Content deleted Content added
Rescuing 1 sources and tagging 0 as dead.) #IABot (v2.0.9.2 |
ElasticSnake (talk | contribs) mNo edit summary |
||
Line 4:
: <math>|\nabla u(x)|=1/f(x) \text{ for } x \in \Omega</math>
: <math>u(x) = 0 \text{ for } x \in \partial \Omega</math>
Typically, such a problem describes the evolution of a closed surface as a function of time <math>u</math> with speed <math>f</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>. The 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.
| |||