Q:

Area of overlap of two circular Gaussian functions

I am trying to write code that finds the overlap of between 3D shapes. 
Each shape is defined by two intersecting normal distributions (one in the x direction, one in the y direction).
Do you have any suggestions of existing code that addresses this question or functions that I can utilize to build this code? Most of my programming experience has been in R, but I am open to solutions in other languages as well.
Thank you in advance for any suggestions and assistance! 

The longer research context on this question: I am studying the use of acoustic space by insects. I want to know whether randomly assembled groups of insects would have calls that are more or less similar than we observe in natural communities (a randomization test). To do so, I need to randomly select insect species and calculate the similarity between their calls. 
For each species, I have a mean and variance for two call characteristics that are approximately normally distributed. I would like to use these two call characteristics to build a 3D probability distribution for the species. I would then like to calculate the amount by which the PDF for one species overlaps with another.
Please accept my apologies if the question is not clear or appropriate for this forum. 

A:

I work in small molecule drug discovery, and I frequently use a program (ROCS, by OpenEye Scientific Software) based on algorithms that represent molecules as collections of spherical Gaussian functions and compute intersection volumes. You might look at the following references, as well as the ROCS documentation:
(1) Grant and Pickup, J. Phys. Chem. 1995, 99, 3503-3510
(2) Grant, Gallardo, and Pickup, J. Comp. Chem. 1996, 17, 1653-1666

