Abstract: Existing displacement mapping techniques operate only in directions normal to the surface, a restriction which limits the richness of the set of representable objects. This work removes that restriction by allowing displacements to be defined along curved trajectories of flow fields. The main contribution of this generalized technique, which will be referred to as flow mapping,is an alternative model of offset surfaces that extends the class of shapes that can be modelled using displacement maps. The paper also discusses methods for synthesizing homogeneous displacement textures. Finally, it introduces the concept of a texture atlas for efficient sampling and reconstruction of distorted textures.