Fourier Transform of a Linear Distribution with Triangular Support and Its Applications in Electromagnetics

Any surface, no matter how irregular, can be well approximated by a union of triangles. Hence, triangles can be used as the elemental shape (a simplex) for a two-dimensional (2-D) surface. A twodimensional linear distribution over each triangle can be used to obtain a piecewise-linear approximation of a function defined over a twodimensional surface. The Fourier transform of the current distribution is needed in many applications, for example, in radar cross section (RCS) calculation, radiation and diffraction in reflector antennas, and spectral Galerkin's method. In this communication, a three-dimensional (3-D) Fourier transform (FT) of a linear function with triangular support is derived in its coordinate free representation.