X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FCardinal.hs;h=9bd8e1df933b592d877d2e1efe810b44d96092ac;hb=618a8b60f67939be66ee7298ae4a47522c83f449;hp=e4e9464e1bddef6ef57fd306d6423c8a707660d5;hpb=f97dbb52b73bd90a89940b9653ff274654aba9de;p=spline3.git

diff --git a/src/Cardinal.hs b/src/Cardinal.hs
index e4e9464..9bd8e1d 100644
--- a/src/Cardinal.hs
+++ b/src/Cardinal.hs
@@ -1,23 +1,188 @@
+-- | The Cardinal module contains the Cardinal data type, representing
+--   a cardinal direction (one of the 26 directions surrounding the
+--   center of a cube. In addition to those 26 directions, we also
+--   include the interior point and a number of composite types that
+--   allow us to perform arithmetic on directions.
 module Cardinal
 where
 
-data Cardinal = F
-              | B
-              | L
-              | R
-              | T
-              | D
-              | Sum Cardinal Cardinal
+import Prelude hiding (LT)
+
+data Cardinal = F   -- ^ Front
+              | B   -- ^ Back
+              | L   -- ^ Left
+              | R   -- ^ Right
+              | D   -- ^ Down
+              | T   -- ^ Top
+              | FL  -- ^ Front Left
+              | FR  -- ^ Front Right
+              | FD  -- ^ Front Down
+              | FT  -- ^ Front Top
+              | BL  -- ^ Back Left
+              | BR  -- ^ Back Right
+              | BD  -- ^ Back Down
+              | BT  -- ^ Back Top
+              | LD  -- ^ Left Down
+              | LT  -- ^ Left Top
+              | RD  -- ^ Right Down
+              | RT  -- ^ Right Top
+              | FLD -- ^ Front Left Down
+              | FLT -- ^ Front Left Top
+              | FRD -- ^ Front Right Down
+              | FRT -- ^ Front Right Top
+              | BLD -- ^ Back Left Down
+              | BLT -- ^ Back Left Top
+              | BRD -- ^ Back Right Down
+              | BRT -- ^ Back Right Top
+              | I   -- ^ Interior
+              | Scalar Double -- ^ A wrapper around a scalar value.
+              | Sum Cardinal Cardinal -- ^ The sum of two directions.
               | Difference Cardinal Cardinal
-              | Product Cardinal Cardinal
-              | ScalarProduct Double Cardinal
+              -- ^ The difference of two directions, the first minus the second.
+              | Product Cardinal Cardinal -- ^ The product of two directions.
+              | Quotient Cardinal Cardinal
+              -- ^ The quotient of two directions, the first divided by the
+              --   second.
                 deriving (Show, Eq)
 
+
+-- | By making Cardinal an instance of 'Num', we gain the ability to
+--   add, subtract, and multiply directions. The results of these
+--   operations are never actually calculated; the types just keep
+--   track of which operations were performed in which order.
 instance Num Cardinal where
     x + y = Sum x y
     x - y = Difference x y
-    x * y = Sum x y
-    negate x = ScalarProduct (-1) x
+    x * y = Product x y
+    negate = Product (Scalar (-1))
     abs x = x
     signum x = x
-    fromInteger _ = F -- Whatever.
+    fromInteger x = Scalar (fromIntegral x)
+
+
+-- | Like the Num instance, the 'Fractional' instance allows us to
+--   take quotients of directions.
+instance Fractional Cardinal where
+    x / y   = Quotient x y
+    recip = Quotient (Scalar 1)
+    fromRational x = Scalar (fromRational x)
+
+
+-- | Rotate a cardinal direction counter-clockwise about the x-axis.
+ccwx :: Cardinal -> Cardinal
+ccwx F = F
+ccwx B = B
+ccwx L = T
+ccwx R = D
+ccwx D = L
+ccwx T = R
+ccwx FL = FT
+ccwx FR = FD
+ccwx FD = FL
+ccwx FT = FR
+ccwx BL = BT
+ccwx BR = BD
+ccwx BD = BL
+ccwx BT = BR
+ccwx LD = LT
+ccwx LT = RT
+ccwx RD = LD
+ccwx RT = RD
+ccwx FLD = FLT
+ccwx FLT = FRT
+ccwx FRD = FLD
+ccwx FRT = FRD
+ccwx BLD = BLT
+ccwx BLT = BRT
+ccwx BRD = BLD
+ccwx BRT = BRD
+ccwx I = I
+ccwx (Scalar s) = (Scalar s)
+ccwx (Sum c0 c1) = Sum (ccwx c0) (ccwx c1)
+ccwx (Difference c0 c1) = Difference (ccwx c0) (ccwx c1)
+ccwx (Product c0 c1) = Product (ccwx c0) (ccwx c1)
+ccwx (Quotient c0 c1) = Quotient (ccwx c0) (ccwx c1)
+
+-- | Rotate a cardinal direction clockwise about the x-axis.
+cwx :: Cardinal -> Cardinal
+cwx = ccwx . ccwx . ccwx
+
+
+-- | Rotate a cardinal direction counter-clockwise about the y-axis.
+ccwy :: Cardinal -> Cardinal
+ccwy F = D
+ccwy B = T
+ccwy L = L
+ccwy R = R
+ccwy D = B
+ccwy T = F
+ccwy FL = LD
+ccwy FR = RD
+ccwy FD = BD
+ccwy FT = FD
+ccwy BL = LT
+ccwy BR = RT
+ccwy BD = BT
+ccwy BT = FT
+ccwy LD = BL
+ccwy LT = FL
+ccwy RD = BR
+ccwy RT = FR
+ccwy FLD = BLD
+ccwy FLT = FLD
+ccwy FRD = BRD
+ccwy FRT = FRD
+ccwy BLD = BLT
+ccwy BLT = FLT
+ccwy BRD = BRT
+ccwy BRT = FRT
+ccwy I = I
+ccwy (Scalar s) = (Scalar s)
+ccwy (Sum c0 c1) = Sum (ccwy c0) (ccwy c1)
+ccwy (Difference c0 c1) = Difference (ccwy c0) (ccwy c1)
+ccwy (Product c0 c1) = Product (ccwy c0) (ccwy c1)
+ccwy (Quotient c0 c1) = Quotient (ccwy c0) (ccwy c1)
+
+-- | Rotate a cardinal direction clockwise about the y-axis.
+cwy :: Cardinal -> Cardinal
+cwy = ccwy . ccwy . ccwy
+
+
+-- | Rotate a cardinal direction counter-clockwise about the z-axis.
+ccwz :: Cardinal -> Cardinal
+ccwz F = L
+ccwz B = R
+ccwz L = B
+ccwz R = F
+ccwz D = D
+ccwz T = T
+ccwz FL = BL
+ccwz FR = FL
+ccwz FD = LD
+ccwz FT = LT
+ccwz BL = BR
+ccwz BR = FR
+ccwz BD = RD
+ccwz BT = RT
+ccwz LD = BD
+ccwz LT = BT
+ccwz RD = FD
+ccwz RT = FT
+ccwz FLD = BLD
+ccwz FLT = BLT
+ccwz FRD = FLD
+ccwz FRT = FLT
+ccwz BLD = BRD
+ccwz BLT = BRT
+ccwz BRD = FRD
+ccwz BRT = FRT
+ccwz I = I
+ccwz (Scalar s) = (Scalar s)
+ccwz (Sum c0 c1) = Sum (ccwz c0) (ccwz c1)
+ccwz (Difference c0 c1) = Difference (ccwz c0) (ccwz c1)
+ccwz (Product c0 c1) = Product (ccwz c0) (ccwz c1)
+ccwz (Quotient c0 c1) = Quotient (ccwz c0) (ccwz c1)
+
+-- | Rotate a cardinal direction clockwise about the z-axis.
+cwz :: Cardinal -> Cardinal
+cwz = ccwz . ccwz . ccwz