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What is the best aspect ratio for a geographical map when considering ease of finding a route from a variable start point to a marked end point?

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By "aspect ratio" do you mean the width/height ratio? If so, doesn't it depend on whether the route follows a more horizontal or vertical path? (I'm sorry if this comment seems daft - i must be missing something very obvious). – Izhaki Aug 27 '13 at 23:16
A variable start point could be above, below or to the sides, it's more a question of what shape gives the most clarity to a person finding a route on a map – Toni Leigh Aug 28 '13 at 5:37
The answer depends on whether the task is 'finding a route' or 'finding a route and navigating along the route from the origin to the destination'. If the task includes navigation, then the mode of movement is also relevant. The research on electronic map displays for aviation, automobiles, and pedestrian overlaps somewhat but not completely. The differences depend on whether you want to emphasize an ego-centered reference frame, world-centered reference frame, or both. Can you describe the task in more detail? – user1757436 Sep 10 '13 at 12:50

A circle with the user's current location at the center.

It places no constraint on the user's choice of direction. Most likely your application is screen based and thus for restrained by some type of square display. The best aspect ratio obviously depends on the device and screen real estate and how it is used and navigated.

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a circle is interesting, don't military applications often map geography onto circles ? – Toni Leigh Sep 30 '13 at 17:56

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