mirror of
https://github.com/TheAlgorithms/Python.git
synced 2025-01-18 00:07:00 +00:00
Fix sphinx/build_docs warnings for maths/volume (#12464)
* Fix sphinx/build_docs warnings for maths/volume * Fix * Fix * Fix * Fix * Fix * Fix * Fix
This commit is contained in:
Maxim Smolskiy
GitHub
parent
b0cb13fea5
commit
04fbfd6eae
149
maths/volume.py
149
maths/volume.py
|
|
@ -1,5 +1,6 @@
|
|||
"""
|
||||
Find the volume of various shapes.
|
||||
|
||||
* https://en.wikipedia.org/wiki/Volume
|
||||
* 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:
|
||||
"""
|
||||
Calculate the Volume of a Cube.
|
||||
|
||||
>>> vol_cube(1)
|
||||
1.0
|
||||
>>> vol_cube(3)
|
||||
|
|
@ -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)
|
||||
|
|
@ -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)
|
||||
|
|
@ -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
|
||||
|
|
@ -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)
|
||||
|
|
@ -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)
|
||||
|
|
@ -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)
|
||||
|
|
@ -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)
|
||||
|
|
@ -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)
|
||||
|
|
@ -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)
|
||||
|
|
@ -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)
|
||||
|
|
@ -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)
|
||||
|
|
@ -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)
|
||||
|
|
@ -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
|
||||
|
|
@ -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)
|
||||
|
|
@ -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)
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user