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Commit 04fbfd6

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Fix sphinx/build_docs warnings for maths/volume (TheAlgorithms#12464)
* Fix sphinx/build_docs warnings for maths/volume * Fix * Fix * Fix * Fix * Fix * Fix * Fix
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‎maths/volume.py‎

Lines changed: 95 additions & 54 deletions
Original file line numberDiff line numberDiff line change
@@ -1,5 +1,6 @@
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"""
22
Find the volume of various shapes.
3+
34
* https://en.wikipedia.org/wiki/Volume
45
* https://en.wikipedia.org/wiki/Spherical_cap
56
"""
@@ -12,6 +13,7 @@
1213
def vol_cube(side_length: float) -> float:
1314
"""
1415
Calculate the Volume of a Cube.
16+
1517
>>> vol_cube(1)
1618
1.0
1719
>>> vol_cube(3)
@@ -33,6 +35,7 @@ def vol_cube(side_length: float) -> float:
3335
def vol_spherical_cap(height: float, radius: float) -> float:
3436
"""
3537
Calculate the volume of the spherical cap.
38+
3639
>>> vol_spherical_cap(1, 2)
3740
5.235987755982988
3841
>>> vol_spherical_cap(1.6, 2.6)
@@ -57,20 +60,29 @@ def vol_spherical_cap(height: float, radius: float) -> float:
5760
def vol_spheres_intersect(
5861
radius_1: float, radius_2: float, centers_distance: float
5962
) -> float:
60-
"""
63+
r"""
6164
Calculate the volume of the intersection of two spheres.
65+
6266
The intersection is composed by two spherical caps and therefore its volume is the
63-
sum of the volumes of the spherical caps. First, it calculates the heights (h1, h2)
64-
of the spherical caps, then the two volumes and it returns the sum.
67+
sum of the volumes of the spherical caps.
68+
First, it calculates the heights :math:`(h_1, h_2)` of the spherical caps,
69+
then the two volumes and it returns the sum.
6570
The height formulas are
66-
h1 = (radius_1 - radius_2 + centers_distance)
67-
* (radius_1 + radius_2 - centers_distance)
68-
/ (2 * centers_distance)
69-
h2 = (radius_2 - radius_1 + centers_distance)
70-
* (radius_2 + radius_1 - centers_distance)
71-
/ (2 * centers_distance)
72-
if centers_distance is 0 then it returns the volume of the smallers sphere
73-
:return vol_spherical_cap(h1, radius_2) + vol_spherical_cap(h2, radius_1)
71+
72+
.. math::
73+
h_1 = \frac{(radius_1 - radius_2 + centers\_distance)
74+
\cdot (radius_1 + radius_2 - centers\_distance)}
75+
{2 \cdot centers\_distance}
76+
77+
h_2 = \frac{(radius_2 - radius_1 + centers\_distance)
78+
\cdot (radius_2 + radius_1 - centers\_distance)}
79+
{2 \cdot centers\_distance}
80+
81+
if `centers_distance` is 0 then it returns the volume of the smallers sphere
82+
83+
:return: ``vol_spherical_cap`` (:math:`h_1`, :math:`radius_2`)
84+
+ ``vol_spherical_cap`` (:math:`h_2`, :math:`radius_1`)
85+
7486
>>> vol_spheres_intersect(2, 2, 1)
7587
21.205750411731103
7688
>>> vol_spheres_intersect(2.6, 2.6, 1.6)
@@ -112,14 +124,18 @@ def vol_spheres_intersect(
112124
def vol_spheres_union(
113125
radius_1: float, radius_2: float, centers_distance: float
114126
) -> float:
115-
"""
127+
r"""
116128
Calculate the volume of the union of two spheres that possibly intersect.
117-
It is the sum of sphere A and sphere B minus their intersection.
118-
First, it calculates the volumes (v1, v2) of the spheres,
119-
then the volume of the intersection (i) and it returns the sum v1+v2-i.
120-
If centers_distance is 0 then it returns the volume of the larger sphere
121-
:return vol_sphere(radius_1) + vol_sphere(radius_2)
122-
- vol_spheres_intersect(radius_1, radius_2, centers_distance)
129+
130+
It is the sum of sphere :math:`A` and sphere :math:`B` minus their intersection.
131+
First, it calculates the volumes :math:`(v_1, v_2)` of the spheres,
132+
then the volume of the intersection :math:`i` and
133+
it returns the sum :math:`v_1 + v_2 - i`.
134+
If `centers_distance` is 0 then it returns the volume of the larger sphere
135+
136+
:return: ``vol_sphere`` (:math:`radius_1`) + ``vol_sphere`` (:math:`radius_2`)
137+
- ``vol_spheres_intersect``
138+
(:math:`radius_1`, :math:`radius_2`, :math:`centers\_distance`)
123139
124140
>>> vol_spheres_union(2, 2, 1)
125141
45.814892864851146
@@ -157,7 +173,9 @@ def vol_spheres_union(
157173
def vol_cuboid(width: float, height: float, length: float) -> float:
158174
"""
159175
Calculate the Volume of a Cuboid.
160-
:return multiple of width, length and height
176+
177+
:return: multiple of `width`, `length` and `height`
178+
161179
>>> vol_cuboid(1, 1, 1)
162180
1.0
163181
>>> vol_cuboid(1, 2, 3)
@@ -185,10 +203,12 @@ def vol_cuboid(width: float, height: float, length: float) -> float:
185203

186204

187205
def vol_cone(area_of_base: float, height: float) -> float:
188-
"""
189-
Calculate the Volume of a Cone.
190-
Wikipedia reference: https://en.wikipedia.org/wiki/Cone
191-
:return (1/3) * area_of_base * height
206+
r"""
207+
| Calculate the Volume of a Cone.
208+
| Wikipedia reference: https://en.wikipedia.org/wiki/Cone
209+
210+
:return: :math:`\frac{1}{3} \cdot area\_of\_base \cdot height`
211+
192212
>>> vol_cone(10, 3)
193213
10.0
194214
>>> vol_cone(1, 1)
@@ -212,10 +232,12 @@ def vol_cone(area_of_base: float, height: float) -> float:
212232

213233

214234
def vol_right_circ_cone(radius: float, height: float) -> float:
215-
"""
216-
Calculate the Volume of a Right Circular Cone.
217-
Wikipedia reference: https://en.wikipedia.org/wiki/Cone
218-
:return (1/3) * pi * radius^2 * height
235+
r"""
236+
| Calculate the Volume of a Right Circular Cone.
237+
| Wikipedia reference: https://en.wikipedia.org/wiki/Cone
238+
239+
:return: :math:`\frac{1}{3} \cdot \pi \cdot radius^2 \cdot height`
240+
219241
>>> vol_right_circ_cone(2, 3)
220242
12.566370614359172
221243
>>> vol_right_circ_cone(0, 0)
@@ -237,10 +259,12 @@ def vol_right_circ_cone(radius: float, height: float) -> float:
237259

238260

239261
def vol_prism(area_of_base: float, height: float) -> float:
240-
"""
241-
Calculate the Volume of a Prism.
242-
Wikipedia reference: https://en.wikipedia.org/wiki/Prism_(geometry)
243-
:return V = Bh
262+
r"""
263+
| Calculate the Volume of a Prism.
264+
| Wikipedia reference: https://en.wikipedia.org/wiki/Prism_(geometry)
265+
266+
:return: :math:`V = B \cdot h`
267+
244268
>>> vol_prism(10, 2)
245269
20.0
246270
>>> vol_prism(11, 1)
@@ -264,10 +288,12 @@ def vol_prism(area_of_base: float, height: float) -> float:
264288

265289

266290
def vol_pyramid(area_of_base: float, height: float) -> float:
267-
"""
268-
Calculate the Volume of a Pyramid.
269-
Wikipedia reference: https://en.wikipedia.org/wiki/Pyramid_(geometry)
270-
:return (1/3) * Bh
291+
r"""
292+
| Calculate the Volume of a Pyramid.
293+
| Wikipedia reference: https://en.wikipedia.org/wiki/Pyramid_(geometry)
294+
295+
:return: :math:`\frac{1}{3} \cdot B \cdot h`
296+
271297
>>> vol_pyramid(10, 3)
272298
10.0
273299
>>> vol_pyramid(1.5, 3)
@@ -291,10 +317,12 @@ def vol_pyramid(area_of_base: float, height: float) -> float:
291317

292318

293319
def vol_sphere(radius: float) -> float:
294-
"""
295-
Calculate the Volume of a Sphere.
296-
Wikipedia reference: https://en.wikipedia.org/wiki/Sphere
297-
:return (4/3) * pi * r^3
320+
r"""
321+
| Calculate the Volume of a Sphere.
322+
| Wikipedia reference: https://en.wikipedia.org/wiki/Sphere
323+
324+
:return: :math:`\frac{4}{3} \cdot \pi \cdot r^3`
325+
298326
>>> vol_sphere(5)
299327
523.5987755982989
300328
>>> vol_sphere(1)
@@ -315,10 +343,13 @@ def vol_sphere(radius: float) -> float:
315343

316344

317345
def vol_hemisphere(radius: float) -> float:
318-
"""Calculate the volume of a hemisphere
319-
Wikipedia reference: https://en.wikipedia.org/wiki/Hemisphere
320-
Other references: https://www.cuemath.com/geometry/hemisphere
321-
:return 2/3 * pi * radius^3
346+
r"""
347+
| Calculate the volume of a hemisphere
348+
| Wikipedia reference: https://en.wikipedia.org/wiki/Hemisphere
349+
| Other references: https://www.cuemath.com/geometry/hemisphere
350+
351+
:return: :math:`\frac{2}{3} \cdot \pi \cdot radius^3`
352+
322353
>>> vol_hemisphere(1)
323354
2.0943951023931953
324355
>>> vol_hemisphere(7)
@@ -339,9 +370,12 @@ def vol_hemisphere(radius: float) -> float:
339370

340371

341372
def vol_circular_cylinder(radius: float, height: float) -> float:
342-
"""Calculate the Volume of a Circular Cylinder.
343-
Wikipedia reference: https://en.wikipedia.org/wiki/Cylinder
344-
:return pi * radius^2 * height
373+
r"""
374+
| Calculate the Volume of a Circular Cylinder.
375+
| Wikipedia reference: https://en.wikipedia.org/wiki/Cylinder
376+
377+
:return: :math:`\pi \cdot radius^2 \cdot height`
378+
345379
>>> vol_circular_cylinder(1, 1)
346380
3.141592653589793
347381
>>> vol_circular_cylinder(4, 3)
@@ -368,7 +402,9 @@ def vol_circular_cylinder(radius: float, height: float) -> float:
368402
def vol_hollow_circular_cylinder(
369403
inner_radius: float, outer_radius: float, height: float
370404
) -> float:
371-
"""Calculate the Volume of a Hollow Circular Cylinder.
405+
"""
406+
Calculate the Volume of a Hollow Circular Cylinder.
407+
372408
>>> vol_hollow_circular_cylinder(1, 2, 3)
373409
28.274333882308138
374410
>>> vol_hollow_circular_cylinder(1.6, 2.6, 3.6)
@@ -405,8 +441,9 @@ def vol_hollow_circular_cylinder(
405441

406442

407443
def vol_conical_frustum(height: float, radius_1: float, radius_2: float) -> float:
408-
"""Calculate the Volume of a Conical Frustum.
409-
Wikipedia reference: https://en.wikipedia.org/wiki/Frustum
444+
"""
445+
| Calculate the Volume of a Conical Frustum.
446+
| Wikipedia reference: https://en.wikipedia.org/wiki/Frustum
410447
411448
>>> vol_conical_frustum(45, 7, 28)
412449
48490.482608158454
@@ -443,9 +480,12 @@ def vol_conical_frustum(height: float, radius_1: float, radius_2: float) -> floa
443480

444481

445482
def vol_torus(torus_radius: float, tube_radius: float) -> float:
446-
"""Calculate the Volume of a Torus.
447-
Wikipedia reference: https://en.wikipedia.org/wiki/Torus
448-
:return 2pi^2 * torus_radius * tube_radius^2
483+
r"""
484+
| Calculate the Volume of a Torus.
485+
| Wikipedia reference: https://en.wikipedia.org/wiki/Torus
486+
487+
:return: :math:`2 \pi^2 \cdot torus\_radius \cdot tube\_radius^2`
488+
449489
>>> vol_torus(1, 1)
450490
19.739208802178716
451491
>>> vol_torus(4, 3)
@@ -471,8 +511,9 @@ def vol_torus(torus_radius: float, tube_radius: float) -> float:
471511

472512

473513
def vol_icosahedron(tri_side: float) -> float:
474-
"""Calculate the Volume of an Icosahedron.
475-
Wikipedia reference: https://en.wikipedia.org/wiki/Regular_icosahedron
514+
"""
515+
| Calculate the Volume of an Icosahedron.
516+
| Wikipedia reference: https://en.wikipedia.org/wiki/Regular_icosahedron
476517
477518
>>> from math import isclose
478519
>>> isclose(vol_icosahedron(2.5), 34.088984228514256)

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