Simple Analytic Geom Question

["Ted Hill" <thill@tomotherapy.com>]

Title: Message

Hello,

 

This is a 2D problem in the x, y plane.

 

My inputs are:

 

circle radius (same for both circles A & B)

center point for circle A

center point for circle B

 

What I want to find are:

 

The corner points of the rectangle that satisfies the following:

 

The four points lie on the circles (2 on each circle, at opposite ends of a diameter) such that

 

2 sides of the rectangle are parallel to the line that joins the center points of the circles.

 

The other two sides of the rectangle are diameters of the circles.

 

I need to run this repeatedly as the mouse moves, so I am looking for a fairly efficient way to calculate the four corners of my rectangle.

 

Thank you,

 

Ted Hill