Ever growing complexity of polygonal models hinders the rendering and manipulation of such models on available graphics hardware resources. LOD management only can make such models suitable for various applications. We propose a new automatic method for generating LODs of a given polygonal model that is based on edge collapse operation. In an edge collapse algorithm, the way how to measure the error introduced as a result of an edge collapse transformation plays a crucial role in determining the ordering of such transformations. We introduce a new measure of geometric deviation, which is based on local evaluation and accumulation of error, and is simple to implement, involves short running times, is memory efficient and preserves geometric features and discontinuities automatically. Results and numerical comparisons show that our algorithm generates simplified models at different LODs of good visual fidelity, which are comparable with those by other methods.