Abstract
Some of the most powerful spatial analysis software solutions (Oracle, Google Earth Engine, PostgreSQL + PostGIS, etc.) are currently performing geometric calculations directly on the ellipsoid (a quadratic surface that models the earth shape), with a double purpose: to attain a high degree of accuracy and to allow the full management of large areas of territory (countries or even continents). It is well known that both objectives are impossible to achieve by means of the traditional approach using local mathematical projections and Cartesian coordinates. This paper demonstrates in a quantitative methodological way that most of the spatial analysis software products make important deviations in calculations regarding to geodesics, being the users unaware of the magnitude of these inaccuracies, which can easily reach meters depending on the distance. This is due to the use of ellipsoid calculations in an approximate way (e.g., using a sphere instead of an ellipsoid). This paper presents the implementation of two algorithms that solve with high accuracy (less than 100 nm) and efficiently (few iterations) two basic geometric calculations on the ellipsoid that are essential to build more complex spatial operators: the intersection of two geodesics and the minimum distance from a point to a geodesic.
Highlights
The most popular vector spatial operations like overlay or intersections of geometries, areas of influence, etc. require calculations that are made up of other basic geometric calculations such as: Operation A: Distance and azimuth between two points. Operation B: Calculation of a second point, from a starting point, an azimuth and a distance. Operation C: Area calculation. Operation D: Line intersection. Operation E: Minimum distance from a point to a line.Any spatial analysis software implements these basic geometric calculations in 2D/3D by itself or through some computational geometry libraries like GDAL, JTS, etc. [1]
We demonstrated that some of the most powerful spatial analysis software solutions perform some geodetic calculations approximately
Two of these operations are the intersection of two geodesics and the minimum distance from a point to a geodesic
Summary
The most popular vector spatial operations like overlay or intersections of geometries, areas of influence (buffer operator), etc. require calculations that are made up of other basic geometric calculations such as:. The most powerful spatial analysis software solutions (Oracle, Google Earth Engine, PostgreSQL + PostGIS, etc.) have implemented some geometric calculations directly on the spheroid. In this way, these software can offer high accuracy over large areas (countries or even continents). For more than a decade the geospatial analysis software products (GIS Desktop, Spatial Databases, and computational geometric libraries) have incorporated quite good 3 of 21 implementations on the ellipsoid of operations A and B with high accuracy (e.g., the methods ST_Azimuth, ST_Project and ST_Distance in PostGIS [15]).
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