地球数字产品的空间数学基础

在分析当前地球数字产品空间数学基础局限性的基础上,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,提出一套适合于大型GIS和地球数字产品的“地图投影”模型的实用模型,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四个方面的需要,从地图投影进到本模型将是方向和技术趋势。

Research on Mathematical Base for Digital Geo-products

Large-scale GIS and the Earth spatial data products are confronted with the problem how to define their space mathematical base in theory and practice, which is also the basic problem of the development of the whole Geographic Information Science. Now, many international academic institutes and famous scholars show much interest in it. 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 GIS take map projections as space mathematical base. Various GIS adopt respective reference systems and map projections adapting to the region and the scale, and all GIS corresponding to the state basic scales take Gauss projection as mathematical base in China. However, lots of practice have 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 and is 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 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, it can show the location of any point of the global exactly and uniquely in form of (B,L,H), it 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.