Fast marching method: Difference between revisions

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Typically, such a problem describes the evolution of a closed surface as a function of time <math>u</math> with speed <math>f(x)</math> in the normal direction at a point <math>x</math> on the propagating surface. The speed function is specified, and the time at which the contour crosses a point <math>x</math> is obtained by solving the equation. Alternatively, <math>u(x)</math> can be thought of as the minimum amount of time it would take to reach <math>\partial\Omega</math> starting from the point <math>x</math>. Fast marching method takes advantage of this [[optimal control]] interpretation of the problem in order to build a solution outwards starting from the "known information", i.e. the boundary values.

The algorithm is similar to [[Dijkstra's algorithm]] and uses the fact that information only flows outward from the seeding area. This problem is a special case of [[level set method]]s. [[Eikonal equation#Computational Algorithmsalgorithms|More general algorithms exist]] but are normally slower.

Extensions to non-flat (triangulated) domains solving: