File(s) under permanent embargo
Reason: This item is currently closed access.
Bounded domain, bi-quadratic rational parametrisations of Dupin cyclides
journal contribution
posted on 2008-08-29, 09:55 authored by Helmut BezDupin cyclides, their applications in geometric modeling and their parametrisation
using bi-quadratic patches bounded by lines of curvature, have been investigated
in recent years by a number of authors - see, for example, Martin et al (1986);
Boehm (1990); Pratt (1990); Degen (1994, 1996). However no completely reliable
and general algorithm for the determination of bi-quadratic cyclide patches has
appeared in the literature. This paper presents a new approach that produces any
required bi-quadratic patch, bounded by lines of curvature, without non-intrinsic
geometric constraints or restrictions. Specifically, if a bi-quadratic parametrisation
exists for the specified region of the cyclide, then it is correctly determined. Explicit
formulæ are given for the Bernstein weights and vectors of the parametrisations.
The method is neither cyclide specific nor specific to the construction of bi-quadratic
rational parametrisations - it may therefore be applied to other surfaces and to
higher-degree rational constructions.
History
School
- Science
Department
- Computer Science
Citation
BEZ, H.E., 2008. Bounded domain, bi-quadratic rational parametrisations of Dupin cyclides. International Journal of Computer Mathematics, 85 (7), pp. 1097 – 1111Publisher
© Taylor & FrancisPublication date
2008Notes
This journal article is Restricted Access. It was published in the journal International Journal of Computer Mathematics and is available at: http://www.tandf.co.uk/journals/titles/00207160.aspISSN
0020-7160;1029-0265Language
- en