This paper presents a novel technique for simplifying a triangulated surface at different levels of resolution. While most existing algorithms based on iterative vertex decimation relies on distance as error metric, the proposed algorithm utilizes an edge criterion for removing a vertex. An {\em interior angle} of a vertex is defined as the maximum value of all possible angles formed by combinations of edges connected to a vertex. Since the surface curvature examined with the interior angle gives more information for deciding the removal of a vertex than the conventional distance measure, the proposed algorithm can approximate the surface with less computation. The height of a triangle that the pair of edges forms is also used as an additional constraint. The computational overload can thus be greatly reduced to linear scale from the exponential scale of the conventional algorithms while yielding a comparable error level.