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cc0405d05c
* Update volume.py with volume of Icosahedron Added function to find volume of a regular Icosahedron * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Apply suggestions from code review * Update volume.py --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
526 lines
17 KiB
Python
526 lines
17 KiB
Python
"""
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Find the volume of various shapes.
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* https://en.wikipedia.org/wiki/Volume
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* https://en.wikipedia.org/wiki/Spherical_cap
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"""
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from __future__ import annotations
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from math import pi, pow
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def vol_cube(side_length: float) -> float:
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"""
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Calculate the Volume of a Cube.
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>>> vol_cube(1)
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1.0
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>>> vol_cube(3)
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27.0
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>>> vol_cube(0)
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0.0
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>>> vol_cube(1.6)
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4.096000000000001
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>>> vol_cube(-1)
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Traceback (most recent call last):
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...
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ValueError: vol_cube() only accepts non-negative values
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"""
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if side_length < 0:
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raise ValueError("vol_cube() only accepts non-negative values")
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return pow(side_length, 3)
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def vol_spherical_cap(height: float, radius: float) -> float:
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"""
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Calculate the volume of the spherical cap.
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>>> vol_spherical_cap(1, 2)
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5.235987755982988
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>>> vol_spherical_cap(1.6, 2.6)
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16.621119532592402
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>>> vol_spherical_cap(0, 0)
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0.0
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>>> vol_spherical_cap(-1, 2)
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Traceback (most recent call last):
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...
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ValueError: vol_spherical_cap() only accepts non-negative values
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>>> vol_spherical_cap(1, -2)
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Traceback (most recent call last):
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...
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ValueError: vol_spherical_cap() only accepts non-negative values
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"""
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if height < 0 or radius < 0:
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raise ValueError("vol_spherical_cap() only accepts non-negative values")
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# Volume is 1/3 pi * height squared * (3 * radius - height)
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return 1 / 3 * pi * pow(height, 2) * (3 * radius - height)
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def vol_spheres_intersect(
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radius_1: float, radius_2: float, centers_distance: float
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) -> float:
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"""
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Calculate the volume of the intersection of two spheres.
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The intersection is composed by two spherical caps and therefore its volume is the
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sum of the volumes of the spherical caps. First, it calculates the heights (h1, h2)
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of the spherical caps, then the two volumes and it returns the sum.
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The height formulas are
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h1 = (radius_1 - radius_2 + centers_distance)
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* (radius_1 + radius_2 - centers_distance)
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/ (2 * centers_distance)
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h2 = (radius_2 - radius_1 + centers_distance)
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* (radius_2 + radius_1 - centers_distance)
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/ (2 * centers_distance)
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if centers_distance is 0 then it returns the volume of the smallers sphere
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:return vol_spherical_cap(h1, radius_2) + vol_spherical_cap(h2, radius_1)
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>>> vol_spheres_intersect(2, 2, 1)
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21.205750411731103
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>>> vol_spheres_intersect(2.6, 2.6, 1.6)
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40.71504079052372
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>>> vol_spheres_intersect(0, 0, 0)
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0.0
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>>> vol_spheres_intersect(-2, 2, 1)
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Traceback (most recent call last):
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...
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ValueError: vol_spheres_intersect() only accepts non-negative values
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>>> vol_spheres_intersect(2, -2, 1)
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Traceback (most recent call last):
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...
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ValueError: vol_spheres_intersect() only accepts non-negative values
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>>> vol_spheres_intersect(2, 2, -1)
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Traceback (most recent call last):
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...
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ValueError: vol_spheres_intersect() only accepts non-negative values
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"""
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if radius_1 < 0 or radius_2 < 0 or centers_distance < 0:
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raise ValueError("vol_spheres_intersect() only accepts non-negative values")
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if centers_distance == 0:
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return vol_sphere(min(radius_1, radius_2))
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h1 = (
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(radius_1 - radius_2 + centers_distance)
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* (radius_1 + radius_2 - centers_distance)
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/ (2 * centers_distance)
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)
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h2 = (
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(radius_2 - radius_1 + centers_distance)
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* (radius_2 + radius_1 - centers_distance)
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/ (2 * centers_distance)
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)
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return vol_spherical_cap(h1, radius_2) + vol_spherical_cap(h2, radius_1)
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def vol_spheres_union(
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radius_1: float, radius_2: float, centers_distance: float
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) -> float:
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"""
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Calculate the volume of the union of two spheres that possibly intersect.
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It is the sum of sphere A and sphere B minus their intersection.
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First, it calculates the volumes (v1, v2) of the spheres,
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then the volume of the intersection (i) and it returns the sum v1+v2-i.
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If centers_distance is 0 then it returns the volume of the larger sphere
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:return vol_sphere(radius_1) + vol_sphere(radius_2)
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- vol_spheres_intersect(radius_1, radius_2, centers_distance)
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>>> vol_spheres_union(2, 2, 1)
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45.814892864851146
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>>> vol_spheres_union(1.56, 2.2, 1.4)
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48.77802773671288
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>>> vol_spheres_union(0, 2, 1)
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Traceback (most recent call last):
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...
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ValueError: vol_spheres_union() only accepts non-negative values, non-zero radius
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>>> vol_spheres_union('1.56', '2.2', '1.4')
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Traceback (most recent call last):
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...
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TypeError: '<=' not supported between instances of 'str' and 'int'
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>>> vol_spheres_union(1, None, 1)
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Traceback (most recent call last):
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...
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TypeError: '<=' not supported between instances of 'NoneType' and 'int'
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"""
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if radius_1 <= 0 or radius_2 <= 0 or centers_distance < 0:
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raise ValueError(
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"vol_spheres_union() only accepts non-negative values, non-zero radius"
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)
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if centers_distance == 0:
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return vol_sphere(max(radius_1, radius_2))
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return (
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vol_sphere(radius_1)
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+ vol_sphere(radius_2)
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- vol_spheres_intersect(radius_1, radius_2, centers_distance)
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)
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def vol_cuboid(width: float, height: float, length: float) -> float:
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"""
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Calculate the Volume of a Cuboid.
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:return multiple of width, length and height
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>>> vol_cuboid(1, 1, 1)
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1.0
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>>> vol_cuboid(1, 2, 3)
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6.0
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>>> vol_cuboid(1.6, 2.6, 3.6)
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14.976
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>>> vol_cuboid(0, 0, 0)
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0.0
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>>> vol_cuboid(-1, 2, 3)
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Traceback (most recent call last):
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...
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ValueError: vol_cuboid() only accepts non-negative values
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>>> vol_cuboid(1, -2, 3)
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Traceback (most recent call last):
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...
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ValueError: vol_cuboid() only accepts non-negative values
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>>> vol_cuboid(1, 2, -3)
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Traceback (most recent call last):
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...
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ValueError: vol_cuboid() only accepts non-negative values
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"""
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if width < 0 or height < 0 or length < 0:
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raise ValueError("vol_cuboid() only accepts non-negative values")
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return float(width * height * length)
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def vol_cone(area_of_base: float, height: float) -> float:
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"""
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Calculate the Volume of a Cone.
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Wikipedia reference: https://en.wikipedia.org/wiki/Cone
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:return (1/3) * area_of_base * height
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>>> vol_cone(10, 3)
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10.0
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>>> vol_cone(1, 1)
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0.3333333333333333
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>>> vol_cone(1.6, 1.6)
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0.8533333333333335
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>>> vol_cone(0, 0)
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0.0
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>>> vol_cone(-1, 1)
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Traceback (most recent call last):
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...
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ValueError: vol_cone() only accepts non-negative values
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>>> vol_cone(1, -1)
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Traceback (most recent call last):
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...
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ValueError: vol_cone() only accepts non-negative values
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"""
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if height < 0 or area_of_base < 0:
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raise ValueError("vol_cone() only accepts non-negative values")
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return area_of_base * height / 3.0
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def vol_right_circ_cone(radius: float, height: float) -> float:
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"""
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Calculate the Volume of a Right Circular Cone.
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Wikipedia reference: https://en.wikipedia.org/wiki/Cone
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:return (1/3) * pi * radius^2 * height
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>>> vol_right_circ_cone(2, 3)
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12.566370614359172
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>>> vol_right_circ_cone(0, 0)
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0.0
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>>> vol_right_circ_cone(1.6, 1.6)
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4.289321169701265
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>>> vol_right_circ_cone(-1, 1)
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Traceback (most recent call last):
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...
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ValueError: vol_right_circ_cone() only accepts non-negative values
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>>> vol_right_circ_cone(1, -1)
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Traceback (most recent call last):
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...
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ValueError: vol_right_circ_cone() only accepts non-negative values
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"""
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if height < 0 or radius < 0:
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raise ValueError("vol_right_circ_cone() only accepts non-negative values")
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return pi * pow(radius, 2) * height / 3.0
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def vol_prism(area_of_base: float, height: float) -> float:
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"""
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Calculate the Volume of a Prism.
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Wikipedia reference: https://en.wikipedia.org/wiki/Prism_(geometry)
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:return V = Bh
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>>> vol_prism(10, 2)
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20.0
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>>> vol_prism(11, 1)
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11.0
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>>> vol_prism(1.6, 1.6)
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2.5600000000000005
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>>> vol_prism(0, 0)
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0.0
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>>> vol_prism(-1, 1)
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Traceback (most recent call last):
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...
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ValueError: vol_prism() only accepts non-negative values
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>>> vol_prism(1, -1)
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Traceback (most recent call last):
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...
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ValueError: vol_prism() only accepts non-negative values
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"""
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if height < 0 or area_of_base < 0:
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raise ValueError("vol_prism() only accepts non-negative values")
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return float(area_of_base * height)
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def vol_pyramid(area_of_base: float, height: float) -> float:
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"""
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Calculate the Volume of a Pyramid.
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Wikipedia reference: https://en.wikipedia.org/wiki/Pyramid_(geometry)
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:return (1/3) * Bh
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>>> vol_pyramid(10, 3)
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10.0
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>>> vol_pyramid(1.5, 3)
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1.5
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>>> vol_pyramid(1.6, 1.6)
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0.8533333333333335
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>>> vol_pyramid(0, 0)
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0.0
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>>> vol_pyramid(-1, 1)
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Traceback (most recent call last):
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...
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ValueError: vol_pyramid() only accepts non-negative values
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>>> vol_pyramid(1, -1)
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Traceback (most recent call last):
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...
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ValueError: vol_pyramid() only accepts non-negative values
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"""
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if height < 0 or area_of_base < 0:
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raise ValueError("vol_pyramid() only accepts non-negative values")
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return area_of_base * height / 3.0
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def vol_sphere(radius: float) -> float:
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"""
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Calculate the Volume of a Sphere.
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Wikipedia reference: https://en.wikipedia.org/wiki/Sphere
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:return (4/3) * pi * r^3
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>>> vol_sphere(5)
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523.5987755982989
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>>> vol_sphere(1)
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4.1887902047863905
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>>> vol_sphere(1.6)
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17.15728467880506
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>>> vol_sphere(0)
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0.0
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>>> vol_sphere(-1)
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Traceback (most recent call last):
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...
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ValueError: vol_sphere() only accepts non-negative values
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"""
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if radius < 0:
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raise ValueError("vol_sphere() only accepts non-negative values")
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# Volume is 4/3 * pi * radius cubed
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return 4 / 3 * pi * pow(radius, 3)
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def vol_hemisphere(radius: float) -> float:
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"""Calculate the volume of a hemisphere
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Wikipedia reference: https://en.wikipedia.org/wiki/Hemisphere
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Other references: https://www.cuemath.com/geometry/hemisphere
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:return 2/3 * pi * radius^3
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>>> vol_hemisphere(1)
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2.0943951023931953
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>>> vol_hemisphere(7)
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718.377520120866
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>>> vol_hemisphere(1.6)
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8.57864233940253
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>>> vol_hemisphere(0)
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0.0
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>>> vol_hemisphere(-1)
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Traceback (most recent call last):
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...
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ValueError: vol_hemisphere() only accepts non-negative values
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"""
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if radius < 0:
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raise ValueError("vol_hemisphere() only accepts non-negative values")
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# Volume is radius cubed * pi * 2/3
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return pow(radius, 3) * pi * 2 / 3
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def vol_circular_cylinder(radius: float, height: float) -> float:
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"""Calculate the Volume of a Circular Cylinder.
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Wikipedia reference: https://en.wikipedia.org/wiki/Cylinder
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:return pi * radius^2 * height
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>>> vol_circular_cylinder(1, 1)
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3.141592653589793
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>>> vol_circular_cylinder(4, 3)
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150.79644737231007
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>>> vol_circular_cylinder(1.6, 1.6)
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12.867963509103795
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>>> vol_circular_cylinder(0, 0)
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0.0
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>>> vol_circular_cylinder(-1, 1)
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Traceback (most recent call last):
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...
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ValueError: vol_circular_cylinder() only accepts non-negative values
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>>> vol_circular_cylinder(1, -1)
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Traceback (most recent call last):
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...
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ValueError: vol_circular_cylinder() only accepts non-negative values
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"""
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if height < 0 or radius < 0:
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raise ValueError("vol_circular_cylinder() only accepts non-negative values")
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# Volume is radius squared * height * pi
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return pow(radius, 2) * height * pi
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def vol_hollow_circular_cylinder(
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inner_radius: float, outer_radius: float, height: float
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) -> float:
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"""Calculate the Volume of a Hollow Circular Cylinder.
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>>> vol_hollow_circular_cylinder(1, 2, 3)
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28.274333882308138
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>>> vol_hollow_circular_cylinder(1.6, 2.6, 3.6)
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47.50088092227767
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>>> vol_hollow_circular_cylinder(-1, 2, 3)
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Traceback (most recent call last):
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...
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ValueError: vol_hollow_circular_cylinder() only accepts non-negative values
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>>> vol_hollow_circular_cylinder(1, -2, 3)
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Traceback (most recent call last):
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...
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ValueError: vol_hollow_circular_cylinder() only accepts non-negative values
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>>> vol_hollow_circular_cylinder(1, 2, -3)
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Traceback (most recent call last):
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...
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ValueError: vol_hollow_circular_cylinder() only accepts non-negative values
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>>> vol_hollow_circular_cylinder(2, 1, 3)
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Traceback (most recent call last):
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...
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ValueError: outer_radius must be greater than inner_radius
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>>> vol_hollow_circular_cylinder(0, 0, 0)
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Traceback (most recent call last):
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...
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ValueError: outer_radius must be greater than inner_radius
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"""
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# Volume - (outer_radius squared - inner_radius squared) * pi * height
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if inner_radius < 0 or outer_radius < 0 or height < 0:
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raise ValueError(
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"vol_hollow_circular_cylinder() only accepts non-negative values"
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)
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if outer_radius <= inner_radius:
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raise ValueError("outer_radius must be greater than inner_radius")
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return pi * (pow(outer_radius, 2) - pow(inner_radius, 2)) * height
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def vol_conical_frustum(height: float, radius_1: float, radius_2: float) -> float:
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"""Calculate the Volume of a Conical Frustum.
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Wikipedia reference: https://en.wikipedia.org/wiki/Frustum
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>>> vol_conical_frustum(45, 7, 28)
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48490.482608158454
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>>> vol_conical_frustum(1, 1, 2)
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7.330382858376184
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>>> vol_conical_frustum(1.6, 2.6, 3.6)
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48.7240076620753
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>>> vol_conical_frustum(0, 0, 0)
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0.0
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>>> vol_conical_frustum(-2, 2, 1)
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Traceback (most recent call last):
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...
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ValueError: vol_conical_frustum() only accepts non-negative values
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>>> vol_conical_frustum(2, -2, 1)
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Traceback (most recent call last):
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...
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ValueError: vol_conical_frustum() only accepts non-negative values
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>>> vol_conical_frustum(2, 2, -1)
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Traceback (most recent call last):
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...
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ValueError: vol_conical_frustum() only accepts non-negative values
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"""
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# Volume is 1/3 * pi * height *
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# (radius_1 squared + radius_2 squared + radius_1 * radius_2)
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if radius_1 < 0 or radius_2 < 0 or height < 0:
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raise ValueError("vol_conical_frustum() only accepts non-negative values")
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return (
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1
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/ 3
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* pi
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* height
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* (pow(radius_1, 2) + pow(radius_2, 2) + radius_1 * radius_2)
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)
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def vol_torus(torus_radius: float, tube_radius: float) -> float:
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"""Calculate the Volume of a Torus.
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Wikipedia reference: https://en.wikipedia.org/wiki/Torus
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:return 2pi^2 * torus_radius * tube_radius^2
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>>> vol_torus(1, 1)
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19.739208802178716
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>>> vol_torus(4, 3)
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710.6115168784338
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>>> vol_torus(3, 4)
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947.4820225045784
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>>> vol_torus(1.6, 1.6)
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80.85179925372404
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>>> vol_torus(0, 0)
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0.0
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>>> vol_torus(-1, 1)
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Traceback (most recent call last):
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...
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ValueError: vol_torus() only accepts non-negative values
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>>> vol_torus(1, -1)
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Traceback (most recent call last):
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...
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ValueError: vol_torus() only accepts non-negative values
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"""
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if torus_radius < 0 or tube_radius < 0:
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raise ValueError("vol_torus() only accepts non-negative values")
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return 2 * pow(pi, 2) * torus_radius * pow(tube_radius, 2)
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|
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def vol_icosahedron(tri_side: float) -> float:
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"""Calculate the Volume of an Icosahedron.
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Wikipedia reference: https://en.wikipedia.org/wiki/Regular_icosahedron
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|
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>>> from math import isclose
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>>> isclose(vol_icosahedron(2.5), 34.088984228514256)
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True
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>>> isclose(vol_icosahedron(10), 2181.694990624912374)
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True
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>>> isclose(vol_icosahedron(5), 272.711873828114047)
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True
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>>> isclose(vol_icosahedron(3.49), 92.740688412033628)
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True
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>>> vol_icosahedron(0)
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|
0.0
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>>> vol_icosahedron(-1)
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Traceback (most recent call last):
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|
...
|
|
ValueError: vol_icosahedron() only accepts non-negative values
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|
>>> vol_icosahedron(-0.2)
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|
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
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|
|
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|
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def main():
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"""Print the Results of Various Volume Calculations."""
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print("Volumes:")
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print(f"Cube: {vol_cube(2) = }") # = 8
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print(f"Cuboid: {vol_cuboid(2, 2, 2) = }") # = 8
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print(f"Cone: {vol_cone(2, 2) = }") # ~= 1.33
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print(f"Right Circular Cone: {vol_right_circ_cone(2, 2) = }") # ~= 8.38
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print(f"Prism: {vol_prism(2, 2) = }") # = 4
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print(f"Pyramid: {vol_pyramid(2, 2) = }") # ~= 1.33
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print(f"Sphere: {vol_sphere(2) = }") # ~= 33.5
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print(f"Hemisphere: {vol_hemisphere(2) = }") # ~= 16.75
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print(f"Circular Cylinder: {vol_circular_cylinder(2, 2) = }") # ~= 25.1
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|
print(f"Torus: {vol_torus(2, 2) = }") # ~= 157.9
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|
print(f"Conical Frustum: {vol_conical_frustum(2, 2, 4) = }") # ~= 58.6
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print(f"Spherical cap: {vol_spherical_cap(1, 2) = }") # ~= 5.24
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print(f"Spheres intersetion: {vol_spheres_intersect(2, 2, 1) = }") # ~= 21.21
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print(f"Spheres union: {vol_spheres_union(2, 2, 1) = }") # ~= 45.81
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print(
|
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f"Hollow Circular Cylinder: {vol_hollow_circular_cylinder(1, 2, 3) = }"
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|
) # ~= 28.3
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print(f"Icosahedron: {vol_icosahedron(2.5) = }") # ~=34.09
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|
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if __name__ == "__main__":
|
|
main()
|