The switching properties of most liquid-crystal electro-optic devices rely mainly on the reorientation of the average molecular direction (director) within the bulk of the liquid-crystal layer . Reorientation of the director at or near the surfaces of the layer usually has an insignificant effect on device performance. Here we describe a different configuration in which a nematic liquid crystal is placed between a flat surface treated to induce a parallel anchoring of the director and a grating surface treated to give a perpendicular anchoring. We show that this configuration leads to an effective azimuthal anchoring at the grating surface that depends on the applied voltage when the nematic phase has negative dielectric anisotropy (that is, the director has a tendency to align perpendicular to the applied field). This leads to a voltage-controlled twist effect in the liquid-crystal cell that is highly sensitive to the grating profile. Furthermore, this twist effect possesses an electro-optic response which is far less dependent on viewing angle compared to many other liquid-crystal display configurations. We therefore suggest that this technology might find application in the next generation of liquid-crystal displays.