Add utility functions for Transform types

src/Data/NumIdr/Transform/Orthonormal.idr

@@ -0,0 +1,51 @@
+module Data.NumIdr.Transform.Orthonormal
+
+import Data.Vect
+import Data.NumIdr.Interfaces
+import Data.NumIdr.Array
+import Data.NumIdr.Vector
+import Data.NumIdr.Matrix
+import Data.NumIdr.Homogeneous
+import Data.NumIdr.Transform.Point
+import Data.NumIdr.Transform.Transform
+
+%default total
+
+
+public export
+Orthonormal : Nat -> Type -> Type
+Orthonormal = Transform TOrthonormal
+
+
+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)
+
+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
+
+
+export
+reflect : {n : _} -> Neg a => Fin n -> Orthonormal n a
+reflect i = unsafeMkTrans $ indexSet [weaken i,weaken i] (-1) identity
+
+export
+reflectX : {n : _} -> Neg a => Orthonormal (1 + n) a
+reflectX = reflect 0
+
+export
+reflectY : {n : _} -> Neg a => Orthonormal (2 + n) a
+reflectY = reflect 1
+
+export
+reflectZ : {n : _} -> Neg a => Orthonormal (3 + n) a
+reflectZ = reflect 2
+
+
+export
+reflectNormal : (Neg a, Fractional a) => Vector n a -> Orthonormal n a
+reflectNormal {n} v with (viewShape v)
+  _ | Shape [n] = unsafeMkTrans $ matrixToH $ (identity - (2 / normSq v) *. outer v v)