Digital distances on the 4-fold pentille tessellation.

Authors

Benedek Nagy, MohammadReza Saadat

Published in

Scientific reports. Volume 15. Issue 1. Pages 35601. Oct 13, 2025. Epub Oct 13, 2025.

Abstract

4-fold pentille tessellation is in two of the known eight classes of periodic tessellations with convex pentagons with side-to-side property and it is also known as Cairo pattern. In these tessellations, the tiles occur in four different orientations and each pentagon tile has five side-neighbors (neighbor pentagons such that a full side is shared) and seven corner-neighbors (pentagons such that there is at least one point shared on the boundary, i.e., at least a corner). Digital, i.e., path-based distances were recently computed on this grid for side-neighbor criteria in Kovács et. al.: Distance on the Cairo pattern. Pattern Recognit. Lett. 145: 141-146 (2021),¹, where the tiles are addressed by coordinate six-tuples. In this paper our aim is twofold, on the one hand, we give a much less complex description of the grid based on coordinate pairs, on the other hand, we compute also the distance based on corner-neighbors. Our result applies to two of the classes of the known 8 periodic side-to-side pentagonal tessellations based on a sole convex pentagon tile.

PMID:
41083474
Bibliographic data and abstract were imported from PubMed on 14 Oct 2025.

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