Rao-Wilton-Glisson basis functions and the electrostatics of triangles & polygons

Rao-Wilton-Glisson basis functions provide one of the most popular and versatile tools for the numerical solution of integral equations in Electromagnetics. They are deeply connected with the problem of calculating the electrostatic potential and field of uniform surface charge distributions existing on polygonal supports. This tutorial reviews the history and relevance of such a calculation, which has been attempted since the 19th century and continues to be the object of new developments, where frequently the physical properties of the problem are hidden by the mathematical complexity of the treatment. Here, a simple geometry-based strategy is used, leading to compact analytical expressions for both potentials and fields, which provide new insights on the singularities associated to the Rao-Wilton-Glisson basis functions.