Bárány, I;
Pór, A;
(2023)
Orientation Preserving Maps of the Square Grid II.
Discrete and Computational Geometry
10.1007/s00454-023-00531-y.
(In press).
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Abstract
For a finite set S⊂ R2 , a map φ: S→ R2 is orientation preserving if for every non-collinear triple u, v, w∈ S the orientation of the triangle u, v, w is the same as that of the triangle φ(u) , φ(v) , φ(w) . Assuming that φ: Gn→ R2 is an orientation preserving map where Gn is the grid { 0 , ± 1 , ⋯ , ± n} 2 and n is large enough we prove that there is a projective transformation μ: R2→ R2 such that ‖ μ∘ φ(z) - z‖ = O(1 / n) for every z∈ Gn .
| Type: | Article |
|---|---|
| Title: | Orientation Preserving Maps of the Square Grid II |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00454-023-00531-y |
| Publisher version: | http://dx.doi.org/10.1007/s00454-023-00531-y |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Order types, Orientation preserving maps, n × n grid |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10188035 |
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