Abstract: There are two ways of ray-tracing space-deformed objects: computing the resulting object and rendering it, or directly rendering the object in its initial space by curving rays. This last approach is advantageous for all non-explicit representations that often should otherwise be facetized (CSG, implicit functions), or for large databases for which too many components should be transformed (particle systems, volumes, complex geometry). We deal here with ray casting in a structured space (voxels, complex geometry in volumetric textures, geometry in grids), focusing on the local illumination evaluation, especially in the anisotropic case. We apply it to the ellipsoidal reflectance model developed for volumetric textures in \cite{neyret95}.