Copyright	(C) 2012-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	non-portable
Safe Haskell	Trustworthy
Language	Haskell98

Linear.V4

Description

4-D Vectors

Synopsis

data V4 a = V4 !a !a !a !a
vector :: Num a => V3 a -> V4 a
point :: Num a => V3 a -> V4 a
normalizePoint :: Fractional a => V4 a -> V3 a
class R1 t where
- _x :: Lens' (t a) a
class R1 t => R2 t where
- _y :: Lens' (t a) a
- _xy :: Lens' (t a) (V2 a)
_yx :: R2 t => Lens' (t a) (V2 a)
class R2 t => R3 t where
- _z :: Lens' (t a) a
- _xyz :: Lens' (t a) (V3 a)
_xz :: R3 t => Lens' (t a) (V2 a)
_yz :: R3 t => Lens' (t a) (V2 a)
_zx :: R3 t => Lens' (t a) (V2 a)
_zy :: R3 t => Lens' (t a) (V2 a)
_xzy :: R3 t => Lens' (t a) (V3 a)
_yxz :: R3 t => Lens' (t a) (V3 a)
_yzx :: R3 t => Lens' (t a) (V3 a)
_zxy :: R3 t => Lens' (t a) (V3 a)
_zyx :: R3 t => Lens' (t a) (V3 a)
class R3 t => R4 t where
- _w :: Lens' (t a) a
- _xyzw :: Lens' (t a) (V4 a)
_xw :: R4 t => Lens' (t a) (V2 a)
_yw :: R4 t => Lens' (t a) (V2 a)
_zw :: R4 t => Lens' (t a) (V2 a)
_wx :: R4 t => Lens' (t a) (V2 a)
_wy :: R4 t => Lens' (t a) (V2 a)
_wz :: R4 t => Lens' (t a) (V2 a)
_xyw :: R4 t => Lens' (t a) (V3 a)
_xzw :: R4 t => Lens' (t a) (V3 a)
_xwy :: R4 t => Lens' (t a) (V3 a)
_xwz :: R4 t => Lens' (t a) (V3 a)
_yxw :: R4 t => Lens' (t a) (V3 a)
_yzw :: R4 t => Lens' (t a) (V3 a)
_ywx :: R4 t => Lens' (t a) (V3 a)
_ywz :: R4 t => Lens' (t a) (V3 a)
_zxw :: R4 t => Lens' (t a) (V3 a)
_zyw :: R4 t => Lens' (t a) (V3 a)
_zwx :: R4 t => Lens' (t a) (V3 a)
_zwy :: R4 t => Lens' (t a) (V3 a)
_wxy :: R4 t => Lens' (t a) (V3 a)
_wxz :: R4 t => Lens' (t a) (V3 a)
_wyx :: R4 t => Lens' (t a) (V3 a)
_wyz :: R4 t => Lens' (t a) (V3 a)
_wzx :: R4 t => Lens' (t a) (V3 a)
_wzy :: R4 t => Lens' (t a) (V3 a)
_xywz :: R4 t => Lens' (t a) (V4 a)
_xzyw :: R4 t => Lens' (t a) (V4 a)
_xzwy :: R4 t => Lens' (t a) (V4 a)
_xwyz :: R4 t => Lens' (t a) (V4 a)
_xwzy :: R4 t => Lens' (t a) (V4 a)
_yxzw :: R4 t => Lens' (t a) (V4 a)
_yxwz :: R4 t => Lens' (t a) (V4 a)
_yzxw :: R4 t => Lens' (t a) (V4 a)
_yzwx :: R4 t => Lens' (t a) (V4 a)
_ywxz :: R4 t => Lens' (t a) (V4 a)
_ywzx :: R4 t => Lens' (t a) (V4 a)
_zxyw :: R4 t => Lens' (t a) (V4 a)
_zxwy :: R4 t => Lens' (t a) (V4 a)
_zyxw :: R4 t => Lens' (t a) (V4 a)
_zywx :: R4 t => Lens' (t a) (V4 a)
_zwxy :: R4 t => Lens' (t a) (V4 a)
_zwyx :: R4 t => Lens' (t a) (V4 a)
_wxyz :: R4 t => Lens' (t a) (V4 a)
_wxzy :: R4 t => Lens' (t a) (V4 a)
_wyxz :: R4 t => Lens' (t a) (V4 a)
_wyzx :: R4 t => Lens' (t a) (V4 a)
_wzxy :: R4 t => Lens' (t a) (V4 a)
_wzyx :: R4 t => Lens' (t a) (V4 a)
ex :: R1 t => E t
ey :: R2 t => E t
ez :: R3 t => E t
ew :: R4 t => E t

Documentation

data V4 a Source #

A 4-dimensional vector.

Constructors

V4 !a !a !a !a

Instances

Monad V4 Source #
Instance details Defined in Linear.V4 Methods (>>=) :: V4 a -> (a -> V4 b) -> V4 b # (>>) :: V4 a -> V4 b -> V4 b # return :: a -> V4 a # fail :: String -> V4 a #
Functor V4 Source #
Instance details Defined in Linear.V4 Methods fmap :: (a -> b) -> V4 a -> V4 b # (<$) :: a -> V4 b -> V4 a #
MonadFix V4 Source #
Instance details Defined in Linear.V4 Methods mfix :: (a -> V4 a) -> V4 a #
Applicative V4 Source #
Instance details Defined in Linear.V4 Methods pure :: a -> V4 a # (<>) :: V4 (a -> b) -> V4 a -> V4 b # liftA2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c # (>) :: V4 a -> V4 b -> V4 b # (<*) :: V4 a -> V4 b -> V4 a #
Foldable V4 Source #
Instance details Defined in Linear.V4 Methods fold :: Monoid m => V4 m -> m # foldMap :: Monoid m => (a -> m) -> V4 a -> m # foldr :: (a -> b -> b) -> b -> V4 a -> b # foldr' :: (a -> b -> b) -> b -> V4 a -> b # foldl :: (b -> a -> b) -> b -> V4 a -> b # foldl' :: (b -> a -> b) -> b -> V4 a -> b # foldr1 :: (a -> a -> a) -> V4 a -> a # foldl1 :: (a -> a -> a) -> V4 a -> a # toList :: V4 a -> [a] # null :: V4 a -> Bool # length :: V4 a -> Int # elem :: Eq a => a -> V4 a -> Bool # maximum :: Ord a => V4 a -> a # minimum :: Ord a => V4 a -> a # sum :: Num a => V4 a -> a # product :: Num a => V4 a -> a #
Traversable V4 Source #
Instance details Defined in Linear.V4 Methods traverse :: Applicative f => (a -> f b) -> V4 a -> f (V4 b) # sequenceA :: Applicative f => V4 (f a) -> f (V4 a) # mapM :: Monad m => (a -> m b) -> V4 a -> m (V4 b) # sequence :: Monad m => V4 (m a) -> m (V4 a) #
Distributive V4 Source #
Instance details Defined in Linear.V4 Methods distribute :: Functor f => f (V4 a) -> V4 (f a) # collect :: Functor f => (a -> V4 b) -> f a -> V4 (f b) # distributeM :: Monad m => m (V4 a) -> V4 (m a) # collectM :: Monad m => (a -> V4 b) -> m a -> V4 (m b) #
Representable V4 Source #
Instance details Defined in Linear.V4 Associated Types type Rep V4 :: Type # Methods tabulate :: (Rep V4 -> a) -> V4 a # index :: V4 a -> Rep V4 -> a #
Eq1 V4 Source #
Instance details Defined in Linear.V4 Methods liftEq :: (a -> b -> Bool) -> V4 a -> V4 b -> Bool #
Ord1 V4 Source #
Instance details Defined in Linear.V4 Methods liftCompare :: (a -> b -> Ordering) -> V4 a -> V4 b -> Ordering #
Read1 V4 Source #
Instance details Defined in Linear.V4 Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V4 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V4 a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V4 a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V4 a] #
Show1 V4 Source #
Instance details Defined in Linear.V4 Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V4 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V4 a] -> ShowS #
MonadZip V4 Source #
Instance details Defined in Linear.V4 Methods mzip :: V4 a -> V4 b -> V4 (a, b) # mzipWith :: (a -> b -> c) -> V4 a -> V4 b -> V4 c # munzip :: V4 (a, b) -> (V4 a, V4 b) #
Serial1 V4 Source #
Instance details Defined in Linear.V4 Methods serializeWith :: MonadPut m => (a -> m ()) -> V4 a -> m () # deserializeWith :: MonadGet m => m a -> m (V4 a) #
Hashable1 V4 Source #
Instance details Defined in Linear.V4 Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> V4 a -> Int #
Apply V4 Source #
Instance details Defined in Linear.V4 Methods (<.>) :: V4 (a -> b) -> V4 a -> V4 b # (.>) :: V4 a -> V4 b -> V4 b # (<.) :: V4 a -> V4 b -> V4 a # liftF2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c #
Traversable1 V4 Source #
Instance details Defined in Linear.V4 Methods traverse1 :: Apply f => (a -> f b) -> V4 a -> f (V4 b) # sequence1 :: Apply f => V4 (f b) -> f (V4 b) #
Foldable1 V4 Source #
Instance details Defined in Linear.V4 Methods fold1 :: Semigroup m => V4 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V4 a -> m # toNonEmpty :: V4 a -> NonEmpty a #
Bind V4 Source #
Instance details Defined in Linear.V4 Methods (>>-) :: V4 a -> (a -> V4 b) -> V4 b # join :: V4 (V4 a) -> V4 a #
Additive V4 Source #
Instance details Defined in Linear.V4 Methods zero :: Num a => V4 a Source # (^+^) :: Num a => V4 a -> V4 a -> V4 a Source # (^-^) :: Num a => V4 a -> V4 a -> V4 a Source # lerp :: Num a => a -> V4 a -> V4 a -> V4 a Source # liftU2 :: (a -> a -> a) -> V4 a -> V4 a -> V4 a Source # liftI2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c Source #
Metric V4 Source #
Instance details Defined in Linear.V4 Methods dot :: Num a => V4 a -> V4 a -> a Source # quadrance :: Num a => V4 a -> a Source # qd :: Num a => V4 a -> V4 a -> a Source # distance :: Floating a => V4 a -> V4 a -> a Source # norm :: Floating a => V4 a -> a Source # signorm :: Floating a => V4 a -> V4 a Source #
Finite V4 Source #
Instance details Defined in Linear.V4 Associated Types type Size V4 :: Nat Source # Methods toV :: V4 a -> V (Size V4) a Source # fromV :: V (Size V4) a -> V4 a Source #
R1 V4 Source #
Instance details Defined in Linear.V4 Methods _x :: Lens' (V4 a) a Source #
R2 V4 Source #
Instance details Defined in Linear.V4 Methods _y :: Lens' (V4 a) a Source # _xy :: Lens' (V4 a) (V2 a) Source #
R3 V4 Source #
Instance details Defined in Linear.V4 Methods _z :: Lens' (V4 a) a Source # _xyz :: Lens' (V4 a) (V3 a) Source #
R4 V4 Source #
Instance details Defined in Linear.V4 Methods _w :: Lens' (V4 a) a Source # _xyzw :: Lens' (V4 a) (V4 a) Source #
Trace V4 Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => V4 (V4 a) -> a Source # diagonal :: V4 (V4 a) -> V4 a Source #
Affine V4 Source #
Instance details Defined in Linear.Affine Associated Types type Diff V4 :: Type -> Type Source # Methods (.-.) :: Num a => V4 a -> V4 a -> Diff V4 a Source # (.+^) :: Num a => V4 a -> Diff V4 a -> V4 a Source # (.-^) :: Num a => V4 a -> Diff V4 a -> V4 a Source #
Unbox a => Vector Vector (V4 a) Source #
Instance details Defined in Linear.V4 Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V4 a) -> m (Vector (V4 a)) # basicUnsafeThaw :: PrimMonad m => Vector (V4 a) -> m (Mutable Vector (PrimState m) (V4 a)) # basicLength :: Vector (V4 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V4 a) -> Vector (V4 a) # basicUnsafeIndexM :: Monad m => Vector (V4 a) -> Int -> m (V4 a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V4 a) -> Vector (V4 a) -> m () # elemseq :: Vector (V4 a) -> V4 a -> b -> b #
Unbox a => MVector MVector (V4 a) Source #
Instance details Defined in Linear.V4 Methods basicLength :: MVector s (V4 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V4 a) -> MVector s (V4 a) # basicOverlaps :: MVector s (V4 a) -> MVector s (V4 a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V4 a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V4 a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V4 a -> m (MVector (PrimState m) (V4 a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V4 a) -> Int -> m (V4 a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V4 a) -> Int -> V4 a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V4 a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V4 a) -> V4 a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V4 a) -> MVector (PrimState m) (V4 a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V4 a) -> MVector (PrimState m) (V4 a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V4 a) -> Int -> m (MVector (PrimState m) (V4 a)) #
Num r => Coalgebra r (E V4) Source #
Instance details Defined in Linear.Algebra Methods comult :: (E V4 -> r) -> E V4 -> E V4 -> r Source # counital :: (E V4 -> r) -> r Source #
Bounded a => Bounded (V4 a) Source #
Instance details Defined in Linear.V4 Methods minBound :: V4 a # maxBound :: V4 a #
Eq a => Eq (V4 a) Source #
Instance details Defined in Linear.V4 Methods (==) :: V4 a -> V4 a -> Bool # (/=) :: V4 a -> V4 a -> Bool #
Floating a => Floating (V4 a) Source #
Instance details Defined in Linear.V4 Methods pi :: V4 a # exp :: V4 a -> V4 a # log :: V4 a -> V4 a # sqrt :: V4 a -> V4 a # (**) :: V4 a -> V4 a -> V4 a # logBase :: V4 a -> V4 a -> V4 a # sin :: V4 a -> V4 a # cos :: V4 a -> V4 a # tan :: V4 a -> V4 a # asin :: V4 a -> V4 a # acos :: V4 a -> V4 a # atan :: V4 a -> V4 a # sinh :: V4 a -> V4 a # cosh :: V4 a -> V4 a # tanh :: V4 a -> V4 a # asinh :: V4 a -> V4 a # acosh :: V4 a -> V4 a # atanh :: V4 a -> V4 a # log1p :: V4 a -> V4 a # expm1 :: V4 a -> V4 a # log1pexp :: V4 a -> V4 a # log1mexp :: V4 a -> V4 a #
Fractional a => Fractional (V4 a) Source #
Instance details Defined in Linear.V4 Methods (/) :: V4 a -> V4 a -> V4 a # recip :: V4 a -> V4 a # fromRational :: Rational -> V4 a #
Data a => Data (V4 a) Source #
Instance details Defined in Linear.V4 Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V4 a -> c (V4 a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V4 a) # toConstr :: V4 a -> Constr # dataTypeOf :: V4 a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (V4 a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V4 a)) # gmapT :: (forall b. Data b => b -> b) -> V4 a -> V4 a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V4 a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V4 a -> r # gmapQ :: (forall d. Data d => d -> u) -> V4 a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> V4 a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> V4 a -> m (V4 a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V4 a -> m (V4 a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V4 a -> m (V4 a) #
Num a => Num (V4 a) Source #
Instance details Defined in Linear.V4 Methods (+) :: V4 a -> V4 a -> V4 a # (-) :: V4 a -> V4 a -> V4 a # (*) :: V4 a -> V4 a -> V4 a # negate :: V4 a -> V4 a # abs :: V4 a -> V4 a # signum :: V4 a -> V4 a # fromInteger :: Integer -> V4 a #
Ord a => Ord (V4 a) Source #
Instance details Defined in Linear.V4 Methods compare :: V4 a -> V4 a -> Ordering # (<) :: V4 a -> V4 a -> Bool # (<=) :: V4 a -> V4 a -> Bool # (>) :: V4 a -> V4 a -> Bool # (>=) :: V4 a -> V4 a -> Bool # max :: V4 a -> V4 a -> V4 a # min :: V4 a -> V4 a -> V4 a #
Read a => Read (V4 a) Source #
Instance details Defined in Linear.V4 Methods readsPrec :: Int -> ReadS (V4 a) # readList :: ReadS [V4 a] # readPrec :: ReadPrec (V4 a) # readListPrec :: ReadPrec [V4 a] #
Show a => Show (V4 a) Source #
Instance details Defined in Linear.V4 Methods showsPrec :: Int -> V4 a -> ShowS # show :: V4 a -> String # showList :: [V4 a] -> ShowS #
Ix a => Ix (V4 a) Source #
Instance details Defined in Linear.V4 Methods range :: (V4 a, V4 a) -> [V4 a] # index :: (V4 a, V4 a) -> V4 a -> Int # unsafeIndex :: (V4 a, V4 a) -> V4 a -> Int inRange :: (V4 a, V4 a) -> V4 a -> Bool # rangeSize :: (V4 a, V4 a) -> Int # unsafeRangeSize :: (V4 a, V4 a) -> Int
Generic (V4 a) Source #
Instance details Defined in Linear.V4 Associated Types type Rep (V4 a) :: Type -> Type # Methods from :: V4 a -> Rep (V4 a) x # to :: Rep (V4 a) x -> V4 a #
Semigroup a => Semigroup (V4 a) Source #
Instance details Defined in Linear.V4 Methods (<>) :: V4 a -> V4 a -> V4 a # sconcat :: NonEmpty (V4 a) -> V4 a # stimes :: Integral b => b -> V4 a -> V4 a #
Monoid a => Monoid (V4 a) Source #
Instance details Defined in Linear.V4 Methods mempty :: V4 a # mappend :: V4 a -> V4 a -> V4 a # mconcat :: [V4 a] -> V4 a #
Lift a => Lift (V4 a) Source #
Instance details Defined in Linear.V4 Methods lift :: V4 a -> Q Exp #
Storable a => Storable (V4 a) Source #
Instance details Defined in Linear.V4 Methods sizeOf :: V4 a -> Int # alignment :: V4 a -> Int # peekElemOff :: Ptr (V4 a) -> Int -> IO (V4 a) # pokeElemOff :: Ptr (V4 a) -> Int -> V4 a -> IO () # peekByteOff :: Ptr b -> Int -> IO (V4 a) # pokeByteOff :: Ptr b -> Int -> V4 a -> IO () # peek :: Ptr (V4 a) -> IO (V4 a) # poke :: Ptr (V4 a) -> V4 a -> IO () #
Binary a => Binary (V4 a) Source #
Instance details Defined in Linear.V4 Methods put :: V4 a -> Put # get :: Get (V4 a) # putList :: [V4 a] -> Put #
Serial a => Serial (V4 a) Source #
Instance details Defined in Linear.V4 Methods serialize :: MonadPut m => V4 a -> m () # deserialize :: MonadGet m => m (V4 a) #
Serialize a => Serialize (V4 a) Source #
Instance details Defined in Linear.V4 Methods put :: Putter (V4 a) # get :: Get (V4 a) #
NFData a => NFData (V4 a) Source #
Instance details Defined in Linear.V4 Methods rnf :: V4 a -> () #
Hashable a => Hashable (V4 a) Source #
Instance details Defined in Linear.V4 Methods hashWithSalt :: Int -> V4 a -> Int # hash :: V4 a -> Int #
Unbox a => Unbox (V4 a) Source #
Instance details Defined in Linear.V4
Ixed (V4 a) Source #
Instance details Defined in Linear.V4 Methods ix :: Index (V4 a) -> Traversal' (V4 a) (IxValue (V4 a)) #
Random a => Random (V4 a) Source #
Instance details Defined in Linear.V4 Methods randomR :: RandomGen g => (V4 a, V4 a) -> g -> (V4 a, g) # random :: RandomGen g => g -> (V4 a, g) # randomRs :: RandomGen g => (V4 a, V4 a) -> g -> [V4 a] # randoms :: RandomGen g => g -> [V4 a] # randomRIO :: (V4 a, V4 a) -> IO (V4 a) # randomIO :: IO (V4 a) #
Epsilon a => Epsilon (V4 a) Source #
Instance details Defined in Linear.V4 Methods nearZero :: V4 a -> Bool Source #
Generic1 V4 Source #
Instance details Defined in Linear.V4 Associated Types type Rep1 V4 :: k -> Type # Methods from1 :: V4 a -> Rep1 V4 a # to1 :: Rep1 V4 a -> V4 a #
FunctorWithIndex (E V4) V4 Source #
Instance details Defined in Linear.V4 Methods imap :: (E V4 -> a -> b) -> V4 a -> V4 b # imapped :: IndexedSetter (E V4) (V4 a) (V4 b) a b #
FoldableWithIndex (E V4) V4 Source #
Instance details Defined in Linear.V4 Methods ifoldMap :: Monoid m => (E V4 -> a -> m) -> V4 a -> m # ifolded :: IndexedFold (E V4) (V4 a) a # ifoldr :: (E V4 -> a -> b -> b) -> b -> V4 a -> b # ifoldl :: (E V4 -> b -> a -> b) -> b -> V4 a -> b # ifoldr' :: (E V4 -> a -> b -> b) -> b -> V4 a -> b # ifoldl' :: (E V4 -> b -> a -> b) -> b -> V4 a -> b #
TraversableWithIndex (E V4) V4 Source #
Instance details Defined in Linear.V4 Methods itraverse :: Applicative f => (E V4 -> a -> f b) -> V4 a -> f (V4 b) # itraversed :: IndexedTraversal (E V4) (V4 a) (V4 b) a b #
Each (V4 a) (V4 b) a b Source #
Instance details Defined in Linear.V4 Methods each :: Traversal (V4 a) (V4 b) a b #
Field1 (V4 a) (V4 a) a a Source #
Instance details Defined in Linear.V4 Methods _1 :: Lens (V4 a) (V4 a) a a #
Field2 (V4 a) (V4 a) a a Source #
Instance details Defined in Linear.V4 Methods _2 :: Lens (V4 a) (V4 a) a a #
Field3 (V4 a) (V4 a) a a Source #
Instance details Defined in Linear.V4 Methods _3 :: Lens (V4 a) (V4 a) a a #
Field4 (V4 a) (V4 a) a a Source #
Instance details Defined in Linear.V4 Methods _4 :: Lens (V4 a) (V4 a) a a #
type Rep V4 Source #
Instance details Defined in Linear.V4 type Rep V4 = E V4
type Size V4 Source #
Instance details Defined in Linear.V4 type Size V4 = 4
type Diff V4 Source #
Instance details Defined in Linear.Affine type Diff V4 = V4
data MVector s (V4 a) Source #
Instance details Defined in Linear.V4 data MVector s (V4 a) = MV_V4 !Int !(MVector s a)
type Rep (V4 a) Source #
Instance details Defined in Linear.V4 type Rep (V4 a) = D1 (MetaData "V4" "Linear.V4" "linear-1.21-8koDM2CeTPQEICbCH921MU" False) (C1 (MetaCons "V4" 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) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a))))
data Vector (V4 a) Source #
Instance details Defined in Linear.V4 data Vector (V4 a) = V_V4 !Int !(Vector a)
type Index (V4 a) Source #
Instance details Defined in Linear.V4 type Index (V4 a) = E V4
type IxValue (V4 a) Source #
Instance details Defined in Linear.V4 type IxValue (V4 a) = a
type Rep1 V4 Source #
Instance details Defined in Linear.V4 type Rep1 V4 = D1 (MetaData "V4" "Linear.V4" "linear-1.21-8koDM2CeTPQEICbCH921MU" False) (C1 (MetaCons "V4" 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 :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1)))

vector :: Num a => V3 a -> V4 a Source #

Convert a 3-dimensional affine vector into a 4-dimensional homogeneous vector, i.e. sets the w coordinate to 0.

point :: Num a => V3 a -> V4 a Source #

Convert a 3-dimensional affine point into a 4-dimensional homogeneous vector, i.e. sets the w coordinate to 1.

normalizePoint :: Fractional a => V4 a -> V3 a Source #

Convert 4-dimensional projective coordinates to a 3-dimensional point. This operation may be denoted, euclidean [x:y:z:w] = (x/w, y/w, z/w) where the projective, homogenous, coordinate [x:y:z:w] is one of many associated with a single point (x/w, y/w, z/w).

class R1 t where Source #

A space that has at least 1 basis vector _x.

Methods

_x :: Lens' (t a) a Source #

>>> V1 2 ^._x
2

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

Instances

R1 Identity Source #
Instance details Defined in Linear.V1 Methods _x :: Lens' (Identity a) a Source #
R1 V1 Source #
Instance details Defined in Linear.V1 Methods _x :: Lens' (V1 a) a Source #
R1 V2 Source #
Instance details Defined in Linear.V2 Methods _x :: Lens' (V2 a) a Source #
R1 V3 Source #
Instance details Defined in Linear.V3 Methods _x :: Lens' (V3 a) a Source #
R1 V4 Source #
Instance details Defined in Linear.V4 Methods _x :: Lens' (V4 a) a Source #
R1 Quaternion Source #
Instance details Defined in Linear.Quaternion Methods _x :: Lens' (Quaternion a) a Source #
R1 f => R1 (Point f) Source #
Instance details Defined in Linear.Affine Methods _x :: Lens' (Point f a) a Source #

class R1 t => R2 t where Source #

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

Minimal complete definition

_xy

Methods

_y :: Lens' (t a) a Source #

>>> V2 1 2 ^._y
2

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

_xy :: Lens' (t a) (V2 a) Source #

Instances

R2 V2 Source #
Instance details Defined in Linear.V2 Methods _y :: Lens' (V2 a) a Source # _xy :: Lens' (V2 a) (V2 a) Source #
R2 V3 Source #
Instance details Defined in Linear.V3 Methods _y :: Lens' (V3 a) a Source # _xy :: Lens' (V3 a) (V2 a) Source #
R2 V4 Source #
Instance details Defined in Linear.V4 Methods _y :: Lens' (V4 a) a Source # _xy :: Lens' (V4 a) (V2 a) Source #
R2 Quaternion Source #
Instance details Defined in Linear.Quaternion Methods _y :: Lens' (Quaternion a) a Source # _xy :: Lens' (Quaternion a) (V2 a) Source #
R2 f => R2 (Point f) Source #
Instance details Defined in Linear.Affine Methods _y :: Lens' (Point f a) a Source # _xy :: Lens' (Point f a) (V2 a) Source #

_yx :: R2 t => Lens' (t a) (V2 a) Source #

>>> V2 1 2 ^. _yx
V2 2 1

class R2 t => R3 t where Source #

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

Methods

_z :: Lens' (t a) a Source #

>>> V3 1 2 3 ^. _z
3

_xyz :: Lens' (t a) (V3 a) Source #

Instances

R3 V3 Source #
Instance details Defined in Linear.V3 Methods _z :: Lens' (V3 a) a Source # _xyz :: Lens' (V3 a) (V3 a) Source #
R3 V4 Source #
Instance details Defined in Linear.V4 Methods _z :: Lens' (V4 a) a Source # _xyz :: Lens' (V4 a) (V3 a) Source #
R3 Quaternion Source #
Instance details Defined in Linear.Quaternion Methods _z :: Lens' (Quaternion a) a Source # _xyz :: Lens' (Quaternion a) (V3 a) Source #
R3 f => R3 (Point f) Source #
Instance details Defined in Linear.Affine Methods _z :: Lens' (Point f a) a Source # _xyz :: Lens' (Point f a) (V3 a) Source #

_xz :: R3 t => Lens' (t a) (V2 a) Source #

_yz :: R3 t => Lens' (t a) (V2 a) Source #

_zx :: R3 t => Lens' (t a) (V2 a) Source #

_zy :: R3 t => Lens' (t a) (V2 a) Source #

_xzy :: R3 t => Lens' (t a) (V3 a) Source #

_yxz :: R3 t => Lens' (t a) (V3 a) Source #

_yzx :: R3 t => Lens' (t a) (V3 a) Source #

_zxy :: R3 t => Lens' (t a) (V3 a) Source #

_zyx :: R3 t => Lens' (t a) (V3 a) Source #

class R3 t => R4 t where Source #

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

Methods

_w :: Lens' (t a) a Source #

>>> V4 1 2 3 4 ^._w
4

_xyzw :: Lens' (t a) (V4 a) Source #

Instances

R4 V4 Source #
Instance details Defined in Linear.V4 Methods _w :: Lens' (V4 a) a Source # _xyzw :: Lens' (V4 a) (V4 a) Source #
R4 Quaternion Source #
Instance details Defined in Linear.Quaternion Methods _w :: Lens' (Quaternion a) a Source # _xyzw :: Lens' (Quaternion a) (V4 a) Source #
R4 f => R4 (Point f) Source #
Instance details Defined in Linear.Affine Methods _w :: Lens' (Point f a) a Source # _xyzw :: Lens' (Point f a) (V4 a) Source #

_xw :: R4 t => Lens' (t a) (V2 a) Source #

_yw :: R4 t => Lens' (t a) (V2 a) Source #

_zw :: R4 t => Lens' (t a) (V2 a) Source #

_wx :: R4 t => Lens' (t a) (V2 a) Source #

_wy :: R4 t => Lens' (t a) (V2 a) Source #

_wz :: R4 t => Lens' (t a) (V2 a) Source #

_xyw :: R4 t => Lens' (t a) (V3 a) Source #

_xzw :: R4 t => Lens' (t a) (V3 a) Source #

_xwy :: R4 t => Lens' (t a) (V3 a) Source #

_xwz :: R4 t => Lens' (t a) (V3 a) Source #

_yxw :: R4 t => Lens' (t a) (V3 a) Source #

_yzw :: R4 t => Lens' (t a) (V3 a) Source #

_ywx :: R4 t => Lens' (t a) (V3 a) Source #

_ywz :: R4 t => Lens' (t a) (V3 a) Source #

_zxw :: R4 t => Lens' (t a) (V3 a) Source #

_zyw :: R4 t => Lens' (t a) (V3 a) Source #

_zwx :: R4 t => Lens' (t a) (V3 a) Source #

_zwy :: R4 t => Lens' (t a) (V3 a) Source #

_wxy :: R4 t => Lens' (t a) (V3 a) Source #

_wxz :: R4 t => Lens' (t a) (V3 a) Source #

_wyx :: R4 t => Lens' (t a) (V3 a) Source #

_wyz :: R4 t => Lens' (t a) (V3 a) Source #

_wzx :: R4 t => Lens' (t a) (V3 a) Source #

_wzy :: R4 t => Lens' (t a) (V3 a) Source #

_xywz :: R4 t => Lens' (t a) (V4 a) Source #

_xzyw :: R4 t => Lens' (t a) (V4 a) Source #

_xzwy :: R4 t => Lens' (t a) (V4 a) Source #

_xwyz :: R4 t => Lens' (t a) (V4 a) Source #

_xwzy :: R4 t => Lens' (t a) (V4 a) Source #

_yxzw :: R4 t => Lens' (t a) (V4 a) Source #

_yxwz :: R4 t => Lens' (t a) (V4 a) Source #

_yzxw :: R4 t => Lens' (t a) (V4 a) Source #

_yzwx :: R4 t => Lens' (t a) (V4 a) Source #

_ywxz :: R4 t => Lens' (t a) (V4 a) Source #

_ywzx :: R4 t => Lens' (t a) (V4 a) Source #

_zxyw :: R4 t => Lens' (t a) (V4 a) Source #

_zxwy :: R4 t => Lens' (t a) (V4 a) Source #

_zyxw :: R4 t => Lens' (t a) (V4 a) Source #

_zywx :: R4 t => Lens' (t a) (V4 a) Source #

_zwxy :: R4 t => Lens' (t a) (V4 a) Source #

_zwyx :: R4 t => Lens' (t a) (V4 a) Source #

_wxyz :: R4 t => Lens' (t a) (V4 a) Source #

_wxzy :: R4 t => Lens' (t a) (V4 a) Source #

_wyxz :: R4 t => Lens' (t a) (V4 a) Source #

_wyzx :: R4 t => Lens' (t a) (V4 a) Source #

_wzxy :: R4 t => Lens' (t a) (V4 a) Source #

_wzyx :: R4 t => Lens' (t a) (V4 a) Source #

ex :: R1 t => E t Source #

ey :: R2 t => E t Source #

ez :: R3 t => E t Source #

ew :: R4 t => E t Source #