Linear.Quaternion

Quaternions

Documentation

data Quaternion a

Quaternions

Constructors

Quaternion !a !(V3 a)

Instances

Monad Quaternion

Methods

(>>=) :: Quaternion a -> (a -> Quaternion b) -> Quaternion b

(>>) :: Quaternion a -> Quaternion b -> Quaternion b

return :: a -> Quaternion a

fail :: String -> Quaternion a

Functor Quaternion

Methods

fmap :: (a -> b) -> Quaternion a -> Quaternion b

(<$) :: a -> Quaternion b -> Quaternion a

MonadFix Quaternion

Methods

mfix :: (a -> Quaternion a) -> Quaternion a

Applicative Quaternion

Methods

pure :: a -> Quaternion a

(<*>) :: Quaternion (a -> b) -> Quaternion a -> Quaternion b

(*>) :: Quaternion a -> Quaternion b -> Quaternion b

(<*) :: Quaternion a -> Quaternion b -> Quaternion a

Foldable Quaternion

Methods

fold :: Monoid m => Quaternion m -> m

foldMap :: Monoid m => (a -> m) -> Quaternion a -> m

foldr :: (a -> b -> b) -> b -> Quaternion a -> b

foldr' :: (a -> b -> b) -> b -> Quaternion a -> b

foldl :: (b -> a -> b) -> b -> Quaternion a -> b

foldl' :: (b -> a -> b) -> b -> Quaternion a -> b

foldr1 :: (a -> a -> a) -> Quaternion a -> a

foldl1 :: (a -> a -> a) -> Quaternion a -> a

toList :: Quaternion a -> [a]

null :: Quaternion a -> Bool

length :: Quaternion a -> Int

elem :: Eq a => a -> Quaternion a -> Bool

maximum :: Ord a => Quaternion a -> a

minimum :: Ord a => Quaternion a -> a

sum :: Num a => Quaternion a -> a

product :: Num a => Quaternion a -> a

Traversable Quaternion

Methods

traverse :: Applicative f => (a -> f b) -> Quaternion a -> f (Quaternion b)

sequenceA :: Applicative f => Quaternion (f a) -> f (Quaternion a)

mapM :: Monad m => (a -> m b) -> Quaternion a -> m (Quaternion b)

sequence :: Monad m => Quaternion (m a) -> m (Quaternion a)

Generic1 Quaternion

Associated Types

type Rep1 (Quaternion :: * -> *) :: * -> *

Methods

from1 :: Quaternion a -> Rep1 Quaternion a

to1 :: Rep1 Quaternion a -> Quaternion a

Distributive Quaternion

Methods

distribute :: Functor f => f (Quaternion a) -> Quaternion (f a)

collect :: Functor f => (a -> Quaternion b) -> f a -> Quaternion (f b)

distributeM :: Monad m => m (Quaternion a) -> Quaternion (m a)

collectM :: Monad m => (a -> Quaternion b) -> m a -> Quaternion (m b)

Representable Quaternion

Associated Types

type Rep (Quaternion :: * -> *) :: *

Methods

tabulate :: (Rep Quaternion -> a) -> Quaternion a

index :: Quaternion a -> Rep Quaternion -> a

Eq1 Quaternion

Methods

liftEq :: (a -> b -> Bool) -> Quaternion a -> Quaternion b -> Bool

Ord1 Quaternion

Methods

liftCompare :: (a -> b -> Ordering) -> Quaternion a -> Quaternion b -> Ordering

Read1 Quaternion

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Quaternion a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Quaternion a]

Show1 Quaternion

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Quaternion a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Quaternion a] -> ShowS

MonadZip Quaternion

Methods

mzip :: Quaternion a -> Quaternion b -> Quaternion (a, b)

mzipWith :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c

munzip :: Quaternion (a, b) -> (Quaternion a, Quaternion b)

Serial1 Quaternion

Methods

serializeWith :: MonadPut m => (a -> m ()) -> Quaternion a -> m ()

deserializeWith :: MonadGet m => m a -> m (Quaternion a)

Apply Quaternion

Methods

(<.>) :: Quaternion (a -> b) -> Quaternion a -> Quaternion b

(.>) :: Quaternion a -> Quaternion b -> Quaternion b

(<.) :: Quaternion a -> Quaternion b -> Quaternion a

Bind Quaternion

Methods

(>>-) :: Quaternion a -> (a -> Quaternion b) -> Quaternion b

join :: Quaternion (Quaternion a) -> Quaternion a

Additive Quaternion

Methods

zero :: Num a => Quaternion a

(^+^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a

(^-^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a

lerp :: Num a => a -> Quaternion a -> Quaternion a -> Quaternion a

liftU2 :: (a -> a -> a) -> Quaternion a -> Quaternion a -> Quaternion a

liftI2 :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c

Metric Quaternion

Methods

dot :: Num a => Quaternion a -> Quaternion a -> a

quadrance :: Num a => Quaternion a -> a

qd :: Num a => Quaternion a -> Quaternion a -> a

distance :: Floating a => Quaternion a -> Quaternion a -> a

norm :: Floating a => Quaternion a -> a

signorm :: Floating a => Quaternion a -> Quaternion a

Finite Quaternion

Associated Types

type Size (Quaternion :: * -> *) :: Nat

Methods

toV :: Quaternion a -> V Nat (Size Quaternion) a

fromV :: V Nat (Size Quaternion) a -> Quaternion a

Hamiltonian Quaternion

Methods

_j :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a)

_k :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a)

_ijk :: Functor f => (V3 a -> f (V3 a)) -> Quaternion a -> f (Quaternion a)

Complicated Quaternion

Methods

_e :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a)

_i :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a)

Trace Quaternion

Methods

trace :: Num a => Quaternion (Quaternion a) -> a

diagonal :: Quaternion (Quaternion a) -> Quaternion a

Affine Quaternion

Associated Types

type Diff (Quaternion :: * -> *) :: * -> *

Methods

(.-.) :: Num a => Quaternion a -> Quaternion a -> Diff Quaternion a

(.+^) :: Num a => Quaternion a -> Diff Quaternion a -> Quaternion a

(.-^) :: Num a => Quaternion a -> Diff Quaternion a -> Quaternion a

Unbox a => Vector Vector (Quaternion a)

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Quaternion a) -> m (Vector (Quaternion a))

basicUnsafeThaw :: PrimMonad m => Vector (Quaternion a) -> m (Mutable Vector (PrimState m) (Quaternion a))

basicLength :: Vector (Quaternion a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Quaternion a) -> Vector (Quaternion a)

basicUnsafeIndexM :: Monad m => Vector (Quaternion a) -> Int -> m (Quaternion a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Quaternion a) -> Vector (Quaternion a) -> m ()

elemseq :: Vector (Quaternion a) -> Quaternion a -> b -> b

Unbox a => MVector MVector (Quaternion a)

Methods

basicLength :: MVector s (Quaternion a) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (Quaternion a) -> MVector s (Quaternion a)

basicOverlaps :: MVector s (Quaternion a) -> MVector s (Quaternion a) -> Bool

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Quaternion a))

basicInitialize :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> m ()

basicUnsafeReplicate :: PrimMonad m => Int -> Quaternion a -> m (MVector (PrimState m) (Quaternion a))

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Int -> m (Quaternion a)

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Int -> Quaternion a -> m ()

basicClear :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Quaternion a -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> MVector (PrimState m) (Quaternion a) -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> MVector (PrimState m) (Quaternion a) -> m ()

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Int -> m (MVector (PrimState m) (Quaternion a))

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

Methods

comult :: (E Quaternion -> r) -> E Quaternion -> E Quaternion -> r

counital :: (E Quaternion -> r) -> r

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

Methods

mult :: (E Quaternion -> E Quaternion -> r) -> E Quaternion -> r

unital :: r -> E Quaternion -> r

Eq a => Eq (Quaternion a)

Methods

(==) :: Quaternion a -> Quaternion a -> Bool

(/=) :: Quaternion a -> Quaternion a -> Bool

RealFloat a => Floating (Quaternion a)

Methods

pi :: Quaternion a

exp :: Quaternion a -> Quaternion a

log :: Quaternion a -> Quaternion a

sqrt :: Quaternion a -> Quaternion a

(**) :: Quaternion a -> Quaternion a -> Quaternion a

logBase :: Quaternion a -> Quaternion a -> Quaternion a

sin :: Quaternion a -> Quaternion a

cos :: Quaternion a -> Quaternion a

tan :: Quaternion a -> Quaternion a

asin :: Quaternion a -> Quaternion a

acos :: Quaternion a -> Quaternion a

atan :: Quaternion a -> Quaternion a

sinh :: Quaternion a -> Quaternion a

cosh :: Quaternion a -> Quaternion a

tanh :: Quaternion a -> Quaternion a

asinh :: Quaternion a -> Quaternion a

acosh :: Quaternion a -> Quaternion a

atanh :: Quaternion a -> Quaternion a

log1p :: Quaternion a -> Quaternion a

expm1 :: Quaternion a -> Quaternion a

log1pexp :: Quaternion a -> Quaternion a

log1mexp :: Quaternion a -> Quaternion a

RealFloat a => Fractional (Quaternion a)

Methods

(/) :: Quaternion a -> Quaternion a -> Quaternion a

recip :: Quaternion a -> Quaternion a

fromRational :: Rational -> Quaternion a

Data a => Data (Quaternion a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Quaternion a -> c (Quaternion a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Quaternion a)

toConstr :: Quaternion a -> Constr

dataTypeOf :: Quaternion a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Quaternion a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Quaternion a))

gmapT :: (forall b. Data b => b -> b) -> Quaternion a -> Quaternion a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Quaternion a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Quaternion a -> r

gmapQ :: (forall d. Data d => d -> u) -> Quaternion a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Quaternion a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Quaternion a -> m (Quaternion a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Quaternion a -> m (Quaternion a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Quaternion a -> m (Quaternion a)

RealFloat a => Num (Quaternion a)

Methods

(+) :: Quaternion a -> Quaternion a -> Quaternion a

(-) :: Quaternion a -> Quaternion a -> Quaternion a

(*) :: Quaternion a -> Quaternion a -> Quaternion a

negate :: Quaternion a -> Quaternion a

abs :: Quaternion a -> Quaternion a

signum :: Quaternion a -> Quaternion a

fromInteger :: Integer -> Quaternion a

Ord a => Ord (Quaternion a)

Methods

compare :: Quaternion a -> Quaternion a -> Ordering

(<) :: Quaternion a -> Quaternion a -> Bool

(<=) :: Quaternion a -> Quaternion a -> Bool

(>) :: Quaternion a -> Quaternion a -> Bool

(>=) :: Quaternion a -> Quaternion a -> Bool

max :: Quaternion a -> Quaternion a -> Quaternion a

min :: Quaternion a -> Quaternion a -> Quaternion a

Read a => Read (Quaternion a)

Methods

readsPrec :: Int -> ReadS (Quaternion a)

readList :: ReadS [Quaternion a]

readPrec :: ReadPrec (Quaternion a)

readListPrec :: ReadPrec [Quaternion a]

Show a => Show (Quaternion a)

Methods

showsPrec :: Int -> Quaternion a -> ShowS

show :: Quaternion a -> String

showList :: [Quaternion a] -> ShowS

Ix a => Ix (Quaternion a)

Methods

range :: (Quaternion a, Quaternion a) -> [Quaternion a]

index :: (Quaternion a, Quaternion a) -> Quaternion a -> Int

unsafeIndex :: (Quaternion a, Quaternion a) -> Quaternion a -> Int

inRange :: (Quaternion a, Quaternion a) -> Quaternion a -> Bool

rangeSize :: (Quaternion a, Quaternion a) -> Int

unsafeRangeSize :: (Quaternion a, Quaternion a) -> Int

Generic (Quaternion a)

Associated Types

type Rep (Quaternion a) :: * -> *

Methods

from :: Quaternion a -> Rep (Quaternion a) x

to :: Rep (Quaternion a) x -> Quaternion a

Storable a => Storable (Quaternion a)

Methods

sizeOf :: Quaternion a -> Int

alignment :: Quaternion a -> Int

peekElemOff :: Ptr (Quaternion a) -> Int -> IO (Quaternion a)

pokeElemOff :: Ptr (Quaternion a) -> Int -> Quaternion a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (Quaternion a)

pokeByteOff :: Ptr b -> Int -> Quaternion a -> IO ()

peek :: Ptr (Quaternion a) -> IO (Quaternion a)

poke :: Ptr (Quaternion a) -> Quaternion a -> IO ()

Binary a => Binary (Quaternion a)

Methods

put :: Quaternion a -> Put

get :: Get (Quaternion a)

putList :: [Quaternion a] -> Put

Serial a => Serial (Quaternion a)

Methods

serialize :: MonadPut m => Quaternion a -> m ()

deserialize :: MonadGet m => m (Quaternion a)

Serialize a => Serialize (Quaternion a)

Methods

put :: Putter (Quaternion a)

get :: Get (Quaternion a)

NFData a => NFData (Quaternion a)

Methods

rnf :: Quaternion a -> ()

Hashable a => Hashable (Quaternion a)

Methods

hashWithSalt :: Int -> Quaternion a -> Int

hash :: Quaternion a -> Int

Unbox a => Unbox (Quaternion a)

Ixed (Quaternion a)

Methods

ix :: Index (Quaternion a) -> Traversal' (Quaternion a) (IxValue (Quaternion a))

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

Methods

nearZero :: Quaternion a -> Bool

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

Methods

conjugate :: Quaternion a -> Quaternion a

FunctorWithIndex (E Quaternion) Quaternion

Methods

imap :: (E Quaternion -> a -> b) -> Quaternion a -> Quaternion b

imapped :: (Indexable (E Quaternion) p, Settable f) => p a (f b) -> Quaternion a -> f (Quaternion b)

FoldableWithIndex (E Quaternion) Quaternion

Methods

ifoldMap :: Monoid m => (E Quaternion -> a -> m) -> Quaternion a -> m

ifolded :: (Indexable (E Quaternion) p, Contravariant f, Applicative f) => p a (f a) -> Quaternion a -> f (Quaternion a)

ifoldr :: (E Quaternion -> a -> b -> b) -> b -> Quaternion a -> b

ifoldl :: (E Quaternion -> b -> a -> b) -> b -> Quaternion a -> b

ifoldr' :: (E Quaternion -> a -> b -> b) -> b -> Quaternion a -> b

ifoldl' :: (E Quaternion -> b -> a -> b) -> b -> Quaternion a -> b

TraversableWithIndex (E Quaternion) Quaternion

Methods

itraverse :: Applicative f => (E Quaternion -> a -> f b) -> Quaternion a -> f (Quaternion b)

itraversed :: (Indexable (E Quaternion) p, Applicative f) => p a (f b) -> Quaternion a -> f (Quaternion b)

Each (Quaternion a) (Quaternion b) a b

Methods

each :: Traversal (Quaternion a) (Quaternion b) a b

type Rep1 Quaternion

type Rep1 Quaternion = D1 (MetaData "Quaternion" "Linear.Quaternion" "linear-1.20.7-5lThnmKUFiyAbTBcmo6MON" False) (C1 (MetaCons "Quaternion" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 (MetaSel (Nothing Symbol) SourceUnpack SourceStrict DecidedUnpack) (Rec1 V3))))

type Rep Quaternion

type Rep Quaternion = E Quaternion

type Size Quaternion

type Size Quaternion = 4

type Diff Quaternion

type Diff Quaternion = Quaternion

data MVector s (Quaternion a)

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

type Rep (Quaternion a)

type Rep (Quaternion a) = D1 (MetaData "Quaternion" "Linear.Quaternion" "linear-1.20.7-5lThnmKUFiyAbTBcmo6MON" False) (C1 (MetaCons "Quaternion" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) SourceUnpack SourceStrict DecidedUnpack) (Rec0 (V3 a)))))

data Vector (Quaternion a)

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

type Index (Quaternion a)

type Index (Quaternion a) = E Quaternion

type IxValue (Quaternion a)

type IxValue (Quaternion a) = a

class Complicated t where

A vector space that includes the basis elements _e and _i

Methods

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

Instances

Complicated Complex

Methods

_e :: Functor f => (a -> f a) -> Complex a -> f (Complex a)

_i :: Functor f => (a -> f a) -> Complex a -> f (Complex a)

Complicated Quaternion

Methods

_e :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a)

_i :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a)

class Complicated t => Hamiltonian t where

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

Methods

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

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

Instances

Hamiltonian Quaternion

Methods

_j :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a)

_k :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a)

_ijk :: Functor f => (V3 a -> f (V3 a)) -> Quaternion a -> f (Quaternion a)

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.