5 ms·

3 https://m.youtube.com/watch?v=_rJdkhlWZVQ https://m.youtube.com/watch?v=_rJdkhlWZVQ

• ww520 5y ago
  I meant in a hexagonal coordinate system, like the hexagon tiles in games.
  • ben_w 5y ago
    It’s still exactly 3, assuming you’re defining it by π´ = c/2r and c = [count of number of hexes that require exactly r hex-boundary crossings to be reached from the starting cell] 6 cells at a distance of 1 hex, 12 at a distance of 2, 18 at a distance of 3, and the underlying growth pattern requires adding 6 on every discrete ring.
    • ww520 5y ago
      Interesting. Good direction in thought with counting the whole cell as a unit. In that case shouldn't the diameter be 3 instead of 2? See the grid in [1]. The center tile counts as distance 1, the left adjacent tile counts as 1, and the right adjacent tile counts as 1, so the total diameter d is 3. Circumference c = 6. c/d = 6/3 = 2. Pi = 2. Then the next ring has 12 tiles. c = 12. d = 5. c/d = 12/5 = 2.4. So Pi = 2.4 for the next ring! [1] https://www.gamedev.net/articles/programming/general-and-gameplay-programming/coordinates-in-hexagon-based-tile-maps-r1800/ https://www.gamedev.net/articles/programming/general-and-gam...
      • ben_w 5y ago
        I’d count the central cell as distance = 0 for the purposes of board game mechanics, and use c=2πr rather than c=πD, but I guess that would make the formula fail my definition of circumference.
        • ww520 5y ago
          If we go from center of the cell to center of the cell, the distance would be 2. I guest that would work.