conrad@cgl.ucsf.edu (Conrad Huang) (02/13/91)
I need to solve the following problem: Given: A probe sphere with center at Cp and radius Rp A set of test spheres with centers at Ci and radii Ri Find: Is there a point that falls on or inside the probe sphere but not in any of the test spheres? This can probably be restated as something like: Vp - sum Vi =/= empty where Vp is the volume of the probe sphere and Vi are the volumes of the test spheres. All I need to know is whether the assertion is true or false. I don't need the actual point/volume that satisfies the assertion. Obviously, I can sample the probe sphere to test the conditions and be "reasonably" certain that the assertion is true or false. But I would really like to get an analytic solution (if there is one). If anyone can tell me how to do this or point me at some references, I'd greatly appreciate it. Conrad Huang conrad@cgl.ucsf.edu