Visual patterns on the surface of an object, such as two dimensional texture, are taken into consideration as part of the geometry remeshing process. Given a parameterized mesh and a texture map, the visual perceptual properties of the texture are first computed using a visual discrimination metric. This precomputation is then used to guide the distribution of samples to the surface mesh. The system automatically distributes few samples to texture areas with strong visual masking properties and more samples to texture areas with weaker visual masking properties. In addition, due to contrast considerations, brighter areas receive fewer samples than do darker surface features. Because of the properties of the human visual system, especially visual masking, the artifacts in the rendered mesh are invisible to the human observer. For a fixed number of polygons, this approach also improves the quality of the rendered mesh since the distribution of the samples is guided by the principles of visual perception. The utility of the system is demonstrated by showing that it can also account for other observable patterns on the surface, besides two dimensional texture, such as those produced by bump mapping, lighting variations, surface reflectance, and interreflections.