From: Michael Orlitzky Date: Sat, 7 May 2011 20:03:14 +0000 (-0400) Subject: Add the rotations about the y and z axes to the Cardinal module. X-Git-Tag: 0.0.1~323 X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=084d6e31ba1eda1e7c206ff8ff23e8567e2339ce;p=spline3.git Add the rotations about the y and z axes to the Cardinal module. Add haddock comments to the Cardinal module. --- diff --git a/src/Cardinal.hs b/src/Cardinal.hs index 0a1b139..42b1260 100644 --- a/src/Cardinal.hs +++ b/src/Cardinal.hs @@ -1,42 +1,55 @@ +-- | The Cardinal module contains the Cardinal data type, representing +-- a cardinal direction (one of the 27 directions surrounding the +-- center of a cube. In addition to those 27 directions, we also +-- include the interior point and a number of composite types that +-- allow us to perform arithmetic on directions. 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 +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 @@ -46,11 +59,15 @@ instance Num Cardinal where 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 fromRational x = Scalar (fromRational x) + -- | Rotate a cardinal direction counter-clockwise about the x-axis. ccwx :: Cardinal -> Cardinal ccwx F = F @@ -92,34 +109,33 @@ 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 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 = BRT -ccwy BRD = BLD -ccwy BRT = BRD +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) @@ -127,6 +143,46 @@ 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. +-- | 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