SpatialMath

Documentation

data Euler a

3-2-1 Euler angle rotation sequence

Constructors

Euler

Fields

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

Instances

Functor Euler

Methods

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

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

Applicative Euler

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

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

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

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)

Methods

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

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

Data a => Data (Euler a)

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)

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)

Methods

showsPrec :: Int -> Euler a -> ShowS

show :: Euler a -> String

showList :: [Euler a] -> ShowS

Generic (Euler a)

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)

Methods

put :: Euler a -> Put

get :: Get (Euler a)

putList :: [Euler a] -> Put

Serialize a => Serialize (Euler a)

Methods

put :: Putter (Euler a)

get :: Get (Euler a)

Generic1 * Euler

Associated Types

type Rep1 Euler (f :: Euler -> *) :: k -> *

Methods

from1 :: f a -> Rep1 Euler f a

to1 :: Rep1 Euler f a -> f a

type Rep (Euler a)

type Rep (Euler a) = D1 * (MetaData "Euler" "Types" "spatial-math-0.5.0.0-COrTBPshcJ1IWPIaDBwva5" False) (C1 * (MetaCons "Euler" PrefixI True) ((:*:) * (S1 * (MetaSel (Just Symbol "eYaw") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)) ((:*:) * (S1 * (MetaSel (Just Symbol "ePitch") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)) (S1 * (MetaSel (Just Symbol "eRoll") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))))

type Rep1 * Euler

type Rep1 * Euler = D1 * (MetaData "Euler" "Types" "spatial-math-0.5.0.0-COrTBPshcJ1IWPIaDBwva5" False) (C1 * (MetaCons "Euler" PrefixI True) ((:*:) * (S1 * (MetaSel (Just Symbol "eYaw") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1) ((:*:) * (S1 * (MetaSel (Just Symbol "ePitch") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1) (S1 * (MetaSel (Just Symbol "eRoll") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))))

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

Methods

arctan2 :: Double -> Double -> Double

ArcTan2 Float

Methods

arctan2 :: Float -> Float -> Float

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

Rotate a vector about the X axis

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

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

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

Rotate a vector about the Y axis

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

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

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

Rotate a vector about the Z axis

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

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

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

Convert quaternion to Euler angles

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

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

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

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

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

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

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

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

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

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

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

Convert DCM to euler angles

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

convert a quaternion to a DCM

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

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

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

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

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

Convert DCM to euler angles

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

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

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

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

convert a DCM to a quaternion

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

>>> quatOfDcm $ V3 (V3 0 1 0) (V3 (-1) 0 0) (V3 0 0 1)
Quaternion 0.7071067811865476 (V3 0.0 0.0 0.7071067811865475)

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

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

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

vec_b = R_a2b * vec_a

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

vec_a = R_a2b^T * vec_b

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

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

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

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

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

re-exported from linear

type M33 a = V3 (V3 a)

A 3x3 matrix with row-major representation

data V3 a :: * -> *

A 3-dimensional vector

Constructors

V3 !a !a !a

Instances

Monad V3

Methods

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

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

return :: a -> V3 a

fail :: String -> V3 a

Functor V3

Methods

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

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

MonadFix V3

Methods

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

Applicative V3

Methods

pure :: a -> V3 a

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

liftA2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c

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

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

Foldable V3

Methods

fold :: Monoid m => V3 m -> m

foldMap :: Monoid m => (a -> m) -> V3 a -> m

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

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

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

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

foldr1 :: (a -> a -> a) -> V3 a -> a

foldl1 :: (a -> a -> a) -> V3 a -> a

toList :: V3 a -> [a]

null :: V3 a -> Bool

length :: V3 a -> Int

elem :: Eq a => a -> V3 a -> Bool

maximum :: Ord a => V3 a -> a

minimum :: Ord a => V3 a -> a

sum :: Num a => V3 a -> a

product :: Num a => V3 a -> a

Traversable V3

Methods

traverse :: Applicative f => (a -> f b) -> V3 a -> f (V3 b)

sequenceA :: Applicative f => V3 (f a) -> f (V3 a)

mapM :: Monad m => (a -> m b) -> V3 a -> m (V3 b)

sequence :: Monad m => V3 (m a) -> m (V3 a)

Distributive V3

Methods

distribute :: Functor f => f (V3 a) -> V3 (f a)

collect :: Functor f => (a -> V3 b) -> f a -> V3 (f b)

distributeM :: Monad m => m (V3 a) -> V3 (m a)

collectM :: Monad m => (a -> V3 b) -> m a -> V3 (m b)

Representable V3

Associated Types

type Rep (V3 :: * -> *) :: *

Methods

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

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

Eq1 V3

Methods

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

Ord1 V3

Methods

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

Read1 V3

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V3 a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V3 a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V3 a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V3 a]

Show1 V3

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V3 a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V3 a] -> ShowS

MonadZip V3

Methods

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

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

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

Serial1 V3

Methods

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

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

Apply 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

Methods

traverse1 :: Apply f => (a -> f b) -> V3 a -> f (V3 b)

sequence1 :: Apply f => V3 (f b) -> f (V3 b)

R3 V3

Methods

_z :: Functor f => (a -> f a) -> V3 a -> f (V3 a)

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

R2 V3

Methods

_y :: Functor f => (a -> f a) -> V3 a -> f (V3 a)

_xy :: Functor f => (V2 a -> f (V2 a)) -> V3 a -> f (V3 a)

R1 V3

Methods

_x :: Functor f => (a -> f a) -> V3 a -> f (V3 a)

Finite V3

Associated Types

type Size (V3 :: * -> *) :: Nat

Methods

toV :: V3 a -> V Nat (Size V3) a

fromV :: V Nat (Size V3) a -> V3 a

Metric V3

Methods

dot :: Num a => V3 a -> V3 a -> a

quadrance :: Num a => V3 a -> a

qd :: Num a => V3 a -> V3 a -> a

distance :: Floating a => V3 a -> V3 a -> a

norm :: Floating a => V3 a -> a

signorm :: Floating a => V3 a -> V3 a

Additive V3

Methods

zero :: Num a => V3 a

(^+^) :: Num a => V3 a -> V3 a -> V3 a

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

lerp :: Num a => a -> V3 a -> V3 a -> V3 a

liftU2 :: (a -> a -> a) -> V3 a -> V3 a -> V3 a

liftI2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c

Foldable1 V3

Methods

fold1 :: Semigroup m => V3 m -> m

foldMap1 :: Semigroup m => (a -> m) -> V3 a -> m

toNonEmpty :: V3 a -> NonEmpty a

Bind V3

Methods

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

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

Unbox a => Vector Vector (V3 a)

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> m (Vector (V3 a))

basicUnsafeThaw :: PrimMonad m => Vector (V3 a) -> m (Mutable Vector (PrimState m) (V3 a))

basicLength :: Vector (V3 a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (V3 a) -> Vector (V3 a)

basicUnsafeIndexM :: Monad m => Vector (V3 a) -> Int -> m (V3 a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> Vector (V3 a) -> m ()

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

Unbox a => MVector MVector (V3 a)

Methods

basicLength :: MVector s (V3 a) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (V3 a) -> MVector s (V3 a)

basicOverlaps :: MVector s (V3 a) -> MVector s (V3 a) -> Bool

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V3 a))

basicInitialize :: PrimMonad m => MVector (PrimState m) (V3 a) -> m ()

basicUnsafeReplicate :: PrimMonad m => Int -> V3 a -> m (MVector (PrimState m) (V3 a))

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (V3 a)

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> V3 a -> m ()

basicClear :: PrimMonad m => MVector (PrimState m) (V3 a) -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) (V3 a) -> V3 a -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m ()

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (MVector (PrimState m) (V3 a))

Bounded a => Bounded (V3 a)

Methods

minBound :: V3 a

maxBound :: V3 a

Eq a => Eq (V3 a)

Methods

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

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

Floating a => Floating (V3 a)

Methods

pi :: V3 a

exp :: V3 a -> V3 a

log :: V3 a -> V3 a

sqrt :: V3 a -> V3 a

(**) :: V3 a -> V3 a -> V3 a

logBase :: V3 a -> V3 a -> V3 a

sin :: V3 a -> V3 a

cos :: V3 a -> V3 a

tan :: V3 a -> V3 a

asin :: V3 a -> V3 a

acos :: V3 a -> V3 a

atan :: V3 a -> V3 a

sinh :: V3 a -> V3 a

cosh :: V3 a -> V3 a

tanh :: V3 a -> V3 a

asinh :: V3 a -> V3 a

acosh :: V3 a -> V3 a

atanh :: V3 a -> V3 a

log1p :: V3 a -> V3 a

expm1 :: V3 a -> V3 a

log1pexp :: V3 a -> V3 a

log1mexp :: V3 a -> V3 a

Fractional a => Fractional (V3 a)

Methods

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

recip :: V3 a -> V3 a

fromRational :: Rational -> V3 a

Data a => Data (V3 a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V3 a -> c (V3 a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V3 a)

toConstr :: V3 a -> Constr

dataTypeOf :: V3 a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (V3 a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V3 a))

gmapT :: (forall b. Data b => b -> b) -> V3 a -> V3 a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r

gmapQ :: (forall d. Data d => d -> u) -> V3 a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> V3 a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a)

Num a => Num (V3 a)

Methods

(+) :: V3 a -> V3 a -> V3 a

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

(*) :: V3 a -> V3 a -> V3 a

negate :: V3 a -> V3 a

abs :: V3 a -> V3 a

signum :: V3 a -> V3 a

fromInteger :: Integer -> V3 a

Ord a => Ord (V3 a)

Methods

compare :: V3 a -> V3 a -> Ordering

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

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

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

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

max :: V3 a -> V3 a -> V3 a

min :: V3 a -> V3 a -> V3 a

Read a => Read (V3 a)

Methods

readsPrec :: Int -> ReadS (V3 a)

readList :: ReadS [V3 a]

readPrec :: ReadPrec (V3 a)

readListPrec :: ReadPrec [V3 a]

Show a => Show (V3 a)

Methods

showsPrec :: Int -> V3 a -> ShowS

show :: V3 a -> String

showList :: [V3 a] -> ShowS

Ix a => Ix (V3 a)

Methods

range :: (V3 a, V3 a) -> [V3 a]

index :: (V3 a, V3 a) -> V3 a -> Int

unsafeIndex :: (V3 a, V3 a) -> V3 a -> Int

inRange :: (V3 a, V3 a) -> V3 a -> Bool

rangeSize :: (V3 a, V3 a) -> Int

unsafeRangeSize :: (V3 a, V3 a) -> Int

Generic (V3 a)

Associated Types

type Rep (V3 a) :: * -> *

Methods

from :: V3 a -> Rep (V3 a) x

to :: Rep (V3 a) x -> V3 a

Storable a => Storable (V3 a)

Methods

sizeOf :: V3 a -> Int

alignment :: V3 a -> Int

peekElemOff :: Ptr (V3 a) -> Int -> IO (V3 a)

pokeElemOff :: Ptr (V3 a) -> Int -> V3 a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (V3 a)

pokeByteOff :: Ptr b -> Int -> V3 a -> IO ()

peek :: Ptr (V3 a) -> IO (V3 a)

poke :: Ptr (V3 a) -> V3 a -> IO ()

Binary a => Binary (V3 a)

Methods

put :: V3 a -> Put

get :: Get (V3 a)

putList :: [V3 a] -> Put

Serial a => Serial (V3 a)

Methods

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

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

Serialize a => Serialize (V3 a)

Methods

put :: Putter (V3 a)

get :: Get (V3 a)

NFData a => NFData (V3 a)

Methods

rnf :: V3 a -> ()

Hashable a => Hashable (V3 a)

Methods

hashWithSalt :: Int -> V3 a -> Int

hash :: V3 a -> Int

Unbox a => Unbox (V3 a)

Ixed (V3 a)

Methods

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

Epsilon a => Epsilon (V3 a)

Methods

nearZero :: V3 a -> Bool

Generic1 * V3

Associated Types

type Rep1 V3 (f :: V3 -> *) :: k -> *

Methods

from1 :: f a -> Rep1 V3 f a

to1 :: Rep1 V3 f a -> f a

FunctorWithIndex (E V3) V3

Methods

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

imapped :: (Indexable (E V3) p, Settable f) => p a (f b) -> V3 a -> f (V3 b)

FoldableWithIndex (E V3) V3

Methods

ifoldMap :: Monoid m => (E V3 -> a -> m) -> V3 a -> m

ifolded :: (Indexable (E V3) p, Contravariant f, Applicative f) => p a (f a) -> V3 a -> f (V3 a)

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

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

ifoldr' :: (E V3 -> a -> b -> b) -> b -> V3 a -> b

ifoldl' :: (E V3 -> b -> a -> b) -> b -> V3 a -> b

TraversableWithIndex (E V3) V3

Methods

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

itraversed :: (Indexable (E V3) p, Applicative f) => p a (f b) -> V3 a -> f (V3 b)

Each (V3 a) (V3 b) a b

Methods

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

Num a => Rotation ((:.) V3 V3) a

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

type Rep V3 = E V3

type Size V3

type Size V3 = 3

data MVector s (V3 a)

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

type Rep (V3 a)

type Rep (V3 a) = D1 * (MetaData "V3" "Linear.V3" "linear-1.20.7-ESPgvMEcP27Jzthlh4sP5X" False) (C1 * (MetaCons "V3" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * a)) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * a)) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * a)))))

data Vector (V3 a)

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

type Index (V3 a)

type Index (V3 a) = E V3

type IxValue (V3 a)

type IxValue (V3 a) = a

type Rep1 * V3

type Rep1 * V3 = D1 * (MetaData "V3" "Linear.V3" "linear-1.20.7-ESPgvMEcP27Jzthlh4sP5X" False) (C1 * (MetaCons "V3" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1))))

data Quaternion a :: * -> *

Quaternions

Constructors

Quaternion !a !(V3 a)

Instances

Monad Quaternion

Methods

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

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

return :: a -> Quaternion a

fail :: String -> Quaternion a

Functor Quaternion

Methods

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

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

MonadFix Quaternion

Methods

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

Applicative Quaternion

Methods

pure :: a -> Quaternion a

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

liftA2 :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c

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

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

Foldable Quaternion

Methods

fold :: Monoid m => Quaternion m -> m

foldMap :: Monoid m => (a -> m) -> Quaternion a -> m

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

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

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

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

foldr1 :: (a -> a -> a) -> Quaternion a -> a

foldl1 :: (a -> a -> a) -> Quaternion a -> a

toList :: Quaternion a -> [a]

null :: Quaternion a -> Bool

length :: Quaternion a -> Int

elem :: Eq a => a -> Quaternion a -> Bool

maximum :: Ord a => Quaternion a -> a

minimum :: Ord a => Quaternion a -> a

sum :: Num a => Quaternion a -> a

product :: Num a => Quaternion a -> a

Traversable Quaternion

Methods

traverse :: Applicative f => (a -> f b) -> Quaternion a -> f (Quaternion b)

sequenceA :: Applicative f => Quaternion (f a) -> f (Quaternion a)

mapM :: Monad m => (a -> m b) -> Quaternion a -> m (Quaternion b)

sequence :: Monad m => Quaternion (m a) -> m (Quaternion a)

Distributive Quaternion

Methods

distribute :: Functor f => f (Quaternion a) -> Quaternion (f a)

collect :: Functor f => (a -> Quaternion b) -> f a -> Quaternion (f b)

distributeM :: Monad m => m (Quaternion a) -> Quaternion (m a)

collectM :: Monad m => (a -> Quaternion b) -> m a -> Quaternion (m b)

Representable Quaternion

Associated Types

type Rep (Quaternion :: * -> *) :: *

Methods

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

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

Eq1 Quaternion

Methods

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

Ord1 Quaternion

Methods

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

Read1 Quaternion

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Quaternion a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Quaternion a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Quaternion a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Quaternion a]

Show1 Quaternion

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Quaternion a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Quaternion a] -> ShowS

MonadZip Quaternion

Methods

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

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

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

Serial1 Quaternion

Methods

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

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

Apply 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

Complicated Quaternion

Methods

_e :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a)

_i :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a)

Hamiltonian Quaternion

Methods

_j :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a)

_k :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a)

_ijk :: Functor f => (V3 a -> f (V3 a)) -> Quaternion a -> f (Quaternion a)

Finite Quaternion

Associated Types

type Size (Quaternion :: * -> *) :: Nat

Methods

toV :: Quaternion a -> V Nat (Size Quaternion) a

fromV :: V Nat (Size Quaternion) a -> Quaternion a

Metric Quaternion

Methods

dot :: Num a => Quaternion a -> Quaternion a -> a

quadrance :: Num a => Quaternion a -> a

qd :: Num a => Quaternion a -> Quaternion a -> a

distance :: Floating a => Quaternion a -> Quaternion a -> a

norm :: Floating a => Quaternion a -> a

signorm :: Floating a => Quaternion a -> Quaternion a

Additive Quaternion

Methods

zero :: Num a => Quaternion a

(^+^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a

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

lerp :: Num a => a -> Quaternion a -> Quaternion a -> Quaternion a

liftU2 :: (a -> a -> a) -> Quaternion a -> Quaternion a -> Quaternion a

liftI2 :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c

Bind Quaternion

Methods

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

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

Num a => Rotation Quaternion a

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)

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Quaternion a) -> m (Vector (Quaternion a))

basicUnsafeThaw :: PrimMonad m => Vector (Quaternion a) -> m (Mutable Vector (PrimState m) (Quaternion a))

basicLength :: Vector (Quaternion a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Quaternion a) -> Vector (Quaternion a)

basicUnsafeIndexM :: Monad m => Vector (Quaternion a) -> Int -> m (Quaternion a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Quaternion a) -> Vector (Quaternion a) -> m ()

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

Unbox a => MVector MVector (Quaternion a)

Methods

basicLength :: MVector s (Quaternion a) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (Quaternion a) -> MVector s (Quaternion a)

basicOverlaps :: MVector s (Quaternion a) -> MVector s (Quaternion a) -> Bool

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Quaternion a))

basicInitialize :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> m ()

basicUnsafeReplicate :: PrimMonad m => Int -> Quaternion a -> m (MVector (PrimState m) (Quaternion a))

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Int -> m (Quaternion a)

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Int -> Quaternion a -> m ()

basicClear :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Quaternion a -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> MVector (PrimState m) (Quaternion a) -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> MVector (PrimState m) (Quaternion a) -> m ()

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Int -> m (MVector (PrimState m) (Quaternion a))

Eq a => Eq (Quaternion a)

Methods

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

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

RealFloat a => Floating (Quaternion a)

Methods

pi :: Quaternion a

exp :: Quaternion a -> Quaternion a

log :: Quaternion a -> Quaternion a

sqrt :: Quaternion a -> Quaternion a

(**) :: Quaternion a -> Quaternion a -> Quaternion a

logBase :: Quaternion a -> Quaternion a -> Quaternion a

sin :: Quaternion a -> Quaternion a

cos :: Quaternion a -> Quaternion a

tan :: Quaternion a -> Quaternion a

asin :: Quaternion a -> Quaternion a

acos :: Quaternion a -> Quaternion a

atan :: Quaternion a -> Quaternion a

sinh :: Quaternion a -> Quaternion a

cosh :: Quaternion a -> Quaternion a

tanh :: Quaternion a -> Quaternion a

asinh :: Quaternion a -> Quaternion a

acosh :: Quaternion a -> Quaternion a

atanh :: Quaternion a -> Quaternion a

log1p :: Quaternion a -> Quaternion a

expm1 :: Quaternion a -> Quaternion a

log1pexp :: Quaternion a -> Quaternion a

log1mexp :: Quaternion a -> Quaternion a

RealFloat a => Fractional (Quaternion a)

Methods

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

recip :: Quaternion a -> Quaternion a

fromRational :: Rational -> Quaternion a

Data a => Data (Quaternion a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Quaternion a -> c (Quaternion a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Quaternion a)

toConstr :: Quaternion a -> Constr

dataTypeOf :: Quaternion a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Quaternion a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Quaternion a))

gmapT :: (forall b. Data b => b -> b) -> Quaternion a -> Quaternion a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Quaternion a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Quaternion a -> r

gmapQ :: (forall d. Data d => d -> u) -> Quaternion a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Quaternion a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Quaternion a -> m (Quaternion a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Quaternion a -> m (Quaternion a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Quaternion a -> m (Quaternion a)

RealFloat a => Num (Quaternion a)

Methods

(+) :: Quaternion a -> Quaternion a -> Quaternion a

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

(*) :: Quaternion a -> Quaternion a -> Quaternion a

negate :: Quaternion a -> Quaternion a

abs :: Quaternion a -> Quaternion a

signum :: Quaternion a -> Quaternion a

fromInteger :: Integer -> Quaternion a

Ord a => Ord (Quaternion a)

Methods

compare :: Quaternion a -> Quaternion a -> Ordering

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

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

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

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

max :: Quaternion a -> Quaternion a -> Quaternion a

min :: Quaternion a -> Quaternion a -> Quaternion a

Read a => Read (Quaternion a)

Methods

readsPrec :: Int -> ReadS (Quaternion a)

readList :: ReadS [Quaternion a]

readPrec :: ReadPrec (Quaternion a)

readListPrec :: ReadPrec [Quaternion a]

Show a => Show (Quaternion a)

Methods

showsPrec :: Int -> Quaternion a -> ShowS

show :: Quaternion a -> String

showList :: [Quaternion a] -> ShowS

Ix a => Ix (Quaternion a)

Methods

range :: (Quaternion a, Quaternion a) -> [Quaternion a]

index :: (Quaternion a, Quaternion a) -> Quaternion a -> Int

unsafeIndex :: (Quaternion a, Quaternion a) -> Quaternion a -> Int

inRange :: (Quaternion a, Quaternion a) -> Quaternion a -> Bool

rangeSize :: (Quaternion a, Quaternion a) -> Int

unsafeRangeSize :: (Quaternion a, Quaternion a) -> Int

Generic (Quaternion a)

Associated Types

type Rep (Quaternion a) :: * -> *

Methods

from :: Quaternion a -> Rep (Quaternion a) x

to :: Rep (Quaternion a) x -> Quaternion a

Storable a => Storable (Quaternion a)

Methods

sizeOf :: Quaternion a -> Int

alignment :: Quaternion a -> Int

peekElemOff :: Ptr (Quaternion a) -> Int -> IO (Quaternion a)

pokeElemOff :: Ptr (Quaternion a) -> Int -> Quaternion a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (Quaternion a)

pokeByteOff :: Ptr b -> Int -> Quaternion a -> IO ()

peek :: Ptr (Quaternion a) -> IO (Quaternion a)

poke :: Ptr (Quaternion a) -> Quaternion a -> IO ()

Binary a => Binary (Quaternion a)

Methods

put :: Quaternion a -> Put

get :: Get (Quaternion a)

putList :: [Quaternion a] -> Put

Serial a => Serial (Quaternion a)

Methods

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

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

Serialize a => Serialize (Quaternion a)

Methods

put :: Putter (Quaternion a)

get :: Get (Quaternion a)

NFData a => NFData (Quaternion a)

Methods

rnf :: Quaternion a -> ()

Hashable a => Hashable (Quaternion a)

Methods

hashWithSalt :: Int -> Quaternion a -> Int

hash :: Quaternion a -> Int

Unbox a => Unbox (Quaternion a)

Ixed (Quaternion a)

Methods

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

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

Methods

nearZero :: Quaternion a -> Bool

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

Methods

conjugate :: Quaternion a -> Quaternion a

Generic1 * Quaternion

Associated Types

type Rep1 Quaternion (f :: Quaternion -> *) :: k -> *

Methods

from1 :: f a -> Rep1 Quaternion f a

to1 :: Rep1 Quaternion f a -> f a

FunctorWithIndex (E Quaternion) Quaternion

Methods

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

imapped :: (Indexable (E Quaternion) p, Settable f) => p a (f b) -> Quaternion a -> f (Quaternion b)

FoldableWithIndex (E Quaternion) Quaternion

Methods

ifoldMap :: Monoid m => (E Quaternion -> a -> m) -> Quaternion a -> m

ifolded :: (Indexable (E Quaternion) p, Contravariant f, Applicative f) => p a (f a) -> Quaternion a -> f (Quaternion a)

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

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

ifoldr' :: (E Quaternion -> a -> b -> b) -> b -> Quaternion a -> b

ifoldl' :: (E Quaternion -> b -> a -> b) -> b -> Quaternion a -> b

TraversableWithIndex (E Quaternion) Quaternion

Methods

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

itraversed :: (Indexable (E Quaternion) p, Applicative f) => p a (f b) -> Quaternion a -> f (Quaternion b)

Each (Quaternion a) (Quaternion b) a b

Methods

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

type Rep Quaternion

type Rep Quaternion = E Quaternion

type Size Quaternion

type Size Quaternion = 4

data MVector s (Quaternion a)

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

type Rep (Quaternion a)

type Rep (Quaternion a) = D1 * (MetaData "Quaternion" "Linear.Quaternion" "linear-1.20.7-ESPgvMEcP27Jzthlh4sP5X" False) (C1 * (MetaCons "Quaternion" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * a)) (S1 * (MetaSel (Nothing Symbol) SourceUnpack SourceStrict DecidedStrict) (Rec0 * (V3 a)))))

data Vector (Quaternion a)

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

type Index (Quaternion a)

type Index (Quaternion a) = E Quaternion

type IxValue (Quaternion a)

type IxValue (Quaternion a) = a

type Rep1 * Quaternion

type Rep1 * Quaternion = D1 * (MetaData "Quaternion" "Linear.Quaternion" "linear-1.20.7-ESPgvMEcP27Jzthlh4sP5X" False) (C1 * (MetaCons "Quaternion" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 * (MetaSel (Nothing Symbol) SourceUnpack SourceStrict DecidedStrict) (Rec1 * V3))))