sphere.py 文件源码

def area(a, b, c):
    """Area of the triangle (a, b, c).

    see :cpp:func:`S2::Area`
    """
    assert is_unit_length(a)
    assert is_unit_length(b)
    assert is_unit_length(c)

    sa = b.angle(c)
    sb = c.angle(a)
    sc = a.angle(b)
    s = 0.5 * (sa + sb + sc)
    if s >= 3e-4:
        s2 = s * s
        dmin = s - max(sa, max(sb, sc))
        if dmin < 1e-2 * s * s2 * s2:
            area = girard_area(a, b, c)
            if dmin < 2 * (0.1 * area):
                return area

    return 4 * math.atan(math.sqrt(
        max(0.0,
            math.tan(0.5 * s) *
            math.tan(0.5 * (s - sa)) *
            math.tan(0.5 * (s - sb)) *
            math.tan(0.5 * (s - sc)))
    ))