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Message: <blockquote data-quote="Rystil Arden" data-source="post: 4105867" data-attributes="member: 29014">Even if you actually had a round room and properly translated it to a square battlemap, you'd still have triangle inequality issues.Pardon the crudely drawn diagrams.  In both diagrams, the square on the right represents the square D&D 4E battlemap (it represents multiple in-game 'squares' on a grid which isn't drawn).  To the left is the supposed circle that represents said square.  In both figures, 4E claims that the blue and red distance in the square are equal length, and the 'Circle Heuristic' claims that if I move everything onto the true circle, it will fix all issues and make the blue and red equal length.  In Figure 1, we see that the circle indeed fixes the problem.  The fact that moving to the upper-left corner of the square takes the same distance as moving straight ahead is entirely accounted for by the circle.  That was my first example.  Now try Figure 2 (my second example).  The guy moving straight ahead moves the radius of the circle or half the length of the big square--sure, fine, no problem.  But the guy moving diagonally 45 degrees up-left and then to the same point is not traveling the same distance on the circle either.  Indeed, two sides of the triangle (in any non-Minkowski space) can never add up to be equal to the third side.  This issue will crop up no matter what shape you use (though props for thinking of the circle, since it does fix the first-order issues, just not the triangle inequality).To summarise: Even if your room is actually honest-to-goodness a circle that you portray as a square, the 4E diagonals still don't work mathematically past a first order movement.  Or in other words, what 4E is doing is not just the same as transforming circles into squares.  You still may be okay with this, and that's fine.</blockquote>

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