Red indicates boundary of P.
Green are trapezoidalization horizonals.
Blue is the case where w_i, w_i - 1 are on different chains
Black is the case where w_i, w_i -1 are on the same chain, and the angle
described by w_i, w_i-1, and u
is convex
Yellow is the case where w_i, w_i -1 are on the same chain, and the
angle described by w_i, w_i-1, and u
is reflex