Safe Haskell	None
Language	Haskell2010

Nonlinear.Quaternion

Synopsis

data Quaternion a = Quaternion !a !(V3 a)
class Complicated t where
- _e, _i :: Lens' (t a) a
class Complicated t => Hamiltonian t where
- _j, _k :: Lens' (t a) a
- _ijk :: Lens' (t a) (V3 a)
slerp :: RealFloat a => Quaternion a -> Quaternion a -> a -> Quaternion a
asinq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a
acosq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a
atanq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a
asinhq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a
acoshq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a
atanhq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a
absi :: Floating a => Quaternion a -> a
pow :: RealFloat a => Quaternion a -> a -> Quaternion a
rotate :: RealFloat a => Quaternion a -> V3 a -> V3 a
axisAngle :: Floating a => V3 a -> a -> Quaternion a

Documentation

data Quaternion a Source #

Quaternions

Constructors

Quaternion !a !(V3 a)

Instances

Instances details

Monad Quaternion Source #
Instance details Defined in Nonlinear.Quaternion Methods (>>=) :: Quaternion a -> (a -> Quaternion b) -> Quaternion b # (>>) :: Quaternion a -> Quaternion b -> Quaternion b # return :: a -> Quaternion a #
Functor Quaternion Source #
Instance details Defined in Nonlinear.Quaternion Methods fmap :: (a -> b) -> Quaternion a -> Quaternion b # (<$) :: a -> Quaternion b -> Quaternion a #
MonadFix Quaternion Source #
Instance details Defined in Nonlinear.Quaternion Methods mfix :: (a -> Quaternion a) -> Quaternion a #
Applicative Quaternion Source #
Instance details 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 Source #
Instance details 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 Source #
Instance details 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 Source #
Instance details Defined in Nonlinear.Quaternion Methods liftEq :: (a -> b -> Bool) -> Quaternion a -> Quaternion b -> Bool #
Ord1 Quaternion Source #
Instance details Defined in Nonlinear.Quaternion Methods liftCompare :: (a -> b -> Ordering) -> Quaternion a -> Quaternion b -> Ordering #
Read1 Quaternion Source #
Instance details 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 Source #
Instance details 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 Source #
Instance details 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 Source #
Instance details Defined in Nonlinear.Quaternion Methods construct :: ((forall b. Lens' (Quaternion b) b) -> a) -> Quaternion a Source #
R1 Quaternion Source #
Instance details Defined in Nonlinear.Quaternion Methods _x :: Lens' (Quaternion a) a Source #
R2 Quaternion Source #
Instance details Defined in Nonlinear.Quaternion Methods _y :: Lens' (Quaternion a) a Source # _xy :: Lens' (Quaternion a) (V2 a) Source #
R3 Quaternion Source #
Instance details Defined in Nonlinear.Quaternion Methods _z :: Lens' (Quaternion a) a Source # _xyz :: Lens' (Quaternion a) (V3 a) Source #
R4 Quaternion Source #
Instance details Defined in Nonlinear.Quaternion Methods _w :: Lens' (Quaternion a) a Source # _xyzw :: Lens' (Quaternion a) (V4 a) Source #
Hamiltonian Quaternion Source #
Instance details Defined in Nonlinear.Quaternion Methods _j :: Lens' (Quaternion a) a Source # _k :: Lens' (Quaternion a) a Source # _ijk :: Lens' (Quaternion a) (V3 a) Source #
Complicated Quaternion Source #
Instance details Defined in Nonlinear.Quaternion Methods _e :: Lens' (Quaternion a) a Source # _i :: Lens' (Quaternion a) a Source #
Eq a => Eq (Quaternion a) Source #
Instance details Defined in Nonlinear.Quaternion Methods (==) :: Quaternion a -> Quaternion a -> Bool # (/=) :: Quaternion a -> Quaternion a -> Bool #
RealFloat a => Floating (Quaternion a) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Nonlinear.Quaternion Methods showsPrec :: Int -> Quaternion a -> ShowS # show :: Quaternion a -> String # showList :: [Quaternion a] -> ShowS #
Ix a => Ix (Quaternion a) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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 Source #
Instance details 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) Source #
Instance details 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 Source #
Instance details 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 Source #

A vector space that includes the basis elements _e and _i

Methods

_e :: Lens' (t a) a Source #

_i :: Lens' (t a) a Source #

Instances

Instances details

Complicated Complex Source #
Instance details Defined in Nonlinear.Quaternion Methods _e :: Lens' (Complex a) a Source # _i :: Lens' (Complex a) a Source #
Complicated Quaternion Source #
Instance details Defined in Nonlinear.Quaternion Methods _e :: Lens' (Quaternion a) a Source # _i :: Lens' (Quaternion a) a Source #

class Complicated t => Hamiltonian t where Source #

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

Methods

_j :: Lens' (t a) a Source #

_k :: Lens' (t a) a Source #

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

Instances

Instances details

Hamiltonian Quaternion Source #
Instance details Defined in Nonlinear.Quaternion Methods _j :: Lens' (Quaternion a) a Source # _k :: Lens' (Quaternion a) a Source # _ijk :: Lens' (Quaternion a) (V3 a) Source #