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src/Data/NumIdr/Transform/Orthonormal.idr

@@ -12,39 +12,54 @@ import Data.NumIdr.Transform.Transform
 %default total
 
 
+||| An orthonormal transform is one that contains an orthonormal matrix,
+||| also known as an improper rotation or rotoreflection.
 public export
 Orthonormal : Nat -> Type -> Type
 Orthonormal = Transform TOrthonormal
 
 
+||| Determine if a matrix represents an orthonormal transform.
 export
 isOrthonormal' : Eq a => Num a => Matrix' n a -> Bool
 isOrthonormal' {n} mat with (viewShape mat)
   _ | Shape [n,n] = identity == fromFunction [n,n] (\[i,j] => getColumn i mat `dot` getColumn j mat)
 
+||| Try to construct an orthonormal transform from a matrix.
 export
 fromMatrix : Eq a => Num a => Matrix' n a -> Maybe (Orthonormal n a)
 fromMatrix mat = if isOrthonormal' mat then Just (unsafeMkTrans (matrixToH mat))
                                        else Nothing
 
 
+--------------------------------------------------------------------------------
+-- Reflections
+--------------------------------------------------------------------------------
+
+
+||| Construct an orthonormal transform that reflects a particular coordinate.
 export
 reflect : {n : _} -> Neg a => Fin n -> Orthonormal n a
 reflect i = unsafeMkTrans $ indexSet [weaken i,weaken i] (-1) identity
 
+||| The orthonormal transform that reflects on the x-coordinate (first coordinate).
 export
 reflectX : {n : _} -> Neg a => Orthonormal (1 + n) a
 reflectX = reflect 0
 
+||| The orthonormal transform that reflects on the y-coordinate (second coordinate).
 export
 reflectY : {n : _} -> Neg a => Orthonormal (2 + n) a
 reflectY = reflect 1
 
+||| The orthonormal transform that reflects on the z-coordinate (third coordinate).
 export
 reflectZ : {n : _} -> Neg a => Orthonormal (3 + n) a
 reflectZ = reflect 2
 
 
+||| Construct an orthonormal transform that reflects along a hyperplane of the
+||| given normal vector. The input does not have to be a unit vector.
 export
 reflectNormal : (Neg a, Fractional a) => Vector n a -> Orthonormal n a
 reflectNormal {n} v with (viewShape v)