The size of spanning disks for polygonal curves

Details The size of spanning disks for polygonal curves The size of spanning disks for polygonal curves

1999-06-28

arxiv.org/abs/math/9906197v2

Discrete and Computational Geometry 29 (2003) 1--17.

Mathematics

Geometric Topology

17 pages, 16 figures

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The size of spanning disks for polygonal curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The size of spanning disks for polygonal curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The size of spanning disks for polygonal curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-422461