This is a very interesting tutorial. It enabled me to really understand both the theoritical foundation as well as the implementation details of the fast marching methods (FMM). Within couple of hours, i managed to implement both the 1st order as well as the second order fast marching methods. I always believed that science is not difficult, we just need to meet either the right professor, right book, or the right tutorial. In my humble opinion, this is the entry point to understanding the FMM. However, if you need to improve the method, i would suggest reading the FMM book by Sethian. Also, you may consider reading the following transaction on sciweavers: Multistencils Fast Marching Methods: A Highly Accurate Solution to the Eikonal Equation on Cartesian Domains. It provides both an improved version of the FMM as well as a survey on the methods that improved that technique.