+-- | 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
- | 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
+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
+ -- ^ 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 = Product x y
- negate x = Product (Scalar (-1)) x
+ negate = Product (Scalar (-1))
abs x = x
signum x = x
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 x = Quotient (Scalar 1) x
+ 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 = R
+ccwz B = L
+ccwz L = F
+ccwz R = B
+ccwz D = D
+ccwz T = T
+ccwz FL = FR
+ccwz FR = BR
+ccwz FD = RD
+ccwz FT = RT
+ccwz BL = FL
+ccwz BR = BL
+ccwz BD = LD
+ccwz BT = LT
+ccwz LD = FD
+ccwz LT = FT
+ccwz RD = BD
+ccwz RT = BT
+ccwz FLD = FRD
+ccwz FLT = FRT
+ccwz FRD = BRD
+ccwz FRT = BRT
+ccwz BLD = FLD
+ccwz BLT = FLT
+ccwz BRD = BLD
+ccwz BRT = BLT
+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
projects / spline3.git / blobdiff