Name: Jhoan T.
I need to know a very simple way to intesect two spheres.
I have their radii and their centres. I know, therefore, their equations.
I am working on brownian dynamics.
The intersection is a circle. The center of the circle will lie along the
line connecting the centers of the spheres. The circle will lie in a plane
perpendicular to this line. You need the location of the center, as well as
the radius of the circle. Choose a coordinate system that has one center at
the origin and the other origin on the x-axis. Draw a circle of appropriate
radius around each center. There will be two points of intersection. For
simplicity, choose the one with y>0. The (x,y) point will be such that
x^2+y^2=r1^2 and (c2-x)^2+y^2=r2^2.
Solve for x. This is the center of the circle you are looking for. Call
this value c, for lack of a better term. In this coordinate system, the
center is at (c,0,0). Solve for y. This is the distance from the x-axis to
the intersection, the radius of the intersection circle. Call this value r.
In this coordinate system, the circle of intersection is the set of points:
(x,y,z) such that x=c and y^2+z^2=r^2.
When you say you want to "intersect" the spheres, exactly what do you want
to know? Do you just want to know if they are close enough to overlap? Do
you want to know the equation or volume of the shared space if they overlap?
Or is it something else?
Richard E. Barrans Jr., Ph.D.
PG Research Foundation, Darien, Illinois
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Update: June 2012