Safe Haskell	None
Language	Haskell2010

SpatialMathT

Contents

re-export for convenience

Synopsis

class Floating a => ArcTan2 a where
data Euler a = Euler {
- eYaw :: a
- ePitch :: a
- eRoll :: a
}
data Quaternion a = Quaternion !a !(V3 a)
data V3 a = V3 !a !a !a
class Rotation g a where
newtype Rot f1 f2 r a = Rot {
- unRot :: r a
}
newtype V3T f a = V3T {
- unV :: V3 a
}
class R1 (t :: * -> *) where
class R1 t => R2 (t :: * -> *) where
class R2 t => R3 (t :: * -> *) where
cross :: Num a => V3T f a -> V3T f a -> V3T f a
orthonormalize :: Floating a => Rot f1 f2 (V3 :. V3) a -> Rot f1 f2 (V3 :. V3) a
dcmOfQuat :: Num a => Rot f g Quaternion a -> Rot f g (V3 :. V3) a
dcmOfEuler321 :: Floating a => Rot f g Euler a -> Rot f g (V3 :. V3) a
quatOfDcm :: (Floating a, Ord a) => Rot f g (V3 :. V3) a -> Rot f g Quaternion a
quatOfEuler321 :: Floating a => Rot f g Euler a -> Rot f g Quaternion a
euler321OfDcm :: (ArcTan2 a, Ord a) => Rot f g (V3 :. V3) a -> Rot f g Euler a
unsafeEuler321OfDcm :: ArcTan2 a => Rot f g (V3 :. V3) a -> Rot f g Euler a
euler321OfQuat :: (ArcTan2 a, Ord a) => Rot f g Quaternion a -> Rot f g Euler a
unsafeEuler321OfQuat :: ArcTan2 a => Rot f g Quaternion a -> Rot f g Euler a
newtype ((g :: k2 -> *) :. (f :: k1 -> k2)) (a :: k1) :: forall k2 k1. (k2 -> *) -> (k1 -> k2) -> k1 -> * = O (g (f a))
unO :: (g :. f) a -> g (f a)

Documentation

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 #

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)))

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)))

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)))

class Rotation g a where #

Minimal complete definition

compose, rot, rot', transpose, identity

Methods

compose :: Rot f1 f2 g a -> Rot f2 f3 g a -> Rot f1 f3 g a #

rot :: Rot f1 f2 g a -> V3T f1 a -> V3T f2 a #

rot' :: Rot f1 f2 g a -> V3T f2 a -> V3T f1 a #

transpose :: Rot f1 f2 g a -> Rot f2 f1 g a #

identity :: Rot f1 f2 g a #

Instances

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 #
(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 #
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 #

newtype Rot f1 f2 r a #

Constructors

Rot
Fields unRot :: r a

Instances

Generic1 (Rot f1 f2 r :: * -> *) #
Instance details Defined in SpatialMathT Associated Types type Rep1 (Rot f1 f2 r) :: k -> * # Methods from1 :: Rot f1 f2 r a -> Rep1 (Rot f1 f2 r) a # to1 :: Rep1 (Rot f1 f2 r) a -> Rot f1 f2 r a #
Functor r => Functor (Rot f1 f2 r) #
Instance details Defined in SpatialMathT Methods fmap :: (a -> b) -> Rot f1 f2 r a -> Rot f1 f2 r b # (<$) :: a -> Rot f1 f2 r b -> Rot f1 f2 r a #
Applicative r => Applicative (Rot f1 f2 r) #
Instance details Defined in SpatialMathT Methods pure :: a -> Rot f1 f2 r a # (<>) :: Rot f1 f2 r (a -> b) -> Rot f1 f2 r a -> Rot f1 f2 r b # liftA2 :: (a -> b -> c) -> Rot f1 f2 r a -> Rot f1 f2 r b -> Rot f1 f2 r c # (>) :: Rot f1 f2 r a -> Rot f1 f2 r b -> Rot f1 f2 r b # (<*) :: Rot f1 f2 r a -> Rot f1 f2 r b -> Rot f1 f2 r a #
Foldable r => Foldable (Rot f1 f2 r) #
Instance details Defined in SpatialMathT Methods fold :: Monoid m => Rot f1 f2 r m -> m # foldMap :: Monoid m => (a -> m) -> Rot f1 f2 r a -> m # foldr :: (a -> b -> b) -> b -> Rot f1 f2 r a -> b # foldr' :: (a -> b -> b) -> b -> Rot f1 f2 r a -> b # foldl :: (b -> a -> b) -> b -> Rot f1 f2 r a -> b # foldl' :: (b -> a -> b) -> b -> Rot f1 f2 r a -> b # foldr1 :: (a -> a -> a) -> Rot f1 f2 r a -> a # foldl1 :: (a -> a -> a) -> Rot f1 f2 r a -> a # toList :: Rot f1 f2 r a -> [a] # null :: Rot f1 f2 r a -> Bool # length :: Rot f1 f2 r a -> Int # elem :: Eq a => a -> Rot f1 f2 r a -> Bool # maximum :: Ord a => Rot f1 f2 r a -> a # minimum :: Ord a => Rot f1 f2 r a -> a # sum :: Num a => Rot f1 f2 r a -> a # product :: Num a => Rot f1 f2 r a -> a #
Traversable r => Traversable (Rot f1 f2 r) #
Instance details Defined in SpatialMathT Methods traverse :: Applicative f => (a -> f b) -> Rot f1 f2 r a -> f (Rot f1 f2 r b) # sequenceA :: Applicative f => Rot f1 f2 r (f a) -> f (Rot f1 f2 r a) # mapM :: Monad m => (a -> m b) -> Rot f1 f2 r a -> m (Rot f1 f2 r b) # sequence :: Monad m => Rot f1 f2 r (m a) -> m (Rot f1 f2 r a) #
Eq (r a) => Eq (Rot f1 f2 r a) #
Instance details Defined in SpatialMathT Methods (==) :: Rot f1 f2 r a -> Rot f1 f2 r a -> Bool # (/=) :: Rot f1 f2 r a -> Rot f1 f2 r a -> Bool #
Fractional (r a) => Fractional (Rot f1 f2 r a) #
Instance details Defined in SpatialMathT Methods (/) :: Rot f1 f2 r a -> Rot f1 f2 r a -> Rot f1 f2 r a # recip :: Rot f1 f2 r a -> Rot f1 f2 r a # fromRational :: Rational -> Rot f1 f2 r a #
Num (r a) => Num (Rot f1 f2 r a) #
Instance details Defined in SpatialMathT Methods (+) :: Rot f1 f2 r a -> Rot f1 f2 r a -> Rot f1 f2 r a # (-) :: Rot f1 f2 r a -> Rot f1 f2 r a -> Rot f1 f2 r a # (*) :: Rot f1 f2 r a -> Rot f1 f2 r a -> Rot f1 f2 r a # negate :: Rot f1 f2 r a -> Rot f1 f2 r a # abs :: Rot f1 f2 r a -> Rot f1 f2 r a # signum :: Rot f1 f2 r a -> Rot f1 f2 r a # fromInteger :: Integer -> Rot f1 f2 r a #
Ord (r a) => Ord (Rot f1 f2 r a) #
Instance details Defined in SpatialMathT Methods compare :: Rot f1 f2 r a -> Rot f1 f2 r a -> Ordering # (<) :: Rot f1 f2 r a -> Rot f1 f2 r a -> Bool # (<=) :: Rot f1 f2 r a -> Rot f1 f2 r a -> Bool # (>) :: Rot f1 f2 r a -> Rot f1 f2 r a -> Bool # (>=) :: Rot f1 f2 r a -> Rot f1 f2 r a -> Bool # max :: Rot f1 f2 r a -> Rot f1 f2 r a -> Rot f1 f2 r a # min :: Rot f1 f2 r a -> Rot f1 f2 r a -> Rot f1 f2 r a #
Show (r a) => Show (Rot f1 f2 r a) #
Instance details Defined in SpatialMathT Methods showsPrec :: Int -> Rot f1 f2 r a -> ShowS # show :: Rot f1 f2 r a -> String # showList :: [Rot f1 f2 r a] -> ShowS #
Generic (Rot f1 f2 r a) #
Instance details Defined in SpatialMathT Associated Types type Rep (Rot f1 f2 r a) :: * -> * # Methods from :: Rot f1 f2 r a -> Rep (Rot f1 f2 r a) x # to :: Rep (Rot f1 f2 r a) x -> Rot f1 f2 r a #
Storable (r a) => Storable (Rot f1 f2 r a) #
Instance details Defined in SpatialMathT Methods sizeOf :: Rot f1 f2 r a -> Int # alignment :: Rot f1 f2 r a -> Int # peekElemOff :: Ptr (Rot f1 f2 r a) -> Int -> IO (Rot f1 f2 r a) # pokeElemOff :: Ptr (Rot f1 f2 r a) -> Int -> Rot f1 f2 r a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Rot f1 f2 r a) # pokeByteOff :: Ptr b -> Int -> Rot f1 f2 r a -> IO () # peek :: Ptr (Rot f1 f2 r a) -> IO (Rot f1 f2 r a) # poke :: Ptr (Rot f1 f2 r a) -> Rot f1 f2 r a -> IO () #
Binary (r a) => Binary (Rot f1 f2 r a) #
Instance details Defined in SpatialMathT Methods put :: Rot f1 f2 r a -> Put # get :: Get (Rot f1 f2 r a) # putList :: [Rot f1 f2 r a] -> Put #
Serialize (r a) => Serialize (Rot f1 f2 r a) #
Instance details Defined in SpatialMathT Methods put :: Putter (Rot f1 f2 r a) # get :: Get (Rot f1 f2 r a) #
type Rep1 (Rot f1 f2 r :: * -> *) #
Instance details Defined in SpatialMathT type Rep1 (Rot f1 f2 r :: * -> *) = D1 (MetaData "Rot" "SpatialMathT" "spatial-math-0.5.0.1-BCf68EO2cdvEFP2DMwbIRL" True) (C1 (MetaCons "Rot" PrefixI True) (S1 (MetaSel (Just "unRot") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 r)))
type Rep (Rot f1 f2 r a) #
Instance details Defined in SpatialMathT type Rep (Rot f1 f2 r a) = D1 (MetaData "Rot" "SpatialMathT" "spatial-math-0.5.0.1-BCf68EO2cdvEFP2DMwbIRL" True) (C1 (MetaCons "Rot" PrefixI True) (S1 (MetaSel (Just "unRot") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (r a))))

newtype V3T f a #

Constructors

V3T
Fields unV :: V3 a

Instances

Functor (V3T f) #
Instance details Defined in SpatialMathT Methods fmap :: (a -> b) -> V3T f a -> V3T f b # (<$) :: a -> V3T f b -> V3T f a #
Applicative (V3T f) #
Instance details Defined in SpatialMathT Methods pure :: a -> V3T f a # (<>) :: V3T f (a -> b) -> V3T f a -> V3T f b # liftA2 :: (a -> b -> c) -> V3T f a -> V3T f b -> V3T f c # (>) :: V3T f a -> V3T f b -> V3T f b # (<*) :: V3T f a -> V3T f b -> V3T f a #
Foldable (V3T f) #
Instance details Defined in SpatialMathT Methods fold :: Monoid m => V3T f m -> m # foldMap :: Monoid m => (a -> m) -> V3T f a -> m # foldr :: (a -> b -> b) -> b -> V3T f a -> b # foldr' :: (a -> b -> b) -> b -> V3T f a -> b # foldl :: (b -> a -> b) -> b -> V3T f a -> b # foldl' :: (b -> a -> b) -> b -> V3T f a -> b # foldr1 :: (a -> a -> a) -> V3T f a -> a # foldl1 :: (a -> a -> a) -> V3T f a -> a # toList :: V3T f a -> [a] # null :: V3T f a -> Bool # length :: V3T f a -> Int # elem :: Eq a => a -> V3T f a -> Bool # maximum :: Ord a => V3T f a -> a # minimum :: Ord a => V3T f a -> a # sum :: Num a => V3T f a -> a # product :: Num a => V3T f a -> a #
Traversable (V3T f) #
Instance details Defined in SpatialMathT Methods traverse :: Applicative f0 => (a -> f0 b) -> V3T f a -> f0 (V3T f b) # sequenceA :: Applicative f0 => V3T f (f0 a) -> f0 (V3T f a) # mapM :: Monad m => (a -> m b) -> V3T f a -> m (V3T f b) # sequence :: Monad m => V3T f (m a) -> m (V3T f a) #
R3 (V3T f) #
Instance details Defined in SpatialMathT Methods _z :: Functor f0 => (a -> f0 a) -> V3T f a -> f0 (V3T f a) # _xyz :: Functor f0 => (V3 a -> f0 (V3 a)) -> V3T f a -> f0 (V3T f a) #
R2 (V3T f) #
Instance details Defined in SpatialMathT Methods _y :: Functor f0 => (a -> f0 a) -> V3T f a -> f0 (V3T f a) # _xy :: Functor f0 => (V2 a -> f0 (V2 a)) -> V3T f a -> f0 (V3T f a) #
R1 (V3T f) #
Instance details Defined in SpatialMathT Methods _x :: Functor f0 => (a -> f0 a) -> V3T f a -> f0 (V3T f a) #
Metric (V3T f) #
Instance details Defined in SpatialMathT Methods dot :: Num a => V3T f a -> V3T f a -> a # quadrance :: Num a => V3T f a -> a # qd :: Num a => V3T f a -> V3T f a -> a # distance :: Floating a => V3T f a -> V3T f a -> a # norm :: Floating a => V3T f a -> a # signorm :: Floating a => V3T f a -> V3T f a #
Additive (V3T f) #
Instance details Defined in SpatialMathT Methods zero :: Num a => V3T f a # (^+^) :: Num a => V3T f a -> V3T f a -> V3T f a # (^-^) :: Num a => V3T f a -> V3T f a -> V3T f a # lerp :: Num a => a -> V3T f a -> V3T f a -> V3T f a # liftU2 :: (a -> a -> a) -> V3T f a -> V3T f a -> V3T f a # liftI2 :: (a -> b -> c) -> V3T f a -> V3T f b -> V3T f c #
Generic1 (V3T f :: * -> *) #
Instance details Defined in SpatialMathT Associated Types type Rep1 (V3T f) :: k -> * # Methods from1 :: V3T f a -> Rep1 (V3T f) a # to1 :: Rep1 (V3T f) a -> V3T f a #
Eq a => Eq (V3T f a) #
Instance details Defined in SpatialMathT Methods (==) :: V3T f a -> V3T f a -> Bool # (/=) :: V3T f a -> V3T f a -> Bool #
Fractional a => Fractional (V3T f a) #
Instance details Defined in SpatialMathT Methods (/) :: V3T f a -> V3T f a -> V3T f a # recip :: V3T f a -> V3T f a # fromRational :: Rational -> V3T f a #
Num a => Num (V3T f a) #
Instance details Defined in SpatialMathT Methods (+) :: V3T f a -> V3T f a -> V3T f a # (-) :: V3T f a -> V3T f a -> V3T f a # (*) :: V3T f a -> V3T f a -> V3T f a # negate :: V3T f a -> V3T f a # abs :: V3T f a -> V3T f a # signum :: V3T f a -> V3T f a # fromInteger :: Integer -> V3T f a #
Ord a => Ord (V3T f a) #
Instance details Defined in SpatialMathT Methods compare :: V3T f a -> V3T f a -> Ordering # (<) :: V3T f a -> V3T f a -> Bool # (<=) :: V3T f a -> V3T f a -> Bool # (>) :: V3T f a -> V3T f a -> Bool # (>=) :: V3T f a -> V3T f a -> Bool # max :: V3T f a -> V3T f a -> V3T f a # min :: V3T f a -> V3T f a -> V3T f a #
Show a => Show (V3T f a) #
Instance details Defined in SpatialMathT Methods showsPrec :: Int -> V3T f a -> ShowS # show :: V3T f a -> String # showList :: [V3T f a] -> ShowS #
Generic (V3T f a) #
Instance details Defined in SpatialMathT Associated Types type Rep (V3T f a) :: * -> * # Methods from :: V3T f a -> Rep (V3T f a) x # to :: Rep (V3T f a) x -> V3T f a #
Storable a => Storable (V3T f a) #
Instance details Defined in SpatialMathT Methods sizeOf :: V3T f a -> Int # alignment :: V3T f a -> Int # peekElemOff :: Ptr (V3T f a) -> Int -> IO (V3T f a) # pokeElemOff :: Ptr (V3T f a) -> Int -> V3T f a -> IO () # peekByteOff :: Ptr b -> Int -> IO (V3T f a) # pokeByteOff :: Ptr b -> Int -> V3T f a -> IO () # peek :: Ptr (V3T f a) -> IO (V3T f a) # poke :: Ptr (V3T f a) -> V3T f a -> IO () #
Binary a => Binary (V3T f a) #
Instance details Defined in SpatialMathT Methods put :: V3T f a -> Put # get :: Get (V3T f a) # putList :: [V3T f a] -> Put #
Serialize a => Serialize (V3T f a) #
Instance details Defined in SpatialMathT Methods put :: Putter (V3T f a) # get :: Get (V3T f a) #
type Rep1 (V3T f :: * -> *) #
Instance details Defined in SpatialMathT type Rep1 (V3T f :: * -> *) = D1 (MetaData "V3T" "SpatialMathT" "spatial-math-0.5.0.1-BCf68EO2cdvEFP2DMwbIRL" True) (C1 (MetaCons "V3T" PrefixI True) (S1 (MetaSel (Just "unV") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 V3)))
type Rep (V3T f a) #
Instance details Defined in SpatialMathT type Rep (V3T f a) = D1 (MetaData "V3T" "SpatialMathT" "spatial-math-0.5.0.1-BCf68EO2cdvEFP2DMwbIRL" True) (C1 (MetaCons "V3T" PrefixI True) (S1 (MetaSel (Just "unV") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (V3 a))))

class R1 (t :: * -> *) where #

A space that has at least 1 basis vector _x.

Minimal complete definition

_x

Methods

_x :: Functor f => (a -> f a) -> t a -> f (t a) #

>>> V1 2 ^._x
2

>>> V1 2 & _x .~ 3
V1 3

Instances

R1 Identity
Instance details Defined in Linear.V1 Methods _x :: Functor f => (a -> f a) -> Identity a -> f (Identity a) #
R1 V4
Instance details Defined in Linear.V4 Methods _x :: Functor f => (a -> f a) -> V4 a -> f (V4 a) #
R1 V3
Instance details Defined in Linear.V3 Methods _x :: Functor f => (a -> f a) -> V3 a -> f (V3 a) #
R1 V2
Instance details Defined in Linear.V2 Methods _x :: Functor f => (a -> f a) -> V2 a -> f (V2 a) #
R1 V1
Instance details Defined in Linear.V1 Methods _x :: Functor f => (a -> f a) -> V1 a -> f (V1 a) #
R1 (V3T f) #
Instance details Defined in SpatialMathT Methods _x :: Functor f0 => (a -> f0 a) -> V3T f a -> f0 (V3T f a) #

class R1 t => R2 (t :: * -> *) where #

A space that distinguishes 2 orthogonal basis vectors _x and _y, but may have more.

Minimal complete definition

_xy

Methods

_y :: Functor f => (a -> f a) -> t a -> f (t a) #

>>> V2 1 2 ^._y
2

>>> V2 1 2 & _y .~ 3
V2 1 3

_xy :: Functor f => (V2 a -> f (V2 a)) -> t a -> f (t a) #

Instances

R2 V4
Instance details Defined in Linear.V4 Methods _y :: Functor f => (a -> f a) -> V4 a -> f (V4 a) # _xy :: Functor f => (V2 a -> f (V2 a)) -> V4 a -> f (V4 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) #
R2 V2
Instance details Defined in Linear.V2 Methods _y :: Functor f => (a -> f a) -> V2 a -> f (V2 a) # _xy :: Functor f => (V2 a -> f (V2 a)) -> V2 a -> f (V2 a) #
R2 (V3T f) #
Instance details Defined in SpatialMathT Methods _y :: Functor f0 => (a -> f0 a) -> V3T f a -> f0 (V3T f a) # _xy :: Functor f0 => (V2 a -> f0 (V2 a)) -> V3T f a -> f0 (V3T f a) #

class R2 t => R3 (t :: * -> *) where #

A space that distinguishes 3 orthogonal basis vectors: _x, _y, and _z. (It may have more)

Minimal complete definition

_z, _xyz

Methods

_z :: Functor f => (a -> f a) -> t a -> f (t a) #

>>> V3 1 2 3 ^. _z
3

_xyz :: Functor f => (V3 a -> f (V3 a)) -> t a -> f (t a) #

Instances

R3 V4
Instance details Defined in Linear.V4 Methods _z :: Functor f => (a -> f a) -> V4 a -> f (V4 a) # _xyz :: Functor f => (V3 a -> f (V3 a)) -> V4 a -> f (V4 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) #
R3 (V3T f) #
Instance details Defined in SpatialMathT Methods _z :: Functor f0 => (a -> f0 a) -> V3T f a -> f0 (V3T f a) # _xyz :: Functor f0 => (V3 a -> f0 (V3 a)) -> V3T f a -> f0 (V3T f a) #

cross :: Num a => V3T f a -> V3T f a -> V3T f a #

orthonormalize :: Floating a => Rot f1 f2 (V3 :. V3) a -> Rot f1 f2 (V3 :. V3) a #

dcmOfQuat :: Num a => Rot f g Quaternion a -> Rot f g (V3 :. V3) a #

dcmOfEuler321 :: Floating a => Rot f g Euler a -> Rot f g (V3 :. V3) a #

quatOfDcm :: (Floating a, Ord a) => Rot f g (V3 :. V3) a -> Rot f g Quaternion a #

quatOfEuler321 :: Floating a => Rot f g Euler a -> Rot f g Quaternion a #

euler321OfDcm :: (ArcTan2 a, Ord a) => Rot f g (V3 :. V3) a -> Rot f g Euler a #

unsafeEuler321OfDcm :: ArcTan2 a => Rot f g (V3 :. V3) a -> Rot f g Euler a #

euler321OfQuat :: (ArcTan2 a, Ord a) => Rot f g Quaternion a -> Rot f g Euler a #

unsafeEuler321OfQuat :: ArcTan2 a => Rot f g Quaternion a -> Rot f g Euler a #

re-export for convenience

newtype ((g :: k2 -> *) :. (f :: k1 -> k2)) (a :: k1) :: forall k2 k1. (k2 -> *) -> (k1 -> k2) -> k1 -> * infixl 9 #

Composition of unary type constructors

There are (at least) two useful Monoid instances, so you'll have to pick one and type-specialize it (filling in all or parts of g and/or f).

    -- standard Monoid instance for Applicative applied to Monoid
    instance (Applicative (g :. f), Monoid a) => Monoid ((g :. f) a) where
      { mempty = pure mempty; mappend = liftA2 mappend }
    -- Especially handy when g is a Monoid_f.
    instance Monoid (g (f a)) => Monoid ((g :. f) a) where
      { mempty = O mempty; mappend = inO2 mappend }

Corresponding to the first and second definitions above,

    instance (Applicative g, Monoid_f f) => Monoid_f (g :. f) where
      { mempty_f = O (pure mempty_f); mappend_f = inO2 (liftA2 mappend_f) }
    instance Monoid_f g => Monoid_f (g :. f) where
      { mempty_f = O mempty_f; mappend_f = inO2 mappend_f }

Similarly, there are two useful Functor instances and two useful ContraFunctor instances.

    instance (      Functor g,       Functor f) => Functor (g :. f) where fmap = fmapFF
    instance (ContraFunctor g, ContraFunctor f) => Functor (g :. f) where fmap = fmapCC

    instance (      Functor g, ContraFunctor f) => ContraFunctor (g :. f) where contraFmap = contraFmapFC
    instance (ContraFunctor g,       Functor f) => ContraFunctor (g :. f) where contraFmap = contraFmapCF

However, it's such a bother to define the Functor instances per composition type, I've left the fmapFF case in. If you want the fmapCC one, you're out of luck for now. I'd love to hear a good solution. Maybe someday Haskell will do Prolog-style search for instances, subgoaling the constraints, rather than just matching instance heads.

Constructors

O (g (f a))

Instances

Functor g => Generic1 (g :. f :: k -> *)
Instance details Defined in Control.Compose Associated Types type Rep1 (g :. f) :: k -> * # Methods from1 :: (g :. f) a -> Rep1 (g :. f) a # to1 :: Rep1 (g :. f) a -> (g :. f) a #
(Functor g, Functor f) => Functor (g :. f)
Instance details Defined in Control.Compose Methods fmap :: (a -> b) -> (g :. f) a -> (g :. f) b # (<$) :: a -> (g :. f) b -> (g :. f) a #
(Applicative g, Applicative f) => Applicative (g :. f)
Instance details Defined in Control.Compose Methods pure :: a -> (g :. f) a # (<>) :: (g :. f) (a -> b) -> (g :. f) a -> (g :. f) b # liftA2 :: (a -> b -> c) -> (g :. f) a -> (g :. f) b -> (g :. f) c # (>) :: (g :. f) a -> (g :. f) b -> (g :. f) b # (<*) :: (g :. f) a -> (g :. f) b -> (g :. f) a #
(Foldable g, Foldable f, Functor g) => Foldable (g :. f)
Instance details Defined in Control.Compose Methods fold :: Monoid m => (g :. f) m -> m # foldMap :: Monoid m => (a -> m) -> (g :. f) a -> m # foldr :: (a -> b -> b) -> b -> (g :. f) a -> b # foldr' :: (a -> b -> b) -> b -> (g :. f) a -> b # foldl :: (b -> a -> b) -> b -> (g :. f) a -> b # foldl' :: (b -> a -> b) -> b -> (g :. f) a -> b # foldr1 :: (a -> a -> a) -> (g :. f) a -> a # foldl1 :: (a -> a -> a) -> (g :. f) a -> a # toList :: (g :. f) a -> [a] # null :: (g :. f) a -> Bool # length :: (g :. f) a -> Int # elem :: Eq a => a -> (g :. f) a -> Bool # maximum :: Ord a => (g :. f) a -> a # minimum :: Ord a => (g :. f) a -> a # sum :: Num a => (g :. f) a -> a # product :: Num a => (g :. f) a -> a #
(Traversable g, Traversable f) => Traversable (g :. f)
Instance details Defined in Control.Compose Methods traverse :: Applicative f0 => (a -> f0 b) -> (g :. f) a -> f0 ((g :. f) b) # sequenceA :: Applicative f0 => (g :. f) (f0 a) -> f0 ((g :. f) a) # mapM :: Monad m => (a -> m b) -> (g :. f) a -> m ((g :. f) b) # sequence :: Monad m => (g :. f) (m a) -> m ((g :. f) 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 #
Eq (g (f a)) => Eq ((g :. f) a)
Instance details Defined in Control.Compose Methods (==) :: (g :. f) a -> (g :. f) a -> Bool # (/=) :: (g :. f) a -> (g :. f) a -> Bool #
Ord (g (f a)) => Ord ((g :. f) a)
Instance details Defined in Control.Compose Methods compare :: (g :. f) a -> (g :. f) a -> Ordering # (<) :: (g :. f) a -> (g :. f) a -> Bool # (<=) :: (g :. f) a -> (g :. f) a -> Bool # (>) :: (g :. f) a -> (g :. f) a -> Bool # (>=) :: (g :. f) a -> (g :. f) a -> Bool # max :: (g :. f) a -> (g :. f) a -> (g :. f) a # min :: (g :. f) a -> (g :. f) a -> (g :. f) a #
Show (g (f a)) => Show ((g :. f) a)
Instance details Defined in Control.Compose Methods showsPrec :: Int -> (g :. f) a -> ShowS # show :: (g :. f) a -> String # showList :: [(g :. f) a] -> ShowS #
Generic ((g :. f) a)
Instance details Defined in Control.Compose Associated Types type Rep ((g :. f) a) :: * -> * # Methods from :: (g :. f) a -> Rep ((g :. f) a) x # to :: Rep ((g :. f) a) x -> (g :. f) a #
type Rep1 (g :. f :: k -> *)
Instance details Defined in Control.Compose type Rep1 (g :. f :: k -> *) = D1 (MetaData ":." "Control.Compose" "TypeCompose-0.9.14-C4jvB97v2tIBqCz3nw48cx" True) (C1 (MetaCons "O" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (g :.: Rec1 f)))
type Rep ((g :. f) a)
Instance details Defined in Control.Compose type Rep ((g :. f) a) = D1 (MetaData ":." "Control.Compose" "TypeCompose-0.9.14-C4jvB97v2tIBqCz3nw48cx" True) (C1 (MetaCons "O" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (g (f a)))))

unO :: (g :. f) a -> g (f a) #

Unwrap a '(:.)'.