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Title: Bounded domain, bi-quadratic rational parametrisations of Dupin cyclides
Authors: Bez, Helmut E.
Issue Date: 2008
Publisher: © Taylor & Francis
Citation: BEZ, H.E., 2008. Bounded domain, bi-quadratic rational parametrisations of Dupin cyclides. International Journal of Computer Mathematics, 85 (7), pp. 1097 – 1111
Abstract: Dupin 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.
Description: 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.asp
URI: https://dspace.lboro.ac.uk/2134/3584
ISSN: 0020-7160
Appears in Collections:Closed Access (Computer Science)

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