Safe Haskell	None
Language	Haskell2010

SpatialMath

Contents

re-exported from linear

Synopsis

Documentation

data Euler a Source #

3-2-1 Euler angle rotation sequence

Constructors

Euler
Fields eYaw :: a ePitch :: a eRoll :: a

Instances

Functor Euler Source #
Methods fmap :: (a -> b) -> Euler a -> Euler b # (<$) :: a -> Euler b -> Euler a #
Applicative Euler Source #
Methods pure :: a -> Euler a # (<>) :: Euler (a -> b) -> Euler a -> Euler b # (>) :: Euler a -> Euler b -> Euler b # (<*) :: Euler a -> Euler b -> Euler a #
Foldable Euler Source #
Methods fold :: Monoid m => Euler m -> m # foldMap :: Monoid m => (a -> m) -> Euler a -> m # foldr :: (a -> b -> b) -> b -> Euler a -> b # foldr' :: (a -> b -> b) -> b -> Euler a -> b # foldl :: (b -> a -> b) -> b -> Euler a -> b # foldl' :: (b -> a -> b) -> b -> Euler a -> b # foldr1 :: (a -> a -> a) -> Euler a -> a # foldl1 :: (a -> a -> a) -> Euler a -> a # toList :: Euler a -> [a] # null :: Euler a -> Bool # length :: Euler a -> Int # elem :: Eq a => a -> Euler a -> Bool # maximum :: Ord a => Euler a -> a # minimum :: Ord a => Euler a -> a # sum :: Num a => Euler a -> a # product :: Num a => Euler a -> a #
Traversable Euler Source #
Methods traverse :: Applicative f => (a -> f b) -> Euler a -> f (Euler b) # sequenceA :: Applicative f => Euler (f a) -> f (Euler a) # mapM :: Monad m => (a -> m b) -> Euler a -> m (Euler b) # sequence :: Monad m => Euler (m a) -> m (Euler a) #
Generic1 Euler Source #
Associated Types type Rep1 (Euler :: * -> ) :: -> * # Methods from1 :: Euler a -> Rep1 Euler a # to1 :: Rep1 Euler a -> Euler a #
(ArcTan2 a, Floating a, Ord a) => Rotation Euler a Source #
Methods compose :: Rot f1 f2 Euler a -> Rot f2 f3 Euler a -> Rot f1 f3 Euler a Source # rot :: Rot f1 f2 Euler a -> V3T f1 a -> V3T f2 a Source # rot' :: Rot f1 f2 Euler a -> V3T f2 a -> V3T f1 a Source # transpose :: Rot f1 f2 Euler a -> Rot f2 f1 Euler a Source # identity :: Rot f1 f2 Euler a Source #
Eq a => Eq (Euler a) Source #
Methods (==) :: Euler a -> Euler a -> Bool # (/=) :: Euler a -> Euler a -> Bool #
Data a => Data (Euler a) Source #
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Euler a -> c (Euler a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Euler a) # toConstr :: Euler a -> Constr # dataTypeOf :: Euler a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Euler a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Euler a)) # gmapT :: (forall b. Data b => b -> b) -> Euler a -> Euler a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Euler a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Euler a -> r # gmapQ :: (forall d. Data d => d -> u) -> Euler a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Euler a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Euler a -> m (Euler a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Euler a -> m (Euler a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Euler a -> m (Euler a) #
Ord a => Ord (Euler a) Source #
Methods compare :: Euler a -> Euler a -> Ordering # (<) :: Euler a -> Euler a -> Bool # (<=) :: Euler a -> Euler a -> Bool # (>) :: Euler a -> Euler a -> Bool # (>=) :: Euler a -> Euler a -> Bool # max :: Euler a -> Euler a -> Euler a # min :: Euler a -> Euler a -> Euler a #
Show a => Show (Euler a) Source #
Methods showsPrec :: Int -> Euler a -> ShowS # show :: Euler a -> String # showList :: [Euler a] -> ShowS #
Generic (Euler a) Source #
Associated Types type Rep (Euler a) :: * -> * # Methods from :: Euler a -> Rep (Euler a) x # to :: Rep (Euler a) x -> Euler a #
Binary a => Binary (Euler a) Source #
Methods put :: Euler a -> Put # get :: Get (Euler a) # putList :: [Euler a] -> Put #
Serialize a => Serialize (Euler a) Source #
Methods put :: Putter (Euler a) # get :: Get (Euler a) #
type Rep1 Euler Source #
type Rep1 Euler = D1 (MetaData "Euler" "Types" "spatial-math-0.3.0.0-Dqp0VTsSbmHILyOQtucnEt" False) (C1 (MetaCons "Euler" PrefixI True) ((::) (S1 (MetaSel (Just Symbol "eYaw") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1) ((::) (S1 (MetaSel (Just Symbol "ePitch") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1) (S1 (MetaSel (Just Symbol "eRoll") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))))
type Rep (Euler a) Source #
type Rep (Euler a) = D1 (MetaData "Euler" "Types" "spatial-math-0.3.0.0-Dqp0VTsSbmHILyOQtucnEt" False) (C1 (MetaCons "Euler" PrefixI True) ((::) (S1 (MetaSel (Just Symbol "eYaw") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) ((::) (S1 (MetaSel (Just Symbol "ePitch") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) (S1 (MetaSel (Just Symbol "eRoll") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))))

class Floating a => ArcTan2 a where Source #

doesn't require RealFloat, used for overloading symbolics

Minimal complete definition

arctan2

Methods

arctan2 :: a -> a -> a Source #

Instances

ArcTan2 Double Source #
Methods arctan2 :: Double -> Double -> Double Source #
ArcTan2 Float Source #
Methods arctan2 :: Float -> Float -> Float Source #

rotateXyzAboutX :: Floating a => V3 a -> a -> V3 a Source #

Rotate a vector about the X axis

>>> trunc $ rotateXyzAboutX (V3 0 1 0) (pi/2)
V3 0.0 0.0 1.0

>>> trunc $ rotateXyzAboutX (V3 0 0 1) (pi/2)
V3 0.0 (-1.0) 0.0

rotateXyzAboutY :: Floating a => V3 a -> a -> V3 a Source #

Rotate a vector about the Y axis

>>> trunc $ rotateXyzAboutY (V3 0 0 1) (pi/2)
V3 1.0 0.0 0.0

>>> trunc $ rotateXyzAboutY (V3 1 0 0) (pi/2)
V3 0.0 0.0 (-1.0)

rotateXyzAboutZ :: Floating a => V3 a -> a -> V3 a Source #

Rotate a vector about the Z axis

>>> trunc $ rotateXyzAboutZ (V3 1 0 0) (pi/2)
V3 0.0 1.0 0.0

>>> trunc $ rotateXyzAboutZ (V3 0 1 0) (pi/2)
V3 (-1.0) 0.0 0.0

euler321OfQuat :: (ArcTan2 a, Ord a) => Quaternion a -> Euler a Source #

Convert quaternion to Euler angles

>>> euler321OfQuat (Quaternion 1.0 (V3 0.0 0.0 0.0))
Euler {eYaw = 0.0, ePitch = -0.0, eRoll = 0.0}

>>> euler321OfQuat (Quaternion (sqrt(2)/2) (V3 (sqrt(2)/2) 0.0 0.0))
Euler {eYaw = 0.0, ePitch = -0.0, eRoll = 1.5707963267948966}

>>> euler321OfQuat (Quaternion (sqrt(2)/2) (V3 0.0 (sqrt(2)/2) 0.0))
Euler {eYaw = 0.0, ePitch = 1.5707963267948966, eRoll = 0.0}

>>> euler321OfQuat (Quaternion (sqrt(2)/2) (V3 0.0 0.0 (sqrt(2)/2)))
Euler {eYaw = 1.5707963267948966, ePitch = -0.0, eRoll = 0.0}

unsafeEuler321OfQuat :: ArcTan2 a => Quaternion a -> Euler a Source #

Convert quaternion to Euler angles. Returns Nan if 2.0*(q1*q3 - q0*q2) is outside [-1, 1].

>>> unsafeEuler321OfQuat (Quaternion 1.0 (V3 0.0 0.0 0.0))
Euler {eYaw = 0.0, ePitch = -0.0, eRoll = 0.0}

>>> unsafeEuler321OfQuat (Quaternion (sqrt(2)/2) (V3 (sqrt(2)/2) 0.0 0.0))
Euler {eYaw = 0.0, ePitch = -0.0, eRoll = 1.5707963267948966}

>>> unsafeEuler321OfQuat (Quaternion (sqrt(2)/2) (V3 0.0 (sqrt(2)/2) 0.0))
Euler {eYaw = 0.0, ePitch = NaN, eRoll = 0.0}

>>> unsafeEuler321OfQuat (Quaternion (sqrt(2)/2) (V3 0.0 0.0 (sqrt(2)/2)))
Euler {eYaw = 1.5707963267948966, ePitch = -0.0, eRoll = 0.0}

euler321OfDcm :: (Ord a, ArcTan2 a) => M33 a -> Euler a Source #

Convert DCM to euler angles

>>> euler321OfDcm $ V3 (V3 1 0 0) (V3 0 1 0) (V3 0 0 1)
Euler {eYaw = 0.0, ePitch = -0.0, eRoll = 0.0}

>>> euler321OfDcm $ V3 (V3 0 1 0) (V3 (-1) 0 0) (V3 0 0 1)
Euler {eYaw = 1.5707963267948966, ePitch = -0.0, eRoll = 0.0}

>>> let s = sqrt(2)/2 in euler321OfDcm $ V3 (V3 s s 0) (V3 (-s) s 0) (V3 0 0 1)
Euler {eYaw = 0.7853981633974483, ePitch = -0.0, eRoll = 0.0}

unsafeEuler321OfDcm :: ArcTan2 a => M33 a -> Euler a Source #

Convert DCM to euler angles. Returns Nan if r[1,3] is outside [-1, 1].

>>> unsafeEuler321OfDcm $ V3 (V3 1 0 0) (V3 0 1 0) (V3 0 0 1)
Euler {eYaw = 0.0, ePitch = -0.0, eRoll = 0.0}

>>> unsafeEuler321OfDcm $ V3 (V3 0 1 0) (V3 (-1) 0 0) (V3 0 0 1)
Euler {eYaw = 1.5707963267948966, ePitch = -0.0, eRoll = 0.0}

>>> let s = sqrt(2)/2 in unsafeEuler321OfDcm $ V3 (V3 s s 0) (V3 (-s) s 0) (V3 0 0 1)
Euler {eYaw = 0.7853981633974483, ePitch = -0.0, eRoll = 0.0}

>>> unsafeEuler321OfDcm $ V3 (V3 0 0 1.1) (V3 0 0 0) (V3 0 0 0)
Euler {eYaw = 0.0, ePitch = NaN, eRoll = 0.0}

quatOfEuler321 :: Floating a => Euler a -> Quaternion a Source #

Convert Euler angles to quaternion. The scalar part of the result may be positive or negative.

>>> quatOfEuler321 (Euler 0 0 0)
Quaternion 1.0 (V3 0.0 0.0 0.0)

>>> quatOfEuler321 (Euler (pi/2) 0 0)
Quaternion 0.7071067811865476 (V3 0.0 0.0 0.7071067811865475)

>>> quatOfEuler321 (Euler 0 (pi/2) 0)
Quaternion 0.7071067811865476 (V3 0.0 0.7071067811865475 0.0)

>>> quatOfEuler321 (Euler 0 0 (pi/2))
Quaternion 0.7071067811865476 (V3 0.7071067811865475 0.0 0.0)

dcmOfQuat :: Num a => Quaternion a -> M33 a Source #

convert a quaternion to a DCM

>>> dcmOfQuat $ Quaternion 1.0 (V3 0.0 0.0 0.0)
V3 (V3 1.0 0.0 0.0) (V3 0.0 1.0 0.0) (V3 0.0 0.0 1.0)

>>> let s = sqrt(2)/2 in fmap trunc $ dcmOfQuat $ Quaternion s (V3 0.0 0.0 s)
V3 (V3 0.0 1.0 0.0) (V3 (-1.0) 0.0 0.0) (V3 0.0 0.0 1.0)

>>> dcmOfQuat $ Quaternion 0.9238795325112867 (V3 0.0 0.0 0.3826834323650898)
V3 (V3 0.7071067811865475 0.7071067811865476 0.0) (V3 (-0.7071067811865476) 0.7071067811865475 0.0) (V3 0.0 0.0 1.0)

dcmOfQuatB2A :: Num a => Quaternion a -> M33 a Source #

dcmOfEuler321 :: Floating a => Euler a -> M33 a Source #

Convert DCM to euler angles

>>> fmap trunc $ dcmOfEuler321 $ Euler {eYaw = 0.0, ePitch = 0, eRoll = 0}
V3 (V3 1.0 0.0 0.0) (V3 0.0 1.0 0.0) (V3 0.0 0.0 1.0)

>>> fmap trunc $ dcmOfEuler321 $ Euler {eYaw = pi/2, ePitch = 0, eRoll = 0}
V3 (V3 0.0 1.0 0.0) (V3 (-1.0) 0.0 0.0) (V3 0.0 0.0 1.0)

>>> fmap trunc $ dcmOfEuler321 $ Euler {eYaw = pi/4, ePitch = 0, eRoll = 0}
V3 (V3 0.7071067811865476 0.7071067811865475 0.0) (V3 (-0.7071067811865475) 0.7071067811865476 0.0) (V3 0.0 0.0 1.0)

quatOfDcm :: Floating a => M33 a -> Quaternion a Source #

convert a DCM to a quaternion

>>> quatOfDcm $ V3 (V3 1 0 0) (V3 0 1 0) (V3 0 0 1)
Quaternion 1.0 (V3 (-0.0) (-0.0) (-0.0))

>>> quatOfDcm $ V3 (V3 0 1 0) (V3 (-1) 0 0) (V3 0 0 1)
Quaternion 0.7071067811865477 (V3 (-0.0) (-0.0) 0.7071067811865474)

>>> let s = sqrt(2)/2 in quatOfDcm $ V3 (V3 s s 0) (V3 (-s) s 0) (V3 0 0 1)
Quaternion 0.9238795325112868 (V3 (-0.0) (-0.0) 0.3826834323650898)

quatOfDcmB2A :: Floating a => M33 a -> Quaternion a Source #

rotVecByDcm :: Num a => M33 a -> V3 a -> V3 a Source #

vec_b = R_a2b * vec_a

rotVecByDcmB2A :: Num a => M33 a -> V3 a -> V3 a Source #

vec_a = R_a2b^T * vec_b

rotVecByQuat :: Num a => Quaternion a -> V3 a -> V3 a Source #

vec_b = q_a2b * vec_a * q_a2b^(-1) vec_b = R(q_a2b) * vec_a

rotVecByQuatB2A :: Num a => Quaternion a -> V3 a -> V3 a Source #

rotVecByEuler :: (Floating a, Ord a) => Euler a -> V3 a -> V3 a Source #

rotVecByEulerB2A :: (Floating a, Ord a) => Euler a -> V3 a -> V3 a Source #

re-exported from linear

type M33 a = V3 (V3 a) #

A 3x3 matrix with row-major representation

data V3 a :: * -> * #

A 3-dimensional vector

Constructors

V3 ~a ~a ~a

Instances

Monad V3
Methods (>>=) :: V3 a -> (a -> V3 b) -> V3 b # (>>) :: V3 a -> V3 b -> V3 b # return :: a -> V3 a # fail :: String -> V3 a #
Functor V3
Methods fmap :: (a -> b) -> V3 a -> V3 b # (<$) :: a -> V3 b -> V3 a #
MonadFix V3
Methods mfix :: (a -> V3 a) -> V3 a #
Applicative V3
Methods pure :: a -> V3 a # (<>) :: V3 (a -> b) -> V3 a -> V3 b # (>) :: V3 a -> V3 b -> V3 b # (<*) :: V3 a -> V3 b -> V3 a #
Foldable V3
Methods fold :: Monoid m => V3 m -> m # foldMap :: Monoid m => (a -> m) -> V3 a -> m # foldr :: (a -> b -> b) -> b -> V3 a -> b # foldr' :: (a -> b -> b) -> b -> V3 a -> b # foldl :: (b -> a -> b) -> b -> V3 a -> b # foldl' :: (b -> a -> b) -> b -> V3 a -> b # foldr1 :: (a -> a -> a) -> V3 a -> a # foldl1 :: (a -> a -> a) -> V3 a -> a # toList :: V3 a -> [a] # null :: V3 a -> Bool # length :: V3 a -> Int # elem :: Eq a => a -> V3 a -> Bool # maximum :: Ord a => V3 a -> a # minimum :: Ord a => V3 a -> a # sum :: Num a => V3 a -> a # product :: Num a => V3 a -> a #
Traversable V3
Methods traverse :: Applicative f => (a -> f b) -> V3 a -> f (V3 b) # sequenceA :: Applicative f => V3 (f a) -> f (V3 a) # mapM :: Monad m => (a -> m b) -> V3 a -> m (V3 b) # sequence :: Monad m => V3 (m a) -> m (V3 a) #
Generic1 V3
Associated Types type Rep1 (V3 :: * -> ) :: -> * # Methods from1 :: V3 a -> Rep1 V3 a # to1 :: Rep1 V3 a -> V3 a #
Distributive V3
Methods distribute :: Functor f => f (V3 a) -> V3 (f a) # collect :: Functor f => (a -> V3 b) -> f a -> V3 (f b) # distributeM :: Monad m => m (V3 a) -> V3 (m a) # collectM :: Monad m => (a -> V3 b) -> m a -> V3 (m b) #
Representable V3
Associated Types type Rep (V3 :: * -> ) :: # Methods tabulate :: (Rep V3 -> a) -> V3 a # index :: V3 a -> Rep V3 -> a #
Eq1 V3
Methods liftEq :: (a -> b -> Bool) -> V3 a -> V3 b -> Bool #
Ord1 V3
Methods liftCompare :: (a -> b -> Ordering) -> V3 a -> V3 b -> Ordering #
Read1 V3
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V3 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V3 a] #
Show1 V3
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V3 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V3 a] -> ShowS #
MonadZip V3
Methods mzip :: V3 a -> V3 b -> V3 (a, b) # mzipWith :: (a -> b -> c) -> V3 a -> V3 b -> V3 c # munzip :: V3 (a, b) -> (V3 a, V3 b) #
Serial1 V3
Methods serializeWith :: MonadPut m => (a -> m ()) -> V3 a -> m () # deserializeWith :: MonadGet m => m a -> m (V3 a) #
Traversable1 V3
Methods traverse1 :: Apply f => (a -> f b) -> V3 a -> f (V3 b) # sequence1 :: Apply f => V3 (f b) -> f (V3 b) #
R3 V3
Methods _z :: Functor f => (a -> f a) -> V3 a -> f (V3 a) # _xyz :: Functor f => (V3 a -> f (V3 a)) -> V3 a -> f (V3 a) #
R2 V3
Methods _y :: Functor f => (a -> f a) -> V3 a -> f (V3 a) # _xy :: Functor f => (V2 a -> f (V2 a)) -> V3 a -> f (V3 a) #
R1 V3
Methods _x :: Functor f => (a -> f a) -> V3 a -> f (V3 a) #
Metric V3
Methods dot :: Num a => V3 a -> V3 a -> a # quadrance :: Num a => V3 a -> a # qd :: Num a => V3 a -> V3 a -> a # distance :: Floating a => V3 a -> V3 a -> a # norm :: Floating a => V3 a -> a # signorm :: Floating a => V3 a -> V3 a #
Additive V3
Methods zero :: Num a => V3 a # (^+^) :: Num a => V3 a -> V3 a -> V3 a # (^-^) :: Num a => V3 a -> V3 a -> V3 a # lerp :: Num a => a -> V3 a -> V3 a -> V3 a # liftU2 :: (a -> a -> a) -> V3 a -> V3 a -> V3 a # liftI2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c #
Apply V3
Methods (<.>) :: V3 (a -> b) -> V3 a -> V3 b # (.>) :: V3 a -> V3 b -> V3 b # (<.) :: V3 a -> V3 b -> V3 a #
Bind V3
Methods (>>-) :: V3 a -> (a -> V3 b) -> V3 b # join :: V3 (V3 a) -> V3 a #
Foldable1 V3
Methods fold1 :: Semigroup m => V3 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V3 a -> m #
Unbox a => Vector Vector (V3 a)
Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> m (Vector (V3 a)) # basicUnsafeThaw :: PrimMonad m => Vector (V3 a) -> m (Mutable Vector (PrimState m) (V3 a)) # basicLength :: Vector (V3 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V3 a) -> Vector (V3 a) # basicUnsafeIndexM :: Monad m => Vector (V3 a) -> Int -> m (V3 a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> Vector (V3 a) -> m () # elemseq :: Vector (V3 a) -> V3 a -> b -> b #
Unbox a => MVector MVector (V3 a)
Methods basicLength :: MVector s (V3 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V3 a) -> MVector s (V3 a) # basicOverlaps :: MVector s (V3 a) -> MVector s (V3 a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V3 a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V3 a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V3 a -> m (MVector (PrimState m) (V3 a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (V3 a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> V3 a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V3 a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V3 a) -> V3 a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (MVector (PrimState m) (V3 a)) #
Bounded a => Bounded (V3 a)
Methods minBound :: V3 a # maxBound :: V3 a #
Eq a => Eq (V3 a)
Methods (==) :: V3 a -> V3 a -> Bool # (/=) :: V3 a -> V3 a -> Bool #
Floating a => Floating (V3 a)
Methods pi :: V3 a # exp :: V3 a -> V3 a # log :: V3 a -> V3 a # sqrt :: V3 a -> V3 a # (**) :: V3 a -> V3 a -> V3 a # logBase :: V3 a -> V3 a -> V3 a # sin :: V3 a -> V3 a # cos :: V3 a -> V3 a # tan :: V3 a -> V3 a # asin :: V3 a -> V3 a # acos :: V3 a -> V3 a # atan :: V3 a -> V3 a # sinh :: V3 a -> V3 a # cosh :: V3 a -> V3 a # tanh :: V3 a -> V3 a # asinh :: V3 a -> V3 a # acosh :: V3 a -> V3 a # atanh :: V3 a -> V3 a # log1p :: V3 a -> V3 a # expm1 :: V3 a -> V3 a # log1pexp :: V3 a -> V3 a # log1mexp :: V3 a -> V3 a #
Fractional a => Fractional (V3 a)
Methods (/) :: V3 a -> V3 a -> V3 a # recip :: V3 a -> V3 a # fromRational :: Rational -> V3 a #
Data a => Data (V3 a)
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V3 a -> c (V3 a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V3 a) # toConstr :: V3 a -> Constr # dataTypeOf :: V3 a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (V3 a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V3 a)) # gmapT :: (forall b. Data b => b -> b) -> V3 a -> V3 a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r # gmapQ :: (forall d. Data d => d -> u) -> V3 a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> V3 a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) #
Num a => Num (V3 a)
Methods (+) :: V3 a -> V3 a -> V3 a # (-) :: V3 a -> V3 a -> V3 a # (*) :: V3 a -> V3 a -> V3 a # negate :: V3 a -> V3 a # abs :: V3 a -> V3 a # signum :: V3 a -> V3 a # fromInteger :: Integer -> V3 a #
Ord a => Ord (V3 a)
Methods compare :: V3 a -> V3 a -> Ordering # (<) :: V3 a -> V3 a -> Bool # (<=) :: V3 a -> V3 a -> Bool # (>) :: V3 a -> V3 a -> Bool # (>=) :: V3 a -> V3 a -> Bool # max :: V3 a -> V3 a -> V3 a # min :: V3 a -> V3 a -> V3 a #
Read a => Read (V3 a)
Methods readsPrec :: Int -> ReadS (V3 a) # readList :: ReadS [V3 a] # readPrec :: ReadPrec (V3 a) # readListPrec :: ReadPrec [V3 a] #
Show a => Show (V3 a)
Methods showsPrec :: Int -> V3 a -> ShowS # show :: V3 a -> String # showList :: [V3 a] -> ShowS #
Ix a => Ix (V3 a)
Methods range :: (V3 a, V3 a) -> [V3 a] # index :: (V3 a, V3 a) -> V3 a -> Int # unsafeIndex :: (V3 a, V3 a) -> V3 a -> Int inRange :: (V3 a, V3 a) -> V3 a -> Bool # rangeSize :: (V3 a, V3 a) -> Int # unsafeRangeSize :: (V3 a, V3 a) -> Int
Generic (V3 a)
Associated Types type Rep (V3 a) :: * -> * # Methods from :: V3 a -> Rep (V3 a) x # to :: Rep (V3 a) x -> V3 a #
Storable a => Storable (V3 a)
Methods sizeOf :: V3 a -> Int # alignment :: V3 a -> Int # peekElemOff :: Ptr (V3 a) -> Int -> IO (V3 a) # pokeElemOff :: Ptr (V3 a) -> Int -> V3 a -> IO () # peekByteOff :: Ptr b -> Int -> IO (V3 a) # pokeByteOff :: Ptr b -> Int -> V3 a -> IO () # peek :: Ptr (V3 a) -> IO (V3 a) # poke :: Ptr (V3 a) -> V3 a -> IO () #
Binary a => Binary (V3 a)
Methods put :: V3 a -> Put # get :: Get (V3 a) # putList :: [V3 a] -> Put #
Serial a => Serial (V3 a)
Methods serialize :: MonadPut m => V3 a -> m () # deserialize :: MonadGet m => m (V3 a) #
Serialize a => Serialize (V3 a)
Methods put :: Putter (V3 a) # get :: Get (V3 a) #
NFData a => NFData (V3 a)
Methods rnf :: V3 a -> () #
Hashable a => Hashable (V3 a)
Methods hashWithSalt :: Int -> V3 a -> Int # hash :: V3 a -> Int #
Unbox a => Unbox (V3 a)

Ixed (V3 a)
Methods ix :: Index (V3 a) -> Traversal' (V3 a) (IxValue (V3 a)) #
Epsilon a => Epsilon (V3 a)
Methods nearZero :: V3 a -> Bool #
FunctorWithIndex (E V3) V3
Methods imap :: (E V3 -> a -> b) -> V3 a -> V3 b # imapped :: (Indexable (E V3) p, Settable f) => p a (f b) -> V3 a -> f (V3 b) #
FoldableWithIndex (E V3) V3
Methods ifoldMap :: Monoid m => (E V3 -> a -> m) -> V3 a -> m # ifolded :: (Indexable (E V3) p, Contravariant f, Applicative f) => p a (f a) -> V3 a -> f (V3 a) # ifoldr :: (E V3 -> a -> b -> b) -> b -> V3 a -> b # ifoldl :: (E V3 -> b -> a -> b) -> b -> V3 a -> b # ifoldr' :: (E V3 -> a -> b -> b) -> b -> V3 a -> b # ifoldl' :: (E V3 -> b -> a -> b) -> b -> V3 a -> b #
TraversableWithIndex (E V3) V3
Methods itraverse :: Applicative f => (E V3 -> a -> f b) -> V3 a -> f (V3 b) # itraversed :: (Indexable (E V3) p, Applicative f) => p a (f b) -> V3 a -> f (V3 b) #
Each (V3 a) (V3 b) a b
Methods each :: Traversal (V3 a) (V3 b) a b #
Num a => Rotation ((:.) V3 V3) a Source #
Methods compose :: Rot f1 f2 (V3 :. V3) a -> Rot f2 f3 (V3 :. V3) a -> Rot f1 f3 (V3 :. V3) a Source # rot :: Rot f1 f2 (V3 :. V3) a -> V3T f1 a -> V3T f2 a Source # rot' :: Rot f1 f2 (V3 :. V3) a -> V3T f2 a -> V3T f1 a Source # transpose :: Rot f1 f2 (V3 :. V3) a -> Rot f2 f1 (V3 :. V3) a Source # identity :: Rot f1 f2 (V3 :. V3) a Source #
type Rep1 V3
type Rep1 V3 = D1 (MetaData "V3" "Linear.V3" "linear-1.20.5-ALqHTYew01KD1PdDd6TYmz" False) (C1 (MetaCons "V3" PrefixI False) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1))))
type Rep V3
type Rep V3 = E V3
data MVector s (V3 a)
data MVector s (V3 a) = MV_V3 ~Int ~(MVector s a)
type Rep (V3 a)
type Rep (V3 a) = D1 (MetaData "V3" "Linear.V3" "linear-1.20.5-ALqHTYew01KD1PdDd6TYmz" False) (C1 (MetaCons "V3" PrefixI False) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)))))
data Vector (V3 a)
data Vector (V3 a) = V_V3 ~Int ~(Vector a)
type Index (V3 a)
type Index (V3 a) = E V3
type IxValue (V3 a)
type IxValue (V3 a) = a

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) #
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) #
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) #
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 #
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 #
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 #
Num a => Rotation Quaternion a Source #
Methods compose :: Rot f1 f2 Quaternion a -> Rot f2 f3 Quaternion a -> Rot f1 f3 Quaternion a Source # rot :: Rot f1 f2 Quaternion a -> V3T f1 a -> V3T f2 a Source # rot' :: Rot f1 f2 Quaternion a -> V3T f2 a -> V3T f1 a Source # transpose :: Rot f1 f2 Quaternion a -> Rot f2 f1 Quaternion a Source # identity :: Rot f1 f2 Quaternion a Source #
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)) #
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)) #
(Conjugate a, RealFloat a) => Conjugate (Quaternion a)
Methods conjugate :: Quaternion a -> Quaternion a #
(RealFloat a, Epsilon a) => Epsilon (Quaternion a)
Methods nearZero :: Quaternion a -> Bool #
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-1.20.5-ALqHTYew01KD1PdDd6TYmz" False) (C1 (MetaCons "Quaternion" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 (MetaSel (Nothing Symbol) SourceUnpack SourceStrict DecidedStrict) (Rec1 V3))))
type Rep Quaternion
type Rep Quaternion = E 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-1.20.5-ALqHTYew01KD1PdDd6TYmz" False) (C1 (MetaCons "Quaternion" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) SourceUnpack SourceStrict DecidedStrict) (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