This is a work-in-progress to explore the possibility of neighbor traversal in the Z7 domain. Z7 is an indexing system for aperature 7 hexagonal discrete global grid systems, as coined in Kmoch et al. (2025). It is based on the Generalized Balanced Ternary (GBT) numeral system described in Lucas, Gibson (1982), van Roessel (1988), and Wikipedia (2025).
Lucas and Gibson (1982) gave examples of GBT with exclusively counter-clockwise (CCW) rotation. The disadvantage of this approach is that the orientation of the hexagons at the different hierarchy levels quickly diverge from each other. White et al. (1992) proposed an alternating rotation direction (CW, CCW, CW, ...) to maintain an alignment of hexagon orientations across hierarchy levels. Kmoch et al. (2025) adopted this alternating rotation pattern for Z7 assigning CW to odd resolutions and CCW to even resolutions.
For reference purposes a rendering of three hierarchies of alternating GBT rotation is included (CW, CCW, CW).
| Counter-clockwise (CCW) | Clockwise (CW) |
|---|---|
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- Kmoch, A., Sahr, K., Chan, W. T., & Uuemaa, E. (2025). IGEO7: A new hierarchically indexed hexagonal equal-area discrete global grid system. AGILE: GIScience Series, 6(32). https://doi.org/10.5194/agile-giss-6-32-2025
- Lucas, D., & Gibson, L. (1982). Automated Analysis of imagery. Air Force Office of Scientific Research. https://apps.dtic.mil/sti/tr/pdf/ADA125710.pdf. (No. AFOSRTR830055).
- Sahr, K. (2011). Hexagonal discrete global grid systems for geospatial computing. Archives of Photogrammetry Cartography and Remote Sensing, 22, 363–376.
- van Roessel, J. W. (1988). Conversion of Cartesian coordinates from and to Generalized Balanced Ternary addresses. Photogrammetric Engineering & Remote Sensing, 54(11), 1565–1570.
- White, D., Kimerling, J. A., & Overton, S. W. (1992). Cartographic and Geometric Components of a Global Sampling Design for Environmental Monitoring. Cartography and Geographic Information Systems, 19(1), 5-22. https://doi.org/10.1559/152304092783786636
- Wikipedia Contributors. (2025, December 16). Generalized balanced ternary. Wikipedia; Wikimedia Foundation.