By differentiation with respect to g1 it may be proved that

w = 0 from g1 = -[oo] to g1 = -2h1,

w = 1/2[pi](2h1 + g1) from g1 = -2h1 to g1 = 0,

w = 1/2[pi](2h1 - g1) from g1 = 0 to g1 = 2h1,

w = 0 from g1 = 2h1 to g1 = [oo].