A geometric approach for DEMs simplification is proposed.The main idea is to uniformly pick points from DEM in the sense of geodesic metric

resulting in terrain-adaptive samples in Euclidean metric.This method randomly sample point from mesh nodes

then judge if the point can be accepted or not according to its geodesic distance from sampled point set

and repeat the whole process until no points can be added.By defining weighted geodesic distance positively related to terrain variation

results with more points in rugged terrain areas and sparse points in flat areas can be obtained.Moreover

the distribution of samples is very fit for high performance terrain visualization.This method is really simple and can retain the topographical details more effectively.