spheresegmentvolume
This tool computes the volume inside a sphere in n dimensions, or inside a sphere cap, or inside any part of a sphere that can be defined by two parallel slicing planes.
Compute the volume of a unit, complete sphere.
In 2-d, the "volume" is pi.
V = spheresegmentvolume([],2)
V =
3.1416
V - pi
ans =
0
In 3-d, compute the volume of an exact unit hemisphere. The volume is pi*2/3, approximately 2.0944
V = spheresegmentvolume([0,1],3)
V =
2.0944
V - 2*pi/3
ans =
-4.4409e-16
In 4-d, compute the volume inside a central band around a hyper-sphere of radius 2, with the band running from -1 to +1. Thus, the parallel planes are separated by 2 units of distance and are symmetric around the center of the sphere.
V = spheresegmentvolume([-1,1],4,2)
V =
58.967
In 50 dimensions, compute the volume inside a unit hemi-spherical cap.
V = spheresegmentvolume([0,1],50)
V =
8.6511e-14
Cite As
John D'Errico (2024). spheresegmentvolume (https://www.mathworks.com/matlabcentral/fileexchange/18641-spheresegmentvolume), MATLAB Central File Exchange. Retrieved .
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Version | Published | Release Notes | |
---|---|---|---|
1.1.0.0 | Repair made for odd dimensionality |