The size of spanning disks for polygonal curves
| dc.creator | Hass, Joel | |
| dc.creator | Snoeyink, Jack | |
| dc.creator | Thurston, William P. | |
| dc.date | 1999-06-28 | |
| dc.date | 2002-03-23 | |
| dc.date.accessioned | 2026-07-07T05:29:42Z | |
| dc.date.available | 2026-07-07T05:29:42Z | |
| dc.description | Let $K$ be a closed polygonal curve in $\RR^3$ consisting of $n$ line segments. Assume that $K$ is unknotted, so that it is the boundary of an embedded disk in $\RR^3$. This paper considers the question: How many triangles are needed to triangulate a Piecewise-Linear (PL) spanning disk of $K$? The main result exhibits a family of unknotted polygons with $n$ edges, $n \to \infty$, such that the minimal number of triangles needed in any triangulated spanning disk grows exponentially with $n$. For each integer $n \ge 0$, there is a closed, unknotted, polygonal curve $K_n$ in $R^3$ having less than $10n+9$ edges, with the property that any Piecewise-Linear triangulated disk spanning the curve contains at least $2^{n-1}$ triangles. | |
| dc.description | 17 pages, 16 figures | |
| dc.identifier | https://arxiv.org/abs/math/9906197 | |
| dc.identifier | http://arxiv.org/abs/math/9906197 | |
| dc.identifier | Discrete and Computational Geometry 29 (2003) 1--17. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78739 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25; 57R05, 68U05 | |
| dc.title | The size of spanning disks for polygonal curves | |
| dc.type | text |