Pythagorean hodographs of ball curves | |
| Author | Napajit Singkorapoom |
| Call Number | AIT Thesis no. CS-94-22 |
| Subject(s) | Computer graphics Computer-aided design |
| Note | A thesis submitted in partial fulfilment of the requirement for the degree of Master of Science, School of Engineering and Technology |
| Publisher | Asian Institute of Technology |
| Abstract | Pythagorean-hodograph (PH) curves are a special class of polynomial curves, distinguished by the property that their arc lengths and offset curves can be computed rationally. The latter property is more useful in applications such as tolerance analysis and numerical control machining. This study carried out adet ailed analysis of these useful properties for Ball curves. The relationship between Ball curves and Bezier curves of which the control points or the basis functions of one can be converted to the other was used to take advantage of some existing results. Moreover, the use of complex representation is a radical different approach which also gives great facilitation in formulating Ball curves to have PH. The necessary and sufficient conditions for cubic and quintic Ball curves to have PH curves were established. These are expressed in terms of the legs of the control polygon concerned. Finally, the arc lengths and offsets to the Ball curves with PH are derived |
| Year | 1994 |
| Type | Thesis |
| School | School of Engineering and Technology (SET) |
| Department | Other Field of Studies (No Department) |
| Academic Program/FoS | Computer Science (CS) |
| Chairperson(s) | Huynh, Ngoc Phien |
| Examination Committee(s) | Bohez, Erik L.J. ;Do, Ba Khang |
| Scholarship Donor(s) | Asian Institute of Technology Partial |
| Degree | Thesis (M.Sc.) - Asian Institute of Technology, 1994 |