Mark Wagner wrote:

> Given the centers and radii of two overlapping spheres, what is the equation
> for the circle where the two spheres intersect?  I need this for a project
> I'm working on.
>
> Mark

What form do you need this equation in?

If r1 and r2 are the radii of the two spheres and d is the distance between
their centers, then the radius of the circle of their intersection should be:

sqrt(-(d+r1+r2)*(d-r1+r2)*(d+r1-r2)*(d-r1-r2))/(2*d)

This circle will be centered on the line connecting the centers of the spheres
and will be

(d+r1-r2)/2

units away from the center of the first sphere and

(d+r2-r1)/2

units away from the center of the second sphere.  The circle will also be
oriented so that it is orthogonal to the line connecting the centers of the
spheres.

I hope that this is helpful.

Post a reply to this message