Multi-Resolution Hexagonal Grid Indexing for Spatial Data
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current spatial data structures, such as square quadtrees, face limitations in efficiently representing and indexing multi-resolution spatial data, particularly when compared to hexagonal grids, which offer better angular resolution and proximity querying but struggle with recursive partitioning and aggregation.
Innovation Solution
The development of multi-resolution indexing systems using mixed-aperture polygons, specifically aperture 3, 4, and 7 hexagons, allowing for arbitrary combinations of resolutions and unique coordinate assignments, enabling efficient location coding and indexing on both flat and spherical surfaces.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If square quadtree structures are used for spatial indexing, then implementation simplicity is maintained, but manufacturing precision and measurement precision of spatial relationships deteriorate
Solution Approach 1:
The patent segments the spatial indexing problem into multiple resolution levels, where each level divides space into discrete cells. This segmentation allows the system to achieve both computational simplicity through discrete operations and spatial precision through hierarchical multi-resolution representation, resolving the contradiction between ease of implementation and spatial relationship accuracy.
2Measurement precision
If hexagonal grids are used for spatial representation, then measurement precision and angular resolution are improved, but device complexity increases due to inability to use simple aggregation or recursive partition
Solution Approach 1:
The patent implements nested hexagonal grids where finer resolution grids are embedded within coarser resolution grids. Each hexagon at one resolution level contains multiple hexagons at the next finer level, creating a hierarchical structure that maintains the geometric advantages of hexagons while enabling efficient aggregation and partitioning operations through the nested organization.
Solution Approach 2:
The patent adds a hierarchical resolution dimension to the two-dimensional hexagonal grid, transforming it from a flat structure to a multi-level hierarchical structure. This dimensional addition enables efficient aggregation and partitioning operations by organizing hexagons across multiple resolution levels, thereby reducing the complexity of hexagonal grid operations while preserving their geometric precision advantages.
3Adaptability or versatility
If multi-resolution indexing is implemented, then adaptability to different spatial requirements is improved, but loss of information increases due to coordinate assignment complexity
Solution Approach 1:
The patent performs preliminary coordinate assignment by establishing a systematic coordinate system for each resolution level before actual spatial indexing occurs. This preliminary action defines the relationship between coordinates at different resolutions, ensuring that coordinate information is preserved and can be accurately transformed across resolution levels, thereby preventing information loss while maintaining adaptability.
Data Source
Figure 1~4
Figure 5~6
Figure 7~8
AI summary
Spatial location systems can be based on multi-resolution grids such as mixed aperture combinations of hexagonal cells. A particular finest resolution can be selected based on a suitable combination of intermediate grid apertures such as arbitrary combinations of aperture 3, aperture 4, and aperture 7 hexagons. Location identifiers can be uniquely assigned by generating child cells from a parent cell so that the generated child cells do not overlap child cells of other parent cells. One or more child blocks can be used at any resolution to avoid such overlap. For aperture three and aperture four hexagonal cells, blocks of four and three child cells, respectively, can be used to provide unique location identifiers.