Geofence Position Determination Using Ray Intersection Counting
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Solution Overview
Problem
Existing methods face challenges in accurately determining if a vehicle's position is within or outside an irregular geofence, particularly for devices with limited data processing resources, as they struggle to correctly represent and process the complex boundaries of such geofences.
Innovation Solution
A method is introduced where a geofence is defined as a closed circuit of straight line boundary segments in a Cartesian coordinate system, and a ray is constructed from the vehicle's position to count intersections with the boundary segments, characterizing the position as within the geofence if the count is odd and outside if it's even, while excluding intersections with boundary segments parallel to the ray and avoiding double counting at vertices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the geofence is defined as an irregular polygon to match real-world boundaries, then the accuracy of boundary representation is improved, but the computational complexity increases for devices with limited resources
Solution Approach 1:
The irregular polygon geofence is segmented into multiple straight line boundary segments. This segmentation allows the complex polygon to be processed as a series of simpler linear segments, reducing the computational burden while maintaining the accuracy of the irregular boundary representation. The ray intersection method processes each segment individually rather than treating the entire polygon as a complex whole.
Solution Approach 2:
The patent uses a ray (a simple geometric construct) to test intersection with the complex polygon boundary. Instead of directly processing the complex polygon geometry, a simplified ray is constructed and its intersections with the polygon segments are counted. This copying approach transforms a complex geometric problem into a simpler intersection counting problem.
2Device complexity
If the polygon is decimated to reduce data processing load, then the device complexity is reduced, but the measurement precision of the geofence boundary deteriorates
Solution Approach 1:
Rather than decimating (reducing) the polygon vertices, the patent segments the polygon into straight line boundaries. This segmentation maintains the fidelity of the original polygon shape while enabling efficient processing through ray intersection methods. Each segment is processed independently, avoiding the need to reduce the overall complexity of the geofence definition.
3Ease of operation
If a ray is constructed from the position to determine geofence status, then the ease of operation is improved, but the risk of double counting intersections at vertices increases
Solution Approach 1:
The patent applies different handling rules to different parts of the boundary segments. Specifically, when a ray passes through a vertex, the intersection is counted differently than when it passes through the middle of a segment. This local differentiation ensures that vertex intersections are not double-counted while maintaining simplicity in the overall algorithm. The rule assigns each vertex to only one adjacent segment for intersection counting purposes.
Data Source
AI summary
A geofence system which locates a position as within or without the complex polygon type geofence using a simplified algorithm. The algorithm obtains a position and compares it to the polygon by establishing a ray from the position constructed in a cardinal direction of the coordinate system. The “polarity” of the count of intersections between the ray and geofence indicates whether the position is inside the geofence or not.