Hoping someone may be able to point me in the right direction so I can research this topic further.


Scenario: You have a vector field (either 2D or 3D) and you wish to find the shortest path between two points located within the vector field.


For example imagine an object floating on the ocean surface. The object has a simple rudder that allows it to steer. How can we find a path that will get the object from its current location (point on vector field) to (or as close to as possible) the destination point.


In this scenario the vector field would represent ocean currents in a 2D space and the desired path should make optimal use of these currents to reach it's final destination (or a point as close to the final destination as possible).


Can anyone offer any suggestions/hints around how this could be calculated?


Note: Post has been edited to improve clarity of question.



Shortest Path finding in vector fields (2D and 3D)
The problem you are struggling to express here is known as Zermelo's navigation problem, and you are not correctly writing it down. You can read about it in Vel Jurdjevic's excellent book **Geometric Control Theory**.


