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中文摘要：
地理空间的度量不宜再采用借助地图投影转换到欧氏空间内的近似解决途径,在定义了大地线尺度作地理空间度量的基础上,采用地图代数完成了全形态（点、线、面）图形在地球尺度空间的精密距离变换,并生成了相应的Voronoi图,为地球上相应于距离的各实际问题的解决提供了严密、合理的解决途径。
英文摘要：
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.
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