src/Cardinal.hs

   1 -- | The Cardinal module contains the Cardinal data type, representing
   2 --   a cardinal direction (one of the 26 directions surrounding the
   3 --   center of a cube. In addition to those 26 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 Control.Monad (liftM, liftM2)
  10 import Prelude hiding (LT)
  11 import Test.QuickCheck (Arbitrary(..), oneof)
  12
  13 data Cardinal = F   -- ^ Front
  14               | B   -- ^ Back
  15               | L   -- ^ Left
  16               | R   -- ^ Right
  17               | D   -- ^ Down
  18               | T   -- ^ Top
  19               | FL  -- ^ Front Left
  20               | FR  -- ^ Front Right
  21               | FD  -- ^ Front Down
  22               | FT  -- ^ Front Top
  23               | BL  -- ^ Back Left
  24               | BR  -- ^ Back Right
  25               | BD  -- ^ Back Down
  26               | BT  -- ^ Back Top
  27               | LD  -- ^ Left Down
  28               | LT  -- ^ Left Top
  29               | RD  -- ^ Right Down
  30               | RT  -- ^ Right Top
  31               | FLD -- ^ Front Left Down
  32               | FLT -- ^ Front Left Top
  33               | FRD -- ^ Front Right Down
  34               | FRT -- ^ Front Right Top
  35               | BLD -- ^ Back Left Down
  36               | BLT -- ^ Back Left Top
  37               | BRD -- ^ Back Right Down
  38               | BRT -- ^ Back Right Top
  39               | I   -- ^ Interior
  40               | Scalar Double -- ^ A wrapper around a scalar value.
  41               | Sum Cardinal Cardinal -- ^ The sum of two directions.
  42               | Difference Cardinal Cardinal
  43               -- ^ The difference of two directions, the first minus the second.
  44               | Product Cardinal Cardinal -- ^ The product of two directions.
  45               | Quotient Cardinal Cardinal
  46               -- ^ The quotient of two directions, the first divided by the
  47               --   second.
  48                 deriving (Show, Eq)
  49
  50
  51 -- | By making Cardinal an instance of 'Num', we gain the ability to
  52 --   add, subtract, and multiply directions. The results of these
  53 --   operations are never actually calculated; the types just keep
  54 --   track of which operations were performed in which order.
  55 instance Num Cardinal where
  56     x + y = Sum x y
  57     x - y = Difference x y
  58     x * y = Product x y
  59     negate = Product (Scalar (-1))
  60     abs x = x
  61     signum x = x
  62     fromInteger x = Scalar (fromIntegral x)
  63
  64
  65 -- | Like the Num instance, the 'Fractional' instance allows us to
  66 --   take quotients of directions.
  67 instance Fractional Cardinal where
  68     x / y   = Quotient x y
  69     recip = Quotient (Scalar 1)
  70     fromRational x = Scalar (fromRational x)
  71
  72
  73
  74 instance Arbitrary Cardinal where
  75     arbitrary = oneof [f,b,l,r,d,t,fl,fr,fd,ft,bl,br,bd,bt,ld,lt,
  76                        rd,rt,fld,flt,frd,frt,bld,blt,brd,brt,i,
  77                        scalar,csum,cdiff,cprod,cquot]
  78         where
  79           f = return F
  80           b = return B
  81           l = return L
  82           r = return R
  83           d = return D
  84           t = return T
  85           fl = return FL
  86           fr = return FR
  87           fd = return FD
  88           ft = return FT
  89           bl = return BL
  90           br = return BR
  91           bd = return BD
  92           bt = return BT
  93           ld = return LD
  94           lt = return LT
  95           rd = return RD
  96           rt = return RT
  97           fld = return FLD
  98           flt = return FLT
  99           frd = return FRD
 100           frt = return FRT
 101           bld = return BLD
 102           blt = return BLT
 103           brd = return BRD
 104           brt = return BRT
 105           i = return I
 106           scalar = liftM Scalar arbitrary
 107           csum = liftM2 Sum arbitrary arbitrary
 108           cdiff = liftM2 Difference arbitrary arbitrary
 109           cprod = liftM2 Product arbitrary arbitrary
 110           cquot = liftM2 Quotient arbitrary arbitrary
 111
 112
 113 -- | Rotate a cardinal direction counter-clockwise about the x-axis.
 114 ccwx :: Cardinal -> Cardinal
 115 ccwx F = F
 116 ccwx B = B
 117 ccwx L = T
 118 ccwx R = D
 119 ccwx D = L
 120 ccwx T = R
 121 ccwx FL = FT
 122 ccwx FR = FD
 123 ccwx FD = FL
 124 ccwx FT = FR
 125 ccwx BL = BT
 126 ccwx BR = BD
 127 ccwx BD = BL
 128 ccwx BT = BR
 129 ccwx LD = LT
 130 ccwx LT = RT
 131 ccwx RD = LD
 132 ccwx RT = RD
 133 ccwx FLD = FLT
 134 ccwx FLT = FRT
 135 ccwx FRD = FLD
 136 ccwx FRT = FRD
 137 ccwx BLD = BLT
 138 ccwx BLT = BRT
 139 ccwx BRD = BLD
 140 ccwx BRT = BRD
 141 ccwx I = I
 142 ccwx (Scalar s) = (Scalar s)
 143 ccwx (Sum c0 c1) = Sum (ccwx c0) (ccwx c1)
 144 ccwx (Difference c0 c1) = Difference (ccwx c0) (ccwx c1)
 145 ccwx (Product c0 c1) = Product (ccwx c0) (ccwx c1)
 146 ccwx (Quotient c0 c1) = Quotient (ccwx c0) (ccwx c1)
 147
 148 -- | Rotate a cardinal direction clockwise about the x-axis.
 149 cwx :: Cardinal -> Cardinal
 150 cwx = ccwx . ccwx . ccwx
 151
 152
 153 -- | Rotate a cardinal direction counter-clockwise about the y-axis.
 154 ccwy :: Cardinal -> Cardinal
 155 ccwy F = D
 156 ccwy B = T
 157 ccwy L = L
 158 ccwy R = R
 159 ccwy D = B
 160 ccwy T = F
 161 ccwy FL = LD
 162 ccwy FR = RD
 163 ccwy FD = BD
 164 ccwy FT = FD
 165 ccwy BL = LT
 166 ccwy BR = RT
 167 ccwy BD = BT
 168 ccwy BT = FT
 169 ccwy LD = BL
 170 ccwy LT = FL
 171 ccwy RD = BR
 172 ccwy RT = FR
 173 ccwy FLD = BLD
 174 ccwy FLT = FLD
 175 ccwy FRD = BRD
 176 ccwy FRT = FRD
 177 ccwy BLD = BLT
 178 ccwy BLT = FLT
 179 ccwy BRD = BRT
 180 ccwy BRT = FRT
 181 ccwy I = I
 182 ccwy (Scalar s) = (Scalar s)
 183 ccwy (Sum c0 c1) = Sum (ccwy c0) (ccwy c1)
 184 ccwy (Difference c0 c1) = Difference (ccwy c0) (ccwy c1)
 185 ccwy (Product c0 c1) = Product (ccwy c0) (ccwy c1)
 186 ccwy (Quotient c0 c1) = Quotient (ccwy c0) (ccwy c1)
 187
 188 -- | Rotate a cardinal direction clockwise about the y-axis.
 189 cwy :: Cardinal -> Cardinal
 190 cwy = ccwy . ccwy . ccwy
 191
 192
 193 -- | Rotate a cardinal direction counter-clockwise about the z-axis.
 194 ccwz :: Cardinal -> Cardinal
 195 ccwz F = R
 196 ccwz B = L
 197 ccwz L = F
 198 ccwz R = B
 199 ccwz D = D
 200 ccwz T = T
 201 ccwz FL = FR
 202 ccwz FR = BR
 203 ccwz FD = RD
 204 ccwz FT = RT
 205 ccwz BL = FL
 206 ccwz BR = BL
 207 ccwz BD = LD
 208 ccwz BT = LT
 209 ccwz LD = FD
 210 ccwz LT = FT
 211 ccwz RD = BD
 212 ccwz RT = BT
 213 ccwz FLD = FRD
 214 ccwz FLT = FRT
 215 ccwz FRD = BRD
 216 ccwz FRT = BRT
 217 ccwz BLD = FLD
 218 ccwz BLT = FLT
 219 ccwz BRD = BLD
 220 ccwz BRT = BLT
 221 ccwz I = I
 222 ccwz (Scalar s) = (Scalar s)
 223 ccwz (Sum c0 c1) = Sum (ccwz c0) (ccwz c1)
 224 ccwz (Difference c0 c1) = Difference (ccwz c0) (ccwz c1)
 225 ccwz (Product c0 c1) = Product (ccwz c0) (ccwz c1)
 226 ccwz (Quotient c0 c1) = Quotient (ccwz c0) (ccwz c1)
 227
 228 -- | Rotate a cardinal direction clockwise about the z-axis.
 229 cwz :: Cardinal -> Cardinal
 230 cwz = ccwz . ccwz . ccwz