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Hex Grid Problems

Hex Grids have LOTS of problems; these problems have been verified for both Horizontal and Vertical Grids. All indicated measurements are taken in Euclidean distance measurements unless indicated otherwise. 1. Hex Grids are not one unit wide. If you measure from one hex to an adjacent hex, the value will be larger than the correct value. If you measure from the center of a hex vertexward to another hex, you get a value of (approximately) two times the unit value. Someone appears to be confusing the hypotenuse with the adjacent leg of the trig triangle; it’s the adjacent leg of the angle that should be 1 unit away, not the hypotenuse; the hypotenuse should be 1*√3 units away. 2. Hexes are not 70 pixels side to side, so as to match square grids. Maps aligned to a square grid will match neither the vertical nor the horizontal distances of the hex grid. Hexes should be 70 pixels side to side, so a token that fits in a square grid fits in the equivalent hex grid. 3. Using a value of 0.2 for grid size does not result in a grid for which there are 5 new cells for every 1 previous cell. Rather, there are only 37 new cells for every previous 4 cells??? Cell count still works for 0.25, and appears to continue to shrink until 0.21, which is the last value at which grid shrinking can still occur. This requires making hex crawl maps bigger to compensate. 4. Manhattan distances do not correctly work for hex grids. Distances to some adjacent hexes do not match distances to other adjacent hexes. Using Euclidean distances reveals that these distances should match.
Just to confirm - yes, we all get this. It seems that everyone has either learnt to live with very borked hexes or doesn't use Roll20.  I'm logging in every month or two, thinking 'they'll get round to it eventually, it's not like I've paid for anything, maybe I should start a d20 game....'