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- Title
Formula for Dupin cyclidic cube and Miquel point.
- Authors
Menjanahary, Jean Michel; Krasauskas, Rimvydas
- Abstract
Dupin cyclides are surfaces conformally equivalent to a torus, a circular cone, or a cylinder. Their patches admit rational bilinear quaternionic Bézier (QB) parametrizations and are used in geometric design and architecture. Dupin cyclidic cubes are a natural trivariate generalization of Dupin cyclide patches. In this article, we derive explicit formulas for control points and weights of rational 3-linear QB parametrizations of Dupin cyclidic cubes and relate them with classical Miquel point construction.
- Subjects
CYLINDER (Shapes); CUBES; GEOMETRIC analysis; GENERALIZATION; PARAMETER estimation
- Publication
Lietuvos Matematikos Rinkinys, 2024, Vol 65, Issue Series A, p1
- ISSN
0132-2818
- Publication type
Academic Journal
- DOI
10.15388/lmd.2024.37366