linear-1.20.2: Linear Algebra

Copyright(C) 2012-2015 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityexperimental
Portabilitynon-portable
Safe HaskellTrustworthy
LanguageHaskell98

Linear.Quaternion

Description

Quaternions

Synopsis

Documentation

data Quaternion a Source

Quaternions

Constructors

Quaternion !a !(V3 a) 

Instances

Monad Quaternion Source 
Functor Quaternion Source 
MonadFix Quaternion Source 
Applicative Quaternion Source 
Foldable Quaternion Source 
Traversable Quaternion Source 
Generic1 Quaternion Source 
Distributive Quaternion Source 
Representable Quaternion Source 
MonadZip Quaternion Source 
Serial1 Quaternion Source 
Apply Quaternion Source 
Bind Quaternion Source 
Eq1 Quaternion Source 
Ord1 Quaternion Source 
Read1 Quaternion Source 
Show1 Quaternion Source 
Additive Quaternion Source 
Metric Quaternion Source 
Hamiltonian Quaternion Source 
Complicated Quaternion Source 
Trace Quaternion Source 
Affine Quaternion Source 
Unbox a => Vector Vector (Quaternion a) Source 
Unbox a => MVector MVector (Quaternion a) Source 
(Num r, TrivialConjugate r) => Coalgebra r (E Quaternion) Source 
(Num r, TrivialConjugate r) => Algebra r (E Quaternion) Source 
Eq a => Eq (Quaternion a) Source 
RealFloat a => Floating (Quaternion a) Source 
RealFloat a => Fractional (Quaternion a) Source 
Data a => Data (Quaternion a) Source 
RealFloat a => Num (Quaternion a) Source 
Ord a => Ord (Quaternion a) Source 
Read a => Read (Quaternion a) Source 
Show a => Show (Quaternion a) Source 
Ix a => Ix (Quaternion a) Source 
Generic (Quaternion a) Source 
Storable a => Storable (Quaternion a) Source 
Binary a => Binary (Quaternion a) Source 
Serial a => Serial (Quaternion a) Source 
Serialize a => Serialize (Quaternion a) Source 
NFData a => NFData (Quaternion a) Source 
Hashable a => Hashable (Quaternion a) Source 
Unbox a => Unbox (Quaternion a) Source 
Ixed (Quaternion a) Source 
(RealFloat a, Epsilon a) => Epsilon (Quaternion a) Source 
(Conjugate a, RealFloat a) => Conjugate (Quaternion a) Source 
FunctorWithIndex (E Quaternion) Quaternion Source 
FoldableWithIndex (E Quaternion) Quaternion Source 
TraversableWithIndex (E Quaternion) Quaternion Source 
Each (Quaternion a) (Quaternion b) a b Source 
type Rep1 Quaternion Source 
type Rep Quaternion = E Quaternion Source 
type Diff Quaternion = Quaternion Source 
data MVector s (Quaternion a) = MV_Quaternion !Int (MVector s a) Source 
type Rep (Quaternion a) Source 
data Vector (Quaternion a) = V_Quaternion !Int (Vector a) Source 
type Index (Quaternion a) = E Quaternion Source 
type IxValue (Quaternion a) = a Source 

class Complicated t where Source

A vector space that includes the basis elements _e and _i

Minimal complete definition

Nothing

Methods

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

Instances

class Complicated t => Hamiltonian t where Source

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

Minimal complete definition

Nothing

Methods

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

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

Instances

ee :: Complicated t => E t Source

ei :: Complicated t => E t Source

ej :: Hamiltonian t => E t Source

ek :: Hamiltonian t => E t Source

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

Spherical linear interpolation between two quaternions.

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

asin with a specified branch cut.

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

acos with a specified branch cut.

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

atan with a specified branch cut.

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

asinh with a specified branch cut.

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

acosh with a specified branch cut.

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

atanh with a specified branch cut.

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

norm of the imaginary component

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

raise a Quaternion to a scalar power

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

Apply a rotation to a vector.

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

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