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