Modulelinear-1.22Haskell2010

Linear.Quaternion

Quaternions

1 type
2 classes
15 values

Packagelinear-1.22
Exports18
LanguageHaskell2010
LicenceBSD-3-Clause
SourceQuaternion.hs

datadata Quaternion a

Quaternions

Constructors

Quaternion !a !(V3 a)

Instances74Monad, Functor, MonadFix, Applicative, Foldable, Traversable, …

Monad QuaternionDefined in linear-1.22 · Linear.Quaternion
Functor QuaternionDefined in linear-1.22 · Linear.Quaternion
MonadFix QuaternionDefined in linear-1.22 · Linear.Quaternion
Applicative QuaternionDefined in linear-1.22 · Linear.Quaternion
Foldable QuaternionDefined in linear-1.22 · Linear.Quaternion
Traversable QuaternionDefined in linear-1.22 · Linear.Quaternion
MonadZip QuaternionDefined in linear-1.22 · Linear.Quaternion
Eq1 QuaternionDefined in linear-1.22 · Linear.Quaternion
Ord1 QuaternionDefined in linear-1.22 · Linear.Quaternion
Read1 QuaternionDefined in linear-1.22 · Linear.Quaternion
Show1 QuaternionDefined in linear-1.22 · Linear.Quaternion
Hashable1 QuaternionDefined in linear-1.22 · Linear.Quaternion
Distributive QuaternionDefined in linear-1.22 · Linear.Quaternion
Apply QuaternionDefined in linear-1.22 · Linear.Quaternion
Bind QuaternionDefined in linear-1.22 · Linear.Quaternion
Representable QuaternionDefined in linear-1.22 · Linear.Quaternion
Serial1 QuaternionDefined in linear-1.22 · Linear.Quaternion
Metric QuaternionDefined in linear-1.22 · Linear.Quaternion
Complicated QuaternionDefined in linear-1.22 · Linear.Quaternion
Hamiltonian QuaternionDefined in linear-1.22 · Linear.Quaternion
Trace QuaternionDefined in linear-1.22 · Linear.Trace
R1 QuaternionDefined in linear-1.22 · Linear.Quaternion
R2 QuaternionDefined in linear-1.22 · Linear.Quaternion
R3 QuaternionDefined in linear-1.22 · Linear.Quaternion
R4 QuaternionDefined in linear-1.22 · Linear.Quaternion
Additive QuaternionDefined in linear-1.22 · Linear.Quaternion
Affine QuaternionDefined in linear-1.22 · Linear.Affine
Finite QuaternionDefined in linear-1.22 · Linear.Quaternion
Generic1 QuaternionDefined in linear-1.22 · Linear.Quaternion
Lift a => Lift (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Unbox a => Vector Vector (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Unbox a => MVector MVector (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
(Num r, TrivialConjugate r) => Algebra r (E Quaternion)Defined in linear-1.22 · Linear.Algebra
(Num r, TrivialConjugate r) => Coalgebra r (E Quaternion)Defined in linear-1.22 · Linear.Algebra
Eq a => Eq (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
RealFloat a => Floating (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
RealFloat a => Fractional (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Data a => Data (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
RealFloat a => Num (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Ord a => Ord (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Read a => Read (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Show a => Show (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Ix a => Ix (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Generic (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Semigroup a => Semigroup (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Monoid a => Monoid (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Storable a => Storable (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
NFData a => NFData (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Random a => Random (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Binary a => Binary (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Hashable a => Hashable (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Unbox a => Unbox (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Serialize a => Serialize (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Ixed (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
Serial a => Serial (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
(Conjugate a, RealFloat a) => Conjugate (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
(RealFloat a, Epsilon a) => Epsilon (Quaternion a)Defined in linear-1.22 · Linear.Quaternion
FoldableWithIndex (E Quaternion) QuaternionDefined in linear-1.22 · Linear.Quaternion
FunctorWithIndex (E Quaternion) QuaternionDefined in linear-1.22 · Linear.Quaternion
TraversableWithIndex (E Quaternion) QuaternionDefined in linear-1.22 · Linear.Quaternion
Each (Quaternion a) (Quaternion b) a bDefined in linear-1.22 · Linear.Quaternion
Field1 (Quaternion a) (Quaternion a) a aDefined in linear-1.22 · Linear.Quaternion
Field2 (Quaternion a) (Quaternion a) a aDefined in linear-1.22 · Linear.Quaternion
Field3 (Quaternion a) (Quaternion a) a aDefined in linear-1.22 · Linear.Quaternion
Field4 (Quaternion a) (Quaternion a) a aDefined in linear-1.22 · Linear.Quaternion
type Rep (Quaternion a) = D1 ('MetaData "Quaternion" "Linear.Quaternion" "linear-1.22-3d3RJcba25gDknnFKeY2an" 'False) (C1 ('MetaCons "Quaternion" 'PrefixI 'False) (S1 ('MetaSel 'Nothing 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel 'Nothing 'SourceUnpack 'SourceStrict 'DecidedUnpack) (Rec0 (V3 a))))Defined in linear-1.22 · Linear.Quaternion
type Rep1 Quaternion = D1 ('MetaData "Quaternion" "Linear.Quaternion" "linear-1.22-3d3RJcba25gDknnFKeY2an" 'False) (C1 ('MetaCons "Quaternion" 'PrefixI 'False) (S1 ('MetaSel 'Nothing 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: S1 ('MetaSel 'Nothing 'SourceUnpack 'SourceStrict 'DecidedUnpack) (Rec1 V3)))Defined in linear-1.22 · Linear.Quaternion
data MVector s (Quaternion a)
- MV_Quaternion !Int (MVector s a)
Defined in linear-1.22 · Linear.Quaternion
data Vector (Quaternion a)
- V_Quaternion !Int (Vector a)
Defined in linear-1.22 · Linear.Quaternion
type Rep Quaternion = E QuaternionDefined in linear-1.22 · Linear.Quaternion
type Index (Quaternion a) = E QuaternionDefined in linear-1.22 · Linear.Quaternion
type IxValue (Quaternion a) = aDefined in linear-1.22 · Linear.Quaternion
type Diff Quaternion = QuaternionDefined in linear-1.22 · Linear.Affine
type Size Quaternion = 4Defined in linear-1.22 · Linear.Quaternion

classclass Complicated (t :: Type -> Type) where

A vector space that includes the basis elements _e and _i

Methods

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

Instances2Complicated

Complicated ComplexDefined in linear-1.22 · Linear.Quaternion
Complicated QuaternionDefined in linear-1.22 · Linear.Quaternion

classclass Complicated t => Hamiltonian (t :: Type -> Type) where

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

Methods

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

Instances1Hamiltonian

Hamiltonian QuaternionDefined in linear-1.22 · Linear.Quaternion

valueee :: Complicated t => E t

valueei :: Complicated t => E t

valueej :: Hamiltonian t => E t

valueek :: Hamiltonian t => E t

valueslerp :: RealFloat a => Quaternion a -> Quaternion a -> a -> Quaternion a

Spherical linear interpolation between two quaternions.

valueasinq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a

asin with a specified branch cut.

valueacosq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a

acos with a specified branch cut.

valueatanq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a

atan with a specified branch cut.

valueasinhq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a

asinh with a specified branch cut.

valueacoshq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a

acosh with a specified branch cut.

valueatanhq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a

atanh with a specified branch cut.

valueabsi :: Floating a => Quaternion a -> a

norm of the imaginary component

valuepow :: RealFloat a => Quaternion a -> a -> Quaternion a

raise a Quaternion to a scalar power

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

Apply a rotation to a vector.

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

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