大型GIS与数字地球的空间数学基础研究

Research on System Space Mathematical Base of Large-scale GIS and the Digital Earth

将地图投影概念由传统的曲面到平面的变换扩展为曲面到曲面的变换 ,并提出一套适合于大型GIS和地球数字产品的实用“地图投影”模型。该模型的视图采用等距离切圆柱投影 ,度量空间是椭球面几何系统 ,符合计算机环境下GIS视图与度量空间分离的特性。鉴于全球多分辨率连续可视化 ,精密可视化量算、三维、多维地球数据统一 ,标准的空间定位框架和只有在统一的空间系统内 ,全球资源、生态环境数据才能进行精确的地理分析等 4个方面的需要 。

The map projection is a kind of topology transformation between two_dimensional fields in order to express the earth surface with limited plane maps.When choosing a concrete type of map projection,we usually consider three factors: map use,map scale,and location,shape,area of the region.Map projections are the space mathematical base of maps.GIS came of cartology,and maps are the main data source of GIS.Currently,most GISs take map projections as space mathematical base.Various GISs adopt respective reference systems and map projections adapting to the region and the scale,and all GISs corresponding to the state basic scales take Gauss projection as mathematical base in China.However,lots of practice has proved that large_scale GIS which take Gauss projection as space mathematical base have a lot of problems,e.g.large region can not be continuously visualized.Since spatial objects are digitized in respective maps which are discontinuous,complex map merging is necessary but hard to handle.Gauss projection is not applicable for integrating maps at different scales over a large rang.The systems are limited to expand and update with development.It is difficult to define the third dimension and the time dimension in such complex two dimension measurement space.The fact that GISs use different reference systems is a main disadvantage for both GIS's development and the form of the Digital Earth. The mathematical base of GIS is essential to unify the GIS established separately.It is also the premise for building the Digital Earth.After analyzing the status quo and the limitations of the space mathematical base of GIS,this paper points out definitely that the geodetic coordinate system is uniform,which can show the location of any point of the global exactly and uniquely in form of ( B,L,H ) and is the most proper reference system of large_scale GIS and Digital Earth.Moreover,this paper also puts forward a set of practical model of the standard “map projection',that is, R multiplied L is X ,and the product of R and B is Y ,where L is the longitude, B is the latitude,and their units are radian. R is the mean curvature radius of the earth. The model is similar in form to the cylindrical equidistant projection,but they differ from each other in essence.The first one is the plane view of the geodetic coordinate system's horizontal projection,and it provides the exact 2D geometry measurement space on the global earth surface.The view system and the measurement space are separate in the model,but the latter is the plane view and the plane measurement system. Finally,this paper introduces a DRG system based on this model.