Variational principles have played an exceptionally important role in the foundations of mathematical physics. Their potential in numerical algorithms should not be underestimated.

In this paper, I interpret the fast marching eikonal solver with the help of Fermat's principle. Two important generalizations follow immediately from that interpretation. First, it allows us to obtain a fast method of first-arrival traveltime computation on triangulated grids. Furthermore, we can obtain a general principle, which extends the fast marching algorithm to other Hamilton-type equations and their variational principles. More research is required to confirm these promises.

In addition, future research should focus on 3-D implementations and on increasing the approximation order of the method.

10/9/1997