On the Parameterization of Rational Ringed Surfaces and Rational Canal Surfaces
| Type of publication: | Article |
| Citation: | |
| Publication status: | Accepted |
| Journal: | Mathematics in Computer Science |
| Year: | 2014 |
| Abstract: | Ringed surfaces and canal surfaces are surfaces that contain a one-parameter fam- ily of circles. Ringed surfaces can be described by a radius function, a directrix curve and vector eld along the directrix curve, which speci es the normals of the planes that contain the circles. In particular, the class of ringed surfaces includes canal surfaces, which can be obtained as the envelopes of a one-parameter family of spheres. Consequently, canal surfaces can be described by a spine curve and a radius function. We present parameterization algorithms for rational ringed surfaces and rational canal surfaces. It is shown that these algorithms may generate any rational parameterization of a ringed (or canal) surface with the property that one family of parameter lines consists of circles. These algorithms are used to obtain rational pa- rameterizations for Darboux cyclides and to construct blends between pairs of canal surfaces and pairs of ringed surfaces. |
| Preprint project: | NCMM |
| Preprint year: | 2014 |
| Preprint number: | 08 |
| Preprint ID: | NCMM/2014/08 |
| Keywords: | blending, canal surface, Darboux cyclide, Dupin cyclide, rational parametrization, Ringed surface |
| Authors | |
| Added by: | [JP] |
| Total mark: | 0 |
|
Attachments
|
|
|
|
|
Notes
|
|
|
|
|
|
Topics
|
|
