| Author | Nguyen Van Phuoc |
| Call Number | AIT Thesis no. CS-93-23 |
| Subject(s) | Computer-aided design
|
| Note | A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science |
| Publisher | Asian Institute of Technology |
| Abstract | By far the most common and useful representation for curves and surfaces in computer-aided
geometric design is parametric representation. If it was easy to convert from implicit to
parametric forms, then parametric representations could usefully supplement implicit
representations, and we would convert between representations as required by the geometric
operation. However, algorithmic conversion from implicit to parametric form is not simple or
complete, and practical problems have forced ongoing researchers to explore effective methods
including deferring and sidestepping symbolic computations to lower the cost before
parameterization can become a routine operation.
This thesis presents the complete algorithms along with the implementations for
parameterizing curves and surfaces up to degree 2 in two and three dimensional spaces by
symbolic algebraic computations. A first geometric transformation approach along with complete
explicit formulae for all cases of quadric have been developed. The study has also studied and
solved successfully the parameterization problem for some classes of cubics and higher degree
varieties. The implementation programs written in Mathematica programming language greatly
speed up the processes of parameterizations and finding intersection curve of two surfaces. |
| Year | 1993 |
| Type | Thesis |
| School | School of Engineering and Technology (SET) |
| Department | Department of Information and Communications Technologies (DICT) |
| Academic Program/FoS | Computer Science (CS) |
| Chairperson(s) | Huynh, Ngoc Phien; |
| Examination Committee(s) | Bohez, Erik L.J.;Kanchana Kanchanasut; |
| Scholarship Donor(s) | Government of Switzerland; |
| Degree | Thesis (M.Sc.) - Asian Institute of Technology, 1993 |