Connection between antennas, beam steering, and the moir\'{e} effect

The moir'{e} effect provides an interpretation for the steering of antennas that form beams through internal spatial interferences. We make an explicit connection between such antennas and the moir'{e} effect, and use it to model six planar antennas that steer by scaling, rotating, or translating operations. Three of the antennas illustrate how to use moir'{e} patterns to generate antenna designs.