Fast marching method
Typically, such a problem describes the evolution of a closed curve as a function of time with speed in the normal direction at a point on the curve. The speed function is specified, and the time at which the contour crosses a point is obtained by solving the equation.
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 methods. More general algorithms exist but are normally slower.
Extensions to non-flat (triangulated) domains solving:
- Djikstra-like Methods for the Eikonal Equation J.N. Tsitsiklis, 1995
- The Fast Marching Method and its Applications by James A. Sethian
- Multi-Stencils Fast Marching Methods
- Multi-Stencils Fast Marching Matlab Implementation
- Implementation Details of the Fast Marching Methods
- Generalized Fast Marching method by Forcadel et al.  for applications in image segmentation.
- See Chapter 8 in Design and Optimization of Nano-Optical Elements by Coupling Fabrication to Optical Behavior
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