Aperture 3 Hexagon Tree Location Coding for Geospatial Grids
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Solution Overview
Problem
Existing location coding systems for geospatial data on icosahedral aperture 3 hexagon discrete global grid systems (DGGS) are inefficient due to the inability to effectively use path addresses, which are necessary for hierarchical algorithms and spatial queries, as aperture 3 hexagon grids do not form traditional trees, limiting the precision and efficiency of location coding.
Innovation Solution
The introduction of modified generalized balanced ternary (MGBT) and aperture 3 hexagon tree (A3HT) methods allows for the assignment of path address-form location codes, enabling efficient tiling of path address hierarchies onto the icosahedron, thereby specifying path address-form location codes for aperture 3 hexagon DGGS as vector, raster, or bucket systems, and providing a transformation to and from existing pyramid code systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If traditional pyramid address systems are used for icosahedral aperture 3 hexagon DGGS, then location codes can be assigned to cells, but hierarchical algorithms cannot operate effectively and spatial queries are inefficient
Solution Approach 1:
The patent segments the icosahedral surface into hierarchical resolutions using aperture 3 hexagon grids, where each cell at resolution K is divided into 7 cells at resolution K+1. This segmentation enables path address formation by creating a tree-like hierarchical structure that allows efficient spatial queries and hierarchical algorithms to operate on the DGGS.
Solution Approach 2:
The patent introduces a new dimensional organization by mapping the 2D hexagon grid cells onto a 1D path address space using modified generalized balanced ternary encoding. This dimensional transformation allows hierarchical algorithms to operate efficiently by converting spatial relationships into linear address sequences that can be processed by standard algorithms.
2Productivity
If path address-form location codes are implemented on aperture 3 hexagon grids, then hierarchical algorithms can operate effectively, but the grids must be reorganized into tree structures
Solution Approach 1:
The patent changes the parameter representation by using modified generalized balanced ternary encoding instead of traditional binary pyramid addresses. This parameter transformation allows each cell to be uniquely identified by a path address that encodes its hierarchical position, enabling efficient spatial queries while maintaining the aperture 3 hexagon grid structure.
Solution Approach 2:
The patent introduces modified generalized balanced ternary encoding as an intermediary system that bridges the aperture 3 hexagon grid structure and path address hierarchies. This intermediary encoding mechanism translates the unique 7-ary subdivision pattern of aperture 3 grids into a form that supports traditional tree-based hierarchical algorithms.
3Measurement precision
If precision of location coding is improved by using finer resolutions, then more detailed geospatial data can be represented, but the complexity of the coding system increases
Solution Approach 1:
The patent implements nested hierarchical resolutions where each cell at resolution K contains exactly 7 cells at resolution K+1, forming a nested structure. This nesting allows progressive refinement of location precision by traversing down the hierarchy, with each level providing finer spatial resolution while maintaining a systematic and manageable code structure through path addresses.
Data Source
AI summary
A method for assigning path address-form location codes to objects represented using aperture 3 hexagon discrete global grid systems in both vector systems and bucket and raster systems in which hexagons in a first resolution are given a linear code and hexagons in subsequent finer resolutions have identifiers added to the linear code, the method iteratively applying the assigning step to further finer resolutions to a maximum resolution. In vector systems each hexagon has seven hexagons in a finer resolution and in raster and bucket systems each hexagon is assigned to be an open or closed generator class, an open generator creating a closed generator in a finer resolution, and a closed generator generating six open generator hexagons and a seventh closed generator hexagon.