Abstract: Shell mapping is a technique to represent three-dimensional surface details. This is achieved by extruding the triangles of an existing mesh along their normals, and mapping a 3D function (e.g., a 3D texture) into the resulting prisms. Unfortunately, such a mapping is nonlinear. Previous approaches perform a piece-wise linear approximation by subdividing the prisms into tetrahedrons. However, such an approximation often leads to severe artifacts. In this paper we present a correct (i.e., smooth) mapping that does not rely on a decomposition into tetrahedrons. We present an efficient GPU ray casting algorithm which provides correct parallax, self-occlusion, and silhouettes, at the cost of longer rendering times. The new formulation also allows modeling shells with smooth curvatures using Coons patches within the prisms. Tangent continuity between adjacent prisms is guaranteed, while the mapping itself remains local, i.e. every curved prism content is modeled at runtime in the GPU without the need for any precomputation. This allows instantly replacing animated triangular meshes with prism-based shells.