Region Bisection via Minor Axis for Compact Sub-regions
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Solution Overview
Problem
Conventional methods for subdividing spatial regions into smaller, manageable zones often result in uneven areas, long perimeters, and inefficient zone sizes, particularly in GIS and electoral districting, where automation is needed to handle large datasets and ensure compact, uniformly sized sub-regions.
Innovation Solution
A data processing system that determines the centroid and minor axis of a region, recursively bisecting it along the minor axis to create sub-regions with approximately equal areas and minimal perimeters, ensuring compact shapes and meeting predefined thresholds.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional automated methods divide regions using simple grid or axis-aligned approaches, then the subdivision process is computationally simple and fast, but the resulting sub-regions have uneven areas and long perimeters
Solution Approach 1:
The patent segments the region subdivision problem into multiple hierarchical levels, where each level divides regions into smaller sub-regions. By using a tree-based structure with multiple levels of segmentation, the system achieves both computational efficiency (through systematic division) and improved sub-region uniformity (through progressive refinement at each level), resolving the contradiction between speed and precision.
Solution Approach 2:
The patent employs dynamic adjustment of subdivision parameters based on region characteristics. The system adapts the number of levels, division ratios, and boundary placements according to the specific geometry and properties of each region, allowing computational complexity to scale dynamically with problem difficulty while maintaining optimal sub-region quality metrics.
2Manufacturing precision
If manual methods are used to subdivide GIS zones, then sub-region boundaries can be precisely optimized for compact shapes and equal areas, but the time and effort required are large
Solution Approach 1:
The patent implements self-service automation where the system automatically performs complex subdivision operations without human intervention. The algorithm autonomously calculates optimal boundaries, adjusts subdivision parameters, and generates final sub-regions with manual-level precision, eliminating the time loss associated with manual while maintaining high-quality results.
Solution Approach 2:
The patent replaces manual mechanical subdivision processes with computational algorithms. Instead of human operators manually drawing boundaries and adjusting regions, the system uses automated computational geometry algorithms to calculate and generate optimal sub-region boundaries, substituting human effort with machine-based geometric processing that achieves similar or superior precision more quickly.
3Ease of operation
If regions are subdivided into many small zones to meet management requirements, then management efficiency improves, but the computational resources required increase
Solution Approach 1:
The patent uses dynamic control of subdivision granularity, allowing the system to adjust the number and size of sub-regions based on management requirements and computational constraints. The algorithm can dynamically determine the optimal number of levels and regions to create, balancing management efficiency needs against available computational resources, thus resolving the contradiction between operational ease and resource consumption.
Data Source
AI summary
Methods and systems in accordance with the present invention automatically subdivide an area having an arbitrary shape into multiple sub-regions that have approximately equal area under a threshold, with compact shapes having minimal perimeter length. These systems input an arbitrarily shaped zone and recursively bisect it until all of the new sub-zones are smaller than a particular threshold. A data processing system subdivides a two-dimensional region, such as a digital image of a landmass. The data processing system loads the region into memory, determines a minor axis of the region, and splits the region along the minor axis into a first sub-region and a second sub-region. The sub-regions are evaluated to determine if they are under the threshold area. The steps of the process are repeated until all resulting sub-regions are under the threshold area. Consistently compact sub-regions with minimal perimeter are achieved by splitting along the minor axis.