## Fast Marching algorithm 341 Pseudocode

The pseudo code of the Fast Marching algorithm is given in table 1. The FM algorithm relies on a partitioning of the C-space in three sets: Accepted configurations for which the distance function u has been computed and frozen, Current configurations for which an estimate v of u has been estimated (and not frozen), and the remaining Unvisited configurations for which u is unknown.

Definitions

Start is the set of start configurations; Goal is the set of goal configurations;

Neigh(S) is the set of neighbours of a set of configurations S;

xtop is the configuration in priority queue Current with the highest priority.

Procedure Initialization()

{02} Unvisited = Q \ Accepted, u(Unvisited) = v(Unvisited) = <x>; {03} Current = Neigh(Start), v(Current) = t (Current);

Procedure Main()

{05} Remove xtop from Current and insert it in Accepted with u(xtop) = v(xtop); {06} FMComputeV(Neigh(xtop));_

### Table 1. Pseudo code of the Fast Marching algorithm

The set of Current configurations is stored in a priority queue. On top of this queue the configuration with the highest priority is called xtop. At each iteration of the exploration process, xtop is moved from Current to Accepted and its Unvisited neighbours are updated and moved from Unvisited to Current. The exploration process expands from the start configuration and ends when the goal configuration is eventually set to Accepted.

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