Quaternionic Bézier curves, surfaces and volume
We extended the rational Bézier construction for linear, bi-linear and threelinear map, by allowing quaternion weights. These objects are Möbius invariant and have halved degree with respect to the real parametrization. In general, these parametrizations are in four dimensional space. We analyse whe...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2013-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Subjects: | |
| Online Access: | https://www.journals.vu.lt/LMR/article/view/14908 |
| _version_ | 1818792124600025088 |
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| author | Severinas Zube |
| author_facet | Severinas Zube |
| author_sort | Severinas Zube |
| collection | DOAJ |
| description | We extended the rational Bézier construction for linear, bi-linear and threelinear map, by allowing quaternion weights. These objects are Möbius invariant and have halved degree with respect to the real parametrization. In general, these parametrizations are in four dimensional space. We analyse when a special the three-linear parametrized volume is in usual three dimensional subspace and gives three orthogonal family of Dupine cyclides. |
| first_indexed | 2024-12-18T15:22:16Z |
| format | Article |
| id | doaj.art-455b161e90834ab880e2a8ab9d8a0e07 |
| institution | Directory Open Access Journal |
| issn | 0132-2818 2335-898X |
| language | English |
| last_indexed | 2024-12-18T15:22:16Z |
| publishDate | 2013-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj.art-455b161e90834ab880e2a8ab9d8a0e072022-12-21T21:03:22ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2013-12-0154A10.15388/LMR.A.2013.17Quaternionic Bézier curves, surfaces and volumeSeverinas Zube0Vilnius UniversityWe extended the rational Bézier construction for linear, bi-linear and threelinear map, by allowing quaternion weights. These objects are Möbius invariant and have halved degree with respect to the real parametrization. In general, these parametrizations are in four dimensional space. We analyse when a special the three-linear parametrized volume is in usual three dimensional subspace and gives three orthogonal family of Dupine cyclides.https://www.journals.vu.lt/LMR/article/view/14908circleDupine cyclideinversionquaternion |
| spellingShingle | Severinas Zube Quaternionic Bézier curves, surfaces and volume Lietuvos Matematikos Rinkinys circle Dupine cyclide inversion quaternion |
| title | Quaternionic Bézier curves, surfaces and volume |
| title_full | Quaternionic Bézier curves, surfaces and volume |
| title_fullStr | Quaternionic Bézier curves, surfaces and volume |
| title_full_unstemmed | Quaternionic Bézier curves, surfaces and volume |
| title_short | Quaternionic Bézier curves, surfaces and volume |
| title_sort | quaternionic bezier curves surfaces and volume |
| topic | circle Dupine cyclide inversion quaternion |
| url | https://www.journals.vu.lt/LMR/article/view/14908 |
| work_keys_str_mv | AT severinaszube quaternionicbeziercurvessurfacesandvolume |