynh Ngoc Phien; |
| Examination Committee(s) | Kanchana Kanchanasut ;Hoang Le Tien; |
| Scholarship Donor(s) | Asian Institute of Technology Partial Scholarship ; |
| Degree | Thesis (M.Sc.) - Asian Institute of Technology, 1998 |