Linear.Quaternion

Quaternions

Documentation

data Quaternion a

Quaternions

Constructors

Quaternion !a !(V3 a)

Instances

Monad Quaternion

Functor Quaternion

MonadFix Quaternion

Applicative Quaternion

Foldable Quaternion

Traversable Quaternion

Generic1 Quaternion

Distributive Quaternion

Representable Quaternion

MonadZip Quaternion

Serial1 Quaternion

Apply Quaternion

Bind Quaternion

Eq1 Quaternion

Ord1 Quaternion

Read1 Quaternion

Show1 Quaternion

Additive Quaternion

Metric Quaternion

Hamiltonian Quaternion

Complicated Quaternion

Trace Quaternion

Affine Quaternion

Unbox a => Vector Vector (Quaternion a)

Unbox a => MVector MVector (Quaternion a)

(Num r, TrivialConjugate r) => Coalgebra r (E Quaternion)

(Num r, TrivialConjugate r) => Algebra r (E Quaternion)

Eq a => Eq (Quaternion a)

RealFloat a => Floating (Quaternion a)

RealFloat a => Fractional (Quaternion a)

Data a => Data (Quaternion a)

RealFloat a => Num (Quaternion a)

Ord a => Ord (Quaternion a)

Read a => Read (Quaternion a)

Show a => Show (Quaternion a)

Ix a => Ix (Quaternion a)

Generic (Quaternion a)

Storable a => Storable (Quaternion a)

Binary a => Binary (Quaternion a)

Serial a => Serial (Quaternion a)

Serialize a => Serialize (Quaternion a)

NFData a => NFData (Quaternion a)

Hashable a => Hashable (Quaternion a)

Unbox a => Unbox (Quaternion a)

Ixed (Quaternion a)

(RealFloat a, Epsilon a) => Epsilon (Quaternion a)

(Conjugate a, RealFloat a) => Conjugate (Quaternion a)

FunctorWithIndex (E Quaternion) Quaternion

FoldableWithIndex (E Quaternion) Quaternion

TraversableWithIndex (E Quaternion) Quaternion

Each (Quaternion a) (Quaternion b) a b

type Rep1 Quaternion

type Rep Quaternion = E Quaternion

type Diff Quaternion = Quaternion

data MVector s (Quaternion a) = MV_Quaternion !Int (MVector s a)

type Rep (Quaternion a)

data Vector (Quaternion a) = V_Quaternion !Int (Vector a)

type Index (Quaternion a) = E Quaternion

type IxValue (Quaternion a) = a

class Complicated t where

A vector space that includes the basis elements _e and _i

Minimal complete definition

Nothing

Methods

_e, _i :: Lens' (t a) a

Instances

Complicated Complex

Complicated Quaternion

class Complicated t => Hamiltonian t where

A vector space that includes the basis elements _e, _i, _j and _k

Minimal complete definition

Nothing

Methods

_j, _k :: Lens' (t a) a

_ijk :: Lens' (t a) (V3 a)

Instances

Hamiltonian Quaternion

ee :: Complicated t => E t

ei :: Complicated t => E t

ej :: Hamiltonian t => E t

ek :: Hamiltonian t => E t

slerp :: RealFloat a => Quaternion a -> Quaternion a -> a -> Quaternion a

Spherical linear interpolation between two quaternions.

asinq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a

asin with a specified branch cut.

acosq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a

acos with a specified branch cut.

atanq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a

atan with a specified branch cut.

asinhq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a

asinh with a specified branch cut.

acoshq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a

acosh with a specified branch cut.

atanhq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a

atanh with a specified branch cut.

absi :: Floating a => Quaternion a -> a

norm of the imaginary component

pow :: RealFloat a => Quaternion a -> a -> Quaternion a

raise a Quaternion to a scalar power

rotate :: (Conjugate a, RealFloat a) => Quaternion a -> V3 a -> V3 a

Apply a rotation to a vector.

axisAngle :: (Epsilon a, Floating a) => V3 a -> a -> Quaternion a

axisAngle axis theta builds a Quaternion representing a rotation of theta radians about axis.