Fast and reliable measurement of material appearance is crucial for many applications ranging from virtual prototyping to visual quality control. The most common appearance representation is BRDF capturing illumination- and viewing-dependent reflectance. One of the approaches to rapid BRDF measurement captures its subspace, using so called slices, by continuous movements of a light and camera in azimuthal directions, while their elevations remain fixed. This records set of slices in the BRDF space while remaining data are unknown. We present a novel approach to BRDF reconstruction based on a concept of anisotropic stencils interpolating values along predicted locations of anisotropic highlights. Our method marks an improvement over the original linear interpolation method, and thus we ascertain it to be a promising variant of interpolation from such sparse yet very effective measurements.