3D Spatial Search Using Polygon Centroid Mapping

The patent divides the three-dimensional space into multiple two-dimensional planes (e.g., x-y planes at different z-heights). Each plane is independently processed to identify polygons containing target data points. This segmentation allows parallel processing of multiple planes simultaneously, reducing overall processing time while maintaining comprehensive spatial coverage and mapping accuracy.

The patent reduces the computational problem from searching in full three-dimensional space to searching in multiple two-dimensional planes. By projecting 3D data points onto 2D planes and identifying containing polygons in each plane, the system achieves O(1) time complexity per plane regardless of the total number of polygons in 3D space, thus solving the time-accuracy contradiction.

The patent segments the large three-dimensional space into multiple manageable two-dimensional planes. Each plane can be processed independently with constant time complexity O(1) per plane using the polygon centroid method. This allows the system to handle increased range and granularity by simply adding more planes to process, rather than increasing computational complexity for the entire space.

The patent processes each 2D plane independently and identifies only the relevant polygons containing target points, rather than processing all polygons in the entire 3D space. This partial action approach ensures that computing power requirements remain constant per plane regardless of the total number of polygons, enabling scalable processing of large-granularity spaces.