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	Haskell2010

Linear.V2

Description

2-D Vectors

Synopsis

data V2 a = V2 !a !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)
ex :: R1 t => E t
ey :: R2 t => E t
perp :: Num a => V2 a -> V2 a
angle :: Floating a => a -> V2 a
unangle :: (Floating a, Ord a) => V2 a -> a
crossZ :: Num a => V2 a -> V2 a -> a

Documentation

data V2 a Source #

A 2-dimensional vector

>>> pure 1 :: V2 Int
V2 1 1

>>> V2 1 2 + V2 3 4
V2 4 6

>>> V2 1 2 * V2 3 4
V2 3 8

>>> sum (V2 1 2)
3

Constructors

V2 !a !a

Instances

Instances details

Representable V2 Source #
Instance details Defined in Linear.V2 Associated Types type Rep V2 Source # Methods tabulate :: (Rep V2 -> a) -> V2 a Source # index :: V2 a -> Rep V2 -> a Source #
MonadFix V2 Source #
Instance details Defined in Linear.V2 Methods mfix :: (a -> V2 a) -> V2 a Source #
MonadZip V2 Source #
Instance details Defined in Linear.V2 Methods mzip :: V2 a -> V2 b -> V2 (a, b) Source # mzipWith :: (a -> b -> c) -> V2 a -> V2 b -> V2 c Source # munzip :: V2 (a, b) -> (V2 a, V2 b) Source #
Foldable V2 Source #
Instance details Defined in Linear.V2 Methods fold :: Monoid m => V2 m -> m Source # foldMap :: Monoid m => (a -> m) -> V2 a -> m Source # foldMap' :: Monoid m => (a -> m) -> V2 a -> m Source # foldr :: (a -> b -> b) -> b -> V2 a -> b Source # foldr' :: (a -> b -> b) -> b -> V2 a -> b Source # foldl :: (b -> a -> b) -> b -> V2 a -> b Source # foldl' :: (b -> a -> b) -> b -> V2 a -> b Source # foldr1 :: (a -> a -> a) -> V2 a -> a Source # foldl1 :: (a -> a -> a) -> V2 a -> a Source # toList :: V2 a -> [a] Source # null :: V2 a -> Bool Source # length :: V2 a -> Int Source # elem :: Eq a => a -> V2 a -> Bool Source # maximum :: Ord a => V2 a -> a Source # minimum :: Ord a => V2 a -> a Source # sum :: Num a => V2 a -> a Source # product :: Num a => V2 a -> a Source #
Eq1 V2 Source #
Instance details Defined in Linear.V2 Methods liftEq :: (a -> b -> Bool) -> V2 a -> V2 b -> Bool Source #
Ord1 V2 Source #
Instance details Defined in Linear.V2 Methods liftCompare :: (a -> b -> Ordering) -> V2 a -> V2 b -> Ordering Source #
Read1 V2 Source #
Instance details Defined in Linear.V2 Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V2 a) Source # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V2 a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V2 a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V2 a] Source #
Show1 V2 Source #
Instance details Defined in Linear.V2 Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V2 a -> ShowS Source # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V2 a] -> ShowS Source #
Traversable V2 Source #
Instance details Defined in Linear.V2 Methods traverse :: Applicative f => (a -> f b) -> V2 a -> f (V2 b) Source # sequenceA :: Applicative f => V2 (f a) -> f (V2 a) Source # mapM :: Monad m => (a -> m b) -> V2 a -> m (V2 b) Source # sequence :: Monad m => V2 (m a) -> m (V2 a) Source #
Applicative V2 Source #
Instance details Defined in Linear.V2 Methods pure :: a -> V2 a Source # (<>) :: V2 (a -> b) -> V2 a -> V2 b Source # liftA2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c Source # (>) :: V2 a -> V2 b -> V2 b Source # (<*) :: V2 a -> V2 b -> V2 a Source #
Functor V2 Source #
Instance details Defined in Linear.V2 Methods fmap :: (a -> b) -> V2 a -> V2 b Source # (<$) :: a -> V2 b -> V2 a Source #
Monad V2 Source #
Instance details Defined in Linear.V2 Methods (>>=) :: V2 a -> (a -> V2 b) -> V2 b Source # (>>) :: V2 a -> V2 b -> V2 b Source # return :: a -> V2 a Source #
Serial1 V2 Source #
Instance details Defined in Linear.V2 Methods serializeWith :: MonadPut m => (a -> m ()) -> V2 a -> m () Source # deserializeWith :: MonadGet m => m a -> m (V2 a) Source #
Distributive V2 Source #
Instance details Defined in Linear.V2 Methods distribute :: Functor f => f (V2 a) -> V2 (f a) Source # collect :: Functor f => (a -> V2 b) -> f a -> V2 (f b) Source # distributeM :: Monad m => m (V2 a) -> V2 (m a) Source # collectM :: Monad m => (a -> V2 b) -> m a -> V2 (m b) Source #
Hashable1 V2 Source #
Instance details Defined in Linear.V2 Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> V2 a -> Int Source #
Affine V2 Source #
Instance details Defined in Linear.Affine Associated Types type Diff V2 :: Type -> Type Source # Methods (.-.) :: Num a => V2 a -> V2 a -> Diff V2 a Source # (.+^) :: Num a => V2 a -> Diff V2 a -> V2 a Source # (.-^) :: Num a => V2 a -> Diff V2 a -> V2 a Source #
Metric V2 Source #
Instance details Defined in Linear.V2 Methods dot :: Num a => V2 a -> V2 a -> a Source # quadrance :: Num a => V2 a -> a Source # qd :: Num a => V2 a -> V2 a -> a Source # distance :: Floating a => V2 a -> V2 a -> a Source # norm :: Floating a => V2 a -> a Source # signorm :: Floating a => V2 a -> V2 a Source #
Trace V2 Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => V2 (V2 a) -> a Source # diagonal :: V2 (V2 a) -> V2 a Source #
Finite V2 Source #
Instance details Defined in Linear.V2 Associated Types type Size V2 :: Nat Source # Methods toV :: V2 a -> V (Size V2) a Source # fromV :: V (Size V2) a -> V2 a Source #
R1 V2 Source #
Instance details Defined in Linear.V2 Methods _x :: Lens' (V2 a) a Source #
R2 V2 Source #
Instance details Defined in Linear.V2 Methods _y :: Lens' (V2 a) a Source # _xy :: Lens' (V2 a) (V2 a) Source #
Additive V2 Source #
Instance details Defined in Linear.V2 Methods zero :: Num a => V2 a Source # (^+^) :: Num a => V2 a -> V2 a -> V2 a Source # (^-^) :: Num a => V2 a -> V2 a -> V2 a Source # lerp :: Num a => a -> V2 a -> V2 a -> V2 a Source # liftU2 :: (a -> a -> a) -> V2 a -> V2 a -> V2 a Source # liftI2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c Source #
Apply V2 Source #
Instance details Defined in Linear.V2 Methods (<.>) :: V2 (a -> b) -> V2 a -> V2 b Source # (.>) :: V2 a -> V2 b -> V2 b Source # (<.) :: V2 a -> V2 b -> V2 a Source # liftF2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c Source #
Bind V2 Source #
Instance details Defined in Linear.V2 Methods (>>-) :: V2 a -> (a -> V2 b) -> V2 b Source # join :: V2 (V2 a) -> V2 a Source #
Foldable1 V2 Source #
Instance details Defined in Linear.V2 Methods fold1 :: Semigroup m => V2 m -> m Source # foldMap1 :: Semigroup m => (a -> m) -> V2 a -> m Source # toNonEmpty :: V2 a -> NonEmpty a Source #
Traversable1 V2 Source #
Instance details Defined in Linear.V2 Methods traverse1 :: Apply f => (a -> f b) -> V2 a -> f (V2 b) Source # sequence1 :: Apply f => V2 (f b) -> f (V2 b) Source #
Num r => Coalgebra r (E V2) Source #
Instance details Defined in Linear.Algebra Methods comult :: (E V2 -> r) -> E V2 -> E V2 -> r Source # counital :: (E V2 -> r) -> r Source #
Lift a => Lift (V2 a :: Type) Source #
Instance details Defined in Linear.V2 Methods lift :: Quote m => V2 a -> m Exp Source # liftTyped :: forall (m :: Type -> Type). Quote m => V2 a -> Code m (V2 a) Source #
Unbox a => Vector Vector (V2 a) Source #
Instance details Defined in Linear.V2 Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V2 a) -> m (Vector (V2 a)) Source # basicUnsafeThaw :: PrimMonad m => Vector (V2 a) -> m (Mutable Vector (PrimState m) (V2 a)) Source # basicLength :: Vector (V2 a) -> Int Source # basicUnsafeSlice :: Int -> Int -> Vector (V2 a) -> Vector (V2 a) Source # basicUnsafeIndexM :: Monad m => Vector (V2 a) -> Int -> m (V2 a) Source # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V2 a) -> Vector (V2 a) -> m () Source # elemseq :: Vector (V2 a) -> V2 a -> b -> b Source #
Unbox a => MVector MVector (V2 a) Source #
Instance details Defined in Linear.V2 Methods basicLength :: MVector s (V2 a) -> Int Source # basicUnsafeSlice :: Int -> Int -> MVector s (V2 a) -> MVector s (V2 a) Source # basicOverlaps :: MVector s (V2 a) -> MVector s (V2 a) -> Bool Source # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V2 a)) Source # basicInitialize :: PrimMonad m => MVector (PrimState m) (V2 a) -> m () Source # basicUnsafeReplicate :: PrimMonad m => Int -> V2 a -> m (MVector (PrimState m) (V2 a)) Source # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> m (V2 a) Source # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> V2 a -> m () Source # basicClear :: PrimMonad m => MVector (PrimState m) (V2 a) -> m () Source # basicSet :: PrimMonad m => MVector (PrimState m) (V2 a) -> V2 a -> m () Source # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V2 a) -> MVector (PrimState m) (V2 a) -> m () Source # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V2 a) -> MVector (PrimState m) (V2 a) -> m () Source # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> m (MVector (PrimState m) (V2 a)) Source #
Data a => Data (V2 a) Source #
Instance details Defined in Linear.V2 Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V2 a -> c (V2 a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V2 a) Source # toConstr :: V2 a -> Constr Source # dataTypeOf :: V2 a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (V2 a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V2 a)) Source # gmapT :: (forall b. Data b => b -> b) -> V2 a -> V2 a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V2 a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V2 a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> V2 a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> V2 a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> V2 a -> m (V2 a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V2 a -> m (V2 a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V2 a -> m (V2 a) Source #
Storable a => Storable (V2 a) Source #
Instance details Defined in Linear.V2 Methods sizeOf :: V2 a -> Int Source # alignment :: V2 a -> Int Source # peekElemOff :: Ptr (V2 a) -> Int -> IO (V2 a) Source # pokeElemOff :: Ptr (V2 a) -> Int -> V2 a -> IO () Source # peekByteOff :: Ptr b -> Int -> IO (V2 a) Source # pokeByteOff :: Ptr b -> Int -> V2 a -> IO () Source # peek :: Ptr (V2 a) -> IO (V2 a) Source # poke :: Ptr (V2 a) -> V2 a -> IO () Source #
Monoid a => Monoid (V2 a) Source #
Instance details Defined in Linear.V2 Methods mempty :: V2 a Source # mappend :: V2 a -> V2 a -> V2 a Source # mconcat :: [V2 a] -> V2 a Source #
Semigroup a => Semigroup (V2 a) Source #
Instance details Defined in Linear.V2 Methods (<>) :: V2 a -> V2 a -> V2 a Source # sconcat :: NonEmpty (V2 a) -> V2 a Source # stimes :: Integral b => b -> V2 a -> V2 a Source #
Bounded a => Bounded (V2 a) Source #
Instance details Defined in Linear.V2 Methods minBound :: V2 a Source # maxBound :: V2 a Source #
Floating a => Floating (V2 a) Source #
Instance details Defined in Linear.V2 Methods pi :: V2 a Source # exp :: V2 a -> V2 a Source # log :: V2 a -> V2 a Source # sqrt :: V2 a -> V2 a Source # (**) :: V2 a -> V2 a -> V2 a Source # logBase :: V2 a -> V2 a -> V2 a Source # sin :: V2 a -> V2 a Source # cos :: V2 a -> V2 a Source # tan :: V2 a -> V2 a Source # asin :: V2 a -> V2 a Source # acos :: V2 a -> V2 a Source # atan :: V2 a -> V2 a Source # sinh :: V2 a -> V2 a Source # cosh :: V2 a -> V2 a Source # tanh :: V2 a -> V2 a Source # asinh :: V2 a -> V2 a Source # acosh :: V2 a -> V2 a Source # atanh :: V2 a -> V2 a Source # log1p :: V2 a -> V2 a Source # expm1 :: V2 a -> V2 a Source # log1pexp :: V2 a -> V2 a Source # log1mexp :: V2 a -> V2 a Source #
Generic (V2 a) Source #
Instance details Defined in Linear.V2 Associated Types type Rep (V2 a) :: Type -> Type Source # Methods from :: V2 a -> Rep (V2 a) x Source # to :: Rep (V2 a) x -> V2 a Source #
Ix a => Ix (V2 a) Source #
Instance details Defined in Linear.V2 Methods range :: (V2 a, V2 a) -> [V2 a] Source # index :: (V2 a, V2 a) -> V2 a -> Int Source # unsafeIndex :: (V2 a, V2 a) -> V2 a -> Int Source # inRange :: (V2 a, V2 a) -> V2 a -> Bool Source # rangeSize :: (V2 a, V2 a) -> Int Source # unsafeRangeSize :: (V2 a, V2 a) -> Int Source #
Num a => Num (V2 a) Source #
Instance details Defined in Linear.V2 Methods (+) :: V2 a -> V2 a -> V2 a Source # (-) :: V2 a -> V2 a -> V2 a Source # (*) :: V2 a -> V2 a -> V2 a Source # negate :: V2 a -> V2 a Source # abs :: V2 a -> V2 a Source # signum :: V2 a -> V2 a Source # fromInteger :: Integer -> V2 a Source #
Read a => Read (V2 a) Source #
Instance details Defined in Linear.V2 Methods readsPrec :: Int -> ReadS (V2 a) Source # readList :: ReadS [V2 a] Source # readPrec :: ReadPrec (V2 a) Source # readListPrec :: ReadPrec [V2 a] Source #
Fractional a => Fractional (V2 a) Source #
Instance details Defined in Linear.V2 Methods (/) :: V2 a -> V2 a -> V2 a Source # recip :: V2 a -> V2 a Source # fromRational :: Rational -> V2 a Source #
Show a => Show (V2 a) Source #
Instance details Defined in Linear.V2 Methods showsPrec :: Int -> V2 a -> ShowS Source # show :: V2 a -> String Source # showList :: [V2 a] -> ShowS Source #
Binary a => Binary (V2 a) Source #
Instance details Defined in Linear.V2 Methods put :: V2 a -> Put Source # get :: Get (V2 a) Source # putList :: [V2 a] -> Put Source #
Serial a => Serial (V2 a) Source #
Instance details Defined in Linear.V2 Methods serialize :: MonadPut m => V2 a -> m () Source # deserialize :: MonadGet m => m (V2 a) Source #
Serialize a => Serialize (V2 a) Source #
Instance details Defined in Linear.V2 Methods put :: Putter (V2 a) Source # get :: Get (V2 a) Source #
NFData a => NFData (V2 a) Source #
Instance details Defined in Linear.V2 Methods rnf :: V2 a -> () Source #
Eq a => Eq (V2 a) Source #
Instance details Defined in Linear.V2 Methods (==) :: V2 a -> V2 a -> Bool Source # (/=) :: V2 a -> V2 a -> Bool Source #
Ord a => Ord (V2 a) Source #
Instance details Defined in Linear.V2 Methods compare :: V2 a -> V2 a -> Ordering Source # (<) :: V2 a -> V2 a -> Bool Source # (<=) :: V2 a -> V2 a -> Bool Source # (>) :: V2 a -> V2 a -> Bool Source # (>=) :: V2 a -> V2 a -> Bool Source # max :: V2 a -> V2 a -> V2 a Source # min :: V2 a -> V2 a -> V2 a Source #
Hashable a => Hashable (V2 a) Source #
Instance details Defined in Linear.V2 Methods hashWithSalt :: Int -> V2 a -> Int Source # hash :: V2 a -> Int Source #
Ixed (V2 a) Source #
Instance details Defined in Linear.V2 Methods ix :: Index (V2 a) -> Traversal' (V2 a) (IxValue (V2 a)) Source #
Epsilon a => Epsilon (V2 a) Source #
Instance details Defined in Linear.V2 Methods nearZero :: V2 a -> Bool Source #
Random a => Random (V2 a) Source #
Instance details Defined in Linear.V2 Methods randomR :: RandomGen g => (V2 a, V2 a) -> g -> (V2 a, g) Source # random :: RandomGen g => g -> (V2 a, g) Source # randomRs :: RandomGen g => (V2 a, V2 a) -> g -> [V2 a] Source # randoms :: RandomGen g => g -> [V2 a] Source #
Unbox a => Unbox (V2 a) Source #
Instance details Defined in Linear.V2
Generic1 V2 Source #
Instance details Defined in Linear.V2 Associated Types type Rep1 V2 :: k -> Type Source # Methods from1 :: forall (a :: k). V2 a -> Rep1 V2 a Source # to1 :: forall (a :: k). Rep1 V2 a -> V2 a Source #
FoldableWithIndex (E V2) V2 Source #
Instance details Defined in Linear.V2 Methods ifoldMap :: Monoid m => (E V2 -> a -> m) -> V2 a -> m Source # ifoldMap' :: Monoid m => (E V2 -> a -> m) -> V2 a -> m Source # ifoldr :: (E V2 -> a -> b -> b) -> b -> V2 a -> b Source # ifoldl :: (E V2 -> b -> a -> b) -> b -> V2 a -> b Source # ifoldr' :: (E V2 -> a -> b -> b) -> b -> V2 a -> b Source # ifoldl' :: (E V2 -> b -> a -> b) -> b -> V2 a -> b Source #
FunctorWithIndex (E V2) V2 Source #
Instance details Defined in Linear.V2 Methods imap :: (E V2 -> a -> b) -> V2 a -> V2 b Source #
TraversableWithIndex (E V2) V2 Source #
Instance details Defined in Linear.V2 Methods itraverse :: Applicative f => (E V2 -> a -> f b) -> V2 a -> f (V2 b) Source #
Each (V2 a) (V2 b) a b Source #
Instance details Defined in Linear.V2 Methods each :: Traversal (V2 a) (V2 b) a b Source #
Field1 (V2 a) (V2 a) a a Source #
Instance details Defined in Linear.V2 Methods _1 :: Lens (V2 a) (V2 a) a a Source #
Field2 (V2 a) (V2 a) a a Source #
Instance details Defined in Linear.V2 Methods _2 :: Lens (V2 a) (V2 a) a a Source #
type Rep V2 Source #
Instance details Defined in Linear.V2 type Rep V2 = E V2
type Diff V2 Source #
Instance details Defined in Linear.Affine type Diff V2 = V2
type Size V2 Source #
Instance details Defined in Linear.V2 type Size V2 = 2
data MVector s (V2 a) Source #
Instance details Defined in Linear.V2 data MVector s (V2 a) = MV_V2 !Int !(MVector s a)
type Rep (V2 a) Source #
Instance details Defined in Linear.V2 type Rep (V2 a) = D1 ('MetaData "V2" "Linear.V2" "linear-1.21.10-BWYLNa1VYXoLpBTdl1DQBL" 'False) (C1 ('MetaCons "V2" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)))
type Index (V2 a) Source #
Instance details Defined in Linear.V2 type Index (V2 a) = E V2
type IxValue (V2 a) Source #
Instance details Defined in Linear.V2 type IxValue (V2 a) = a
data Vector (V2 a) Source #
Instance details Defined in Linear.V2 data Vector (V2 a) = V_V2 !Int !(Vector a)
type Rep1 V2 Source #
Instance details Defined in Linear.V2 type Rep1 V2 = D1 ('MetaData "V2" "Linear.V2" "linear-1.21.10-BWYLNa1VYXoLpBTdl1DQBL" 'False) (C1 ('MetaCons "V2" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1))

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

Instances details

R1 Identity Source #
Instance details Defined in Linear.V1 Methods _x :: Lens' (Identity a) a Source #
R1 Quaternion Source #
Instance details Defined in Linear.Quaternion Methods _x :: Lens' (Quaternion 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 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

Instances details

R2 Quaternion Source #
Instance details Defined in Linear.Quaternion Methods _y :: Lens' (Quaternion a) a Source # _xy :: Lens' (Quaternion a) (V2 a) Source #
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 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

ex :: R1 t => E t Source #

ey :: R2 t => E t Source #

perp :: Num a => V2 a -> V2 a Source #

the counter-clockwise perpendicular vector

>>> perp $ V2 10 20
V2 (-20) 10

angle :: Floating a => a -> V2 a Source #

unangle :: (Floating a, Ord a) => V2 a -> a Source #

crossZ :: Num a => V2 a -> V2 a -> a Source #

The Z-component of the cross product of two vectors in the XY-plane.

>>> crossZ (V2 1 0) (V2 0 1)
1