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<blockquote data-quote="Nom" data-source="post: 4046137" data-attributes="member: 56980">Maximum deviation from direct line is 30 degrees on a hex grid and 45 degrees on a manhattan grid.&nbsp; Thus, if we call the distance moved 1 (conveniently making it the hypotenuse), then the straight-line distance is cos 30 (0.87), 13% less, for hex and cos 45 (0.71), 29% less, for manhattan.Yep, hexes are more accurate.&nbsp; I've also noticed 5 or more sided regular polyhedrons tend to be approximated by the brain as &quot;sorta-circular&quot; while 3 or 4 sided figures are not.However, both hexes and manhattan feel - at least to me - restricted, that I'm moving in allies rather than freely.&nbsp; The 3.5 metric felt - to me - like &quot;real&quot; distance.&nbsp; Whether that was because the deviation was only 22.5 degress or that the uneven metric obscured the grid I don't know.&nbsp; Deviation is trickier, since (for example) moving 2 up and 1 across costs 2.5 squares of movement (1 diagonal, 1 straight) rather than 2.41 - the straight line is thus 10.5% shorter that what you actually pay, which is pretty close to that for hexes.Quite true.&nbsp; Nor is it played in only 3 axes.&nbsp; Any game on a gride ultimately fixates around the axes of the grid, which is one reason that more axes (even with non-simple metrics) provides fewer restrictions to play.Beyond that, I find it easier to think in the 8 cardinal directions, which is why deviation on a diagonal square grid feels less &quot;annoying&quot; to me than deviation on a hex grid.&nbsp; The inherent limitation of the grid is off-axis and thus not as visible.Huh?&nbsp; How does that work if I run a long line across two adjacent hexrows, where it spends a large amount of time clipping alternate hexes?&nbsp; Yes, you could rule on the 50% crossing point, assuming you can eyeball this accurately, but that isn't nearly as simple as &quot;if it clips it, it's in&quot;.Obviously you're better at on-the-fly trig than I am; I struggled with it for about 6 years of playing Battletech, and is why I loathe mixing hexes and LoS.It's a function of degrees of freedom.&nbsp; With 2 axes, you only need 2 people to block half the movement options.&nbsp; With 3, you need 3.&nbsp; With 4, you need four.&nbsp; Try your example again with hexes by rotating onto the hex-row - you either need to block along a hex-row (and thus not truly normal to movement) or have a double row in the same way as diagonals need a double row.The number of &quot;extra&quot; people compared to a &quot;true&quot; example is dependent on the error of grid-row to actual path. The 1.5 case is a little odd, due to the difference in movement metrics in each axis.</blockquote>

[QUOTE="Nom, post: 4046137, member: 56980"] Maximum deviation from direct line is 30 degrees on a hex grid and 45 degrees on a manhattan grid. Thus, if we call the distance moved 1 (conveniently making it the hypotenuse), then the straight-line distance is cos 30 (0.87), 13% less, for hex and cos 45 (0.71), 29% less, for manhattan. Yep, hexes are more accurate. I've also noticed 5 or more sided regular polyhedrons tend to be approximated by the brain as "sorta-circular" while 3 or 4 sided figures are not. However, both hexes and manhattan feel - at least to me - restricted, that I'm moving in allies rather than freely. The 3.5 metric felt - to me - like "real" distance. Whether that was because the deviation was only 22.5 degress or that the uneven metric obscured the grid I don't know. Deviation is trickier, since (for example) moving 2 up and 1 across costs 2.5 squares of movement (1 diagonal, 1 straight) rather than 2.41 - the straight line is thus 10.5% shorter that what you actually pay, which is pretty close to that for hexes. Quite true. Nor is it played in only 3 axes. Any game on a gride ultimately fixates around the axes of the grid, which is one reason that more axes (even with non-simple metrics) provides fewer restrictions to play. Beyond that, I find it easier to think in the 8 cardinal directions, which is why deviation on a diagonal square grid feels less "annoying" to me than deviation on a hex grid. The inherent limitation of the grid is off-axis and thus not as visible. Huh? How does that work if I run a long line across two adjacent hexrows, where it spends a large amount of time clipping alternate hexes? Yes, you could rule on the 50% crossing point, assuming you can eyeball this accurately, but that isn't nearly as simple as "if it clips it, it's in". Obviously you're better at on-the-fly trig than I am; I struggled with it for about 6 years of playing Battletech, and is why I loathe mixing hexes and LoS. It's a function of degrees of freedom. With 2 axes, you only need 2 people to block half the movement options. With 3, you need 3. With 4, you need four. Try your example again with hexes by rotating onto the hex-row - you either need to block along a hex-row (and thus not truly normal to movement) or have a double row in the same way as diagonals need a double row. The number of "extra" people compared to a "true" example is dependent on the error of grid-row to actual path. The 1.5 case is a little odd, due to the difference in movement metrics in each axis. [/QUOTE]

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