Formula for Dupin cyclidic cube and Miquel point
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 cyc...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Vilnius University Press
2024-12-01
|
| Series: | Lietuvos Matematikos Rinkinys |
| Subjects: | |
| Online Access: | https://ojs.test/index.php/LMR/article/view/37366 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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.
|
|---|---|
| ISSN: | 0132-2818 2335-898X |