| Digital Elevation Model (DEM) is the most important spatial geography information in the geography information system (GIS) database and also the core data that the geography analysis depends on. It is a high-tech outcome with many academics crosses with and permeates. DEM plays a more and more important role in much area, such as mapping, environment, disaster prevention, digital battlefield, national economy realm which relevant with geography analysis and so on.The DEM surface interpolate function influence the DEM quality directly, is the core problem of the DEM. It pierces through to the sector of DEM produce, quality control, accuracy evaluate and apply. The terrain surface based on TIN have a lot of advantages according to based on Grid and it is a method that the lifelike terrain surface expression usually adopts. But currently the DEM surface based on TIN existence problems such as singularity,not smooth,could not reach higher accuracy etc.This paper studies how to build the smooth surface model and accuracy valuation of DEM based on TIN.A model of surface interpolation with c~1 continuities of DEM is given based on TIN. Then a mathematical surface is used to evaluate the accuracy of the model, and the model is applied to the representation of actual terrain. The main results have:(1) Analyze the foundation mathematics knowledge which involved in the DEM surface interpolation based on TIN. The qualification of two adjoining triangle areas to connect together smooth and a kind of method that solves the vertex information of the triangle slice are given.(2) Analyze the continuous but not smooth surface interpolate function, the model of 2D Gauss wavelet function interpolation and Triangular Bézier Patch interpolation are given and the result of interpolate is analyzed.(3) According to the smoothness of the terrain and correlation between adjacency data points, the method of construct surface by the weighted combination of biquadrate polynomial is given. A model of surface interpolation with c~1 continuities of DEM based on TIN is given. Then a mathematical surface is used to evaluate the accuracy of the model, and the model is applied to the representation of actual terrain.(4) We discussed the factors which influence DEM model accuracy and the method of the DEM accuracy valuation. A method of evaluate interpolate function is given and the advantage also disadvantage of each interpolation model are analyzed. |
