| Author | Chuang, Chen-chang |
| Call Number | AIT Thesis no.CS-89-11 |
| Subject(s) | Computer-aided design
|
| Note | A thesis submitted in partial fulfillment of the requirements for
the degree of Master of Engineering |
| Publisher | Asian Institute of Technology |
| Abstract | The Beta-spline developed by Barsky is to combine uniform
cubic B-splines with geometric continuity using the unit tangent
vector and curvature vector. Two shape parameters called bias and
tension respectively were introduced to take care of the geometric
continuity constraints. The effects of these two parameters
on the shape of the curve have been studied. Uniformly-shaped β-spline
has fixed shape parameters which affect the curve over
the whole length. For a more “local” sense, continuous-shaped
β-spline is formed by introducing quintic interpolating polynomial
between the distinct β values at each knot. Some “kinks” is
created in case of wildly varying adjacent β values. This is not
a desired situation in Computer Aided Geometric Modeling.
Later, Goodman gave a general definition of β -splines. The
basic properties of convex hull and variation diminishing have
been shown. An explicit formula for cubic β-splines has been
given. Starting from this definition and the explicit formula, a
B- β spline concept was suggested for computational efficiency
thanks to its recurrence relation. The computation scheme and
implementation were also given.
Analogous to β-splines, discrete β-splines with the technique
of subdivision and the knots insertion on the β-spline
curves have been studied, based on the above general definition
of B-spline. A computation scheme of the above two methods was
discussed. |
| Year | 1989 |
| 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.;Phan, Minh Dung; |
| Scholarship Donor(s) | Goverment of R.O.C.; |
| Degree | Thesis (M.Eng.) - Asian Institute of Technology, 1989 |