Cartographers have long been interested in the representation of various movements such as migration, commercial exchanges and transportation. There are several techniques for visualizing this information; this paper focuses on flow mapping. A flow map is a type of map that shows a set of movements through line symbols connecting an origin to a destination. Each link is associated with a value that corresponds to the volume of the movement. However, once a certain volume of data is reached, the maps quickly become cluttered and can be difficult to read and understand. Moreover, the values of the movements must be correctly represented so as not to induce biased interpretations. The objective of this paper is to create flow maps in which the flows have highly variable thicknesses so that the associated value is correctly represented. The technique used to create the flow paths does not create crossings between flows. In order to remove any visual clutter, such as overlaps between flows and geographic features, some areas of the map are distorted. In other words, our method of map distortion adapts the polygon vector base map to the flows, the central information of the visualization, and not the other way around.