A method if provided for determining a sail path of at least one vessel on a map representative of a marine geographic area, to perform a turn between a start point and an end point. The start point is associated with a start circle, and the end point is associated with an end circle having a predefined radius of curvature. The sail path is curvilinear and composed of arc segments and straight segments. The method includes: detecting, in the map, obstacles likely to interfere with the at least one vessel; encompassing each obstacle into a curvilinear geometric form; determining a sail path of the given vessel by minimizing, under constraints, a cost function including: a first term representative of the length of arc segments making up the sail path and a second term representative of the length of straight segments making up the sail path, taking into account the start and end circles and the curvilinear geometric form into which is encompassed each obstacle.