Abstract
Given a set of planar curves (Jordan arcs), each pair of which meets — either crosses or touches — exactly once, we establish an upper bound on the number of touchings. We show that such a curve family has O(t 2n) touchings, where t is the number of faces in the curve arrangement that contains at least one endpoint of one of the curves. Our method relies on finding special subsets of curves called quasi-grids in curve families; this gives some structural insight into curve families with a high number of touchings.
Original language | English |
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Pages (from-to) | 29-37 |
Number of pages | 9 |
Journal | Computational Geometry |
Volume | 67 |
Issue number | Januari 2018 |
DOIs | |
Publication status | Published - Jan 2018 |
Keywords
- Combinatorial geometry;
- Touching curves;
- Pseudo-segments
- Touching curves
- Combinatorial geometry