Ordering Points for Incremental TIN Construction from DEMs

The standard method of building compact triangulated surface approximations to terrain surfaces (TINs) from dense digital elevation models(DEMs) adds points to an initial sparse triangulation or removes points from a dense initial mesh. Typically, in each triangle in the current TIN, the worst tting point, in terms of vertical distance, is selected. The order of insertion of the points is determined by the magnitude of the maximum vertical diierence. This measure produces triangulations that minimize the maximum vertical distance between the TIN and the source DEM. Other approximation criteria are often used, however, including the root-mean-squared error or the mean absolute error, both for the vertical diierence and normal diierence, i.e. the distance in the direction of the normal to the triangular approximation. For these approximation criteria, we still select the worst t point, but determine the insertion order by various sums of errors over the triangle. Experiments show that using these better evaluation measures signiicantly reduces the size of the TIN for a given approximation error.