Density Mapping System Using Geodetic Distance for Projection Accuracy
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Solution Overview
Problem
Existing computer-based geospatial applications fail to accurately represent density surfaces on maps due to projection distortions, particularly when displaying large geographic areas like the whole Earth, leading to inaccurate visualization of geographic areas and density falloff.
Innovation Solution
A density mapping system that uses geodetic distances and kernel density functions to generate and display density surfaces, accounting for projection distortions by transforming geographic coordinates into planar coordinates and back, ensuring accurate representation of geographic areas and density falloff.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If planar distance-based approach is used to generate density surfaces, then the density surface generation is simple and computationally efficient, but the representation of geographic area and density falloff becomes inaccurate due to projection distortions
Solution Approach 1:
The patent introduces geodetic distance as an intermediary measurement that accounts for the curved surface of the Earth. Instead of using planar distances directly from map projections, the system calculates distances along the geodesic paths on the Earth's surface, thereby mediating between the simplicity of planar calculations and the accuracy of spherical geometry.
Solution Approach 2:
The patent changes the fundamental parameter from planar distance to geodetic distance. By transforming the distance calculation method to account for Earth's curvature through spherical geometry formulas, the system maintains computational efficiency while significantly improving the accuracy of density surface representation across large geographic areas.
2Speed
If planar distance-based approach is used, then the processing speed is fast, but the density falloff representation becomes significantly inaccurate over large geographic areas
Solution Approach 1:
The patent changes the distance parameter from planar Euclidean distance to geodetic distance calculated using spherical geometry. This parameter change ensures that density falloff is computed along the actual surface paths on Earth, maintaining processing speed while dramatically improving accuracy for large-scale geographic representations.
3Device complexity
If density surfaces are generated irrespective of projection distortions, then the generation process is simple, but the visual representation on maps becomes significantly inaccurate
Solution Approach 1:
The patent uses geodetic distance calculation as an intermediary step that bridges the gap between simple density surface generation and accurate visual representation. By incorporating spherical geometry calculations, the system maintains relatively simple generation processes while achieving accurate visual representation that respects Earth's curvature and eliminates projection distortion effects.
Data Source
AI summary
Techniques in a data processor for drawing a density surface on a map in a manner that more accurately accounts for projection distortion in the map. According to one embodiment, data is maintained that represents a geotagged event. A map plane is divided into a plurality of cells and an origin cell corresponding to the geotagged event is identified. Density values are allocated to cells surrounding the origin cell based on geodetic distances between geographic coordinates corresponding to surrounding cells and the geographic coordinate of the geotagged event. A density surface based on the cell allocations is then displayed on a map. By allocating density values to cells based on geodetic distances, the resulting density surface displayed on the map more accurately accounts for projection distortions in the area of the map on which density surface is displayed.