Displacement mapping is ideal for modern GPUs since it enables high-frequency geometric surface detail on models with low memory I/O. However, problems such as texture seams, normal re-computation, and under-sampling artifacts have limited its adoption. We provide a comprehensive solution to these problems by introducing a smooth analytic displacement function. Coefficients are stored in a GPU-friendly tile based texture format, and a multi-resolution mip hierarchy of this function is formed. We propose a novel level-of-detail scheme by computing per vertex adaptive tessellation factors and select the appropriate pre-filtered mip levels of the displacement function. Our method obviates the need for a pre-computed normal map since normals are directly derived from the displacements. Thus, we are able to perform authoring and rendering simultaneously without typical displacement map extraction from a dense triangle mesh. This not only is more flexible than the traditional combination of discrete displacements and normal maps, but also provides faster runtime due to reduced memory I/O.