3D Cartesian Geospatial Indexing for Pole Accuracy
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Solution Overview
Problem
Conventional geospatial databases using two-dimensional models experience accuracy degradation at the North and South Poles and 180-degree East/West meridian lines, necessitating improved methods for geospatial search and indexing.
Innovation Solution
The system employs a three-dimensional Cartesian space using space-filling curves and modified GeoHash indexing, calculating polygon boundaries and intersections in Cartesian coordinates, which treats all points on the spherical surface equally, including the poles and meridian lines, enabling accurate geospatial searches without special handling.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a two-dimensional model based on latitudes and longitudes is used for geospatial indexing, then the system is simple to implement, but geospatial accuracy degrades at the North and South Poles and at the 180-degree East/West meridian lines
Solution Approach 1:
The patent transitions from a two-dimensional latitude/longitude model to a three-dimensional Cartesian coordinate system. By representing Earth as a unit sphere with x, y, z coordinates, the system eliminates the mathematical singularities that occur at poles and meridian lines in 2D projections, thereby maintaining consistent geospatial accuracy across all locations.
Solution Approach 2:
The patent changes the coordinate representation parameters from angular measurements (latitudes and longitudes) to Cartesian coordinates (x, y, z). This parameter transformation allows for uniform distance calculations and boundary intersections throughout the entire Earth surface, including previously problematic regions like the poles and 180-degree meridian.
2Measurement precision
If special handling is implemented for poles and meridian lines in two-dimensional models, then geospatial accuracy at critical points is improved, but the system complexity increases
Solution Approach 1:
The three-dimensional Cartesian coordinate system provides a universal framework that handles all geospatial locations uniformly, including poles and meridian lines, without requiring location-specific logic. The same distance and intersection calculations work everywhere on the sphere, eliminating the need for special-case handling code.
3Measurement precision
If conventional two-dimensional geospatial indexing is used, then search operations are straightforward, but accuracy degradation occurs at critical Earth locations
Solution Approach 1:
The patent replaces the geometric projection-based two-dimensional indexing mechanism with a three-dimensional Cartesian coordinate system. This substitution enables the use of standard Euclidean distance calculations and linear algebra for boundary intersections, providing both improved accuracy and computational efficiency through numeric index lookups.
Data Source
AI summary
Embodiments of a system and method for indexing of geospatial data using three-dimensional Cartesian space are generally described herein. In an aspect, such example methods may include calculating endpoints of a segment, wherein the endpoints are specified in Cartesian coordinates and are located on a substantially spherical surface, defining a boundary of a polygon according to the segment, computing one or more normals corresponding to one or more planes, wherein each of the one or more planes contain a test point and a boundary point associated with the boundary, obtaining a boundary sine value of an angle defined by an arc subtended by the endpoints, summing each of a group of angle values derived from the boundary sine value to obtain an angle sum, wherein the group contains the boundary sine value, and determining whether the test point is inside the polygon based on the angle sum.