Function vol_spheres_union

maths/volume.py:124–170

r""" Calculate the volume of the union of two spheres that possibly intersect. It is the sum of sphere :math:`A` and sphere :math:`B` minus their intersection. First, it calculates the volumes :math:`(v_1, v_2)` of the spheres, then the volume of the intersection :math:`i` and i

(
    radius_1: float, radius_2: float, centers_distance: float
)

def vol_spheres_union(
    radius_1: float, radius_2: float, centers_distance: float
) -> float:
    r"""
    Calculate the volume of the union of two spheres that possibly intersect.

    It is the sum of sphere :math:`A` and sphere :math:`B` minus their intersection.
    First, it calculates the volumes :math:`(v_1, v_2)` of the spheres,
    then the volume of the intersection :math:`i` and
    it returns the sum :math:`v_1 + v_2 - i`.
    If `centers_distance` is 0 then it returns the volume of the larger sphere

    :return: ``vol_sphere`` (:math:`radius_1`) + ``vol_sphere`` (:math:`radius_2`)
             - ``vol_spheres_intersect``
             (:math:`radius_1`, :math:`radius_2`, :math:`centers\_distance`)

    >>> vol_spheres_union(2, 2, 1)
    45.814892864851146
    >>> vol_spheres_union(1.56, 2.2, 1.4)
    48.77802773671288
    >>> vol_spheres_union(0, 2, 1)
    Traceback (most recent call last):
        ...
    ValueError: vol_spheres_union() only accepts non-negative values, non-zero radius
    >>> vol_spheres_union('1.56', '2.2', '1.4')
    Traceback (most recent call last):
        ...
    TypeError: '<=' not supported between instances of 'str' and 'int'
    >>> vol_spheres_union(1, None, 1)
    Traceback (most recent call last):
        ...
    TypeError: '<=' not supported between instances of 'NoneType' and 'int'
    """

    if radius_1 <= 0 or radius_2 <= 0 or centers_distance < 0:
        raise ValueError(
            "vol_spheres_union() only accepts non-negative values, non-zero radius"
        )

    if centers_distance == 0:
        return vol_sphere(max(radius_1, radius_2))

    return (
        vol_sphere(radius_1)
        + vol_sphere(radius_2)
        - vol_spheres_intersect(radius_1, radius_2, centers_distance)
    )


def vol_cuboid(width: float, height: float, length: float) -> float: