maths/volume.py - master - ksushaksusha/Python

maths/volume.py
567 строк18 KB
Omkaar
Fix a few typos (#13346)
15 окт 2025, 20:35
15 окт 2025, 20:353cea941
"""
Find the volume of various shapes.

* https://en.wikipedia.org/wiki/Volume
* https://en.wikipedia.org/wiki/Spherical_cap
"""

from __future__ import annotations

from math import pi, pow  # noqa: A004


def vol_cube(side_length: float) -> float:
    """
    Calculate the Volume of a Cube.

    >>> vol_cube(1)
    1.0
    >>> vol_cube(3)
    27.0
    >>> vol_cube(0)
    0.0
    >>> vol_cube(1.6)
    4.096000000000001
    >>> vol_cube(-1)
    Traceback (most recent call last):
        ...
    ValueError: vol_cube() only accepts non-negative values
    """
    if side_length < 0:
        raise ValueError("vol_cube() only accepts non-negative values")
    return pow(side_length, 3)


def vol_spherical_cap(height: float, radius: float) -> float:
    """
    Calculate the volume of the spherical cap.

    >>> vol_spherical_cap(1, 2)
    5.235987755982988
    >>> vol_spherical_cap(1.6, 2.6)
    16.621119532592402
    >>> vol_spherical_cap(0, 0)
    0.0
    >>> vol_spherical_cap(-1, 2)
    Traceback (most recent call last):
        ...
    ValueError: vol_spherical_cap() only accepts non-negative values
    >>> vol_spherical_cap(1, -2)
    Traceback (most recent call last):
        ...
    ValueError: vol_spherical_cap() only accepts non-negative values
    """
    if height < 0 or radius < 0:
        raise ValueError("vol_spherical_cap() only accepts non-negative values")
    # Volume is 1/3 pi * height squared * (3 * radius - height)
    return 1 / 3 * pi * pow(height, 2) * (3 * radius - height)


def vol_spheres_intersect(
    radius_1: float, radius_2: float, centers_distance: float
) -> float:
    r"""
    Calculate the volume of the intersection of two spheres.

    The intersection is composed by two spherical caps and therefore its volume is the
    sum of the volumes of the spherical caps.
    First, it calculates the heights :math:`(h_1, h_2)` of the spherical caps,
    then the two volumes and it returns the sum.
    The height formulas are

    .. math::
        h_1 = \frac{(radius_1 - radius_2 + centers\_distance)
                    \cdot (radius_1 + radius_2 - centers\_distance)}
                   {2 \cdot centers\_distance}

        h_2 = \frac{(radius_2 - radius_1 + centers\_distance)
                    \cdot (radius_2 + radius_1 - centers\_distance)}
                   {2 \cdot centers\_distance}

    if `centers_distance` is 0 then it returns the volume of the smallers sphere

    :return: ``vol_spherical_cap`` (:math:`h_1`, :math:`radius_2`)
             + ``vol_spherical_cap`` (:math:`h_2`, :math:`radius_1`)

    >>> vol_spheres_intersect(2, 2, 1)
    21.205750411731103
    >>> vol_spheres_intersect(2.6, 2.6, 1.6)
    40.71504079052372
    >>> vol_spheres_intersect(0, 0, 0)
    0.0
    >>> vol_spheres_intersect(-2, 2, 1)
    Traceback (most recent call last):
        ...
    ValueError: vol_spheres_intersect() only accepts non-negative values
    >>> vol_spheres_intersect(2, -2, 1)
    Traceback (most recent call last):
        ...
    ValueError: vol_spheres_intersect() only accepts non-negative values
    >>> vol_spheres_intersect(2, 2, -1)
    Traceback (most recent call last):
        ...
    ValueError: vol_spheres_intersect() only accepts non-negative values
    """
    if radius_1 < 0 or radius_2 < 0 or centers_distance < 0:
        raise ValueError("vol_spheres_intersect() only accepts non-negative values")
    if centers_distance == 0:
        return vol_sphere(min(radius_1, radius_2))

    h1 = (
        (radius_1 - radius_2 + centers_distance)
        * (radius_1 + radius_2 - centers_distance)
        / (2 * centers_distance)
    )
    h2 = (
        (radius_2 - radius_1 + centers_distance)
        * (radius_2 + radius_1 - centers_distance)
        / (2 * centers_distance)
    )

    return vol_spherical_cap(h1, radius_2) + vol_spherical_cap(h2, radius_1)


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:
    """
    Calculate the Volume of a Cuboid.

    :return: multiple of `width`, `length` and `height`

    >>> vol_cuboid(1, 1, 1)
    1.0
    >>> vol_cuboid(1, 2, 3)
    6.0
    >>> vol_cuboid(1.6, 2.6, 3.6)
    14.976
    >>> vol_cuboid(0, 0, 0)
    0.0
    >>> vol_cuboid(-1, 2, 3)
    Traceback (most recent call last):
        ...
    ValueError: vol_cuboid() only accepts non-negative values
    >>> vol_cuboid(1, -2, 3)
    Traceback (most recent call last):
        ...
    ValueError: vol_cuboid() only accepts non-negative values
    >>> vol_cuboid(1, 2, -3)
    Traceback (most recent call last):
        ...
    ValueError: vol_cuboid() only accepts non-negative values
    """
    if width < 0 or height < 0 or length < 0:
        raise ValueError("vol_cuboid() only accepts non-negative values")
    return float(width * height * length)


def vol_cone(area_of_base: float, height: float) -> float:
    r"""
    | Calculate the Volume of a Cone.
    | Wikipedia reference: https://en.wikipedia.org/wiki/Cone

    :return: :math:`\frac{1}{3} \cdot area\_of\_base \cdot height`

    >>> vol_cone(10, 3)
    10.0
    >>> vol_cone(1, 1)
    0.3333333333333333
    >>> vol_cone(1.6, 1.6)
    0.8533333333333335
    >>> vol_cone(0, 0)
    0.0
    >>> vol_cone(-1, 1)
    Traceback (most recent call last):
        ...
    ValueError: vol_cone() only accepts non-negative values
    >>> vol_cone(1, -1)
    Traceback (most recent call last):
        ...
    ValueError: vol_cone() only accepts non-negative values
    """
    if height < 0 or area_of_base < 0:
        raise ValueError("vol_cone() only accepts non-negative values")
    return area_of_base * height / 3.0


def vol_right_circ_cone(radius: float, height: float) -> float:
    r"""
    | Calculate the Volume of a Right Circular Cone.
    | Wikipedia reference: https://en.wikipedia.org/wiki/Cone

    :return: :math:`\frac{1}{3} \cdot \pi \cdot radius^2 \cdot height`

    >>> vol_right_circ_cone(2, 3)
    12.566370614359172
    >>> vol_right_circ_cone(0, 0)
    0.0
    >>> vol_right_circ_cone(1.6, 1.6)
    4.289321169701265
    >>> vol_right_circ_cone(-1, 1)
    Traceback (most recent call last):
        ...
    ValueError: vol_right_circ_cone() only accepts non-negative values
    >>> vol_right_circ_cone(1, -1)
    Traceback (most recent call last):
        ...
    ValueError: vol_right_circ_cone() only accepts non-negative values
    """
    if height < 0 or radius < 0:
        raise ValueError("vol_right_circ_cone() only accepts non-negative values")
    return pi * pow(radius, 2) * height / 3.0


def vol_prism(area_of_base: float, height: float) -> float:
    r"""
    | Calculate the Volume of a Prism.
    | Wikipedia reference: https://en.wikipedia.org/wiki/Prism_(geometry)

    :return: :math:`V = B \cdot h`

    >>> vol_prism(10, 2)
    20.0
    >>> vol_prism(11, 1)
    11.0
    >>> vol_prism(1.6, 1.6)
    2.5600000000000005
    >>> vol_prism(0, 0)
    0.0
    >>> vol_prism(-1, 1)
    Traceback (most recent call last):
        ...
    ValueError: vol_prism() only accepts non-negative values
    >>> vol_prism(1, -1)
    Traceback (most recent call last):
        ...
    ValueError: vol_prism() only accepts non-negative values
    """
    if height < 0 or area_of_base < 0:
        raise ValueError("vol_prism() only accepts non-negative values")
    return float(area_of_base * height)


def vol_pyramid(area_of_base: float, height: float) -> float:
    r"""
    | Calculate the Volume of a Pyramid.
    | Wikipedia reference: https://en.wikipedia.org/wiki/Pyramid_(geometry)

    :return: :math:`\frac{1}{3} \cdot B \cdot h`

    >>> vol_pyramid(10, 3)
    10.0
    >>> vol_pyramid(1.5, 3)
    1.5
    >>> vol_pyramid(1.6, 1.6)
    0.8533333333333335
    >>> vol_pyramid(0, 0)
    0.0
    >>> vol_pyramid(-1, 1)
    Traceback (most recent call last):
        ...
    ValueError: vol_pyramid() only accepts non-negative values
    >>> vol_pyramid(1, -1)
    Traceback (most recent call last):
        ...
    ValueError: vol_pyramid() only accepts non-negative values
    """
    if height < 0 or area_of_base < 0:
        raise ValueError("vol_pyramid() only accepts non-negative values")
    return area_of_base * height / 3.0


def vol_sphere(radius: float) -> float:
    r"""
    | Calculate the Volume of a Sphere.
    | Wikipedia reference: https://en.wikipedia.org/wiki/Sphere

    :return: :math:`\frac{4}{3} \cdot \pi \cdot r^3`

    >>> vol_sphere(5)
    523.5987755982989
    >>> vol_sphere(1)
    4.1887902047863905
    >>> vol_sphere(1.6)
    17.15728467880506
    >>> vol_sphere(0)
    0.0
    >>> vol_sphere(-1)
    Traceback (most recent call last):
        ...
    ValueError: vol_sphere() only accepts non-negative values
    """
    if radius < 0:
        raise ValueError("vol_sphere() only accepts non-negative values")
    # Volume is 4/3 * pi * radius cubed
    return 4 / 3 * pi * pow(radius, 3)


def vol_hemisphere(radius: float) -> float:
    r"""
    | Calculate the volume of a hemisphere
    | Wikipedia reference: https://en.wikipedia.org/wiki/Hemisphere
    | Other references: https://www.cuemath.com/geometry/hemisphere

    :return: :math:`\frac{2}{3} \cdot \pi \cdot radius^3`

    >>> vol_hemisphere(1)
    2.0943951023931953
    >>> vol_hemisphere(7)
    718.377520120866
    >>> vol_hemisphere(1.6)
    8.57864233940253
    >>> vol_hemisphere(0)
    0.0
    >>> vol_hemisphere(-1)
    Traceback (most recent call last):
        ...
    ValueError: vol_hemisphere() only accepts non-negative values
    """
    if radius < 0:
        raise ValueError("vol_hemisphere() only accepts non-negative values")
    # Volume is radius cubed * pi * 2/3
    return pow(radius, 3) * pi * 2 / 3


def vol_circular_cylinder(radius: float, height: float) -> float:
    r"""
    | Calculate the Volume of a Circular Cylinder.
    | Wikipedia reference: https://en.wikipedia.org/wiki/Cylinder

    :return: :math:`\pi \cdot radius^2 \cdot height`

    >>> vol_circular_cylinder(1, 1)
    3.141592653589793
    >>> vol_circular_cylinder(4, 3)
    150.79644737231007
    >>> vol_circular_cylinder(1.6, 1.6)
    12.867963509103795
    >>> vol_circular_cylinder(0, 0)
    0.0
    >>> vol_circular_cylinder(-1, 1)
    Traceback (most recent call last):
        ...
    ValueError: vol_circular_cylinder() only accepts non-negative values
    >>> vol_circular_cylinder(1, -1)
    Traceback (most recent call last):
        ...
    ValueError: vol_circular_cylinder() only accepts non-negative values
    """
    if height < 0 or radius < 0:
        raise ValueError("vol_circular_cylinder() only accepts non-negative values")
    # Volume is radius squared * height * pi
    return pow(radius, 2) * height * pi


def vol_hollow_circular_cylinder(
    inner_radius: float, outer_radius: float, height: float
) -> float:
    """
    Calculate the Volume of a Hollow Circular Cylinder.

    >>> vol_hollow_circular_cylinder(1, 2, 3)
    28.274333882308138
    >>> vol_hollow_circular_cylinder(1.6, 2.6, 3.6)
    47.50088092227767
    >>> vol_hollow_circular_cylinder(-1, 2, 3)
    Traceback (most recent call last):
        ...
    ValueError: vol_hollow_circular_cylinder() only accepts non-negative values
    >>> vol_hollow_circular_cylinder(1, -2, 3)
    Traceback (most recent call last):
        ...
    ValueError: vol_hollow_circular_cylinder() only accepts non-negative values
    >>> vol_hollow_circular_cylinder(1, 2, -3)
    Traceback (most recent call last):
        ...
    ValueError: vol_hollow_circular_cylinder() only accepts non-negative values
    >>> vol_hollow_circular_cylinder(2, 1, 3)
    Traceback (most recent call last):
        ...
    ValueError: outer_radius must be greater than inner_radius
    >>> vol_hollow_circular_cylinder(0, 0, 0)
    Traceback (most recent call last):
        ...
    ValueError: outer_radius must be greater than inner_radius
    """
    # Volume - (outer_radius squared - inner_radius squared) * pi * height
    if inner_radius < 0 or outer_radius < 0 or height < 0:
        raise ValueError(
            "vol_hollow_circular_cylinder() only accepts non-negative values"
        )
    if outer_radius <= inner_radius:
        raise ValueError("outer_radius must be greater than inner_radius")
    return pi * (pow(outer_radius, 2) - pow(inner_radius, 2)) * height


def vol_conical_frustum(height: float, radius_1: float, radius_2: float) -> float:
    """
    | Calculate the Volume of a Conical Frustum.
    | Wikipedia reference: https://en.wikipedia.org/wiki/Frustum

    >>> vol_conical_frustum(45, 7, 28)
    48490.482608158454
    >>> vol_conical_frustum(1, 1, 2)
    7.330382858376184
    >>> vol_conical_frustum(1.6, 2.6, 3.6)
    48.7240076620753
    >>> vol_conical_frustum(0, 0, 0)
    0.0
    >>> vol_conical_frustum(-2, 2, 1)
    Traceback (most recent call last):
        ...
    ValueError: vol_conical_frustum() only accepts non-negative values
    >>> vol_conical_frustum(2, -2, 1)
    Traceback (most recent call last):
        ...
    ValueError: vol_conical_frustum() only accepts non-negative values
    >>> vol_conical_frustum(2, 2, -1)
    Traceback (most recent call last):
        ...
    ValueError: vol_conical_frustum() only accepts non-negative values
    """
    # Volume is 1/3 * pi * height *
    #           (radius_1 squared + radius_2 squared + radius_1 * radius_2)
    if radius_1 < 0 or radius_2 < 0 or height < 0:
        raise ValueError("vol_conical_frustum() only accepts non-negative values")
    return (
        1
        / 3
        * pi
        * height
        * (pow(radius_1, 2) + pow(radius_2, 2) + radius_1 * radius_2)
    )


def vol_torus(torus_radius: float, tube_radius: float) -> float:
    r"""
    | Calculate the Volume of a Torus.
    | Wikipedia reference: https://en.wikipedia.org/wiki/Torus

    :return: :math:`2 \pi^2 \cdot torus\_radius \cdot tube\_radius^2`

    >>> vol_torus(1, 1)
    19.739208802178716
    >>> vol_torus(4, 3)
    710.6115168784338
    >>> vol_torus(3, 4)
    947.4820225045784
    >>> vol_torus(1.6, 1.6)
    80.85179925372404
    >>> vol_torus(0, 0)
    0.0
    >>> vol_torus(-1, 1)
    Traceback (most recent call last):
        ...
    ValueError: vol_torus() only accepts non-negative values
    >>> vol_torus(1, -1)
    Traceback (most recent call last):
        ...
    ValueError: vol_torus() only accepts non-negative values
    """
    if torus_radius < 0 or tube_radius < 0:
        raise ValueError("vol_torus() only accepts non-negative values")
    return 2 * pow(pi, 2) * torus_radius * pow(tube_radius, 2)


def vol_icosahedron(tri_side: float) -> float:
    """
    | Calculate the Volume of an Icosahedron.
    | Wikipedia reference: https://en.wikipedia.org/wiki/Regular_icosahedron

    >>> from math import isclose
    >>> isclose(vol_icosahedron(2.5), 34.088984228514256)
    True
    >>> isclose(vol_icosahedron(10), 2181.694990624912374)
    True
    >>> isclose(vol_icosahedron(5), 272.711873828114047)
    True
    >>> isclose(vol_icosahedron(3.49), 92.740688412033628)
    True
    >>> vol_icosahedron(0)
    0.0
    >>> vol_icosahedron(-1)
    Traceback (most recent call last):
        ...
    ValueError: vol_icosahedron() only accepts non-negative values
    >>> vol_icosahedron(-0.2)
    Traceback (most recent call last):
        ...
    ValueError: vol_icosahedron() only accepts non-negative values
    """
    if tri_side < 0:
        raise ValueError("vol_icosahedron() only accepts non-negative values")
    return tri_side**3 * (3 + 5**0.5) * 5 / 12


def main():
    """Print the Results of Various Volume Calculations."""
    print("Volumes:")
    print(f"Cube: {vol_cube(2) = }")  # = 8
    print(f"Cuboid: {vol_cuboid(2, 2, 2) = }")  # = 8
    print(f"Cone: {vol_cone(2, 2) = }")  # ~= 1.33
    print(f"Right Circular Cone: {vol_right_circ_cone(2, 2) = }")  # ~= 8.38
    print(f"Prism: {vol_prism(2, 2) = }")  # = 4
    print(f"Pyramid: {vol_pyramid(2, 2) = }")  # ~= 1.33
    print(f"Sphere: {vol_sphere(2) = }")  # ~= 33.5
    print(f"Hemisphere: {vol_hemisphere(2) = }")  # ~= 16.75
    print(f"Circular Cylinder: {vol_circular_cylinder(2, 2) = }")  # ~= 25.1
    print(f"Torus: {vol_torus(2, 2) = }")  # ~= 157.9
    print(f"Conical Frustum: {vol_conical_frustum(2, 2, 4) = }")  # ~= 58.6
    print(f"Spherical cap: {vol_spherical_cap(1, 2) = }")  # ~= 5.24
    print(f"Spheres intersection: {vol_spheres_intersect(2, 2, 1) = }")  # ~= 21.21
    print(f"Spheres union: {vol_spheres_union(2, 2, 1) = }")  # ~= 45.81
    print(
        f"Hollow Circular Cylinder: {vol_hollow_circular_cylinder(1, 2, 3) = }"
    )  # ~= 28.3
    print(f"Icosahedron: {vol_icosahedron(2.5) = }")  # ~=34.09


if __name__ == "__main__":
    main()