Copyright	(C) 2012-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <[email protected]>
Stability	experimental
Portability	non-portable
Safe Haskell	Trustworthy
Language	Haskell2010

Linear.V3

Description

3-D Vectors

Synopsis

data V3 a = V3 !a !a !a
cross :: Num a => V3 a -> V3 a -> V3 a
triple :: Num a => V3 a -> V3 a -> V3 a -> a
class R1 (t :: Type -> Type) where
- _x :: Lens' (t a) a
class R1 t => R2 (t :: Type -> Type) where
- _y :: Lens' (t a) a
- _xy :: Lens' (t a) (V2 a)
_yx :: forall (t :: Type -> Type) a. R2 t => Lens' (t a) (V2 a)
class R2 t => R3 (t :: Type -> Type) where
- _z :: Lens' (t a) a
- _xyz :: Lens' (t a) (V3 a)
_xz :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a)
_yz :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a)
_zx :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a)
_zy :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a)
_xzy :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a)
_yxz :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a)
_yzx :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a)
_zxy :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a)
_zyx :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a)
ex :: forall (t :: Type -> Type). R1 t => E t
ey :: forall (t :: Type -> Type). R2 t => E t
ez :: forall (t :: Type -> Type). R3 t => E t

Documentation

data V3 a Source #

A 3-dimensional vector

Constructors

V3 !a !a !a

Instances

Instances details

Representable V3 Source #

Instance details

Defined in Linear.V3

Associated Types

type Rep V3
Instance details Defined in Linear.V3 type Rep V3 = E V3

Methods

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

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

MonadFix V3 Source #

Instance details

Defined in Linear.V3

Methods

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

MonadZip V3 Source #

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) #

Foldable V3 Source #

Instance details

Defined in Linear.V3

Methods

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

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

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

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

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

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

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

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

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

toList :: V3 a -> [a] #

null :: V3 a -> Bool #

length :: V3 a -> Int #

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

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

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

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

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

Foldable1 V3 Source #

Instance details

Defined in Linear.V3

Methods

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

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

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

toNonEmpty :: V3 a -> NonEmpty a #

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

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

head :: V3 a -> a #

last :: V3 a -> a #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> V3 a -> b #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> V3 a -> b #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> V3 a -> b #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> V3 a -> b #

Eq1 V3 Source #

Instance details

Defined in Linear.V3

Methods

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

Ord1 V3 Source #

Instance details

Defined in Linear.V3

Methods

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

Read1 V3 Source #

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 Source #

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 #

Traversable V3 Source #

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) #

Applicative V3 Source #

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 #

Functor V3 Source #

Instance details

Defined in Linear.V3

Methods

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

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

Monad V3 Source #

Instance details

Defined in Linear.V3

Methods

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

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

return :: a -> V3 a #

Serial1 V3 Source #

Instance details

Defined in Linear.V3

Methods

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

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

Distributive V3 Source #

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) #

Hashable1 V3 Source #

Instance details

Defined in Linear.V3

Methods

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

Affine V3 Source #

Instance details

Defined in Linear.Affine

Associated Types

type Diff V3
Instance details Defined in Linear.Affine type Diff V3 = V3

Methods

(.-.) :: Num a => V3 a -> V3 a -> Diff V3 a Source #

(.+^) :: Num a => V3 a -> Diff V3 a -> V3 a Source #

(.-^) :: Num a => V3 a -> Diff V3 a -> V3 a Source #

Metric V3 Source #

Instance details

Defined in Linear.V3

Methods

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

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

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

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

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

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

Trace V3 Source #

Instance details

Defined in Linear.Trace

Methods

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

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

Finite V3 Source #

Instance details

Defined in Linear.V3

Associated Types

type Size V3
Instance details Defined in Linear.V3 type Size V3 = 3

Methods

toV :: V3 a -> V (Size V3) a Source #

fromV :: V (Size V3) a -> V3 a Source #

R1 V3 Source #

Instance details

Defined in Linear.V3

Methods

_x :: Lens' (V3 a) 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 #

R3 V3 Source #

Instance details

Defined in Linear.V3

Methods

_z :: Lens' (V3 a) a Source #

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

Additive V3 Source #

Instance details

Defined in Linear.V3

Methods

zero :: Num a => V3 a Source #

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

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

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

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

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

Apply V3 Source #

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 #

Bind V3 Source #

Instance details

Defined in Linear.V3

Methods

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

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

Traversable1 V3 Source #

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) #

Generic1 V3 Source #

Instance details

Defined in Linear.V3

Associated Types

type Rep1 V3

Instance details

Defined in Linear.V3

type Rep1 V3 = D1 ('MetaData "V3" "Linear.V3" "linear-1.23.2-8abSSbh6WhfAkxshm17ZVU" '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)))

Methods

from1 :: V3 a -> Rep1 V3 a #

to1 :: Rep1 V3 a -> V3 a #

Num r => Coalgebra r (E V3) Source #

Instance details

Defined in Linear.Algebra

Methods

comult :: (E V3 -> r) -> E V3 -> E V3 -> r Source #

counital :: (E V3 -> r) -> r Source #

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

Instance details

Defined in Linear.V3

Methods

lift :: Quote m => V3 a -> m Exp #

liftTyped :: forall (m :: Type -> Type). Quote m => V3 a -> Code m (V3 a) #

Unbox a => Vector Vector (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

basicUnsafeFreeze :: Mutable Vector s (V3 a) -> ST s (Vector (V3 a))

basicUnsafeThaw :: Vector (V3 a) -> ST s (Mutable Vector s (V3 a))

basicLength :: Vector (V3 a) -> Int

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

basicUnsafeIndexM :: Vector (V3 a) -> Int -> Box (V3 a)

basicUnsafeCopy :: Mutable Vector s (V3 a) -> Vector (V3 a) -> ST s ()

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

Unbox a => MVector MVector (V3 a) Source #

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

basicInitialize :: MVector s (V3 a) -> ST s ()

basicUnsafeReplicate :: Int -> V3 a -> ST s (MVector s (V3 a))

basicUnsafeRead :: MVector s (V3 a) -> Int -> ST s (V3 a)

basicUnsafeWrite :: MVector s (V3 a) -> Int -> V3 a -> ST s ()

basicClear :: MVector s (V3 a) -> ST s ()

basicSet :: MVector s (V3 a) -> V3 a -> ST s ()

basicUnsafeCopy :: MVector s (V3 a) -> MVector s (V3 a) -> ST s ()

basicUnsafeMove :: MVector s (V3 a) -> MVector s (V3 a) -> ST s ()

basicUnsafeGrow :: MVector s (V3 a) -> Int -> ST s (MVector s (V3 a))

Data a => Data (V3 a) Source #

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

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

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

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

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

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

Storable a => Storable (V3 a) Source #

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 () #

Monoid a => Monoid (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

mempty :: V3 a #

mappend :: V3 a -> V3 a -> V3 a #

mconcat :: [V3 a] -> V3 a #

Semigroup a => Semigroup (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

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

sconcat :: NonEmpty (V3 a) -> V3 a #

stimes :: Integral b => b -> V3 a -> V3 a #

Bounded a => Bounded (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

minBound :: V3 a #

maxBound :: V3 a #

Floating a => Floating (V3 a) Source #

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 #

Generic (V3 a) Source #

Instance details

Defined in Linear.V3

Associated Types

type Rep (V3 a)

Instance details

Defined in Linear.V3

type Rep (V3 a) = D1 ('MetaData "V3" "Linear.V3" "linear-1.23.2-8abSSbh6WhfAkxshm17ZVU" '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))))

Methods

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

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

Ix a => Ix (V3 a) Source #

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 #

Num a => Num (V3 a) Source #

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 #

Read a => Read (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

readsPrec :: Int -> ReadS (V3 a) #

readList :: ReadS [V3 a] #

readPrec :: ReadPrec (V3 a) #

readListPrec :: ReadPrec [V3 a] #

Fractional a => Fractional (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

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

recip :: V3 a -> V3 a #

fromRational :: Rational -> V3 a #

Show a => Show (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

showsPrec :: Int -> V3 a -> ShowS #

show :: V3 a -> String #

showList :: [V3 a] -> ShowS #

Binary a => Binary (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

put :: V3 a -> Put #

get :: Get (V3 a) #

putList :: [V3 a] -> Put #

Serial a => Serial (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

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

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

Serialize a => Serialize (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

put :: Putter (V3 a) #

get :: Get (V3 a) #

NFData a => NFData (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

rnf :: V3 a -> () #

Eq a => Eq (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

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

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

Ord a => Ord (V3 a) Source #

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 #

Hashable a => Hashable (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

hashWithSalt :: Int -> V3 a -> Int #

hash :: V3 a -> Int #

Ixed (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

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

Epsilon a => Epsilon (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

nearZero :: V3 a -> Bool Source #

Random a => Random (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

randomR :: RandomGen g => (V3 a, V3 a) -> g -> (V3 a, g) #

random :: RandomGen g => g -> (V3 a, g) #

randomRs :: RandomGen g => (V3 a, V3 a) -> g -> [V3 a] #

randoms :: RandomGen g => g -> [V3 a] #

Uniform a => Uniform (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

uniformM :: StatefulGen g m => g -> m (V3 a) #

UniformRange a => UniformRange (V3 a) Source #

Instance details

Defined in Linear.V3

Methods

uniformRM :: StatefulGen g m => (V3 a, V3 a) -> g -> m (V3 a) #

isInRange :: (V3 a, V3 a) -> V3 a -> Bool #

Unbox a => Unbox (V3 a) Source #

Instance details

Defined in Linear.V3

FoldableWithIndex (E V3) V3 Source #

Instance details

Defined in Linear.V3

Methods

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

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

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

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

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

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

FunctorWithIndex (E V3) V3 Source #

Instance details

Defined in Linear.V3

Methods

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

TraversableWithIndex (E V3) V3 Source #

Instance details

Defined in Linear.V3

Methods

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

Each (V3 a) (V3 b) a b Source #

Instance details

Defined in Linear.V3

Methods

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

Field1 (V3 a) (V3 a) a a Source #

Instance details

Defined in Linear.V3

Methods

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

Field2 (V3 a) (V3 a) a a Source #

Instance details

Defined in Linear.V3

Methods

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

Field3 (V3 a) (V3 a) a a Source #

Instance details

Defined in Linear.V3

Methods

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

type Rep V3 Source #

Instance details

Defined in Linear.V3

type Rep V3 = E V3

type Diff V3 Source #

Instance details

Defined in Linear.Affine

type Diff V3 = V3

type Size V3 Source #

Instance details

Defined in Linear.V3

type Size V3 = 3

type Rep1 V3 Source #

Instance details

Defined in Linear.V3

type Rep1 V3 = D1 ('MetaData "V3" "Linear.V3" "linear-1.23.2-8abSSbh6WhfAkxshm17ZVU" 'False) (C1 ('MetaCons "V3" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1)))

data MVector s (V3 a) Source #

Instance details

Defined in Linear.V3

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

type Rep (V3 a) Source #

Instance details

Defined in Linear.V3

type Rep (V3 a) = D1 ('MetaData "V3" "Linear.V3" "linear-1.23.2-8abSSbh6WhfAkxshm17ZVU" 'False) (C1 ('MetaCons "V3" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a))))

type Index (V3 a) Source #

Instance details

Defined in Linear.V3

type Index (V3 a) = E V3

type IxValue (V3 a) Source #

Instance details

Defined in Linear.V3

type IxValue (V3 a) = a

data Vector (V3 a) Source #

Instance details

Defined in Linear.V3

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

cross :: Num a => V3 a -> V3 a -> V3 a Source #

cross product

triple :: Num a => V3 a -> V3 a -> V3 a -> a Source #

scalar triple product

class R1 (t :: Type -> Type) 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 :: Type -> Type) 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 :: forall (t :: Type -> Type) a. R2 t => Lens' (t a) (V2 a) Source #

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

class R2 t => R3 (t :: Type -> Type) 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

Instances details

R3 Quaternion Source #
Instance details Defined in Linear.Quaternion Methods _z :: Lens' (Quaternion a) a Source # _xyz :: Lens' (Quaternion a) (V3 a) Source #
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 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 :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a) Source #

_yz :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a) Source #

_zx :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a) Source #

_zy :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a) Source #

_xzy :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a) Source #

_yxz :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a) Source #

_yzx :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a) Source #

_zxy :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a) Source #

_zyx :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a) Source #

ex :: forall (t :: Type -> Type). R1 t => E t Source #

ey :: forall (t :: Type -> Type). R2 t => E t Source #

ez :: forall (t :: Type -> Type). R3 t => E t Source #