| Title |
Formula for Dupin cyclidic cube and Miquel point |
| Translation of Title |
Dupino ciklidinio kubo formulė ir Miquelio taškas. |
| Authors |
Menjanahary, Jean Michel ; Krasauskas, Rimvydas |
| DOI |
10.15388/LMD.2024.37366 |
| Full Text |
|
| Is Part of |
Lietuvos matematikos rinkinys. Ser. A.. Vilnius : Vilniaus universiteto leidykla. 2024, t. 65, p. 1-8.. ISSN 0132-2818. eISSN 2335-898X |
| Keywords [eng] |
Dupin cyclide ; Dupin cyclidic cube ; quaternionic-Bézier formula |
| Abstract [eng] |
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. |
| Published |
Vilnius : Vilniaus universiteto leidykla |
| Type |
Journal article |
| Language |
English |
| Publication date |
2024 |
| CC license |
|
