I exchanged some messages with someone who was vaguely familiar with the code. It seems as though this implementation is very stubborn on using DLLs, so compiling for 64-bit Ubuntu servers requires some work, including the change of MATLAB code such as loadlibrary([geodesic_library '.dll'], hfile); and the addition of libraries to compilation, including Boost which is 86MB (compressed). Some of the C++ code has been changed a bit and since non-Windows platforms are listed as not supported, there is no guarantee that this is going to work. For exact geodesics, many searches around the Web brought nothing up, not even links from within peer-reviewed papers.
After several hours hacking around the code to make it suitable for compilation on Linux and 64-bit platforms it still seems rather elusive because the Boost library is quite a major dependency and notorious in this regard. In general, many searches around the Web (quite exhaustive) reveal almost no other public implementation of exact geodesics for MATLAB (except the one which in turn latches onto peripheral binaries for Windows, requiring Windows servers and perhaps forking). No MakeFile is provided, so making this code cross-platform would possibly require a great deal of deviation from the original (last updated in early 2008 by Danil Kirsanov).
Roy Schestowitz 2012-01-08