module Cardinal
where
+import Prelude hiding (LT)
+
data Cardinal = F
| B
| L
| R
- | T
| 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
- | ScalarProduct Double Cardinal
+ | Quotient Cardinal Cardinal
deriving (Show, Eq)
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 x = Product (Scalar (-1)) x
abs x = x
signum x = x
- fromInteger _ = F -- Whatever.
+ 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