/sci/ - Science & Math

Let's say I have a cube of size [math]2 \times 2 \times 2[/math], with its center at [math](0, 0, 0)[/math].

Given a sphere with center at [math](x, y, z)[/math] and radius [math]r[/math], is there a general formula for the surface area of the part of the sphere that is inside of the cube? I want the red part of picrel, but in 3D.

For cases where it only touches one side, it seems like I can use the formula for spherical caps, and for cases where the center intersects the edge of the cube it's a spherical wedge. Is there a formula for when it's cut off by two or more sides at an arbitrary location?

Also, is there a similar formula for hyperspheres intersected by hypercubes, or higher dimensions?

Note: I don't need a symbolic answer. An integral that I can paste into a solver and get a rough numeric answer is more than fine.
>>15043131
You can't; LG's search is terrible. Wildcards are the best you can get AFAIK.