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Sphere intersection and spherical cap volumes (#5579)

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* sphere intersection + spherical cap volume formulas

* reformatted

* Update volume.py

Co-authored-by: Christian Clauss <cclauss@me.com>
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Matteo Messmer 2021-10-27 00:28:26 +02:00 committed by GitHub
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maths/volume.py
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@ -20,6 +20,56 @@ def vol_cube(side_length: int | float) -> float:
return pow(side_length, 3)
def vol_spherical_cap(height: float, radius: float) -> float:
"""
Calculate the Volume of the spherical cap.
:return 1/3 pi * height ^ 2 * (3 * radius - height)
>>> vol_spherical_cap(1, 2)
5.235987755982988
"""
return 1 / 3 * pi * pow(height, 2) * (3 * radius - height)
def vol_spheres_intersect(
radius_1: float, radius_2: float, centers_distance: float
) -> float:
"""
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 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)
>>> vol_spheres_intersect(2, 2, 1)
21.205750411731103
"""
if centers_distance == 0:
return vol_sphere(min(radius_1, radius_2))
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)
)
return vol_spherical_cap(h1, radius_2) + vol_spherical_cap(h2, radius_1)
def vol_cuboid(width: float, height: float, length: float) -> float:
"""
Calculate the Volume of a Cuboid.
@ -127,6 +177,8 @@ def main():
print("Pyramid: " + str(vol_pyramid(2, 2))) # ~= 1.33
print("Sphere: " + str(vol_sphere(2))) # ~= 33.5
print("Circular Cylinder: " + str(vol_circular_cylinder(2, 2))) # ~= 25.1
print("Spherical cap: " + str(vol_spherical_cap(1, 2))) # ~= 5.24
print("Spheres intersetion: " + str(vol_spheres_intersect(2, 2, 1))) # ~= 21.21
if __name__ == "__main__":