Point-in-Polygon Determination Using Hierarchical Region Approximation
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Solution Overview
Problem
Current methods for determining whether a point lies within a polygon in a multidimensional space are inefficient in terms of processor resource usage, particularly when dealing with complex polygons, as they do not effectively utilize the information generated during polygon approximation for subsequent point-in-polygon analysis.
Innovation Solution
The method involves approximating a complex polygon by generating regions that encompass portions of the polygon, using algorithms like Ramer-Douglas-Peucker, and analyzing the intersection of a ray projected from the point with these regions to determine if the point is inside or outside the polygon, thereby efficiently utilizing the information for point-in-polygon determination.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional point-in-polygon algorithms are used, then determination accuracy is maintained, but processor resource usage increases
Solution Approach 1:
The patent applies preliminary action by pre-processing the polygon into a hierarchical structure of bounding boxes and regions before point-in-polygon queries are performed. This pre-computed structure enables rapid rejection of points outside the polygon without requiring full geometric analysis, thereby reducing processor resources during actual determination while maintaining accuracy.
Solution Approach 2:
The patent segments the polygon into multiple hierarchical levels of bounding boxes and regions. This segmentation allows the algorithm to process points at different levels of detail, quickly eliminating points that fall outside outer bounding boxes without performing computationally intensive operations, thus reducing overall processor resource usage while preserving determination accuracy.
2Loss of information
If complex polygon approximation is performed, then data description sufficiency is improved, but processor resource usage increases
Solution Approach 1:
The patent performs preliminary approximation of the complex polygon by generating bounding boxes and regional structures before point-in-polygon determination. This pre-computed approximation structure captures the essential geometric information needed for accurate determination while enabling efficient processing, thus reducing processor resource usage during actual queries.
Solution Approach 2:
The patent extracts key geometric information from the complex polygon by creating a hierarchical structure of bounding boxes and regions. This extracted structure contains the essential spatial information needed for point-in-polygon determination, allowing the algorithm to work with a simplified representation that reduces computational overhead while maintaining determination accuracy.
Data Source
AI summary
A computer-implemented method for determining whether a point lies within a first polygon in a multidimensional space and an electronic device for carrying out the method is disclosed. The method comprises accessing first polygon coordinates defining each of a position and a shape of the first polygon in the multidimensional space; accessing the point coordinates defining the position of the point in the multidimensional space; identifying regions of the multidimensional space each encompassing a respective portion of the first polygon coordinates, the regions approximating the first polygon; and storing, in a non-transitory computer-readable medium, region coordinates of at least one of the regions; whereby an analysis of the region coordinates and point coordinates is executable to generate an indication that the point lies within the first polygon and an indication that the point does not lie within the first polygon. Some implementations comprise executing the analysis and providing the indication.