Moved 3D rotation matrices from ...Matrix.

Rotation.hs

@@ -0,0 +1,44 @@
+{-# LANGUAGE TypeOperators #-}
+
+module Rotation where
+
+import Data.HList ((:*:))
+import Numeric.Units.Dimensional.Prelude
+import Numeric.Units.Dimensional.LinearAlgebra
+import qualified Prelude
+
+-- | The type of homogenous vectors with three elements.
+type Homo3 d = Vec (d:*:d:*.d)
+
+-- | Cartesian unit vectors.
+unit_x, unit_y, unit_z :: Num a => Homo3 DOne a
+unit_x = vCons _1 $ vCons _0 $ vSing _0
+unit_y = vCons _0 $ vCons _1 $ vSing _0
+unit_z = vCons _0 $ vCons _0 $ vSing _1
+
+
+-- Rotation matrices (cartesian)
+-- =============================
+
+-- | Convenience type for homogeneous 3x3 matrices.
+type Homo33 d = Mat ((d:*:d:*.d) :*:
+                     (d:*:d:*.d) :*.
+                     (d:*:d:*.d))
+
+-- Rotation matrices. Rotates a vector by the given angle (analogous
+-- to rotating the coordinate system in opposite direction).
+
+rotX :: Floating a => PlaneAngle a -> Homo33 DOne a
+rotX a = consRow   (vCons _1 $ vCons _0      $ vSing _0)
+       $ consRow   (vCons _0 $ vCons (cos a) $ vSing (negate (sin a)))
+       $ rowMatrix (vCons _0 $ vCons (sin a) $ vSing (cos a))
+
+rotY :: Floating a => PlaneAngle a -> Homo33 DOne a
+rotY a = consRow   (vCons (cos a)          $ vCons _0 $ vSing (sin a))
+       $ consRow   (vCons _0               $ vCons _1 $ vSing _0)
+       $ rowMatrix (vCons (negate (sin a)) $ vCons _0 $ vSing (cos a))
+
+rotZ :: Floating a => PlaneAngle a -> Homo33 DOne a
+rotZ a = consRow   (vCons (cos a) $ vCons (negate (sin a)) $ vSing _0)
+       $ consRow   (vCons (sin a) $ vCons (cos a)          $ vSing _0)
+       $ rowMatrix (vCons _0      $ vCons _0               $ vSing _1)