Nonlinear.Quaternion

Documentation

data Quaternion a

Quaternions

Constructors

Quaternion !a !(V3 a)

Instances

Monad Quaternion

Defined in Nonlinear.Quaternion

Methods

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

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

return :: a -> Quaternion a

Functor Quaternion

Defined in Nonlinear.Quaternion

Methods

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

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

MonadFix Quaternion

Defined in Nonlinear.Quaternion

Methods

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

Applicative Quaternion

Defined in Nonlinear.Quaternion

Methods

pure :: a -> Quaternion a

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

liftA2 :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c

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

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

Foldable Quaternion

Defined in Nonlinear.Quaternion

Methods

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

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

Defined in Nonlinear.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)

Eq1 Quaternion

Defined in Nonlinear.Quaternion

Methods

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

Ord1 Quaternion

Defined in Nonlinear.Quaternion

Methods

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

Read1 Quaternion

Defined in Nonlinear.Quaternion

Methods

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

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

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Quaternion a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Quaternion a]

Show1 Quaternion

Defined in Nonlinear.Quaternion

Methods

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

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

MonadZip Quaternion

Defined in Nonlinear.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)

Vec Quaternion

Defined in Nonlinear.Quaternion

Methods

construct :: ((forall b. Lens' (Quaternion b) b) -> a) -> Quaternion a

R1 Quaternion

Defined in Nonlinear.Quaternion

Methods

_x :: Lens' (Quaternion a) a

R2 Quaternion

Defined in Nonlinear.Quaternion

Methods

_y :: Lens' (Quaternion a) a

_xy :: Lens' (Quaternion a) (V2 a)

R3 Quaternion

Defined in Nonlinear.Quaternion

Methods

_z :: Lens' (Quaternion a) a

_xyz :: Lens' (Quaternion a) (V3 a)

R4 Quaternion

Defined in Nonlinear.Quaternion

Methods

_w :: Lens' (Quaternion a) a

_xyzw :: Lens' (Quaternion a) (V4 a)

Hamiltonian Quaternion

Defined in Nonlinear.Quaternion

Methods

_j :: Lens' (Quaternion a) a

_k :: Lens' (Quaternion a) a

_ijk :: Lens' (Quaternion a) (V3 a)

Complicated Quaternion

Defined in Nonlinear.Quaternion

Methods

_e :: Lens' (Quaternion a) a

_i :: Lens' (Quaternion a) a

Eq a => Eq (Quaternion a)

Defined in Nonlinear.Quaternion

Methods

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

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

RealFloat a => Floating (Quaternion a)

Defined in Nonlinear.Quaternion

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)

Defined in Nonlinear.Quaternion

Methods

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

recip :: Quaternion a -> Quaternion a

fromRational :: Rational -> Quaternion a

Data a => Data (Quaternion a)

Defined in Nonlinear.Quaternion

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 :: forall r r'. (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)

Defined in Nonlinear.Quaternion

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)

Defined in Nonlinear.Quaternion

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)

Defined in Nonlinear.Quaternion

Methods

readsPrec :: Int -> ReadS (Quaternion a)

readList :: ReadS [Quaternion a]

readPrec :: ReadPrec (Quaternion a)

readListPrec :: ReadPrec [Quaternion a]

Show a => Show (Quaternion a)

Defined in Nonlinear.Quaternion

Methods

showsPrec :: Int -> Quaternion a -> ShowS

show :: Quaternion a -> String

showList :: [Quaternion a] -> ShowS

Ix a => Ix (Quaternion a)

Defined in Nonlinear.Quaternion

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)

Defined in Nonlinear.Quaternion

Associated Types

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

Methods

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

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

Semigroup a => Semigroup (Quaternion a)

Defined in Nonlinear.Quaternion

Methods

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

sconcat :: NonEmpty (Quaternion a) -> Quaternion a

stimes :: Integral b => b -> Quaternion a -> Quaternion a

Monoid a => Monoid (Quaternion a)

Defined in Nonlinear.Quaternion

Methods

mempty :: Quaternion a

mappend :: Quaternion a -> Quaternion a -> Quaternion a

mconcat :: [Quaternion a] -> Quaternion a

Storable a => Storable (Quaternion a)

Defined in Nonlinear.Quaternion

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 ()

Generic1 Quaternion

Defined in Nonlinear.Quaternion

Associated Types

type Rep1 Quaternion :: k -> Type

Methods

from1 :: forall (a :: k). Quaternion a -> Rep1 Quaternion a

to1 :: forall (a :: k). Rep1 Quaternion a -> Quaternion a

type Rep (Quaternion a)

Defined in Nonlinear.Quaternion

type Rep (Quaternion a) = D1 ('MetaData "Quaternion" "Nonlinear.Quaternion" "nonlinear-0.1.0-dd7wbAvLl3JZC37BHOks3" 'False) (C1 ('MetaCons "Quaternion" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 (V3 a))))

type Rep1 Quaternion

Defined in Nonlinear.Quaternion

type Rep1 Quaternion = D1 ('MetaData "Quaternion" "Nonlinear.Quaternion" "nonlinear-0.1.0-dd7wbAvLl3JZC37BHOks3" 'False) (C1 ('MetaCons "Quaternion" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec1 V3)))

class Complicated t where

A vector space that includes the basis elements _e and _i

Methods

_e :: Lens' (t a) a

_i :: Lens' (t a) a

Instances

Complicated Complex

Defined in Nonlinear.Quaternion

Methods

_e :: Lens' (Complex a) a

_i :: Lens' (Complex a) a

Complicated Quaternion

Defined in Nonlinear.Quaternion

Methods

_e :: Lens' (Quaternion a) a

_i :: Lens' (Quaternion a) a

class Complicated t => Hamiltonian t 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)

Instances

Hamiltonian Quaternion

Defined in Nonlinear.Quaternion

Methods

_j :: Lens' (Quaternion a) a

_k :: Lens' (Quaternion a) a

_ijk :: Lens' (Quaternion a) (V3 a)

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 :: RealFloat a => Quaternion a -> V3 a -> V3 a

Apply a rotation to a vector.

axisAngle :: Floating a => V3 a -> a -> Quaternion a

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