Safe Haskell	None
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
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
unsafeEuler321OfQuat :: ArcTan2 a => Quaternion a -> Euler a
euler321OfDcm :: (Ord a, ArcTan2 a) => M33 a -> Euler a
unsafeEuler321OfDcm :: ArcTan2 a => M33 a -> Euler a
quatOfEuler321 :: Floating 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, Ord a) => M33 a -> Quaternion a
quatOfDcmB2A :: (Floating a, Ord 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 #

3-2-1 Euler angle rotation sequence

Constructors

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

Instances

Functor Euler #
Instance details Defined in Types Methods fmap :: (a -> b) -> Euler a -> Euler b # (<$) :: a -> Euler b -> Euler a #
Applicative Euler #
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 #
Foldable Euler #
Instance details Defined in Types 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 #
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) #
(ArcTan2 a, Floating a, Ord a) => Rotation Euler a #
Instance details Defined in SpatialMathT Methods compose :: Rot f1 f2 Euler a -> Rot f2 f3 Euler a -> Rot f1 f3 Euler a # rot :: Rot f1 f2 Euler a -> V3T f1 a -> V3T f2 a # rot' :: Rot f1 f2 Euler a -> V3T f2 a -> V3T f1 a # transpose :: Rot f1 f2 Euler a -> Rot f2 f1 Euler a # identity :: Rot f1 f2 Euler a #
Eq a => Eq (Euler a) #
Instance details Defined in Types Methods (==) :: Euler a -> Euler a -> Bool # (/=) :: Euler a -> Euler a -> Bool #
Data a => Data (Euler a) #
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 :: (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) #
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 #
Show a => Show (Euler a) #
Instance details Defined in Types Methods showsPrec :: Int -> Euler a -> ShowS # show :: Euler a -> String # showList :: [Euler a] -> ShowS #
Generic (Euler a) #
Instance details Defined in Types 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) #
Instance details Defined in Types Methods put :: Euler a -> Put # get :: Get (Euler a) # putList :: [Euler a] -> Put #
Serialize a => Serialize (Euler a) #
Instance details Defined in Types Methods put :: Putter (Euler a) # get :: Get (Euler a) #
Generic1 Euler #
Instance details Defined in Types Associated Types type Rep1 Euler :: k -> * # Methods from1 :: Euler a -> Rep1 Euler a # to1 :: Rep1 Euler a -> Euler a #
type Rep (Euler a) #
Instance details Defined in Types type Rep (Euler a) = D1 (MetaData "Euler" "Types" "spatial-math-0.5.0.1-BCf68EO2cdvEFP2DMwbIRL" 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))))
type Rep1 Euler #
Instance details Defined in Types type Rep1 Euler = D1 (MetaData "Euler" "Types" "spatial-math-0.5.0.1-BCf68EO2cdvEFP2DMwbIRL" 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)))

class Floating a => ArcTan2 a where #

doesn't require RealFloat, used for overloading symbolics

Minimal complete definition

arctan2

Methods

arctan2 :: a -> a -> a #

arctan2 y x computes the arctangent from two arguments. The Double and Float instances call out to a sufficiently recent version of libm to compute this.

The following test cases are the full set of recommended function properties specified for function atan2Pi() on page 45 of the IEEE Std 754-2008 document.

>>> arctan2 0 (-0) :: Double
3.141592653589793
>>> arctan2 (-0) (-0) :: Double
-3.141592653589793
>>> arctan2 0 0 :: Double
0.0
>>> arctan2 (-0) 0 :: Double
-0.0

\x -> x < 0 ==> arctan2 (-0) x == (-pi :: Double)

\x -> x < 0 ==> arctan2 0 x == (pi :: Double)

\x -> x > 0 ==> arctan2 (-0) x == (-0 :: Double)

\x -> x > 0 ==> arctan2 0 x == (0 :: Double)

\y -> y < 0 ==> arctan2 y (-0) == (-pi / 2 :: Double)

\y -> y > 0 ==> arctan2 y 0 == (pi / 2 :: Double)

\y -> y > 0 && not (isNaN y || isInfinite y) ==> arctan2 y (negate $ 1/0) == (pi :: Double)

\y -> y < 0 && not (isNaN y || isInfinite y) ==> arctan2 y (negate $ 1/0) == (-pi :: Double)

\y -> y > 0 && not (isNaN y || isInfinite y) ==> arctan2 y (1/0) == (0 :: Double)

\y -> y < 0 && not (isNaN y || isInfinite y) ==> arctan2 y (1/0) == (-0 :: Double)

\x -> not (isNaN x || isInfinite x) ==> arctan2 (negate $ 1/0) x == (-pi/2 :: Double)

\x -> not (isNaN x || isInfinite x) ==> arctan2 (1/0) x == (pi/2 :: Double)

>>> arctan2 neginf neginf :: Double
-2.356194490192345
>>> arctan2 inf neginf :: Double
2.356194490192345
>>> arctan2 neginf inf :: Double
-0.7853981633974483
>>> arctan2 inf inf :: Double
0.7853981633974483

Instances

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

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

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 #

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 #

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 #

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 #

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 #

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 #

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 #

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 #

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 #

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

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, Ord a) => M33 a -> Quaternion a #

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 0.7071067811865476 (V3 0.0 0.0 0.7071067811865475)

>>> let s = sqrt(2)/2 in quatOfDcm $ V3 (V3 s s 0) (V3 (-s) s 0) (V3 0 0 1)
Quaternion 0.9238795325112867 (V3 0.0 0.0 0.3826834323650898)

quatOfDcmB2A :: (Floating a, Ord a) => M33 a -> Quaternion a #

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

vec_b = R_a2b * vec_a

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

vec_a = R_a2b^T * vec_b

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

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 #

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

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

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
Instance details Defined in Linear.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
Instance details Defined in Linear.V3 Methods fmap :: (a -> b) -> V3 a -> V3 b # (<$) :: a -> V3 b -> V3 a #
MonadFix V3
Instance details Defined in Linear.V3 Methods mfix :: (a -> V3 a) -> 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 #
Foldable V3
Instance details Defined in Linear.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
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) #
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) #
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 #
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 #
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) #
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) #
Hashable1 V3
Instance details Defined in Linear.V3 Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> V3 a -> Int #
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 #
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) #
Trace V3
Instance details Defined in Linear.Trace Methods trace :: Num a => V3 (V3 a) -> a # diagonal :: V3 (V3 a) -> V3 a #
R3 V3
Instance details Defined in Linear.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
Instance details Defined in Linear.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
Instance details Defined in Linear.V3 Methods _x :: Functor f => (a -> f a) -> V3 a -> f (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 #
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 #
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 #
Foldable1 V3
Instance details Defined in Linear.V3 Methods fold1 :: Semigroup m => V3 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V3 a -> m # toNonEmpty :: V3 a -> NonEmpty a #
Bind V3
Instance details Defined in Linear.V3 Methods (>>-) :: V3 a -> (a -> V3 b) -> V3 b # join :: V3 (V3 a) -> V3 a #
Unbox a => Vector Vector (V3 a)
Instance details Defined in Linear.V3 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 #
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 => 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 :: 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)
Instance details Defined in Linear.V3 Methods minBound :: V3 a # maxBound :: V3 a #
Eq a => Eq (V3 a)
Instance details Defined in Linear.V3 Methods (==) :: V3 a -> V3 a -> Bool # (/=) :: V3 a -> V3 a -> Bool #
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 #
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 #
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 :: (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)
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 #
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 #
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] #
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 #
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
Generic (V3 a)
Instance details Defined in Linear.V3 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)
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 () #
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 -> () #
Hashable a => Hashable (V3 a)
Instance details Defined in Linear.V3 Methods hashWithSalt :: Int -> V3 a -> Int # hash :: V3 a -> Int #
Unbox a => Unbox (V3 a)
Instance details Defined in Linear.V3
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 #
Generic1 V3
Instance details Defined in Linear.V3 Associated Types type Rep1 V3 :: k -> * # Methods from1 :: V3 a -> Rep1 V3 a # to1 :: Rep1 V3 a -> V3 a #
FunctorWithIndex (E V3) V3
Instance details Defined in Linear.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
Instance details Defined in Linear.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
Instance details Defined in Linear.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
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 #
Num a => Rotation (V3 :. V3) a #
Instance details Defined in SpatialMathT Methods compose :: Rot f1 f2 (V3 :. V3) a -> Rot f2 f3 (V3 :. V3) a -> Rot f1 f3 (V3 :. V3) a # rot :: Rot f1 f2 (V3 :. V3) a -> V3T f1 a -> V3T f2 a # rot' :: Rot f1 f2 (V3 :. V3) a -> V3T f2 a -> V3T f1 a # transpose :: Rot f1 f2 (V3 :. V3) a -> Rot f2 f1 (V3 :. V3) a # identity :: Rot f1 f2 (V3 :. V3) 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
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-1.20.8-71KE8HaDWJk9VTUReACBrP" 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))))
data Vector (V3 a)
Instance details Defined in Linear.V3 data Vector (V3 a) = V_V3 !Int !(Vector 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
type Rep1 V3
Instance details Defined in Linear.V3 type Rep1 V3 = D1 (MetaData "V3" "Linear.V3" "linear-1.20.8-71KE8HaDWJk9VTUReACBrP" 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 Quaternion a #

Quaternions

Constructors

Quaternion !a !(V3 a)

Instances

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 # fail :: String -> Quaternion a #
Functor Quaternion
Instance details Defined in Linear.Quaternion Methods fmap :: (a -> b) -> Quaternion a -> Quaternion b # (<$) :: a -> Quaternion b -> Quaternion a #
MonadFix Quaternion
Instance details Defined in Linear.Quaternion Methods mfix :: (a -> Quaternion a) -> 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 #
Foldable Quaternion
Instance details Defined in Linear.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
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) #
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) #
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 #
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 #
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) #
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) #
Hashable1 Quaternion
Instance details Defined in Linear.Quaternion Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> Quaternion a -> Int #
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 #
Trace Quaternion
Instance details Defined in Linear.Trace Methods trace :: Num a => Quaternion (Quaternion a) -> a # diagonal :: Quaternion (Quaternion a) -> Quaternion a #
Complicated Quaternion
Instance details Defined in Linear.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
Instance details Defined in Linear.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) #
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 #
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 #
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 #
Bind Quaternion
Instance details Defined in Linear.Quaternion Methods (>>-) :: Quaternion a -> (a -> Quaternion b) -> Quaternion b # join :: Quaternion (Quaternion a) -> Quaternion a #
Num a => Rotation Quaternion a #
Instance details Defined in SpatialMathT Methods compose :: Rot f1 f2 Quaternion a -> Rot f2 f3 Quaternion a -> Rot f1 f3 Quaternion a # rot :: Rot f1 f2 Quaternion a -> V3T f1 a -> V3T f2 a # rot' :: Rot f1 f2 Quaternion a -> V3T f2 a -> V3T f1 a # transpose :: Rot f1 f2 Quaternion a -> Rot f2 f1 Quaternion a # identity :: Rot f1 f2 Quaternion a #
Unbox a => Vector Vector (Quaternion a)
Instance details Defined in Linear.Quaternion 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 #
(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 => 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 :: 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)
Instance details Defined in Linear.Quaternion Methods (==) :: Quaternion a -> Quaternion a -> Bool # (/=) :: Quaternion a -> Quaternion a -> Bool #
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 #
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 #
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 :: (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)
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 #
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 #
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] #
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 #
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
Generic (Quaternion a)
Instance details Defined in Linear.Quaternion 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)
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 () #
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 -> () #
Hashable a => Hashable (Quaternion a)
Instance details Defined in Linear.Quaternion Methods hashWithSalt :: Int -> Quaternion a -> Int # hash :: Quaternion a -> Int #
Unbox a => Unbox (Quaternion a)
Instance details Defined in Linear.Quaternion
Ixed (Quaternion a)
Instance details Defined in Linear.Quaternion Methods ix :: Index (Quaternion a) -> Traversal' (Quaternion a) (IxValue (Quaternion a)) #
(RealFloat a, Epsilon a) => Epsilon (Quaternion a)
Instance details Defined in Linear.Quaternion Methods nearZero :: Quaternion a -> Bool #
(Conjugate a, RealFloat a) => Conjugate (Quaternion a)
Instance details Defined in Linear.Quaternion Methods conjugate :: Quaternion a -> Quaternion a #
Generic1 Quaternion
Instance details Defined in Linear.Quaternion Associated Types type Rep1 Quaternion :: k -> * # Methods from1 :: Quaternion a -> Rep1 Quaternion a # to1 :: Rep1 Quaternion a -> Quaternion a #
FunctorWithIndex (E Quaternion) Quaternion
Instance details Defined in Linear.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
Instance details Defined in Linear.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
Instance details Defined in Linear.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
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
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-1.20.8-71KE8HaDWJk9VTUReACBrP" False) (C1 (MetaCons "Quaternion" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) SourceUnpack SourceStrict DecidedUnpack) (Rec0 (V3 a))))
data Vector (Quaternion a)
Instance details Defined in Linear.Quaternion data Vector (Quaternion a) = V_Quaternion !Int (Vector 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
type Rep1 Quaternion
Instance details Defined in Linear.Quaternion type Rep1 Quaternion = D1 (MetaData "Quaternion" "Linear.Quaternion" "linear-1.20.8-71KE8HaDWJk9VTUReACBrP" False) (C1 (MetaCons "Quaternion" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1 :*: S1 (MetaSel (Nothing :: Maybe Symbol) SourceUnpack SourceStrict DecidedUnpack) (Rec1 V3)))