Distance Transformation and Voronoi Generation on Earth Ellipsoid——Metrics of Geographic Space

The accurate measurement of distance between features on surface of the Earth ellipsoid and its visualization is one of the most important challenges in geometry.It is related to status determination of moving objects on the Earth surface,and is thus the fundamental for other spatial metrics and spatial analysis.It is inexact and inefficient to use Euclidian distance on a map projection as a substitute for measurement of distance on the surface of Earth ellipsoid.An approach based on map algebra is developed to achieve accurate distance transformation for whole type of shapes(i.e.points,lines,and polygon) on the metric space of Earth ellipsoid.And Voronoi diagrams can be then generated.The approach proposed gives an accurate and applicable solution to issues about measurement of distance on the Earth surface.