分析了空间插值模型，数字地面模型和它们与地理信息系统集成的研究进展，存在的缺陷和需要解决的理论问题，论述了建立基于曲面论和遥感反演方法数字模型及实现其与地理信息系统有效集成的必要性和可行性。

The existing digital models can be classified into spatial interpolation models and digital terrain models. Spatial interpolation can be defined as the procedure of estimating the value of properties at unsampled sites within the area covered by existing point observation. The methods for spatial interpolation include interpolation by drawing boundaries, trend surface analysis, spline functions, moving averages and Kriging interpolation. A digital terrain model is an ordered array of numbers that represent the spatial distribution of terrain attributes. Three exiting principal ways of structuring a digital terrain model are triangulated irregular networks, regular grid networks and contour|based networks. Issues on errors of digital terrain models and spatial interpolation models have been important research topics since the late 1960s and many methods for analyzing and measuring errors have been developed. However, the error problem is not attacked at the root. Although relative studies have found that slope, aspect and curvature are the most important variables for a surface, these variables are not used in formulation of the relative models. In fact, the first and the second fundamental forms are determinants of a surface, while the slope, aspect and curvature only are determinants of the thalweg of a surface according to differential geometry. The digital model of the 4th generation GIS is based on the fundamental theorem of surfaces and approach of remote sensing inversion, which can integrate theory of differential geometry with expertise, remote sensing information over an area and monitoring information at points.