From c88ec8e43960514d27a6368d864a68e07eb18e50 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 6 May 2011 16:37:52 -0400
Subject: [PATCH] Add the counter-clockwise rotations (with respect to the
 x-axis) to the Cardinal module.

---
 src/Cardinal.hs | 41 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 41 insertions(+)

diff --git a/src/Cardinal.hs b/src/Cardinal.hs
index f62896f..c6f7e8f 100644
--- a/src/Cardinal.hs
+++ b/src/Cardinal.hs
@@ -1,6 +1,8 @@
 module Cardinal
 where
 
+import Prelude hiding (LT)
+
 data Cardinal = F
               | B
               | L
@@ -48,3 +50,42 @@ 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
-- 
2.43.2