Geospatial Cluster Border Approximation via Triangulation
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Solution Overview
Problem
Mapping service providers face challenges in automatically approximating the borders between clusters of geospatial data points, particularly in areas with gaps without geospatial points, such as parks or farm lands, which affects the definition of franchise service areas.
Innovation Solution
A method involving tessellating geospatial points to generate triangles, determining triangle edges connecting points with different codes, adding new points along these edges to their centroids, and forming polygons to represent borders between code sets, thereby approximating the borders between clusters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional clustering methods are used to group geospatial data points, then clusters can be formed, but the borders between clusters cannot be accurately determined in areas with gaps without geospatial points
Solution Approach 1:
The patent segments the geospatial space by tessellating points into triangles, dividing the continuous space into discrete triangular elements. This segmentation allows border approximation to proceed element-by-element through the triangulation mesh, enabling precise tracking of cluster boundaries even in gap areas where no original geospatial points exist.
Solution Approach 2:
The patent introduces triangles as intermediary geometric structures that mediate between the discrete geospatial points and the continuous cluster borders. These triangles fill the gap areas without points, providing a mathematical framework to infer and approximate borders in regions where direct measurement is impossible.
2Manufacturing precision
If manual border definition is used to accurately define franchise service areas, then precision can be achieved, but the process becomes time-consuming and labor-intensive
Solution Approach 1:
The system performs self-service by automatically computing cluster borders through algorithmic processing of the triangulated geospatial data. The border approximation is generated autonomously by the system itself through mathematical operations on the triangle mesh, eliminating the need for manual intervention while maintaining high precision.
Solution Approach 2:
The patent replaces the mechanical manual process of border definition with an automated computational system. Instead of human operators manually drawing borders, the system uses algorithmic processing of triangulated geospatial data to automatically generate precise border approximations, substituting mechanical human labor with computational automation.
3Measurement precision
If geospatial points are densely distributed to improve border accuracy, then measurement precision increases, but data collection complexity and costs increase
Solution Approach 1:
The patent transitions from measuring borders directly in the geospatial point distribution space to measuring them in the triangulation mesh space. By lifting the problem to a higher dimensional mathematical construction (the triangle mesh), the system can approximate borders with the same accuracy as dense point distribution would provide, but using the existing sparse points combined with mathematical interpolation.
Data Source
AI summary
An approach is provided for approximating border(s) between clusters of geospatial points based on triangulation. The approach involves receiving geospatial points respectively associated with at least one of a plurality of codes representing an identifiable characteristic. The approach also involves tessellating the points to generate triangles. The approach further involves processing the triangles to determine triangle edge(s) that connects a first point associated with a first code set and a second point associated with a second code set. The approach further involves, for each of the determined triangle edge(s), adding a new point along the determined triangle edge and generating a new edge from the new point to a centroid of a respective triangle. The approach further involves determining a polygon based on the new edge. The polygon represents a border between the points associated with the first code set and the points associated with the second code set.