Data.NumIdr.Transform.Orthonormal

Definitions

Orthonormal : Nat -> Type -> Type

  An orthonormal transform is one that contains an orthonormal matrix,
  also known as an improper rotation or rotoreflection.

Totality: total
Visibility: public export

isOrthonormal' : Eq a => Num a => Matrix' n a -> Bool

  Determine if a matrix represents an orthonormal transform.

Totality: total
Visibility: export

fromMatrix : Eq a => Num a => Matrix' n a -> Maybe (Orthonormal n a)

  Try to construct an orthonormal transform from a matrix.

Totality: total
Visibility: export

isOrthonormal : Eq a => Num a => HMatrix' n a -> Bool

  Determine if a homogeneous matrix represents a rotation.

Totality: total
Visibility: export

fromHMatrix : Eq a => Num a => HMatrix' n a -> Maybe (Orthonormal n a)

Totality: total
Visibility: export

reflect : Neg a => Fin n -> Orthonormal n a

  Construct an orthonormal transform that reflects a particular coordinate.

Totality: total
Visibility: export

reflectX : Neg a => Orthonormal (1 + n) a

  The orthonormal transform that reflects on the x-coordinate (first coordinate).

Totality: total
Visibility: export

reflectY : Neg a => Orthonormal (2 + n) a

  The orthonormal transform that reflects on the y-coordinate (second coordinate).

Totality: total
Visibility: export

reflectZ : Neg a => Orthonormal (3 + n) a

  The orthonormal transform that reflects on the z-coordinate (third coordinate).

Totality: total
Visibility: export

reflectNormal : (Neg a, Fractional a) => Vector n a -> Orthonormal n a

  Construct an orthonormal transform that reflects along a hyperplane of the
  given normal vector. The input does not have to be a unit vector.

Totality: total
Visibility: export