Abstract: A new method of mesh simplification of non uniform sampling is presented, which considers some important viewpoints in the viewpoint space, and which uses the quadric error metrics simplification algorithm of Garland and Heckbert. In this simplification method, similarity of appearance is considered. Two theorems that discriminate boundary of a model are proposed so that sampling could be based on them in theory. In the simplification process, the model would be sampled by considering some important viewpoints of the viewpoint space, so that pairs of vertices near contours would be sampled and be preserved. The algorithm performs at extremely low levels of simplification, and preserves similarity of appearance whenever possible. This method is tested through experiments. Experimental results show that this method is effective. Finally, the time and space complexity of this algorithm is analyzed.