Algebraic and geometric approximation of waves among obstacles

Complex phenomena, such as the wave propagation in a medium, are thought to require highly sophisticated machineries for understanding their mechanics. In this paper, two wave phenomena, diffraction and interference, are implemented using solid modeling operations. The geometric model for the waves from a source is a cone. A trimmed cone is the DIFFERENCE between a cone and the given boundary. The wave propagation is modelled by the UNION of the cones (or trimmed cones). The intellectual contribution of this paper is on the dynamics of interface evolution. It answers the question of how a symmetric wave in the near field becomes asymmetric in a field far from the source. The analytical contribution is on the algebraic and geometric structures. Seemingly complex phenomena can be modelled with set operations on simple geometry such as cones.