Some geometrical aspects of control points for toric patches
| dc.creator | Craciun, Gheorghe | |
| dc.creator | Garcia-Puente, Luis | |
| dc.creator | Sottile, Frank | |
| dc.date | 2008-12-06 | |
| dc.date | 2009-03-04 | |
| dc.date.accessioned | 2026-07-07T12:48:28Z | |
| dc.date.available | 2026-07-07T12:48:28Z | |
| dc.description | We use ideas from algebraic geometry and dynamical systems to explain some ways that control points influence the shape of a Bézier curve or patch. In particular, we establish a generalization of Birch's Theorem and use it to deduce sufficient conditions on the control points for a patch to be injective. We also explain a way that the control points influence the shape via degenerations to regular control polytopes. The natural objects of this investigation are irrational patches, which are a generalization of Krasauskas's toric patches, and include Bézier and tensor product patches as important special cases. | |
| dc.description | 24 pages, many color figures | |
| dc.identifier | https://arxiv.org/abs/0812.1275 | |
| dc.identifier | http://arxiv.org/abs/0812.1275 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222063 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 65D17, 14M25 | |
| dc.title | Some geometrical aspects of control points for toric patches | |
| dc.type | text |