Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Intersecting Spheres
Name: Jhoan T.
Status: student	
Age:  N/A
Location: N/A
Country: N/A
Date: N/A 


Question:
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.



Replies:
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.

Kenneth Mellendorf


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.
Assistant Director
PG Research Foundation, Darien, Illinois



Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs

NEWTON AND ASK A SCIENTIST
Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory