src/Cardinal.hs

   1 module Cardinal
   2 where
   3
   4 import Prelude hiding (LT)
   5
   6 data Cardinal = F
   7               | B
   8               | L
   9               | R
  10               | D
  11               | T
  12               | FL
  13               | FR
  14               | FD
  15               | FT
  16               | BL
  17               | BR
  18               | BD
  19               | BT
  20               | LD
  21               | LT
  22               | RD
  23               | RT
  24               | FLD
  25               | FLT
  26               | FRD
  27               | FRT
  28               | BLD
  29               | BLT
  30               | BRD
  31               | BRT
  32               | I
  33               | Scalar Double
  34               | Sum Cardinal Cardinal
  35               | Difference Cardinal Cardinal
  36               | Product Cardinal Cardinal
  37               | Quotient Cardinal Cardinal
  38                 deriving (Show, Eq)
  39
  40 instance Num Cardinal where
  41     x + y = Sum x y
  42     x - y = Difference x y
  43     x * y = Product x y
  44     negate x = Product (Scalar (-1)) x
  45     abs x = x
  46     signum x = x
  47     fromInteger x = Scalar (fromIntegral x)
  48
  49 instance Fractional Cardinal where
  50     x / y   = Quotient x y
  51     recip x = Quotient (Scalar 1) x
  52     fromRational x = Scalar (fromRational x)
  53
  54 -- | Rotate a cardinal direction counter-clockwise about the x-axis.
  55 ccwx :: Cardinal -> Cardinal
  56 ccwx F = F
  57 ccwx B = B
  58 ccwx L = T
  59 ccwx R = D
  60 ccwx D = L
  61 ccwx T = R
  62 ccwx FL = FT
  63 ccwx FR = FD
  64 ccwx FD = FL
  65 ccwx FT = FR
  66 ccwx BL = BT
  67 ccwx BR = BD
  68 ccwx BD = BL
  69 ccwx BT = BR
  70 ccwx LD = LT
  71 ccwx LT = RT
  72 ccwx RD = LD
  73 ccwx RT = RD
  74 ccwx FLD = FLT
  75 ccwx FLT = FRT
  76 ccwx FRD = FLD
  77 ccwx FRT = FRD
  78 ccwx BLD = BLT
  79 ccwx BLT = BRT
  80 ccwx BRD = BLD
  81 ccwx BRT = BRD
  82 ccwx I = I
  83 ccwx (Scalar s) = (Scalar s)
  84 ccwx (Sum c0 c1) = Sum (ccwx c0) (ccwx c1)
  85 ccwx (Difference c0 c1) = Difference (ccwx c0) (ccwx c1)
  86 ccwx (Product c0 c1) = Product (ccwx c0) (ccwx c1)
  87 ccwx (Quotient c0 c1) = Quotient (ccwx c0) (ccwx c1)
  88
  89 -- | Rotate a cardinal direction clockwise about the x-axis.
  90 cwx :: Cardinal -> Cardinal
  91 cwx = ccwx . ccwx . ccwx