module Cardinal
where

import Prelude hiding (LT)

data Cardinal = F
              | B
              | L
              | R
              | D
              | T
              | FL
              | FR
              | FD
              | FT
              | BL
              | BR
              | BD
              | BT
              | LD
              | LT
              | RD
              | RT
              | FLD
              | FLT
              | FRD
              | FRT
              | BLD
              | BLT
              | BRD
              | BRT
              | I
              | Scalar Double
              | Sum Cardinal Cardinal
              | Difference Cardinal Cardinal
              | Product Cardinal Cardinal
              | Quotient Cardinal Cardinal
                deriving (Show, Eq)

instance Num Cardinal where
    x + y = Sum x y
    x - y = Difference x y
    x * y = Product x y
    negate x = Product (Scalar (-1)) x
    abs x = x
    signum x = x
    fromInteger x = Scalar (fromIntegral x)

instance Fractional Cardinal where
    x / y   = Quotient x y
    recip x = Quotient (Scalar 1) x
    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.
--   TODO: Fix these; they still use the x-axis values.
ccwy :: Cardinal -> Cardinal
ccwy F = F
ccwy B = B
ccwy L = T
ccwy R = D
ccwy D = L
ccwy T = R
ccwy FL = FT
ccwy FR = FD
ccwy FD = FL
ccwy FT = FR
ccwy BL = BT
ccwy BR = BD
ccwy BD = BL
ccwy BT = BR
ccwy LD = LT
ccwy LT = RT
ccwy RD = LD
ccwy RT = RD
ccwy FLD = FLT
ccwy FLT = FRT
ccwy FRD = FLD
ccwy FRT = FRD
ccwy BLD = BLT
ccwy BLT = BRT
ccwy BRD = BLD
ccwy BRT = BRD
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 x-axis.
cwy :: Cardinal -> Cardinal
cwy = ccwy . ccwy . ccwy