TY  - JOUR
T1  - On the Parameterization of Rational Ringed Surfaces and Rational Canal Surfaces
A1  - Bastl, Bohumír
A1  - Jüttler, Bert
A1  - Lávička, Miroslav
A1  - Schulz, Tino
A1  - Šír, Zbyněk
JA  - Mathematics in Computer Science
Y1  - 2014
KW  - blending
KW  - canal surface
KW  - Darboux cyclide
KW  - Dupin cyclide
KW  - rational parametrization
KW  - Ringed surface
N2  - 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.
M1  - Preprint project = NCMM
M1  - Preprint year = 2014
M1  - Preprint number = 08
M1  - Preprint ID = NCMM/2014/08
ER  -