Orientation Preserving Maps of the Square Grid II

Bárány, Imre and Pór, Attila (2023) Orientation Preserving Maps of the Square Grid II. DISCRETE AND COMPUTATIONAL GEOMETRY. ISSN 0179-5376


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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 . © 2023, Crown.

Item Type: Article
Additional Information: Alfréd Rényi Institute of Mathematics, 13 Reáltanoda Street, Budapest, 1053, Hungary Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, United Kingdom Department of Mathematics, Western Kentucky University, 1906 College Heights Blvd. #11078, Bowling Green, 42101, KY, United States Export Date: 22 November 2023; Cited By: 0; Correspondence Address: I. Bárány; Department of Mathematics, University College London, London, Gower Street, WC1E 6BT, United Kingdom; email:
Uncontrolled Keywords: ORDER TYPES; n×n grid; Orientation preserving maps;
Subjects: Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria
Depositing User: MTMT SWORD
Date Deposited: 22 Nov 2023 17:34
Last Modified: 22 Nov 2023 17:34

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