Abstract: The present invention includes a method and apparatus which determines the tree-dimensional (x, y, z coordinate) position of the receiving position of a GPS antenna on an earth-moving machine or a vehicle, determines the tilt of the machine or vehicle in real time (tilt may vary from point to point), and utilizes this data to calculate the three-dimesional (x, y, z coordinate) position of a point of the earth's surface disposed beneath the machine or vehicle. In a preferred embodiment, the present invention derives and displays the distance between the actual elevation of this point and the desired surface elevation.

Abstract: A scanning array antenna employs a solid rotating core having an anisotropic refractive index within an apertured waveguide that emits radiation in response to an input beam propagating through the waveguide. Rotating the core changes its refractive index relative to the input beam, causing the radiated beams to undergo an angular scanning. The solid rotating waveguide core can be formed from a dispersion of aligned elongate conductive members in an isotropic dielectric, from a liquid crystal medium, or from a dispersion of aligned elongate conductive members in a liquid crystal medium. The antenna is operable in reciprocal transmission and reception modes.