Navigation maps from several centuries ago often feature a network of straight lines overlaid on the oceans, converging in a number of stars. Here is an example (JPEG file).
What was the purpose of these lines? My only guess is that cartographers included them to point out predominent winds on the seas. I don’t see, however, why the lines would converge in those star-shaped pivots then.
The stars look like compass roses. I’d say that they’re on the maps so that you can easily determine the bearing from your starting point to your destination, in the days before handy tools to do so.
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“Portolan chart” and “rhumb line” seem to be key phrases to begin your investigation.
Rhumb lines being the line generated on a map by following a constant bearing from a given point (e.g., the kind of knowledge you’d want if you were sailing). Because of the need to project a spherical object onto a flat surface entails some distortion, if you lay a ruler on many such maps the “straight line” described on the map would be curved on the globe. Mercator-projection maps have the useful attribute that a line that appears straight on the map can be followed, on your ship, with a constant bearing.
