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Non-Euclidean Geometry in 4E?
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<blockquote data-quote="Imban" data-source="post: 4047522" data-attributes="member: 29206"><p>To borrow your own pictures, my solution requires you to assume that in Figure B, the distance is 6 squares, but its actual distance: approximately 42.4 feet. The real distance is 42.4 feet. It's just that characters are <strong>actually notably faster</strong> along diagonals, capable of covering 30 feet in 6 seconds with orthagonal movement in Figure A and 42.4 feet in 6 seconds with diagonal movement in Figure B, and somewhere in between if they engage in a mixture of both.</p><p></p><p></p><p></p><p>Yeah, 1-1-1-1 can actually be any combination of 5ft orthagonal and 7ft diagonal steps. In order for this to make "sense" - though it posits a very strange world - there has to be an absolute grid of reference, so rotating the grid isn't really an issue.</p><p></p><p>If you don't know how you line up as regards to the absolute grid (say, you have a random outdoor encounter) you have to determine it based on ranges, which I suppose calls into play the "doesn't map exactly" thing I mentioned earlier. This means you will actually be <strong>closer in squares</strong> if you choose to lay out the grid diagonally than if you choose to lay it out orthagonally, because if you need to base your battle map on known ranges rather than a premade grid, you need it to obey known ranges.</p></blockquote><p></p>
[QUOTE="Imban, post: 4047522, member: 29206"] To borrow your own pictures, my solution requires you to assume that in Figure B, the distance is 6 squares, but its actual distance: approximately 42.4 feet. The real distance is 42.4 feet. It's just that characters are [b]actually notably faster[/b] along diagonals, capable of covering 30 feet in 6 seconds with orthagonal movement in Figure A and 42.4 feet in 6 seconds with diagonal movement in Figure B, and somewhere in between if they engage in a mixture of both. Yeah, 1-1-1-1 can actually be any combination of 5ft orthagonal and 7ft diagonal steps. In order for this to make "sense" - though it posits a very strange world - there has to be an absolute grid of reference, so rotating the grid isn't really an issue. If you don't know how you line up as regards to the absolute grid (say, you have a random outdoor encounter) you have to determine it based on ranges, which I suppose calls into play the "doesn't map exactly" thing I mentioned earlier. This means you will actually be [b]closer in squares[/b] if you choose to lay out the grid diagonally than if you choose to lay it out orthagonally, because if you need to base your battle map on known ranges rather than a premade grid, you need it to obey known ranges. [/QUOTE]
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