On the Parameterization of Rational Ringed Surfaces and Rational Canal Surfaces |
| |
Authors: | Bohumír Bastl Bert Jüttler Miroslav Lávička Tino Schulz Zbyněk Šír |
| |
Affiliation: | 1. University of West Bohemia, Plzeň, Czech Republic 2. Johannes Kepler University of Linz, Linz, Austria 3. INRIA Méditerranée, Sophia-Antipolis, Valbonne, France 4. Charles University in Prague, Prague, Czech Republic
|
| |
Abstract: | Ringed surfaces and canal surfaces are surfaces that contain a one-parameter family of circles. Ringed surfaces can be described by a radius function, a directrix curve and vector field along the directrix curve, which specifies 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 parameterizations for Darboux cyclides and to construct blends between pairs of canal surfaces and pairs of ringed surfaces. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|