The purpose of this work is to synthesize textures of rough, real world surfaces under freely chosen viewing and illumination directions. Moreover, such textures are produced for continuously changing directions in such a way that the different textures are mutually consistent, i.e. emulate the same piece of surface. This is necessary for 3D animation. It is assumed that the mesostructure (small-scale) geometry of a surface is not known, and that the only input consists of a set of images, taken under different viewing and illumination directions. These are automatically aligned to build an appropriate Bidirectional Texture Function (BTF). Directly extending 2D synthesis methods for pixels to complete BTF columns has drawbacks which are exposed, and a superior sequential but highly parallelizable algorithm is proposed. Examples demonstrate the quality of the results.