A new method of surface modeling and its application to DEM construction

A new method of surface modelling based on the fundamental theorem of surfaces (SMTS) is presented. Eight different test surfaces are employed to comparatively analyze the simulation errors of SMTS and the classical methods of surface modeling in GIS, including TLI (triangulated irregular network with linear interpolation), SPLINE, IDW (inverse distance weighted) and KRIGING. Numerical tests show that SMTS is much more accurate than the classical methods. SMTS theoretically gives a solution to the error problem that has long troubled DEM construction. As a real-world example, SMTS is used to construct a DEM of the Da-Fo-Si coal mine in Shaan-Xi Province, China. Its root mean square error (RMSE) is compared with those of DEMs constructed by the four classical methods. The results show that although SMTS also has a higher accuracy in the real-world example, the improvement of accuracy is less distinct than that expected from the numerical tests. The accuracy loss seems to be caused by location differences between sampling points and the central points of lattices of the simulated surfaces. Two alternative ways are proposed to solve this problem.