src/Cardinal.hs

   1 -- | The Cardinal module contains the Cardinal data type, representing
   2 --   a cardinal direction (one of the 27 directions surrounding the
   3 --   center of a cube. In addition to those 27 directions, we also
   4 --   include the interior point and a number of composite types that
   5 --   allow us to perform arithmetic on directions.
   6 module Cardinal
   7 where
   8
   9 import Prelude hiding (LT)
  10
  11 data Cardinal = F   -- ^ Front
  12               | B   -- ^ Back
  13               | L   -- ^ Left
  14               | R   -- ^ Right
  15               | D   -- ^ Down
  16               | T   -- ^ Top
  17               | FL  -- ^ Front Left
  18               | FR  -- ^ Front Right
  19               | FD  -- ^ Front Down
  20               | FT  -- ^ Front Top
  21               | BL  -- ^ Back Left
  22               | BR  -- ^ Back Right
  23               | BD  -- ^ Back Down
  24               | BT  -- ^ Back Top
  25               | LD  -- ^ Left Down
  26               | LT  -- ^ Left Top
  27               | RD  -- ^ Right Down
  28               | RT  -- ^ Right Top
  29               | FLD -- ^ Front Left Down
  30               | FLT -- ^ Front Left Top
  31               | FRD -- ^ Front Right Down
  32               | FRT -- ^ Front Right Top
  33               | BLD -- ^ Back Left Down
  34               | BLT -- ^ Back Left Top
  35               | BRD -- ^ Back Right Down
  36               | BRT -- ^ Back Right Top
  37               | I   -- ^ Interior
  38               | Scalar Double -- ^ A wrapper around a scalar value.
  39               | Sum Cardinal Cardinal -- ^ The sum of two directions.
  40               | Difference Cardinal Cardinal
  41               -- ^ The difference of two directions, the first minus the second.
  42               | Product Cardinal Cardinal -- ^ The product of two directions.
  43               | Quotient Cardinal Cardinal
  44               -- ^ The quotient of two directions, the first divided by the
  45               --   second.
  46                 deriving (Show, Eq)
  47
  48
  49 -- | By making Cardinal an instance of 'Num', we gain the ability to
  50 --   add, subtract, and multiply directions. The results of these
  51 --   operations are never actually calculated; the types just keep
  52 --   track of which operations were performed in which order.
  53 instance Num Cardinal where
  54     x + y = Sum x y
  55     x - y = Difference x y
  56     x * y = Product x y
  57     negate = Product (Scalar (-1))
  58     abs x = x
  59     signum x = x
  60     fromInteger x = Scalar (fromIntegral x)
  61
  62
  63 -- | Like the Num instance, the Fractional instance allows us to
  64 --   take quotients of directions.
  65 instance Fractional Cardinal where
  66     x / y   = Quotient x y
  67     recip = Quotient (Scalar 1)
  68     fromRational x = Scalar (fromRational x)
  69
  70
  71 -- | Rotate a cardinal direction counter-clockwise about the x-axis.
  72 ccwx :: Cardinal -> Cardinal
  73 ccwx F = F
  74 ccwx B = B
  75 ccwx L = T
  76 ccwx R = D
  77 ccwx D = L
  78 ccwx T = R
  79 ccwx FL = FT
  80 ccwx FR = FD
  81 ccwx FD = FL
  82 ccwx FT = FR
  83 ccwx BL = BT
  84 ccwx BR = BD
  85 ccwx BD = BL
  86 ccwx BT = BR
  87 ccwx LD = LT
  88 ccwx LT = RT
  89 ccwx RD = LD
  90 ccwx RT = RD
  91 ccwx FLD = FLT
  92 ccwx FLT = FRT
  93 ccwx FRD = FLD
  94 ccwx FRT = FRD
  95 ccwx BLD = BLT
  96 ccwx BLT = BRT
  97 ccwx BRD = BLD
  98 ccwx BRT = BRD
  99 ccwx I = I
 100 ccwx (Scalar s) = (Scalar s)
 101 ccwx (Sum c0 c1) = Sum (ccwx c0) (ccwx c1)
 102 ccwx (Difference c0 c1) = Difference (ccwx c0) (ccwx c1)
 103 ccwx (Product c0 c1) = Product (ccwx c0) (ccwx c1)
 104 ccwx (Quotient c0 c1) = Quotient (ccwx c0) (ccwx c1)
 105
 106 -- | Rotate a cardinal direction clockwise about the x-axis.
 107 cwx :: Cardinal -> Cardinal
 108 cwx = ccwx . ccwx . ccwx
 109
 110
 111 -- | Rotate a cardinal direction counter-clockwise about the y-axis.
 112 ccwy :: Cardinal -> Cardinal
 113 ccwy F = D
 114 ccwy B = T
 115 ccwy L = L
 116 ccwy R = R
 117 ccwy D = B
 118 ccwy T = F
 119 ccwy FL = LD
 120 ccwy FR = RD
 121 ccwy FD = BD
 122 ccwy FT = FD
 123 ccwy BL = LT
 124 ccwy BR = RT
 125 ccwy BD = BT
 126 ccwy BT = FT
 127 ccwy LD = BL
 128 ccwy LT = FL
 129 ccwy RD = BR
 130 ccwy RT = FR
 131 ccwy FLD = BLD
 132 ccwy FLT = FLD
 133 ccwy FRD = BRD
 134 ccwy FRT = FRD
 135 ccwy BLD = BLT
 136 ccwy BLT = FLT
 137 ccwy BRD = BRT
 138 ccwy BRT = FRT
 139 ccwy I = I
 140 ccwy (Scalar s) = (Scalar s)
 141 ccwy (Sum c0 c1) = Sum (ccwy c0) (ccwy c1)
 142 ccwy (Difference c0 c1) = Difference (ccwy c0) (ccwy c1)
 143 ccwy (Product c0 c1) = Product (ccwy c0) (ccwy c1)
 144 ccwy (Quotient c0 c1) = Quotient (ccwy c0) (ccwy c1)
 145
 146 -- | Rotate a cardinal direction clockwise about the y-axis.
 147 cwy :: Cardinal -> Cardinal
 148 cwy = ccwy . ccwy . ccwy
 149
 150
 151 -- | Rotate a cardinal direction counter-clockwise about the z-axis.
 152 ccwz :: Cardinal -> Cardinal
 153 ccwz F = L
 154 ccwz B = R
 155 ccwz L = B
 156 ccwz R = F
 157 ccwz D = D
 158 ccwz T = T
 159 ccwz FL = BL
 160 ccwz FR = FL
 161 ccwz FD = LD
 162 ccwz FT = LT
 163 ccwz BL = BR
 164 ccwz BR = FR
 165 ccwz BD = RD
 166 ccwz BT = RT
 167 ccwz LD = BD
 168 ccwz LT = BT
 169 ccwz RD = FD
 170 ccwz RT = FT
 171 ccwz FLD = BLD
 172 ccwz FLT = BLT
 173 ccwz FRD = FLD
 174 ccwz FRT = FLT
 175 ccwz BLD = BRD
 176 ccwz BLT = BRT
 177 ccwz BRD = FRD
 178 ccwz BRT = FRT
 179 ccwz I = I
 180 ccwz (Scalar s) = (Scalar s)
 181 ccwz (Sum c0 c1) = Sum (ccwz c0) (ccwz c1)
 182 ccwz (Difference c0 c1) = Difference (ccwz c0) (ccwz c1)
 183 ccwz (Product c0 c1) = Product (ccwz c0) (ccwz c1)
 184 ccwz (Quotient c0 c1) = Quotient (ccwz c0) (ccwz c1)
 185
 186 -- | Rotate a cardinal direction clockwise about the z-axis.
 187 cwz :: Cardinal -> Cardinal
 188 cwz = ccwz . ccwz . ccwz