Many applications in computer graphics require complex and highly detailed models. However, the level of detail actually necessary may vary considerably. It is often desirable to use approximations in place of excessively detailed models to control processing time. A new polygonal mesh simplification algorithm is presented for colored or textured models based on vertex clustering, and a more accurate error-measuring method for vertex clustering is introduced. The algorithm can produce high quality approximations of polygonal models. It makes adaptive subdivision of the bounding box in the original model using octree structure and performs vertex clustering in an error range specified by users. The color or texture information defined over the mesh can be preserved during simplification by constructing a texture map for the simplified mesh. To make a continuous transition between level of detail (LoD) models possible, an efficient interpolating method is also proposed. The efficiency of the algorithm is demonstrated in the experimental results.