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Giving Birth to the International Society for Geometry and Graphics—A Documentation of the Years 1988–1994 Read chapter Read first chapter

2019 | OriginalPaper | Chapter

Parametrizing 3-Webs of Circles on Darboux Cyclides

Author : Rimvydas Krasauskas

Published in: ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics

Publisher: Springer International Publishing

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Abstract

In 2012 Pottmann et al. presented full classification of 3-webs (hexagonal webs) of circles on Darboux cyclides into 5 types. We provide rational trigonometric bilinear parametrizations of these webs of circles in all cases except for the general case of type 3, which has a parametrization involving square root. As a direct corollary, analytic formulas for discrete 3-webs can be easily extracted from these parametrizations.

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Literature
1.
Blaschke, W., Bol, G.: Geometrie der Gewebe. Springer, Berlin (1938)MATH
2.
Krasauskas, R., Zube, S.: Rational Bézier formulas with quaternion and Clifford algebra weights. In: SAGA—Advances in ShApes, Geometry, and Algebra, Geometry and Computing, vol. 10, pp. 147–166. Springer, Cham (2014)
3.
4.
5.
Pottmann, H., Shia, L., Skopenkov, M.: Darboux cyclides and webs from circles. Comput. Aided Geom. Des. 29, 77–97 (2012)MathSciNetCrossRef
Metadata
Title
Parametrizing 3-Webs of Circles on Darboux Cyclides
Author
Rimvydas Krasauskas
Copyright Year
2019
Book
ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics

Print ISBN: 978-3-319-95587-2

Electronic ISBN: 978-3-319-95588-9

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-95588-9_201

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