Finding intersection of two spheres
- by Onkar Deshpande
Hi,
Consider the following problem - I am given 2 links of length L0 and L1. P0 is the point that the first link starts at and P1 is the point that I want the end of second link to be at in 3-D space. I am supposed to write a function that should take in these 3-D points (P0 and P1) as inputs and should find all configurations of the links that put the second link's end point at P1.
My understanding of how to go about it is - Each link L0 and L1 will create a sphere S0 and S1 around itself. I should find out the intersection of those two spheres (which will be a circle) and print all points that are on the circumference of that circle.
I saw gmatt's first reply on the http://stackoverflow.com/questions/1406375/finding-intersection-points-between-3-spheres but could not understand it properly since the images did not show up. I also saw a formula for finding out the intersection at mathworld[dot]wolfram[dot]com/Sphere-SphereIntersection[dot]html .
I could find the radius of intersection by the method given on mathworld. Also I can find the center of that circle and then use the parametric equation of circle to find the points. The only doubt that I have is will this method work for the points P0 and P1 mentioned above ?
Please comment and let me know your thoughts.
