MAPP - Board & Card Geometry Calculations

- Copyright 2007, Hogwash Design. All Rights Reserved.


(1) Hexagon Dimesions

              w
          |<----->|
      _
      |      / \
      |    /     \     _
      |   |       |    |
    h |   |       |    | s
      |   |       |    _
      |    \     /
      _      \ /
                       

    For regular hexagon of side 's', the above dimension are:
      
      w  =  2.s.cos(30 deg)  =  s.sqrt(3).(1/2) = (1.732).s (approximately)
      
      h  =  s + 2.s.sin(30 deg)  =  s + 2.s.(1/2)  =  s + s  =  2.s


    For some values of s:
    
      s      w    h
      --     --   --
      10     17   20
      20     35   40
      30     52   60

      34     59   68
      35     61   70

      40     69   80    

    For our needs, we should be able to deviate slighty from these
     proportions without any issues.


(2) Tiling Offsets
    

              w
          |<----->|

      _                _
      |      / \       |
      |    /     \     |
      |   |       |    | Sep-V
    h |   |       |    | 
      |   |       |    _
      |    \     / \
      _      \ /     \
              |       |
              |       |
              |       |
               \     / 
                 \ / 
          |<->|
            Sep-H



     When tiling the hexagons, the separation offset from one hexagon
     to the one to it's bottom right is:
     
     Sep-V  =  h.(3/4)
     
     Sep-H  =  w.(1/2)



(3) Board Dimensions vs Grid Size
    

                           Bw
          |<------------------------------------>|

           C=1       2         ...       NC
    _
    |            / \     / \                / \
    |          /     \ /     \            /     \
    |         |       |       |          |       |
    | R=1     |       |       |          |       |
    |         |       |       |          |       |
    |        / \     / \     /          / \     /
    |      /     \ /     \            /     \ /
    |     |       |       |          |       |
    |   2 |       |       |          |       |
    |     |       |       |          |       |
    |      \     / \     / \          \     / \
    |        \ /     \ /     \          \ /     \
    |
 BH |
    |
    |        / \     / \     /          / \     /
    |      /     \ /     \            /     \ /
    |     |       |       |          |       |
    |  NR |       |       |          |       |
    |     |       |       |          |       |
    |      \     / \     / \          \     /
    _        \ /     \ /                \ /



    For a board with NC columns and NR rows, the board dimensions are:
    
      BW  =  NC.w + w/2  =  w.(NC + 1/2)

      BH  =  NR.h.(3/4) + h.(1/4)  =  h.(3.NR + 1)/4


    Assuming that the top-left corner of the bounding rectangle for the
    top-left hexagon is (0,0), the top and left for the hexagon in
    column C and row R is calculated as follows:

    
      Top   =  (R-1).h.(3/4)

      Left  =  (C-1).w + w/2        (when R is odd)
                 OR
               (C-1).w              (when R is even)




(4A) Outer Board size and formula for s=40:

      For s=40: w=69->70 and h=80

      Using NR=10 and NC=5, we get:
      
        BW  =  70.(5 + 1/2)  =  385
      
        BH  =  80.( (3).(10) + 1 ) )/4  =  620
      
      And:
      
        Top   =  (R-1).80.(3/4)  =  (R-1).60

        Left  =  (C-1).70 + 35                (when R is odd)
                   OR
                 (C-1).70                     (when R is even)
       

(4B) Inner Board size and formula for s=40:

      For s=40: w=69->70 and h=80

      Using NR=8 and NC=5, we get:
      
        BW  =  70.(5 + 1/2)  =  385
      
        BH  =  80.( (3).(8) + 1 ) )/4  =  500
      
      And:
      
        Top   =  (R-1).80.(3/4)  =  (R-1).60

        Left  =  (C-1).70                     (when R is odd)
                   OR
                 (C-1).70 + 35                (when R is even)





(5A) Outer Board size and formula for s=34:

      For s=34: w=59->60 and h=68

      Using NR=10 and NC=8, we get:
      
        BW  =  60.(8 + 1/2)  =  510
      
        BH  =  68.( (3).(10) + 1 ) )/4  =  527
      
      And:
      
        Top   =  (R-1).68.(3/4)  =  (R-1).51

        Left  =  (C-1).60 + 30                (when R is odd)
                   OR
                 (C-1).60                     (when R is even)
       

(5B) Inner Board size and formula for s=34:

      For s=34: w=59->60 and h=68

      Using NR=8 and NC=8, we get:
      
        BW  =  60.(8 + 1/2)  =  510
      
        BH  =  70.( (3).(8) + 1 ) )/4  =  425
      
      And:
      
        Top   =  (R-1).68.(3/4)  =  (R-1).51

        Left  =  (C-1).60                     (when R is odd)
                   OR
                 (C-1).60 + 30                (when R is even)