Input: A regular N-gon P_N, and a point (x,y). Output: Membership of (x,y) relative to P_N. Description: Center P_N on the origin, and determine bounding lines as { (x,y) : L_n(x,y) = 0}, with n from 1 to N. The polynomial H(x,y) = L1*L2*...LN gives a height to any point (x,y). By simple bounds on the height and norm of (x,y), it is possible to tell whether or not (x,y) falls interior to the N-gon, or on a boundary ( either point-like or line-like ). The trade-off is that this algorithm requires ~N additional multiplications in order to replace ~N logical operations with only two or three. It is easy to program, but possibly non-optimal. For a use case see: Wolfram Community, "Fixing RegionMember & A302176 at once", https://community.wolfram.com/groups/-/m/t/1854034 --Brad