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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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@MaximSmolskiy
MaximSmolskiy authored Dec 24, 2024
1 parent b0cb13f commit 04fbfd6
Showing 1 changed file with 95 additions and 54 deletions.
149 changes: 95 additions & 54 deletions maths/volume.py
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Original file line number Diff line number Diff line change
@@ -1,5 +1,6 @@
"""
Find the volume of various shapes.
* https://en.wikipedia.org/wiki/Volume
* https://en.wikipedia.org/wiki/Spherical_cap
"""
Expand All @@ -12,6 +13,7 @@
def vol_cube(side_length: float) -> float:
"""
Calculate the Volume of a Cube.
>>> vol_cube(1)
1.0
>>> vol_cube(3)
Expand All @@ -33,6 +35,7 @@ def vol_cube(side_length: float) -> float:
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)
Expand All @@ -57,20 +60,29 @@ def vol_spherical_cap(height: float, radius: float) -> float:
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 (h1, h2)
of the spherical caps, then the two volumes and it returns the sum.
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
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)
if centers_distance is 0 then it returns the volume of the smallers sphere
:return vol_spherical_cap(h1, radius_2) + vol_spherical_cap(h2, radius_1)
.. 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)
Expand Down Expand Up @@ -112,14 +124,18 @@ def vol_spheres_intersect(
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 A and sphere B minus their intersection.
First, it calculates the volumes (v1, v2) of the spheres,
then the volume of the intersection (i) and it returns the sum v1+v2-i.
If centers_distance is 0 then it returns the volume of the larger sphere
:return vol_sphere(radius_1) + vol_sphere(radius_2)
- vol_spheres_intersect(radius_1, radius_2, centers_distance)
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
Expand Down Expand Up @@ -157,7 +173,9 @@ def vol_spheres_union(
def vol_cuboid(width: float, height: float, length: float) -> float:
"""
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)
1.0
>>> vol_cuboid(1, 2, 3)
Expand Down Expand Up @@ -185,10 +203,12 @@ def vol_cuboid(width: float, height: float, length: float) -> float:


def vol_cone(area_of_base: float, height: float) -> float:
"""
Calculate the Volume of a Cone.
Wikipedia reference: https://en.wikipedia.org/wiki/Cone
:return (1/3) * area_of_base * height
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)
Expand All @@ -212,10 +232,12 @@ def vol_cone(area_of_base: float, height: float) -> float:


def vol_right_circ_cone(radius: float, height: float) -> float:
"""
Calculate the Volume of a Right Circular Cone.
Wikipedia reference: https://en.wikipedia.org/wiki/Cone
:return (1/3) * pi * radius^2 * height
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)
Expand All @@ -237,10 +259,12 @@ def vol_right_circ_cone(radius: float, height: float) -> float:


def vol_prism(area_of_base: float, height: float) -> float:
"""
Calculate the Volume of a Prism.
Wikipedia reference: https://en.wikipedia.org/wiki/Prism_(geometry)
:return V = Bh
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)
Expand All @@ -264,10 +288,12 @@ def vol_prism(area_of_base: float, height: float) -> float:


def vol_pyramid(area_of_base: float, height: float) -> float:
"""
Calculate the Volume of a Pyramid.
Wikipedia reference: https://en.wikipedia.org/wiki/Pyramid_(geometry)
:return (1/3) * Bh
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)
Expand All @@ -291,10 +317,12 @@ def vol_pyramid(area_of_base: float, height: float) -> float:


def vol_sphere(radius: float) -> float:
"""
Calculate the Volume of a Sphere.
Wikipedia reference: https://en.wikipedia.org/wiki/Sphere
:return (4/3) * pi * r^3
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)
Expand All @@ -315,10 +343,13 @@ def vol_sphere(radius: float) -> float:


def vol_hemisphere(radius: float) -> float:
"""Calculate the volume of a hemisphere
Wikipedia reference: https://en.wikipedia.org/wiki/Hemisphere
Other references: https://www.cuemath.com/geometry/hemisphere
:return 2/3 * pi * radius^3
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)
Expand All @@ -339,9 +370,12 @@ def vol_hemisphere(radius: float) -> float:


def vol_circular_cylinder(radius: float, height: float) -> float:
"""Calculate the Volume of a Circular Cylinder.
Wikipedia reference: https://en.wikipedia.org/wiki/Cylinder
:return pi * radius^2 * height
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)
Expand All @@ -368,7 +402,9 @@ def vol_circular_cylinder(radius: float, height: float) -> float:
def vol_hollow_circular_cylinder(
inner_radius: float, outer_radius: float, height: 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)
28.274333882308138
>>> vol_hollow_circular_cylinder(1.6, 2.6, 3.6)
Expand Down Expand Up @@ -405,8 +441,9 @@ def vol_hollow_circular_cylinder(


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)
48490.482608158454
Expand Down Expand Up @@ -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:
"""Calculate the Volume of a Torus.
Wikipedia reference: https://en.wikipedia.org/wiki/Torus
:return 2pi^2 * torus_radius * tube_radius^2
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)
Expand All @@ -471,8 +511,9 @@ def vol_torus(torus_radius: float, tube_radius: 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
>>> isclose(vol_icosahedron(2.5), 34.088984228514256)
Expand Down

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