| 释义 |
Sphere-Sphere IntersectionLet two spheres of Radii  and  be located along the x-Axis centered at  and , respectively. Not surprisingly, the analysis is very similar to the case of the Circle-Circle Intersection.The equations of the two Spheres are
Combining (1) and (2) gives
 | (3) |
 | (4) |
 gives
 | (5) |
 -plane at asingle -coordinate. Plugging this back into (1) gives
which is a Circle with Radius
The Volume of the 3-D Lens common to the two spheres can be found by adding the two SphericalCaps. The distances from the Spheres' centers to the bases of the caps are
so the heights of the caps are
The Volume of a Spherical Cap of height  for a Sphere of Radius  is
 | (12) |
 and  and summing the two caps gives
 | (13) |
 for  as it must. In the special case  , the Volume simplifies to
 | (14) |
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