Accurate Algorithms for Spatial Operations on the Spheroid in a Spatial Database Management System

Some of the most powerful spatial analysis software solutions (Oracle, Google Earth Engine, PostgreSQL + PostGIS, etc.) are currently performing geometric calculations directly on ellipsoid (a quadratic surface that models earth shape), with a double purpose: to attain high degree accuracy and allow full management large areas territory (countries or even continents). It is well known both objectives impossible achieve by means traditional approach using local mathematical projections Cartesian coordinates. This paper demonstrates in quantitative methodological way products make important deviations regarding geodesics, being users unaware magnitude these inaccuracies, which can easily reach meters depending distance. due use an approximate (e.g., sphere instead ellipsoid). presents implementation two algorithms solve (less than 100 nm) efficiently (few iterations) basic essential build more complex operators: intersection geodesics minimum distance from point geodesic.