Existing solid texture synthesis algorithms generate a full volume of color content from a set of 2D example images. We introduce a new algorithm with the unique ability to restrict synthesis to a subset of the voxels, while enforcing spatial determinism. This is especially useful when texturing objects, since only a thick layer around the surface needs to be synthesized. A major difficulty lies in reducing the dependency chain of neighborhood matching, so that each voxel only depends on a small number of other voxels. Our key idea is to synthesize a volume from a set of pre-computed 3D candidates, each being a triple of interleaved 2D neighborhoods. We present an efficient algorithm to carefully select in a pre-process only those candidates forming consistent triples. This significantly reduces the search space during subsequent synthesis. The result is a new parallel, spatially deterministic solid texture synthesis algorithm which runs efficiently on the GPU. Our approach generates ...