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

Formula for Dupin cyclidic cube and Miquel point.

Menjanahary, Jean Michel; Krasauskas, Rimvydas