SpatialMath

Documentation

data Euler a

3-2-1 Euler angle rotation sequence

Constructors

Euler

Fields

• eYaw :: a
• ePitch :: a
• eRoll :: a

Instances

Foldable Euler

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

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

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

Defined in Types

Methods

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

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

Generic1 Euler

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)

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)

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)

Defined in Types

Methods

showsPrec :: Int -> Euler a -> ShowS

show :: Euler a -> String

showList :: [Euler a] -> ShowS

Binary a => Binary (Euler a)

Defined in Types

Methods

put :: Euler a -> Put

get :: Get (Euler a)

putList :: [Euler a] -> Put

Serialize a => Serialize (Euler a)

Defined in Types

Methods

put :: Putter (Euler a)

get :: Get (Euler a)

Eq a => Eq (Euler a)

Defined in Types

Methods

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

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

Ord a => Ord (Euler a)

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

Defined in Types

type Rep1 Euler = D1 ('MetaData "Euler" "Types" "SpatialMath-0.2.7.1-FJ8akJ7FKV75UBVB9UHiZk" '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)

Defined in Types

type Rep (Euler a) = D1 ('MetaData "Euler" "Types" "SpatialMath-0.2.7.1-FJ8akJ7FKV75UBVB9UHiZk" '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

doesn't require RealFloat, used for overloading symbolics

Methods

arctan2 :: a -> a -> a

Instances

ArcTan2 Double

Defined in SpatialMath

Methods

arctan2 :: Double -> Double -> Double

ArcTan2 Float

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}

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

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

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 => 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 0.7071067811865477 (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

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

Representable V3

Defined in Linear.V3

Associated Types

type Rep V3

Methods

tabulate :: (Rep V3 -> a) -> V3 a

index :: V3 a -> Rep V3 -> a

MonadFix V3

Defined in Linear.V3

Methods

mfix :: (a -> V3 a) -> V3 a

MonadZip V3

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

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

Defined in Linear.V3

Methods

liftEq :: (a -> b -> Bool) -> V3 a -> V3 b -> Bool

Ord1 V3

Defined in Linear.V3

Methods

liftCompare :: (a -> b -> Ordering) -> V3 a -> V3 b -> Ordering

Read1 V3

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

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

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

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

Defined in Linear.V3

Methods

fmap :: (a -> b) -> V3 a -> V3 b

(<$) :: a -> V3 b -> V3 a

Monad V3

Defined in Linear.V3

Methods

(>>=) :: V3 a -> (a -> V3 b) -> V3 b

(>>) :: V3 a -> V3 b -> V3 b

return :: a -> V3 a

Serial1 V3

Defined in Linear.V3

Methods

serializeWith :: MonadPut m => (a -> m ()) -> V3 a -> m ()

deserializeWith :: MonadGet m => m a -> m (V3 a)

Distributive V3

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

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

Defined in Linear.V3

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> V3 a -> Int

Metric V3

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

Defined in Linear.Trace

Methods

trace :: Num a => V3 (V3 a) -> a

diagonal :: V3 (V3 a) -> V3 a

Finite V3

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

Defined in Linear.V3

Methods

_x :: Lens' (V3 a) a

R2 V3

Defined in Linear.V3

Methods

_y :: Lens' (V3 a) a

_xy :: Lens' (V3 a) (V2 a)

R3 V3

Defined in Linear.V3

Methods

_z :: Lens' (V3 a) a

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

Additive V3

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

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

Defined in Linear.V3

Methods

(>>-) :: V3 a -> (a -> V3 b) -> V3 b

join :: V3 (V3 a) -> V3 a

Traversable1 V3

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

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)

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)

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)

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)

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)

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)

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)

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)

Defined in Linear.V3

Methods

minBound :: V3 a

maxBound :: V3 a

Floating a => Floating (V3 a)

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)

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)

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)

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)

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)

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)

Defined in Linear.V3

Methods

showsPrec :: Int -> V3 a -> ShowS

show :: V3 a -> String

showList :: [V3 a] -> ShowS

Binary a => Binary (V3 a)

Defined in Linear.V3

Methods

put :: V3 a -> Put

get :: Get (V3 a)

putList :: [V3 a] -> Put

Serial a => Serial (V3 a)

Defined in Linear.V3

Methods

serialize :: MonadPut m => V3 a -> m ()

deserialize :: MonadGet m => m (V3 a)

Serialize a => Serialize (V3 a)

Defined in Linear.V3

Methods

put :: Putter (V3 a)

get :: Get (V3 a)

NFData a => NFData (V3 a)

Defined in Linear.V3

Methods

rnf :: V3 a -> ()

Eq a => Eq (V3 a)

Defined in Linear.V3

Methods

(==) :: V3 a -> V3 a -> Bool

(/=) :: V3 a -> V3 a -> Bool

Ord a => Ord (V3 a)

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)

Defined in Linear.V3

Methods

hashWithSalt :: Int -> V3 a -> Int

hash :: V3 a -> Int

Ixed (V3 a)

Defined in Linear.V3

Methods

ix :: Index (V3 a) -> Traversal' (V3 a) (IxValue (V3 a))

Epsilon a => Epsilon (V3 a)

Defined in Linear.V3

Methods

nearZero :: V3 a -> Bool

Random a => Random (V3 a)

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)

Defined in Linear.V3

Num a => Rotation (M33 a) a

Defined in SpatialMathT

Methods

compose :: Rot f1 f2 (M33 a) -> Rot f2 f3 (M33 a) -> Rot f1 f3 (M33 a)

rot :: Rot f1 f2 (M33 a) -> V3T f1 a -> V3T f2 a

rot' :: Rot f1 f2 (M33 a) -> V3T f2 a -> V3T f1 a

toDcm :: Rot f1 f2 (M33 a) -> Rot f1 f2 (M33 a)

transpose :: Rot f1 f2 (M33 a) -> Rot f2 f1 (M33 a)

FoldableWithIndex (E V3) V3

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

Defined in Linear.V3

Methods

imap :: (E V3 -> a -> b) -> V3 a -> V3 b

TraversableWithIndex (E V3) V3

Defined in Linear.V3

Methods

itraverse :: Applicative f => (E V3 -> a -> f b) -> V3 a -> f (V3 b)

Lift a => Lift (V3 a :: Type)

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

Defined in Linear.V3

Methods

each :: Traversal (V3 a) (V3 b) a b

Field1 (V3 a) (V3 a) a a

Defined in Linear.V3

Methods

_1 :: Lens (V3 a) (V3 a) a a

Field2 (V3 a) (V3 a) a a

Defined in Linear.V3

Methods

_2 :: Lens (V3 a) (V3 a) a a

Field3 (V3 a) (V3 a) a a

Defined in Linear.V3

Methods

_3 :: Lens (V3 a) (V3 a) a a

type Rep V3

Defined in Linear.V3

type Rep V3 = E V3

type Size V3

Defined in Linear.V3

type Size V3 = 3

type Rep1 V3

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)

Defined in Linear.V3

data MVector s (V3 a) = MV_V3 !Int !(MVector s a)

type Rep (V3 a)

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)

Defined in Linear.V3

type Index (V3 a) = E V3

type IxValue (V3 a)

Defined in Linear.V3

type IxValue (V3 a) = a

data Vector (V3 a)

Defined in Linear.V3

data Vector (V3 a) = V_V3 !Int !(Vector a)

data Quaternion a

Quaternions

Constructors

Quaternion !a !(V3 a)

Instances

Representable Quaternion

Defined in Linear.Quaternion

Associated Types

type Rep Quaternion

Methods

tabulate :: (Rep Quaternion -> a) -> Quaternion a

index :: Quaternion a -> Rep Quaternion -> a

MonadFix Quaternion

Defined in Linear.Quaternion

Methods

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

MonadZip Quaternion

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

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

Defined in Linear.Quaternion

Methods

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

Ord1 Quaternion

Defined in Linear.Quaternion

Methods

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

Read1 Quaternion

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

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

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

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

Defined in Linear.Quaternion

Methods

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

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

Monad Quaternion

Defined in Linear.Quaternion

Methods

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

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

return :: a -> Quaternion a

Serial1 Quaternion

Defined in Linear.Quaternion

Methods

serializeWith :: MonadPut m => (a -> m ()) -> Quaternion a -> m ()

deserializeWith :: MonadGet m => m a -> m (Quaternion a)

Distributive Quaternion

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

Defined in Linear.Quaternion

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> Quaternion a -> Int

Metric Quaternion

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

Defined in Linear.Quaternion

Methods

_e :: Lens' (Quaternion a) a

_i :: Lens' (Quaternion a) a

Hamiltonian Quaternion

Defined in Linear.Quaternion

Methods

_j :: Lens' (Quaternion a) a

_k :: Lens' (Quaternion a) a

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

Trace Quaternion

Defined in Linear.Trace

Methods

trace :: Num a => Quaternion (Quaternion a) -> a

diagonal :: Quaternion (Quaternion a) -> Quaternion a

Finite Quaternion

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

Defined in Linear.Quaternion

Methods

_x :: Lens' (Quaternion a) a

R2 Quaternion

Defined in Linear.Quaternion

Methods

_y :: Lens' (Quaternion a) a

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

R3 Quaternion

Defined in Linear.Quaternion

Methods

_z :: Lens' (Quaternion a) a

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

R4 Quaternion

Defined in Linear.Quaternion

Methods

_w :: Lens' (Quaternion a) a

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

Additive Quaternion

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

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

Defined in Linear.Quaternion

Methods

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

join :: Quaternion (Quaternion a) -> Quaternion a

Generic1 Quaternion

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

Defined in Linear.Quaternion

Methods

showsPrec :: Int -> Quaternion a -> ShowS

show :: Quaternion a -> String

showList :: [Quaternion a] -> ShowS

Binary a => Binary (Quaternion a)

Defined in Linear.Quaternion

Methods

put :: Quaternion a -> Put

get :: Get (Quaternion a)

putList :: [Quaternion a] -> Put

Serial a => Serial (Quaternion a)

Defined in Linear.Quaternion

Methods

serialize :: MonadPut m => Quaternion a -> m ()

deserialize :: MonadGet m => m (Quaternion a)

Serialize a => Serialize (Quaternion a)

Defined in Linear.Quaternion

Methods

put :: Putter (Quaternion a)

get :: Get (Quaternion a)

NFData a => NFData (Quaternion a)

Defined in Linear.Quaternion

Methods

rnf :: Quaternion a -> ()

Eq a => Eq (Quaternion a)

Defined in Linear.Quaternion

Methods

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

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

Ord a => Ord (Quaternion a)

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)

Defined in Linear.Quaternion

Methods

hashWithSalt :: Int -> Quaternion a -> Int

hash :: Quaternion a -> Int

Ixed (Quaternion a)

Defined in Linear.Quaternion

Methods

ix :: Index (Quaternion a) -> Traversal' (Quaternion a) (IxValue (Quaternion a))

(Conjugate a, RealFloat a) => Conjugate (Quaternion a)

Defined in Linear.Quaternion

Methods

conjugate :: Quaternion a -> Quaternion a

(RealFloat a, Epsilon a) => Epsilon (Quaternion a)

Defined in Linear.Quaternion

Methods

nearZero :: Quaternion a -> Bool

Random a => Random (Quaternion a)

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)

Defined in Linear.Quaternion

Num a => Rotation (Quaternion a) a

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

toDcm :: Rot f1 f2 (Quaternion a) -> Rot f1 f2 (M33 a)

transpose :: Rot f1 f2 (Quaternion a) -> Rot f2 f1 (Quaternion a)

FoldableWithIndex (E Quaternion) Quaternion

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

Defined in Linear.Quaternion

Methods

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

TraversableWithIndex (E Quaternion) Quaternion

Defined in Linear.Quaternion

Methods

itraverse :: Applicative f => (E Quaternion -> a -> f b) -> Quaternion a -> f (Quaternion b)

Lift a => Lift (Quaternion a :: Type)

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

Defined in Linear.Quaternion

Methods

each :: Traversal (Quaternion a) (Quaternion b) a b

Field1 (Quaternion a) (Quaternion a) a a

Defined in Linear.Quaternion

Methods

_1 :: Lens (Quaternion a) (Quaternion a) a a

Field2 (Quaternion a) (Quaternion a) a a

Defined in Linear.Quaternion

Methods

_2 :: Lens (Quaternion a) (Quaternion a) a a

Field3 (Quaternion a) (Quaternion a) a a

Defined in Linear.Quaternion

Methods

_3 :: Lens (Quaternion a) (Quaternion a) a a

Field4 (Quaternion a) (Quaternion a) a a

Defined in Linear.Quaternion

Methods

_4 :: Lens (Quaternion a) (Quaternion a) a a

type Rep Quaternion

Defined in Linear.Quaternion

type Rep Quaternion = E Quaternion

type Size Quaternion

Defined in Linear.Quaternion

type Size Quaternion = 4

type Rep1 Quaternion

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)

Defined in Linear.Quaternion

data MVector s (Quaternion a) = MV_Quaternion !Int (MVector s a)

type Rep (Quaternion a)

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)

Defined in Linear.Quaternion

type Index (Quaternion a) = E Quaternion

type IxValue (Quaternion a)

Defined in Linear.Quaternion

type IxValue (Quaternion a) = a

data Vector (Quaternion a)

Defined in Linear.Quaternion

data Vector (Quaternion a) = V_Quaternion !Int (Vector a)