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arXiv · 1601.06865

Convex-Arc Drawings of Pseudolines

David Eppstein·Mereke van Garderen·Bettina Speckmann·Torsten Ueckerdt
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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.

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David Eppstein, Mereke van Garderen, Bettina Speckmann, Torsten Ueckerdt. 2016-01-26. Convex-Arc Drawings of Pseudolines. https://arxiv.org/abs/1601.06865

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