Small 3D Vector Math Library

Vector.hs

-- file: Vectors.hs
--
-- Contains vector functions

data Vector a = Vector a a a 
              deriving (Show)
                       
vecPlus3D :: (Num t) => Vector t -> Vector t -> Vector t
(Vector i j k) `vecPlus3D` (Vector l m n) = Vector (i+l) (j+m) (k+n)

vecMult3D :: (Num t) => Vector t -> t -> Vector t
(Vector i j k) `vecMult3D` c = Vector (i*c) (j*c) (k*c)

scalMult3D :: (Num t) => Vector t -> Vector t -> t
(Vector i j k) `scalMult3D` (Vector l m n) = i*l + j*m + k*n

magnitude3D :: (Floating t) => Vector t -> t
magnitude3D (Vector i j k) = sqrt (i**2 + j**2 + k**2)

dot3D :: (Floating t) => Vector t -> Vector t -> t
(Vector i j k) `dot3D` (Vector l m n) = (i*l + j*m + k*n)

theta3D :: (Floating t) => Vector t -> Vector t -> t
theta3D (Vector i j k) (Vector l m n) = (asin . magnitude3D $ crossProduct) * 
                                        (180/pi)
    where crossProduct = (Vector i j k) `cross` (Vector l m n)

-- cross does not follow the [..]3D naming convention
-- because cross products only exist for 3D vectors
cross :: (Num t) => Vector t -> Vector t -> Vector t
(Vector i j k) `cross` (Vector l m n) = Vector (j*n - m*k)
                                               (k*l - n*i)
                                               (i*m - l*j)