Safe Haskell	Safe-Inferred
Language	Haskell2010

SpatialMath

Contents

re-exported from linear

Synopsis

data Euler a = Euler {
- eYaw :: a
- ePitch :: a
- eRoll :: a
}
class Floating a => ArcTan2 a where
- arctan2 :: a -> a -> a
rotateXyzAboutX :: Floating a => V3 a -> a -> V3 a
rotateXyzAboutY :: Floating a => V3 a -> a -> V3 a
rotateXyzAboutZ :: Floating a => V3 a -> a -> V3 a
euler321OfQuat :: (ArcTan2 a, Ord a) => Quaternion a -> Euler a
euler321OfDcm :: (Ord a, ArcTan2 a) => M33 a -> Euler a
unsafeEuler321OfDcm :: ArcTan2 a => M33 a -> Euler a
quatOfEuler321 :: (Floating a, Ord a) => Euler a -> Quaternion a
dcmOfQuat :: Num a => Quaternion a -> M33 a
dcmOfQuatB2A :: Num a => Quaternion a -> M33 a
dcmOfEuler321 :: Floating a => Euler a -> M33 a
quatOfDcm :: Floating a => M33 a -> Quaternion a
quatOfDcmB2A :: Floating a => M33 a -> Quaternion a
rotVecByDcm :: Num a => M33 a -> V3 a -> V3 a
rotVecByDcmB2A :: Num a => M33 a -> V3 a -> V3 a
rotVecByQuat :: Num a => Quaternion a -> V3 a -> V3 a
rotVecByQuatB2A :: Num a => Quaternion a -> V3 a -> V3 a
rotVecByEuler :: (Floating a, Ord a) => Euler a -> V3 a -> V3 a
rotVecByEulerB2A :: (Floating a, Ord a) => Euler a -> V3 a -> V3 a
type M33 a = V3 (V3 a)
data V3 a = V3 !a !a !a
data Quaternion a = Quaternion !a !(V3 a)

Documentation

data Euler a Source #

3-2-1 Euler angle rotation sequence

Constructors

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

Instances

Instances details

Foldable Euler Source #
Instance details Defined in Types Methods fold :: Monoid m => Euler m -> m # foldMap :: Monoid m => (a -> m) -> Euler a -> 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 #
Instance details Defined in Types 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) #
Applicative Euler Source #
Instance details Defined in Types Methods pure :: a -> Euler a # (<>) :: Euler (a -> b) -> Euler a -> Euler b # liftA2 :: (a -> b -> c) -> Euler a -> Euler b -> Euler c # (>) :: Euler a -> Euler b -> Euler b # (<*) :: Euler a -> Euler b -> Euler a #
Functor Euler Source #
Instance details Defined in Types Methods fmap :: (a -> b) -> Euler a -> Euler b # (<$) :: a -> Euler b -> Euler a #
Generic1 Euler Source #
Instance details Defined in Types Associated Types type Rep1 Euler :: k -> Type # Methods from1 :: forall (a :: k). Euler a -> Rep1 Euler a # to1 :: forall (a :: k). Rep1 Euler a -> Euler a #
Data a => Data (Euler a) Source #
Instance details Defined in Types 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 :: forall r r'. (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) #
Generic (Euler a) Source #
Instance details Defined in Types Associated Types type Rep (Euler a) :: Type -> Type # Methods from :: Euler a -> Rep (Euler a) x # to :: Rep (Euler a) x -> Euler a #
Show a => Show (Euler a) Source #
Instance details Defined in Types Methods showsPrec :: Int -> Euler a -> ShowS # show :: Euler a -> String # showList :: [Euler a] -> ShowS #
Binary a => Binary (Euler a) Source #
Instance details Defined in Types Methods put :: Euler a -> Put # get :: Get (Euler a) # putList :: [Euler a] -> Put #
Serialize a => Serialize (Euler a) Source #
Instance details Defined in Types Methods put :: Putter (Euler a) # get :: Get (Euler a) #
Eq a => Eq (Euler a) Source #
Instance details Defined in Types Methods (==) :: Euler a -> Euler a -> Bool # (/=) :: Euler a -> Euler a -> Bool #
Ord a => Ord (Euler a) Source #
Instance details Defined in Types 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 #
type Rep1 Euler Source #
Instance details Defined in Types type Rep1 Euler = D1 ('MetaData "Euler" "Types" "SpatialMath-0.2.7.0-GZqIaMCJq0F5jaw9AzNN8p" 'False) (C1 ('MetaCons "Euler" 'PrefixI 'True) (S1 ('MetaSel ('Just "eYaw") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1 :: (S1 ('MetaSel ('Just "ePitch") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1 :: S1 ('MetaSel ('Just "eRoll") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)))
type Rep (Euler a) Source #
Instance details Defined in Types type Rep (Euler a) = D1 ('MetaData "Euler" "Types" "SpatialMath-0.2.7.0-GZqIaMCJq0F5jaw9AzNN8p" 'False) (C1 ('MetaCons "Euler" 'PrefixI 'True) (S1 ('MetaSel ('Just "eYaw") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :: (S1 ('MetaSel ('Just "ePitch") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :: S1 ('MetaSel ('Just "eRoll") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a))))

class Floating a => ArcTan2 a where Source #

doesn't require RealFloat, used for overloading symbolics

Methods

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

Instances

Instances details

ArcTan2 Double Source #
Instance details Defined in SpatialMath Methods arctan2 :: Double -> Double -> Double Source #
ArcTan2 Float Source #
Instance details Defined in SpatialMath 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}

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, Ord a) => Euler a -> Quaternion a Source #

Convert Euler angles to quaternion

>>> 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

Instances details

Representable V3
Instance details Defined in Linear.V3 Associated Types type Rep V3 # Methods tabulate :: (Rep V3 -> a) -> V3 a # index :: V3 a -> Rep V3 -> a #
MonadFix V3
Instance details Defined in Linear.V3 Methods mfix :: (a -> V3 a) -> V3 a #
MonadZip V3
Instance details Defined in Linear.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) #
Foldable V3
Instance details Defined in Linear.V3 Methods fold :: Monoid m => V3 m -> m # foldMap :: Monoid m => (a -> m) -> V3 a -> 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 #
Eq1 V3
Instance details Defined in Linear.V3 Methods liftEq :: (a -> b -> Bool) -> V3 a -> V3 b -> Bool #
Ord1 V3
Instance details Defined in Linear.V3 Methods liftCompare :: (a -> b -> Ordering) -> V3 a -> V3 b -> Ordering #
Read1 V3
Instance details Defined in Linear.V3 Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V3 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V3 a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V3 a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V3 a] #
Show1 V3
Instance details Defined in Linear.V3 Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V3 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V3 a] -> ShowS #
Traversable V3
Instance details Defined in Linear.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) #
Applicative V3
Instance details Defined in Linear.V3 Methods pure :: a -> V3 a # (<>) :: V3 (a -> b) -> V3 a -> V3 b # liftA2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c # (>) :: V3 a -> V3 b -> V3 b # (<*) :: V3 a -> V3 b -> V3 a #
Functor V3
Instance details Defined in Linear.V3 Methods fmap :: (a -> b) -> V3 a -> V3 b # (<$) :: a -> V3 b -> V3 a #
Monad V3
Instance details Defined in Linear.V3 Methods (>>=) :: V3 a -> (a -> V3 b) -> V3 b # (>>) :: V3 a -> V3 b -> V3 b # return :: a -> V3 a #
Serial1 V3
Instance details Defined in Linear.V3 Methods serializeWith :: MonadPut m => (a -> m ()) -> V3 a -> m () # deserializeWith :: MonadGet m => m a -> m (V3 a) #
Distributive V3
Instance details Defined in Linear.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) #
Foldable1 V3
Instance details Defined in Linear.V3 Methods fold1 :: Semigroup m => V3 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V3 a -> m # foldMap1' :: Semigroup m => (a -> m) -> V3 a -> m # toNonEmpty :: V3 a -> NonEmpty a # maximum :: Ord a => V3 a -> a # minimum :: Ord a => V3 a -> a # head :: V3 a -> a # last :: V3 a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> V3 a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> V3 a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> V3 a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> V3 a -> b #
Hashable1 V3
Instance details Defined in Linear.V3 Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> V3 a -> Int #
Metric V3
Instance details Defined in Linear.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 #
Trace V3
Instance details Defined in Linear.Trace Methods trace :: Num a => V3 (V3 a) -> a # diagonal :: V3 (V3 a) -> V3 a #
Finite V3
Instance details Defined in Linear.V3 Associated Types type Size V3 :: Nat # Methods toV :: V3 a -> V (Size V3) a # fromV :: V (Size V3) a -> V3 a #
R1 V3
Instance details Defined in Linear.V3 Methods _x :: Lens' (V3 a) a #
R2 V3
Instance details Defined in Linear.V3 Methods _y :: Lens' (V3 a) a # _xy :: Lens' (V3 a) (V2 a) #
R3 V3
Instance details Defined in Linear.V3 Methods _z :: Lens' (V3 a) a # _xyz :: Lens' (V3 a) (V3 a) #
Additive V3
Instance details Defined in Linear.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
Instance details Defined in Linear.V3 Methods (<.>) :: V3 (a -> b) -> V3 a -> V3 b # (.>) :: V3 a -> V3 b -> V3 b # (<.) :: V3 a -> V3 b -> V3 a # liftF2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c #
Bind V3
Instance details Defined in Linear.V3 Methods (>>-) :: V3 a -> (a -> V3 b) -> V3 b # join :: V3 (V3 a) -> V3 a #
Traversable1 V3
Instance details Defined in Linear.V3 Methods traverse1 :: Apply f => (a -> f b) -> V3 a -> f (V3 b) # sequence1 :: Apply f => V3 (f b) -> f (V3 b) #
Generic1 V3
Instance details Defined in Linear.V3 Associated Types type Rep1 V3 :: k -> Type # Methods from1 :: forall (a :: k). V3 a -> Rep1 V3 a # to1 :: forall (a :: k). Rep1 V3 a -> V3 a #
Num r => Coalgebra r (E V3)
Instance details Defined in Linear.Algebra Methods comult :: (E V3 -> r) -> E V3 -> E V3 -> r # counital :: (E V3 -> r) -> r #
Unbox a => Vector Vector (V3 a)
Instance details Defined in Linear.V3 Methods basicUnsafeFreeze :: Mutable Vector s (V3 a) -> ST s (Vector (V3 a)) # basicUnsafeThaw :: Vector (V3 a) -> ST s (Mutable Vector s (V3 a)) # basicLength :: Vector (V3 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V3 a) -> Vector (V3 a) # basicUnsafeIndexM :: Vector (V3 a) -> Int -> Box (V3 a) # basicUnsafeCopy :: Mutable Vector s (V3 a) -> Vector (V3 a) -> ST s () # elemseq :: Vector (V3 a) -> V3 a -> b -> b #
Unbox a => MVector MVector (V3 a)
Instance details Defined in Linear.V3 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 :: Int -> ST s (MVector s (V3 a)) # basicInitialize :: MVector s (V3 a) -> ST s () # basicUnsafeReplicate :: Int -> V3 a -> ST s (MVector s (V3 a)) # basicUnsafeRead :: MVector s (V3 a) -> Int -> ST s (V3 a) # basicUnsafeWrite :: MVector s (V3 a) -> Int -> V3 a -> ST s () # basicClear :: MVector s (V3 a) -> ST s () # basicSet :: MVector s (V3 a) -> V3 a -> ST s () # basicUnsafeCopy :: MVector s (V3 a) -> MVector s (V3 a) -> ST s () # basicUnsafeMove :: MVector s (V3 a) -> MVector s (V3 a) -> ST s () # basicUnsafeGrow :: MVector s (V3 a) -> Int -> ST s (MVector s (V3 a)) #
Data a => Data (V3 a)
Instance details Defined in Linear.V3 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 :: forall r r'. (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) #
Storable a => Storable (V3 a)
Instance details Defined in Linear.V3 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 () #
Monoid a => Monoid (V3 a)
Instance details Defined in Linear.V3 Methods mempty :: V3 a # mappend :: V3 a -> V3 a -> V3 a # mconcat :: [V3 a] -> V3 a #
Semigroup a => Semigroup (V3 a)
Instance details Defined in Linear.V3 Methods (<>) :: V3 a -> V3 a -> V3 a # sconcat :: NonEmpty (V3 a) -> V3 a # stimes :: Integral b => b -> V3 a -> V3 a #
Bounded a => Bounded (V3 a)
Instance details Defined in Linear.V3 Methods minBound :: V3 a # maxBound :: V3 a #
Floating a => Floating (V3 a)
Instance details Defined in Linear.V3 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 #
Generic (V3 a)
Instance details Defined in Linear.V3 Associated Types type Rep (V3 a) :: Type -> Type # Methods from :: V3 a -> Rep (V3 a) x # to :: Rep (V3 a) x -> V3 a #
Ix a => Ix (V3 a)
Instance details Defined in Linear.V3 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 #
Num a => Num (V3 a)
Instance details Defined in Linear.V3 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 #
Read a => Read (V3 a)
Instance details Defined in Linear.V3 Methods readsPrec :: Int -> ReadS (V3 a) # readList :: ReadS [V3 a] # readPrec :: ReadPrec (V3 a) # readListPrec :: ReadPrec [V3 a] #
Fractional a => Fractional (V3 a)
Instance details Defined in Linear.V3 Methods (/) :: V3 a -> V3 a -> V3 a # recip :: V3 a -> V3 a # fromRational :: Rational -> V3 a #
Show a => Show (V3 a)
Instance details Defined in Linear.V3 Methods showsPrec :: Int -> V3 a -> ShowS # show :: V3 a -> String # showList :: [V3 a] -> ShowS #
Binary a => Binary (V3 a)
Instance details Defined in Linear.V3 Methods put :: V3 a -> Put # get :: Get (V3 a) # putList :: [V3 a] -> Put #
Serial a => Serial (V3 a)
Instance details Defined in Linear.V3 Methods serialize :: MonadPut m => V3 a -> m () # deserialize :: MonadGet m => m (V3 a) #
Serialize a => Serialize (V3 a)
Instance details Defined in Linear.V3 Methods put :: Putter (V3 a) # get :: Get (V3 a) #
NFData a => NFData (V3 a)
Instance details Defined in Linear.V3 Methods rnf :: V3 a -> () #
Eq a => Eq (V3 a)
Instance details Defined in Linear.V3 Methods (==) :: V3 a -> V3 a -> Bool # (/=) :: V3 a -> V3 a -> Bool #
Ord a => Ord (V3 a)
Instance details Defined in Linear.V3 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 #
Hashable a => Hashable (V3 a)
Instance details Defined in Linear.V3 Methods hashWithSalt :: Int -> V3 a -> Int # hash :: V3 a -> Int #
Ixed (V3 a)
Instance details Defined in Linear.V3 Methods ix :: Index (V3 a) -> Traversal' (V3 a) (IxValue (V3 a)) #
Epsilon a => Epsilon (V3 a)
Instance details Defined in Linear.V3 Methods nearZero :: V3 a -> Bool #
Random a => Random (V3 a)
Instance details Defined in Linear.V3 Methods randomR :: RandomGen g => (V3 a, V3 a) -> g -> (V3 a, g) # random :: RandomGen g => g -> (V3 a, g) # randomRs :: RandomGen g => (V3 a, V3 a) -> g -> [V3 a] # randoms :: RandomGen g => g -> [V3 a] #
Unbox a => Unbox (V3 a)
Instance details Defined in Linear.V3
Num a => Rotation (M33 a) a Source #
Instance details Defined in SpatialMathT Methods compose :: Rot f1 f2 (M33 a) -> Rot f2 f3 (M33 a) -> Rot f1 f3 (M33 a) Source # rot :: Rot f1 f2 (M33 a) -> V3T f1 a -> V3T f2 a Source # rot' :: Rot f1 f2 (M33 a) -> V3T f2 a -> V3T f1 a Source # toDcm :: Rot f1 f2 (M33 a) -> Rot f1 f2 (M33 a) Source # transpose :: Rot f1 f2 (M33 a) -> Rot f2 f1 (M33 a) Source #
FoldableWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods ifoldMap :: Monoid m => (E V3 -> a -> m) -> V3 a -> m # ifoldMap' :: Monoid m => (E V3 -> a -> m) -> V3 a -> m # 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 #
FunctorWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods imap :: (E V3 -> a -> b) -> V3 a -> V3 b #
TraversableWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods itraverse :: Applicative f => (E V3 -> a -> f b) -> V3 a -> f (V3 b) #
Lift a => Lift (V3 a :: Type)
Instance details Defined in Linear.V3 Methods lift :: Quote m => V3 a -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => V3 a -> Code m (V3 a) #
Each (V3 a) (V3 b) a b
Instance details Defined in Linear.V3 Methods each :: Traversal (V3 a) (V3 b) a b #
Field1 (V3 a) (V3 a) a a
Instance details Defined in Linear.V3 Methods _1 :: Lens (V3 a) (V3 a) a a #
Field2 (V3 a) (V3 a) a a
Instance details Defined in Linear.V3 Methods _2 :: Lens (V3 a) (V3 a) a a #
Field3 (V3 a) (V3 a) a a
Instance details Defined in Linear.V3 Methods _3 :: Lens (V3 a) (V3 a) a a #
type Rep V3
Instance details Defined in Linear.V3 type Rep V3 = E V3
type Size V3
Instance details Defined in Linear.V3 type Size V3 = 3
type Rep1 V3
Instance details Defined in Linear.V3 type Rep1 V3 = D1 ('MetaData "V3" "Linear.V3" "linear-1.22-1g9bkrZLtgG1Kif13VBuPE" 'False) (C1 ('MetaCons "V3" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1)))
data MVector s (V3 a)
Instance details Defined in Linear.V3 data MVector s (V3 a) = MV_V3 !Int !(MVector s a)
type Rep (V3 a)
Instance details Defined in Linear.V3 type Rep (V3 a) = D1 ('MetaData "V3" "Linear.V3" "linear-1.22-1g9bkrZLtgG1Kif13VBuPE" 'False) (C1 ('MetaCons "V3" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a))))
type Index (V3 a)
Instance details Defined in Linear.V3 type Index (V3 a) = E V3
type IxValue (V3 a)
Instance details Defined in Linear.V3 type IxValue (V3 a) = a
data Vector (V3 a)
Instance details Defined in Linear.V3 data Vector (V3 a) = V_V3 !Int !(Vector a)

data Quaternion a #

Quaternions

Constructors

Quaternion !a !(V3 a)

Instances

Instances details

Representable Quaternion
Instance details Defined in Linear.Quaternion Associated Types type Rep Quaternion # Methods tabulate :: (Rep Quaternion -> a) -> Quaternion a # index :: Quaternion a -> Rep Quaternion -> a #
MonadFix Quaternion
Instance details Defined in Linear.Quaternion Methods mfix :: (a -> Quaternion a) -> Quaternion a #
MonadZip Quaternion
Instance details Defined in Linear.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) #
Foldable Quaternion
Instance details Defined in Linear.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 #
Eq1 Quaternion
Instance details Defined in Linear.Quaternion Methods liftEq :: (a -> b -> Bool) -> Quaternion a -> Quaternion b -> Bool #
Ord1 Quaternion
Instance details Defined in Linear.Quaternion Methods liftCompare :: (a -> b -> Ordering) -> Quaternion a -> Quaternion b -> Ordering #
Read1 Quaternion
Instance details Defined in Linear.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
Instance details Defined in Linear.Quaternion Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Quaternion a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Quaternion a] -> ShowS #
Traversable Quaternion
Instance details Defined in Linear.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) #
Applicative Quaternion
Instance details Defined in Linear.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 #
Functor Quaternion
Instance details Defined in Linear.Quaternion Methods fmap :: (a -> b) -> Quaternion a -> Quaternion b # (<$) :: a -> Quaternion b -> Quaternion a #
Monad Quaternion
Instance details Defined in Linear.Quaternion Methods (>>=) :: Quaternion a -> (a -> Quaternion b) -> Quaternion b # (>>) :: Quaternion a -> Quaternion b -> Quaternion b # return :: a -> Quaternion a #
Serial1 Quaternion
Instance details Defined in Linear.Quaternion Methods serializeWith :: MonadPut m => (a -> m ()) -> Quaternion a -> m () # deserializeWith :: MonadGet m => m a -> m (Quaternion a) #
Distributive Quaternion
Instance details Defined in Linear.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) #
Hashable1 Quaternion
Instance details Defined in Linear.Quaternion Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> Quaternion a -> Int #
Metric Quaternion
Instance details Defined in Linear.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 #
Complicated Quaternion
Instance details Defined in Linear.Quaternion Methods _e :: Lens' (Quaternion a) a # _i :: Lens' (Quaternion a) a #
Hamiltonian Quaternion
Instance details Defined in Linear.Quaternion Methods _j :: Lens' (Quaternion a) a # _k :: Lens' (Quaternion a) a # _ijk :: Lens' (Quaternion a) (V3 a) #
Trace Quaternion
Instance details Defined in Linear.Trace Methods trace :: Num a => Quaternion (Quaternion a) -> a # diagonal :: Quaternion (Quaternion a) -> Quaternion a #
Finite Quaternion
Instance details Defined in Linear.Quaternion Associated Types type Size Quaternion :: Nat # Methods toV :: Quaternion a -> V (Size Quaternion) a # fromV :: V (Size Quaternion) a -> Quaternion a #
R1 Quaternion
Instance details Defined in Linear.Quaternion Methods _x :: Lens' (Quaternion a) a #
R2 Quaternion
Instance details Defined in Linear.Quaternion Methods _y :: Lens' (Quaternion a) a # _xy :: Lens' (Quaternion a) (V2 a) #
R3 Quaternion
Instance details Defined in Linear.Quaternion Methods _z :: Lens' (Quaternion a) a # _xyz :: Lens' (Quaternion a) (V3 a) #
R4 Quaternion
Instance details Defined in Linear.Quaternion Methods _w :: Lens' (Quaternion a) a # _xyzw :: Lens' (Quaternion a) (V4 a) #
Additive Quaternion
Instance details Defined in Linear.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
Instance details Defined in Linear.Quaternion Methods (<.>) :: Quaternion (a -> b) -> Quaternion a -> Quaternion b # (.>) :: Quaternion a -> Quaternion b -> Quaternion b # (<.) :: Quaternion a -> Quaternion b -> Quaternion a # liftF2 :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c #
Bind Quaternion
Instance details Defined in Linear.Quaternion Methods (>>-) :: Quaternion a -> (a -> Quaternion b) -> Quaternion b # join :: Quaternion (Quaternion a) -> Quaternion a #
Generic1 Quaternion
Instance details Defined in Linear.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 #
(Num r, TrivialConjugate r) => Algebra r (E Quaternion)
Instance details Defined in Linear.Algebra Methods mult :: (E Quaternion -> E Quaternion -> r) -> E Quaternion -> r # unital :: r -> E Quaternion -> r #
(Num r, TrivialConjugate r) => Coalgebra r (E Quaternion)
Instance details Defined in Linear.Algebra Methods comult :: (E Quaternion -> r) -> E Quaternion -> E Quaternion -> r # counital :: (E Quaternion -> r) -> r #
Unbox a => Vector Vector (Quaternion a)
Instance details Defined in Linear.Quaternion Methods basicUnsafeFreeze :: Mutable Vector s (Quaternion a) -> ST s (Vector (Quaternion a)) # basicUnsafeThaw :: Vector (Quaternion a) -> ST s (Mutable Vector s (Quaternion a)) # basicLength :: Vector (Quaternion a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Quaternion a) -> Vector (Quaternion a) # basicUnsafeIndexM :: Vector (Quaternion a) -> Int -> Box (Quaternion a) # basicUnsafeCopy :: Mutable Vector s (Quaternion a) -> Vector (Quaternion a) -> ST s () # elemseq :: Vector (Quaternion a) -> Quaternion a -> b -> b #
Unbox a => MVector MVector (Quaternion a)
Instance details Defined in Linear.Quaternion 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 :: Int -> ST s (MVector s (Quaternion a)) # basicInitialize :: MVector s (Quaternion a) -> ST s () # basicUnsafeReplicate :: Int -> Quaternion a -> ST s (MVector s (Quaternion a)) # basicUnsafeRead :: MVector s (Quaternion a) -> Int -> ST s (Quaternion a) # basicUnsafeWrite :: MVector s (Quaternion a) -> Int -> Quaternion a -> ST s () # basicClear :: MVector s (Quaternion a) -> ST s () # basicSet :: MVector s (Quaternion a) -> Quaternion a -> ST s () # basicUnsafeCopy :: MVector s (Quaternion a) -> MVector s (Quaternion a) -> ST s () # basicUnsafeMove :: MVector s (Quaternion a) -> MVector s (Quaternion a) -> ST s () # basicUnsafeGrow :: MVector s (Quaternion a) -> Int -> ST s (MVector s (Quaternion a)) #
Data a => Data (Quaternion a)
Instance details Defined in Linear.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) #
Storable a => Storable (Quaternion a)
Instance details Defined in Linear.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 () #
Monoid a => Monoid (Quaternion a)
Instance details Defined in Linear.Quaternion Methods mempty :: Quaternion a # mappend :: Quaternion a -> Quaternion a -> Quaternion a # mconcat :: [Quaternion a] -> Quaternion a #
Semigroup a => Semigroup (Quaternion a)
Instance details Defined in Linear.Quaternion Methods (<>) :: Quaternion a -> Quaternion a -> Quaternion a # sconcat :: NonEmpty (Quaternion a) -> Quaternion a # stimes :: Integral b => b -> Quaternion a -> Quaternion a #
RealFloat a => Floating (Quaternion a)
Instance details Defined in Linear.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 #
Generic (Quaternion a)
Instance details Defined in Linear.Quaternion Associated Types type Rep (Quaternion a) :: Type -> Type # Methods from :: Quaternion a -> Rep (Quaternion a) x # to :: Rep (Quaternion a) x -> Quaternion a #
Ix a => Ix (Quaternion a)
Instance details Defined in Linear.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 #
RealFloat a => Num (Quaternion a)
Instance details Defined in Linear.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 #
Read a => Read (Quaternion a)
Instance details Defined in Linear.Quaternion Methods readsPrec :: Int -> ReadS (Quaternion a) # readList :: ReadS [Quaternion a] # readPrec :: ReadPrec (Quaternion a) # readListPrec :: ReadPrec [Quaternion a] #
RealFloat a => Fractional (Quaternion a)
Instance details Defined in Linear.Quaternion Methods (/) :: Quaternion a -> Quaternion a -> Quaternion a # recip :: Quaternion a -> Quaternion a # fromRational :: Rational -> Quaternion a #
Show a => Show (Quaternion a)
Instance details Defined in Linear.Quaternion Methods showsPrec :: Int -> Quaternion a -> ShowS # show :: Quaternion a -> String # showList :: [Quaternion a] -> ShowS #
Binary a => Binary (Quaternion a)
Instance details Defined in Linear.Quaternion Methods put :: Quaternion a -> Put # get :: Get (Quaternion a) # putList :: [Quaternion a] -> Put #
Serial a => Serial (Quaternion a)
Instance details Defined in Linear.Quaternion Methods serialize :: MonadPut m => Quaternion a -> m () # deserialize :: MonadGet m => m (Quaternion a) #
Serialize a => Serialize (Quaternion a)
Instance details Defined in Linear.Quaternion Methods put :: Putter (Quaternion a) # get :: Get (Quaternion a) #
NFData a => NFData (Quaternion a)
Instance details Defined in Linear.Quaternion Methods rnf :: Quaternion a -> () #
Eq a => Eq (Quaternion a)
Instance details Defined in Linear.Quaternion Methods (==) :: Quaternion a -> Quaternion a -> Bool # (/=) :: Quaternion a -> Quaternion a -> Bool #
Ord a => Ord (Quaternion a)
Instance details Defined in Linear.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 #
Hashable a => Hashable (Quaternion a)
Instance details Defined in Linear.Quaternion Methods hashWithSalt :: Int -> Quaternion a -> Int # hash :: Quaternion a -> Int #
Ixed (Quaternion a)
Instance details Defined in Linear.Quaternion Methods ix :: Index (Quaternion a) -> Traversal' (Quaternion a) (IxValue (Quaternion a)) #
(Conjugate a, RealFloat a) => Conjugate (Quaternion a)
Instance details Defined in Linear.Quaternion Methods conjugate :: Quaternion a -> Quaternion a #
(RealFloat a, Epsilon a) => Epsilon (Quaternion a)
Instance details Defined in Linear.Quaternion Methods nearZero :: Quaternion a -> Bool #
Random a => Random (Quaternion a)
Instance details Defined in Linear.Quaternion Methods randomR :: RandomGen g => (Quaternion a, Quaternion a) -> g -> (Quaternion a, g) # random :: RandomGen g => g -> (Quaternion a, g) # randomRs :: RandomGen g => (Quaternion a, Quaternion a) -> g -> [Quaternion a] # randoms :: RandomGen g => g -> [Quaternion a] #
Unbox a => Unbox (Quaternion a)
Instance details Defined in Linear.Quaternion
Num a => Rotation (Quaternion a) a Source #
Instance details Defined in SpatialMathT 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 # toDcm :: Rot f1 f2 (Quaternion a) -> Rot f1 f2 (M33 a) Source # transpose :: Rot f1 f2 (Quaternion a) -> Rot f2 f1 (Quaternion a) Source #
FoldableWithIndex (E Quaternion) Quaternion
Instance details Defined in Linear.Quaternion Methods ifoldMap :: Monoid m => (E Quaternion -> a -> m) -> Quaternion a -> m # ifoldMap' :: Monoid m => (E Quaternion -> a -> m) -> Quaternion a -> m # 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 #
FunctorWithIndex (E Quaternion) Quaternion
Instance details Defined in Linear.Quaternion Methods imap :: (E Quaternion -> a -> b) -> Quaternion a -> Quaternion b #
TraversableWithIndex (E Quaternion) Quaternion
Instance details Defined in Linear.Quaternion Methods itraverse :: Applicative f => (E Quaternion -> a -> f b) -> Quaternion a -> f (Quaternion b) #
Lift a => Lift (Quaternion a :: Type)
Instance details Defined in Linear.Quaternion Methods lift :: Quote m => Quaternion a -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Quaternion a -> Code m (Quaternion a) #
Each (Quaternion a) (Quaternion b) a b
Instance details Defined in Linear.Quaternion Methods each :: Traversal (Quaternion a) (Quaternion b) a b #
Field1 (Quaternion a) (Quaternion a) a a
Instance details Defined in Linear.Quaternion Methods _1 :: Lens (Quaternion a) (Quaternion a) a a #
Field2 (Quaternion a) (Quaternion a) a a
Instance details Defined in Linear.Quaternion Methods _2 :: Lens (Quaternion a) (Quaternion a) a a #
Field3 (Quaternion a) (Quaternion a) a a
Instance details Defined in Linear.Quaternion Methods _3 :: Lens (Quaternion a) (Quaternion a) a a #
Field4 (Quaternion a) (Quaternion a) a a
Instance details Defined in Linear.Quaternion Methods _4 :: Lens (Quaternion a) (Quaternion a) a a #
type Rep Quaternion
Instance details Defined in Linear.Quaternion type Rep Quaternion = E Quaternion
type Size Quaternion
Instance details Defined in Linear.Quaternion type Size Quaternion = 4
type Rep1 Quaternion
Instance details Defined in Linear.Quaternion type Rep1 Quaternion = D1 ('MetaData "Quaternion" "Linear.Quaternion" "linear-1.22-1g9bkrZLtgG1Kif13VBuPE" '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)))
data MVector s (Quaternion a)
Instance details Defined in Linear.Quaternion data MVector s (Quaternion a) = MV_Quaternion !Int (MVector s a)
type Rep (Quaternion a)
Instance details Defined in Linear.Quaternion type Rep (Quaternion a) = D1 ('MetaData "Quaternion" "Linear.Quaternion" "linear-1.22-1g9bkrZLtgG1Kif13VBuPE" '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 Index (Quaternion a)
Instance details Defined in Linear.Quaternion type Index (Quaternion a) = E Quaternion
type IxValue (Quaternion a)
Instance details Defined in Linear.Quaternion type IxValue (Quaternion a) = a
data Vector (Quaternion a)
Instance details Defined in Linear.Quaternion data Vector (Quaternion a) = V_Quaternion !Int (Vector a)