Convex-Arc Drawings of Pseudolines
David Eppstein, Mereke van Garderen, Bettina Speckmann and, Torsten Ueckerdt

TL;DR
This paper explores various geometric representations of pseudoline arrangements, including convex arc drawings, and characterizes which arrangements can be represented by different convex curves and polygons.
Contribution
It introduces new geometric representations for pseudoline arrangements, especially for outerplanar and simple arrangements, expanding understanding of their visualizations.
Findings
Outerplanar arrangements can be represented by circle chords, convex chains, or hyperbolic lines.
Simple non-outerplanar arrangements can be represented by convex polygonal chains or smooth convex curves.
The paper characterizes the types of arrangements that admit these convex arc representations.
Abstract
A weak pseudoline arrangement is a topological generalization of a line arrangement, consisting of curves topologically equivalent to lines that cross each other at most once. We consider arrangements that are outerplanar---each crossing is incident to an unbounded face---and simple---each crossing point is the crossing of only two curves. We show that these arrangements can be represented by chords of a circle, by convex polygonal chains with only two bends, or by hyperbolic lines. Simple but non-outerplanar arrangements (non-weak) can be represented by convex polygonal chains or convex smooth curves of linear complexity.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Computational Geometry and Mesh Generation · Mathematics and Applications
