Give an example of a monotone simple polygon for which the set of directions with respect to which
it is monotone consists of at least two distinct "double cones" of directions. more precisely, show a simple polygon p that
is monotone with respect to the line y = x and with respect to the line y = −x, but is not x-monotone or y-monotone. 1
(optional question to provoke thought: for an n-gon, what is the maximum number (in terms of n) of double cones of
directions of monotonicity? i know that it can grow like ω(n), but can you get a tight exact bound? )
(b). suppose that p is a simple rectilinear polygon (all edges are parallel to the coordinate axes). ca