The disclosure describes one or more embodiments of systems, methods, and non-transitory computer-readable media that utilize a sharpness map that includes information on how to filter a displacement map on a per-texel basis to preserve sharp features while sampling a displacement map. For instance, the disclosed systems utilize a sharpness map that encodes combinable patterns to represent discontinuities of features within a displacement map. In some embodiments, the disclosed systems generate a sharpness map having texels encoded with discontinuity configurations that are referenced to control filtering (e.g., via interpolation) of a displacement map such that sharp features within the displacement map are not lost (due to smoothing during interpolation). For example, the disclosed systems filter feature values of a displacement map using discontinuities identified within a sharpness map to interpolate when the feature value(s) and a sampling point are identified as being on the same side of a discontinuity.