How to get the height according to EGM96 for a point?

GeographicLib includes classes to compute the geoid height via interpolation on a grid of values (the Geoid class) and via summing the spherical harmonic sum (the GravityModel class). The interpolation method is pretty straightforward; see the associated documentation, Geoid height. I agree that the NGA programs for computing the geoid height via spherical harmonics are poorly documented. I've tried to explain the method on the documentation page, Gravity models. More to the point, I'm happy to answer questions. (I've had no luck getting NGA to answer questions about its programs!)

Pardon if I'm cross-posting a link from Stack Overflow. I asked a similar question on Stack Overflow with regards how to do the calculations for an IOS application. I actually ended up answering my own question but I've posted a link here which gives you both C and Objective C code to complete this task.

Code is here:
https://stackoverflow.com/questions/22196714/wgs84-geoid-height-altitude-offset-for-external-gps-data-on-ios

Somebody ported a Fortran program to do these calculations into C and I then ported it over to Objective C

Here is a C# library for calculating geoid EGM96 undulations: https://github.com/MatejFranceskin/GeoidHeightsDotNet

Available also as Nuget packet: GeoidHeightsDotNet

There is a JavaScript conversion library here: https://www.npmjs.com/package/egm96-universal