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Fix sphinx/build_docs warnings for maths/volume (#12464)

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* Fix sphinx/build_docs warnings for maths/volume

* Fix

* Fix

* Fix

* Fix

* Fix

* Fix

* Fix
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Maxim Smolskiy 2024-12-24 03:14:11 +03:00 committed by GitHub
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maths/volume.py
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@ -1,5 +1,6 @@
""" """
Find the volume of various shapes. Find the volume of various shapes.
* https://en.wikipedia.org/wiki/Volume * https://en.wikipedia.org/wiki/Volume
* https://en.wikipedia.org/wiki/Spherical_cap * https://en.wikipedia.org/wiki/Spherical_cap
""" """
@ -12,6 +13,7 @@ from math import pi, pow # noqa: A004
def vol_cube(side_length: float) -> float: def vol_cube(side_length: float) -> float:
""" """
Calculate the Volume of a Cube. Calculate the Volume of a Cube.
>>> vol_cube(1) >>> vol_cube(1)
1.0 1.0
>>> vol_cube(3) >>> vol_cube(3)
@ -33,6 +35,7 @@ def vol_cube(side_length: float) -> float:
def vol_spherical_cap(height: float, radius: float) -> float: def vol_spherical_cap(height: float, radius: float) -> float:
""" """
Calculate the volume of the spherical cap. Calculate the volume of the spherical cap.
>>> vol_spherical_cap(1, 2) >>> vol_spherical_cap(1, 2)
5.235987755982988 5.235987755982988
>>> vol_spherical_cap(1.6, 2.6) >>> vol_spherical_cap(1.6, 2.6)
@ -57,20 +60,29 @@ def vol_spherical_cap(height: float, radius: float) -> float:
def vol_spheres_intersect( def vol_spheres_intersect(
radius_1: float, radius_2: float, centers_distance: float radius_1: float, radius_2: float, centers_distance: float
) -> float: ) -> float:
""" r"""
Calculate the volume of the intersection of two spheres. Calculate the volume of the intersection of two spheres.
The intersection is composed by two spherical caps and therefore its volume is the 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 (h1, h2) sum of the volumes of the spherical caps.
of the spherical caps, then the two volumes and it returns the sum. 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 The height formulas are
h1 = (radius_1 - radius_2 + centers_distance)
* (radius_1 + radius_2 - centers_distance) .. math::
/ (2 * centers_distance) h_1 = \frac{(radius_1 - radius_2 + centers\_distance)
h2 = (radius_2 - radius_1 + centers_distance) \cdot (radius_1 + radius_2 - centers\_distance)}
* (radius_2 + radius_1 - centers_distance) {2 \cdot centers\_distance}
/ (2 * centers_distance)
if centers_distance is 0 then it returns the volume of the smallers sphere h_2 = \frac{(radius_2 - radius_1 + centers\_distance)
:return vol_spherical_cap(h1, radius_2) + vol_spherical_cap(h2, radius_1) \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) >>> vol_spheres_intersect(2, 2, 1)
21.205750411731103 21.205750411731103
>>> vol_spheres_intersect(2.6, 2.6, 1.6) >>> vol_spheres_intersect(2.6, 2.6, 1.6)
@ -112,14 +124,18 @@ def vol_spheres_intersect(
def vol_spheres_union( def vol_spheres_union(
radius_1: float, radius_2: float, centers_distance: float radius_1: float, radius_2: float, centers_distance: float
) -> float: ) -> float:
""" r"""
Calculate the volume of the union of two spheres that possibly intersect. Calculate the volume of the union of two spheres that possibly intersect.
It is the sum of sphere A and sphere B minus their intersection.
First, it calculates the volumes (v1, v2) of the spheres, It is the sum of sphere :math:`A` and sphere :math:`B` minus their intersection.
then the volume of the intersection (i) and it returns the sum v1+v2-i. First, it calculates the volumes :math:`(v_1, v_2)` of the spheres,
If centers_distance is 0 then it returns the volume of the larger sphere then the volume of the intersection :math:`i` and
:return vol_sphere(radius_1) + vol_sphere(radius_2) it returns the sum :math:`v_1 + v_2 - i`.
- vol_spheres_intersect(radius_1, radius_2, centers_distance) 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) >>> vol_spheres_union(2, 2, 1)
45.814892864851146 45.814892864851146
@ -157,7 +173,9 @@ def vol_spheres_union(
def vol_cuboid(width: float, height: float, length: float) -> float: def vol_cuboid(width: float, height: float, length: float) -> float:
""" """
Calculate the Volume of a Cuboid. Calculate the Volume of a Cuboid.
:return multiple of width, length and height
:return: multiple of `width`, `length` and `height`
>>> vol_cuboid(1, 1, 1) >>> vol_cuboid(1, 1, 1)
1.0 1.0
>>> vol_cuboid(1, 2, 3) >>> vol_cuboid(1, 2, 3)
@ -185,10 +203,12 @@ def vol_cuboid(width: float, height: float, length: float) -> float:
def vol_cone(area_of_base: float, height: float) -> float: def vol_cone(area_of_base: float, height: float) -> float:
""" r"""
Calculate the Volume of a Cone. | Calculate the Volume of a Cone.
Wikipedia reference: https://en.wikipedia.org/wiki/Cone | Wikipedia reference: https://en.wikipedia.org/wiki/Cone
:return (1/3) * area_of_base * height
:return: :math:`\frac{1}{3} \cdot area\_of\_base \cdot height`
>>> vol_cone(10, 3) >>> vol_cone(10, 3)
10.0 10.0
>>> vol_cone(1, 1) >>> vol_cone(1, 1)
@ -212,10 +232,12 @@ def vol_cone(area_of_base: float, height: float) -> float:
def vol_right_circ_cone(radius: float, height: float) -> float: def vol_right_circ_cone(radius: float, height: float) -> float:
""" r"""
Calculate the Volume of a Right Circular Cone. | Calculate the Volume of a Right Circular Cone.
Wikipedia reference: https://en.wikipedia.org/wiki/Cone | Wikipedia reference: https://en.wikipedia.org/wiki/Cone
:return (1/3) * pi * radius^2 * height
:return: :math:`\frac{1}{3} \cdot \pi \cdot radius^2 \cdot height`
>>> vol_right_circ_cone(2, 3) >>> vol_right_circ_cone(2, 3)
12.566370614359172 12.566370614359172
>>> vol_right_circ_cone(0, 0) >>> vol_right_circ_cone(0, 0)
@ -237,10 +259,12 @@ def vol_right_circ_cone(radius: float, height: float) -> float:
def vol_prism(area_of_base: float, height: float) -> float: def vol_prism(area_of_base: float, height: float) -> float:
""" r"""
Calculate the Volume of a Prism. | Calculate the Volume of a Prism.
Wikipedia reference: https://en.wikipedia.org/wiki/Prism_(geometry) | Wikipedia reference: https://en.wikipedia.org/wiki/Prism_(geometry)
:return V = Bh
:return: :math:`V = B \cdot h`
>>> vol_prism(10, 2) >>> vol_prism(10, 2)
20.0 20.0
>>> vol_prism(11, 1) >>> vol_prism(11, 1)
@ -264,10 +288,12 @@ def vol_prism(area_of_base: float, height: float) -> float:
def vol_pyramid(area_of_base: float, height: float) -> float: def vol_pyramid(area_of_base: float, height: float) -> float:
""" r"""
Calculate the Volume of a Pyramid. | Calculate the Volume of a Pyramid.
Wikipedia reference: https://en.wikipedia.org/wiki/Pyramid_(geometry) | Wikipedia reference: https://en.wikipedia.org/wiki/Pyramid_(geometry)
:return (1/3) * Bh
:return: :math:`\frac{1}{3} \cdot B \cdot h`
>>> vol_pyramid(10, 3) >>> vol_pyramid(10, 3)
10.0 10.0
>>> vol_pyramid(1.5, 3) >>> vol_pyramid(1.5, 3)
@ -291,10 +317,12 @@ def vol_pyramid(area_of_base: float, height: float) -> float:
def vol_sphere(radius: float) -> float: def vol_sphere(radius: float) -> float:
""" r"""
Calculate the Volume of a Sphere. | Calculate the Volume of a Sphere.
Wikipedia reference: https://en.wikipedia.org/wiki/Sphere | Wikipedia reference: https://en.wikipedia.org/wiki/Sphere
:return (4/3) * pi * r^3
:return: :math:`\frac{4}{3} \cdot \pi \cdot r^3`
>>> vol_sphere(5) >>> vol_sphere(5)
523.5987755982989 523.5987755982989
>>> vol_sphere(1) >>> vol_sphere(1)
@ -315,10 +343,13 @@ def vol_sphere(radius: float) -> float:
def vol_hemisphere(radius: float) -> float: def vol_hemisphere(radius: float) -> float:
"""Calculate the volume of a hemisphere r"""
Wikipedia reference: https://en.wikipedia.org/wiki/Hemisphere | Calculate the volume of a hemisphere
Other references: https://www.cuemath.com/geometry/hemisphere | Wikipedia reference: https://en.wikipedia.org/wiki/Hemisphere
:return 2/3 * pi * radius^3 | Other references: https://www.cuemath.com/geometry/hemisphere
:return: :math:`\frac{2}{3} \cdot \pi \cdot radius^3`
>>> vol_hemisphere(1) >>> vol_hemisphere(1)
2.0943951023931953 2.0943951023931953
>>> vol_hemisphere(7) >>> vol_hemisphere(7)
@ -339,9 +370,12 @@ def vol_hemisphere(radius: float) -> float:
def vol_circular_cylinder(radius: float, height: float) -> float: def vol_circular_cylinder(radius: float, height: float) -> float:
"""Calculate the Volume of a Circular Cylinder. r"""
Wikipedia reference: https://en.wikipedia.org/wiki/Cylinder | Calculate the Volume of a Circular Cylinder.
:return pi * radius^2 * height | Wikipedia reference: https://en.wikipedia.org/wiki/Cylinder
:return: :math:`\pi \cdot radius^2 \cdot height`
>>> vol_circular_cylinder(1, 1) >>> vol_circular_cylinder(1, 1)
3.141592653589793 3.141592653589793
>>> vol_circular_cylinder(4, 3) >>> vol_circular_cylinder(4, 3)
@ -368,7 +402,9 @@ def vol_circular_cylinder(radius: float, height: float) -> float:
def vol_hollow_circular_cylinder( def vol_hollow_circular_cylinder(
inner_radius: float, outer_radius: float, height: float inner_radius: float, outer_radius: float, height: float
) -> float: ) -> float:
"""Calculate the Volume of a Hollow Circular Cylinder. """
Calculate the Volume of a Hollow Circular Cylinder.
>>> vol_hollow_circular_cylinder(1, 2, 3) >>> vol_hollow_circular_cylinder(1, 2, 3)
28.274333882308138 28.274333882308138
>>> vol_hollow_circular_cylinder(1.6, 2.6, 3.6) >>> vol_hollow_circular_cylinder(1.6, 2.6, 3.6)
@ -405,8 +441,9 @@ def vol_hollow_circular_cylinder(
def vol_conical_frustum(height: float, radius_1: float, radius_2: float) -> float: 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 | Calculate the Volume of a Conical Frustum.
| Wikipedia reference: https://en.wikipedia.org/wiki/Frustum
>>> vol_conical_frustum(45, 7, 28) >>> vol_conical_frustum(45, 7, 28)
48490.482608158454 48490.482608158454
@ -443,9 +480,12 @@ def vol_conical_frustum(height: float, radius_1: float, radius_2: float) -> floa
def vol_torus(torus_radius: float, tube_radius: float) -> float: def vol_torus(torus_radius: float, tube_radius: float) -> float:
"""Calculate the Volume of a Torus. r"""
Wikipedia reference: https://en.wikipedia.org/wiki/Torus | Calculate the Volume of a Torus.
:return 2pi^2 * torus_radius * tube_radius^2 | Wikipedia reference: https://en.wikipedia.org/wiki/Torus
:return: :math:`2 \pi^2 \cdot torus\_radius \cdot tube\_radius^2`
>>> vol_torus(1, 1) >>> vol_torus(1, 1)
19.739208802178716 19.739208802178716
>>> vol_torus(4, 3) >>> vol_torus(4, 3)
@ -471,8 +511,9 @@ def vol_torus(torus_radius: float, tube_radius: float) -> float:
def vol_icosahedron(tri_side: float) -> float: def vol_icosahedron(tri_side: float) -> float:
"""Calculate the Volume of an Icosahedron. """
Wikipedia reference: https://en.wikipedia.org/wiki/Regular_icosahedron | Calculate the Volume of an Icosahedron.
| Wikipedia reference: https://en.wikipedia.org/wiki/Regular_icosahedron
>>> from math import isclose >>> from math import isclose
>>> isclose(vol_icosahedron(2.5), 34.088984228514256) >>> isclose(vol_icosahedron(2.5), 34.088984228514256)