We present a new algorithm for appearance-preserving simplification. Not only does it generate a low-polygon-count approximation of a model, but it also preserves the appearance. This is accomplished for a particular display resolution in the sense that we properly sample the surface position, curvature, and color attributes of the input surface. We convert the input surface to a representation that decouples the sampling of these three attributes, storing the colors and normals in texture and normal maps, respectively. Our simplification algorithm employs a new texture deviation metric, which guarantees that these maps shift by no more than a user-specified number of pixels on the screen. The simplification process filters the surface position, while the runtime system filters the colors and normals on a per-pixel basis. We have applied our simplification technique to several large models achieving significant amounts of simplification with little or no loss in rendering quality.