Calculate area/fraction on sky

sky_frac.py

def test_sky_frac(self):

    frac = go.sky_frac(-90, 90, 0, 360)
    self.assertTrue(frac > 0.99999999999)

    frac = go.sky_frac(0, 90, 0, 360)
    self.assertTrue(0.49 < frac < 0.51)

    frac = go.sky_frac(0, 90, 0, 90)
    self.assertTrue(0.124 < frac < 0.126)

    frac = go.sky_frac(-90, 90, 0, 180)
    self.assertTrue(0.49 < frac < 0.51)


def sky_frac(d_min, d_max, r_min, r_max):
    """
    Calculate the fraction of the sky that an area subtends
    """

    d_min = math.radians(d_min)
    d_max = math.radians(d_max)
    r_min = math.radians(r_min)
    r_max = math.radians(r_max)

    # Calculate fractional surface area
    def area(d_min, d_max, r_min, r_max):
        return (-math.cos(d_max)+math.cos(d_min))*(r_max-r_min)/(4*math.pi)

    if d_min < 0:
        top = area(0, d_max, r_min, r_max)
        bottom = area(0, abs(d_min), r_min, r_max)
        a = top + bottom
    else:
        a = area(d_min, d_max, r_min, r_max)

    return a