| Title: |
Some geometrical aspects of control points for toric patches |
| Authors: |
Craciun, Gheorghe, Garcia-Puente, Luis, Sottile, Frank |
| Publication Year: |
2008 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Algebraic Geometry, 65D17, 14M25 |
| More Details: |
We use ideas from algebraic geometry and dynamical systems to explain some ways that control points influence the shape of a B\'ezier 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 B\'ezier and tensor product patches as important special cases.
Comment: 24 pages, many color figures |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/0812.1275 |
| Accession Number: |
edsarx.0812.1275 |
| Database: |
arXiv |
