linear-1.7: Linear Algebra

Portability	non-portable
Stability	experimental
Maintainer	Edward Kmett <[email protected]>
Safe Haskell	Trustworthy

Linear.Quaternion

Description

Quaternions

Synopsis

Documentation

data Quaternion a Source

Quaternions

Constructors

Quaternion !a !(V3 a)

Instances

Monad Quaternion
Functor Quaternion
Typeable1 Quaternion
Applicative Quaternion
Foldable Quaternion
Traversable Quaternion
Generic1 Quaternion
Distributive Quaternion
Representable Quaternion
Apply Quaternion
Bind Quaternion
Additive Quaternion
Metric Quaternion
Hamiltonian Quaternion
Complicated Quaternion
Trace Quaternion
Affine Quaternion
(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)
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

class Complicated t whereSource

A vector space that includes the basis elements _e and _i

Methods

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

Instances

Complicated Complex
Complicated Quaternion

class Complicated t => Hamiltonian t whereSource

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

Methods

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

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

Instances

Hamiltonian Quaternion

ee :: Complicated t => E tSource

ei :: Complicated t => E tSource

ej :: Hamiltonian t => E tSource

ek :: Hamiltonian t => E tSource

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

Spherical linear interpolation between two quaternions.

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

asin with a specified branch cut.

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

acos with a specified branch cut.

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

atan with a specified branch cut.

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

asinh with a specified branch cut.

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

acosh with a specified branch cut.

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

atanh with a specified branch cut.

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

norm of the imaginary component

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

raise a Quaternion to a scalar power

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

Apply a rotation to a vector.

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

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