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!
|
| _version_ | 1841561107512164352 |
|---|---|
| author | Jean Michel Menjanahary Rimvydas Krasauskas |
| author_facet | Jean Michel Menjanahary Rimvydas Krasauskas |
| author_sort | Jean Michel Menjanahary |
| collection | DOAJ |
| description |
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.
|
| format | Article |
| id | doaj-art-463af6b3bf2f4db2aa462f6000782f5a |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-463af6b3bf2f4db2aa462f6000782f5a2025-01-03T06:33:49ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2024-12-0165A10.15388/LMD.2024.37366Formula for Dupin cyclidic cube and Miquel pointJean Michel Menjanahary0https://orcid.org/0009-0007-4180-993XRimvydas Krasauskas1https://orcid.org/0000-0002-4464-8146Vilnius UniversityVilnius University 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. https://ojs.test/index.php/LMR/article/view/37366Dupin cyclideDupin cyclidic cubequaternionic-Bézier formula |
| spellingShingle | Jean Michel Menjanahary Rimvydas Krasauskas Formula for Dupin cyclidic cube and Miquel point Lietuvos Matematikos Rinkinys Dupin cyclide Dupin cyclidic cube quaternionic-Bézier formula |
| title | Formula for Dupin cyclidic cube and Miquel point |
| title_full | Formula for Dupin cyclidic cube and Miquel point |
| title_fullStr | Formula for Dupin cyclidic cube and Miquel point |
| title_full_unstemmed | Formula for Dupin cyclidic cube and Miquel point |
| title_short | Formula for Dupin cyclidic cube and Miquel point |
| title_sort | formula for dupin cyclidic cube and miquel point |
| topic | Dupin cyclide Dupin cyclidic cube quaternionic-Bézier formula |
| url | https://ojs.test/index.php/LMR/article/view/37366 |
| work_keys_str_mv | AT jeanmichelmenjanahary formulafordupincyclidiccubeandmiquelpoint AT rimvydaskrasauskas formulafordupincyclidiccubeandmiquelpoint |