Data.QuadTree

Documentation

data QuadTree a

A type mapping values at (infinitely precise) locations in 2D space. That is, you can consider an QuadTree to be a function V2 Rational -> a, equipped with efficient means of querying the space.

QuadTrees should usually be constructed using their Monoidal or Applicative interfaces, as well as by way of the fill function.

Constructors

QuadTree

Fields

• ot_default :: a
• ot_root_pow :: Integer
• ot_tree :: Free a

Instances

Applicative QuadTree

Defined in Data.QuadTree

Methods

pure :: a -> QuadTree a

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

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

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

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

Functor QuadTree

Defined in Data.QuadTree

Methods

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

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

Monoid a => Monoid (QuadTree a)

Defined in Data.QuadTree

Methods

mempty :: QuadTree a

mappend :: QuadTree a -> QuadTree a -> QuadTree a

mconcat :: [QuadTree a] -> QuadTree a

Semigroup a => Semigroup (QuadTree a)

Defined in Data.QuadTree

Methods

(<>) :: QuadTree a -> QuadTree a -> QuadTree a

sconcat :: NonEmpty (QuadTree a) -> QuadTree a

stimes :: Integral b => b -> QuadTree a -> QuadTree a

Num a => Num (QuadTree a)

Defined in Data.QuadTree

Methods

(+) :: QuadTree a -> QuadTree a -> QuadTree a

(-) :: QuadTree a -> QuadTree a -> QuadTree a

(*) :: QuadTree a -> QuadTree a -> QuadTree a

negate :: QuadTree a -> QuadTree a

abs :: QuadTree a -> QuadTree a

signum :: QuadTree a -> QuadTree a

fromInteger :: Integer -> QuadTree a

Show a => Show (QuadTree a)

Defined in Data.QuadTree

Methods

showsPrec :: Int -> QuadTree a -> ShowS

show :: QuadTree a -> String

showList :: [QuadTree a] -> ShowS

Eq a => Eq (QuadTree a)

Defined in Data.QuadTree

Methods

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

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

Semilattice a => Semilattice (QuadTree a)

Defined in Data.QuadTree

Methods

(/\) :: QuadTree a -> QuadTree a -> QuadTree a

Constructing QuadTrees

fill :: forall a. Rect Rational -> a -> QuadTree a -> QuadTree a

Fill a Rect with the given value in an QuadTree

combineAla :: forall n a. (Coercible a n, Semigroup n) => (a -> n) -> QuadTree a -> QuadTree a -> QuadTree a

Combine two QuadTrees using a different semigroup than usual. For example, in order to replace any values in qt1 with those covered by qt2, we can use:

combineAla Last qt1 qt2

Spatially Querying QuadTrees

lookup :: V2 Rational -> QuadTree a -> a

Get the value at the given position in the QuadTree.

query :: Semilattice s => (a -> s) -> Rect Rational -> QuadTree a -> s

Query a region of space in an QuadTree. This method is a special case of foldMap, specialized to finite regions.

For example, if you'd like to check if everything in the Rect has a specific value, use All as your choice of Semilattice. If you'd like to check whether anything in the space has a value, instead use Any.

Eliminating QuadTrees

fuse :: Eq a => QuadTree a -> QuadTree a

Fuse together all adjacent regions of space which contain the same value. This will speed up subsequent queries, but requires traversing the entire tree.

elements :: Ord a => QuadTree a -> Set a

Get the unique elements contained in the QuadTree.

toRects :: QuadTree a -> [(Rect Rational, a)]

Partition the QuadTree into contiguous, singular-valued Rects. Satsifies the law

foldr (uncurry fill) (pure $ defaultValue ot) (toRects ot) == ot

boundingRect :: QuadTree a -> Rect Rational

Get a Rect guaranteed to bound all of the non-defaulted values in the QuadTree.

defaultValue :: QuadTree a -> a

Get the value used to fill the infinity of space in an QuadTree.

Constructing Rects

data Rect a

An axis-aligned bounding box in 3-space.

Constructors

Rect

Fields

• r_pos :: !(V2 a)
• r_size :: !(V2 a)

Instances

Functor Rect

Defined in Data.QuadTree.Internal

Methods

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

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

Generic (Rect a)

Defined in Data.QuadTree.Internal

Associated Types

type Rep (Rect a) :: Type -> Type

Methods

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

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

Read a => Read (Rect a)

Defined in Data.QuadTree.Internal

Methods

readsPrec :: Int -> ReadS (Rect a)

readList :: ReadS [Rect a]

readPrec :: ReadPrec (Rect a)

readListPrec :: ReadPrec [Rect a]

Show a => Show (Rect a)

Defined in Data.QuadTree.Internal

Methods

showsPrec :: Int -> Rect a -> ShowS

show :: Rect a -> String

showList :: [Rect a] -> ShowS

Eq a => Eq (Rect a)

Defined in Data.QuadTree.Internal

Methods

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

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

Ord a => Ord (Rect a)

Defined in Data.QuadTree.Internal

Methods

compare :: Rect a -> Rect a -> Ordering

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

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

(>) :: Rect a -> Rect a -> Bool

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

max :: Rect a -> Rect a -> Rect a

min :: Rect a -> Rect a -> Rect a

type Rep (Rect a)

Defined in Data.QuadTree.Internal

type Rep (Rect a) = D1 ('MetaData "Rect" "Data.QuadTree.Internal" "nspace-0.2.0.0-JcrzAw5ubjR6TX1H0E6SmC" 'False) (C1 ('MetaCons "Rect" 'PrefixI 'True) (S1 ('MetaSel ('Just "r_pos") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (V2 a)) :*: S1 ('MetaSel ('Just "r_size") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (V2 a))))

mkRectByPow :: Integer -> Rect Rational

Construct a Rect centered around $(0, 0, 0)$, with side length $2n$.

Eliminating Rects

midpoint :: Fractional a => Rect a -> V2 a

Compute the center of a Rect.

subdivide :: Fractional a => Rect a -> V4 (Rect a)

Subdivide a Rect into four Rects which fill up the same volume.

rectCorners :: Num a => Rect a -> V4 (V2 a)

Get the co-ordinates of the corners of a Rect.

Indexing Types

data V2 a

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

Representable V2

Defined in Linear.V2

Associated Types

type Rep V2

Methods

tabulate :: (Rep V2 -> a) -> V2 a

index :: V2 a -> Rep V2 -> a

MonadFix V2

Defined in Linear.V2

Methods

mfix :: (a -> V2 a) -> V2 a

MonadZip V2

Defined in Linear.V2

Methods

mzip :: V2 a -> V2 b -> V2 (a, b)

mzipWith :: (a -> b -> c) -> V2 a -> V2 b -> V2 c

munzip :: V2 (a, b) -> (V2 a, V2 b)

Foldable V2

Defined in Linear.V2

Methods

fold :: Monoid m => V2 m -> m

foldMap :: Monoid m => (a -> m) -> V2 a -> m

foldMap' :: Monoid m => (a -> m) -> V2 a -> m

foldr :: (a -> b -> b) -> b -> V2 a -> b

foldr' :: (a -> b -> b) -> b -> V2 a -> b

foldl :: (b -> a -> b) -> b -> V2 a -> b

foldl' :: (b -> a -> b) -> b -> V2 a -> b

foldr1 :: (a -> a -> a) -> V2 a -> a

foldl1 :: (a -> a -> a) -> V2 a -> a

toList :: V2 a -> [a]

null :: V2 a -> Bool

length :: V2 a -> Int

elem :: Eq a => a -> V2 a -> Bool

maximum :: Ord a => V2 a -> a

minimum :: Ord a => V2 a -> a

sum :: Num a => V2 a -> a

product :: Num a => V2 a -> a

Eq1 V2

Defined in Linear.V2

Methods

liftEq :: (a -> b -> Bool) -> V2 a -> V2 b -> Bool

Ord1 V2

Defined in Linear.V2

Methods

liftCompare :: (a -> b -> Ordering) -> V2 a -> V2 b -> Ordering

Read1 V2

Defined in Linear.V2

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V2 a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V2 a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V2 a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V2 a]

Show1 V2

Defined in Linear.V2

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V2 a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V2 a] -> ShowS

Traversable V2

Defined in Linear.V2

Methods

traverse :: Applicative f => (a -> f b) -> V2 a -> f (V2 b)

sequenceA :: Applicative f => V2 (f a) -> f (V2 a)

mapM :: Monad m => (a -> m b) -> V2 a -> m (V2 b)

sequence :: Monad m => V2 (m a) -> m (V2 a)

Applicative V2

Defined in Linear.V2

Methods

pure :: a -> V2 a

(<*>) :: V2 (a -> b) -> V2 a -> V2 b

liftA2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c

(*>) :: V2 a -> V2 b -> V2 b

(<*) :: V2 a -> V2 b -> V2 a

Functor V2

Defined in Linear.V2

Methods

fmap :: (a -> b) -> V2 a -> V2 b

(<$) :: a -> V2 b -> V2 a

Monad V2

Defined in Linear.V2

Methods

(>>=) :: V2 a -> (a -> V2 b) -> V2 b

(>>) :: V2 a -> V2 b -> V2 b

return :: a -> V2 a

Serial1 V2

Defined in Linear.V2

Methods

serializeWith :: MonadPut m => (a -> m ()) -> V2 a -> m ()

deserializeWith :: MonadGet m => m a -> m (V2 a)

Distributive V2

Defined in Linear.V2

Methods

distribute :: Functor f => f (V2 a) -> V2 (f a)

collect :: Functor f => (a -> V2 b) -> f a -> V2 (f b)

distributeM :: Monad m => m (V2 a) -> V2 (m a)

collectM :: Monad m => (a -> V2 b) -> m a -> V2 (m b)

Foldable1 V2

Defined in Linear.V2

Methods

fold1 :: Semigroup m => V2 m -> m

foldMap1 :: Semigroup m => (a -> m) -> V2 a -> m

foldMap1' :: Semigroup m => (a -> m) -> V2 a -> m

toNonEmpty :: V2 a -> NonEmpty a

maximum :: Ord a => V2 a -> a

minimum :: Ord a => V2 a -> a

head :: V2 a -> a

last :: V2 a -> a

foldrMap1 :: (a -> b) -> (a -> b -> b) -> V2 a -> b

foldlMap1' :: (a -> b) -> (b -> a -> b) -> V2 a -> b

foldlMap1 :: (a -> b) -> (b -> a -> b) -> V2 a -> b

foldrMap1' :: (a -> b) -> (a -> b -> b) -> V2 a -> b

Hashable1 V2

Defined in Linear.V2

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> V2 a -> Int

Metric V2

Defined in Linear.V2

Methods

dot :: Num a => V2 a -> V2 a -> a

quadrance :: Num a => V2 a -> a

qd :: Num a => V2 a -> V2 a -> a

distance :: Floating a => V2 a -> V2 a -> a

norm :: Floating a => V2 a -> a

signorm :: Floating a => V2 a -> V2 a

Finite V2

Defined in Linear.V2

Associated Types

type Size V2 :: Nat

Methods

toV :: V2 a -> V (Size V2) a

fromV :: V (Size V2) a -> V2 a

R1 V2

Defined in Linear.V2

Methods

_x :: Lens' (V2 a) a

R2 V2

Defined in Linear.V2

Methods

_y :: Lens' (V2 a) a

_xy :: Lens' (V2 a) (V2 a)

Additive V2

Defined in Linear.V2

Methods

zero :: Num a => V2 a

(^+^) :: Num a => V2 a -> V2 a -> V2 a

(^-^) :: Num a => V2 a -> V2 a -> V2 a

lerp :: Num a => a -> V2 a -> V2 a -> V2 a

liftU2 :: (a -> a -> a) -> V2 a -> V2 a -> V2 a

liftI2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c

Apply V2

Defined in Linear.V2

Methods

(<.>) :: V2 (a -> b) -> V2 a -> V2 b

(.>) :: V2 a -> V2 b -> V2 b

(<.) :: V2 a -> V2 b -> V2 a

liftF2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c

Bind V2

Defined in Linear.V2

Methods

(>>-) :: V2 a -> (a -> V2 b) -> V2 b

join :: V2 (V2 a) -> V2 a

Traversable1 V2

Defined in Linear.V2

Methods

traverse1 :: Apply f => (a -> f b) -> V2 a -> f (V2 b)

sequence1 :: Apply f => V2 (f b) -> f (V2 b)

Generic1 V2

Defined in Linear.V2

Associated Types

type Rep1 V2 :: k -> Type

Methods

from1 :: forall (a :: k). V2 a -> Rep1 V2 a

to1 :: forall (a :: k). Rep1 V2 a -> V2 a

Unbox a => Vector Vector (V2 a)

Defined in Linear.V2

Methods

basicUnsafeFreeze :: Mutable Vector s (V2 a) -> ST s (Vector (V2 a))

basicUnsafeThaw :: Vector (V2 a) -> ST s (Mutable Vector s (V2 a))

basicLength :: Vector (V2 a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (V2 a) -> Vector (V2 a)

basicUnsafeIndexM :: Vector (V2 a) -> Int -> Box (V2 a)

basicUnsafeCopy :: Mutable Vector s (V2 a) -> Vector (V2 a) -> ST s ()

elemseq :: Vector (V2 a) -> V2 a -> b -> b

Unbox a => MVector MVector (V2 a)

Defined in Linear.V2

Methods

basicLength :: MVector s (V2 a) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (V2 a) -> MVector s (V2 a)

basicOverlaps :: MVector s (V2 a) -> MVector s (V2 a) -> Bool

basicUnsafeNew :: Int -> ST s (MVector s (V2 a))

basicInitialize :: MVector s (V2 a) -> ST s ()

basicUnsafeReplicate :: Int -> V2 a -> ST s (MVector s (V2 a))

basicUnsafeRead :: MVector s (V2 a) -> Int -> ST s (V2 a)

basicUnsafeWrite :: MVector s (V2 a) -> Int -> V2 a -> ST s ()

basicClear :: MVector s (V2 a) -> ST s ()

basicSet :: MVector s (V2 a) -> V2 a -> ST s ()

basicUnsafeCopy :: MVector s (V2 a) -> MVector s (V2 a) -> ST s ()

basicUnsafeMove :: MVector s (V2 a) -> MVector s (V2 a) -> ST s ()

basicUnsafeGrow :: MVector s (V2 a) -> Int -> ST s (MVector s (V2 a))

Data a => Data (V2 a)

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)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V2 a)

toConstr :: V2 a -> Constr

dataTypeOf :: V2 a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (V2 a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V2 a))

gmapT :: (forall b. Data b => b -> b) -> V2 a -> V2 a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V2 a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V2 a -> r

gmapQ :: (forall d. Data d => d -> u) -> V2 a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> V2 a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> V2 a -> m (V2 a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V2 a -> m (V2 a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V2 a -> m (V2 a)

Storable a => Storable (V2 a)

Defined in Linear.V2

Methods

sizeOf :: V2 a -> Int

alignment :: V2 a -> Int

peekElemOff :: Ptr (V2 a) -> Int -> IO (V2 a)

pokeElemOff :: Ptr (V2 a) -> Int -> V2 a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (V2 a)

pokeByteOff :: Ptr b -> Int -> V2 a -> IO ()

peek :: Ptr (V2 a) -> IO (V2 a)

poke :: Ptr (V2 a) -> V2 a -> IO ()

Monoid a => Monoid (V2 a)

Defined in Linear.V2

Methods

mempty :: V2 a

mappend :: V2 a -> V2 a -> V2 a

mconcat :: [V2 a] -> V2 a

Semigroup a => Semigroup (V2 a)

Defined in Linear.V2

Methods

(<>) :: V2 a -> V2 a -> V2 a

sconcat :: NonEmpty (V2 a) -> V2 a

stimes :: Integral b => b -> V2 a -> V2 a

Bounded a => Bounded (V2 a)

Defined in Linear.V2

Methods

minBound :: V2 a

maxBound :: V2 a

Floating a => Floating (V2 a)

Defined in Linear.V2

Methods

pi :: V2 a

exp :: V2 a -> V2 a

log :: V2 a -> V2 a

sqrt :: V2 a -> V2 a

(**) :: V2 a -> V2 a -> V2 a

logBase :: V2 a -> V2 a -> V2 a

sin :: V2 a -> V2 a

cos :: V2 a -> V2 a

tan :: V2 a -> V2 a

asin :: V2 a -> V2 a

acos :: V2 a -> V2 a

atan :: V2 a -> V2 a

sinh :: V2 a -> V2 a

cosh :: V2 a -> V2 a

tanh :: V2 a -> V2 a

asinh :: V2 a -> V2 a

acosh :: V2 a -> V2 a

atanh :: V2 a -> V2 a

log1p :: V2 a -> V2 a

expm1 :: V2 a -> V2 a

log1pexp :: V2 a -> V2 a

log1mexp :: V2 a -> V2 a

Generic (V2 a)

Defined in Linear.V2

Associated Types

type Rep (V2 a) :: Type -> Type

Methods

from :: V2 a -> Rep (V2 a) x

to :: Rep (V2 a) x -> V2 a

Ix a => Ix (V2 a)

Defined in Linear.V2

Methods

range :: (V2 a, V2 a) -> [V2 a]

index :: (V2 a, V2 a) -> V2 a -> Int

unsafeIndex :: (V2 a, V2 a) -> V2 a -> Int

inRange :: (V2 a, V2 a) -> V2 a -> Bool

rangeSize :: (V2 a, V2 a) -> Int

unsafeRangeSize :: (V2 a, V2 a) -> Int

Num a => Num (V2 a)

Defined in Linear.V2

Methods

(+) :: V2 a -> V2 a -> V2 a

(-) :: V2 a -> V2 a -> V2 a

(*) :: V2 a -> V2 a -> V2 a

negate :: V2 a -> V2 a

abs :: V2 a -> V2 a

signum :: V2 a -> V2 a

fromInteger :: Integer -> V2 a

Read a => Read (V2 a)

Defined in Linear.V2

Methods

readsPrec :: Int -> ReadS (V2 a)

readList :: ReadS [V2 a]

readPrec :: ReadPrec (V2 a)

readListPrec :: ReadPrec [V2 a]

Fractional a => Fractional (V2 a)

Defined in Linear.V2

Methods

(/) :: V2 a -> V2 a -> V2 a

recip :: V2 a -> V2 a

fromRational :: Rational -> V2 a

Show a => Show (V2 a)

Defined in Linear.V2

Methods

showsPrec :: Int -> V2 a -> ShowS

show :: V2 a -> String

showList :: [V2 a] -> ShowS

Binary a => Binary (V2 a)

Defined in Linear.V2

Methods

put :: V2 a -> Put

get :: Get (V2 a)

putList :: [V2 a] -> Put

Serial a => Serial (V2 a)

Defined in Linear.V2

Methods

serialize :: MonadPut m => V2 a -> m ()

deserialize :: MonadGet m => m (V2 a)

Serialize a => Serialize (V2 a)

Defined in Linear.V2

Methods

put :: Putter (V2 a)

get :: Get (V2 a)

NFData a => NFData (V2 a)

Defined in Linear.V2

Methods

rnf :: V2 a -> ()

Eq a => Eq (V2 a)

Defined in Linear.V2

Methods

(==) :: V2 a -> V2 a -> Bool

(/=) :: V2 a -> V2 a -> Bool

Ord a => Ord (V2 a)

Defined in Linear.V2

Methods

compare :: V2 a -> V2 a -> Ordering

(<) :: V2 a -> V2 a -> Bool

(<=) :: V2 a -> V2 a -> Bool

(>) :: V2 a -> V2 a -> Bool

(>=) :: V2 a -> V2 a -> Bool

max :: V2 a -> V2 a -> V2 a

min :: V2 a -> V2 a -> V2 a

Hashable a => Hashable (V2 a)

Defined in Linear.V2

Methods

hashWithSalt :: Int -> V2 a -> Int

hash :: V2 a -> Int

Ixed (V2 a)

Defined in Linear.V2

Methods

ix :: Index (V2 a) -> Traversal' (V2 a) (IxValue (V2 a))

Epsilon a => Epsilon (V2 a)

Defined in Linear.V2

Methods

nearZero :: V2 a -> Bool

Random a => Random (V2 a)

Defined in Linear.V2

Methods

randomR :: RandomGen g => (V2 a, V2 a) -> g -> (V2 a, g)

random :: RandomGen g => g -> (V2 a, g)

randomRs :: RandomGen g => (V2 a, V2 a) -> g -> [V2 a]

randoms :: RandomGen g => g -> [V2 a]

Unbox a => Unbox (V2 a)

Defined in Linear.V2

FoldableWithIndex (E V2) V2

Defined in Linear.V2

Methods

ifoldMap :: Monoid m => (E V2 -> a -> m) -> V2 a -> m

ifoldMap' :: Monoid m => (E V2 -> a -> m) -> V2 a -> m

ifoldr :: (E V2 -> a -> b -> b) -> b -> V2 a -> b

ifoldl :: (E V2 -> b -> a -> b) -> b -> V2 a -> b

ifoldr' :: (E V2 -> a -> b -> b) -> b -> V2 a -> b

ifoldl' :: (E V2 -> b -> a -> b) -> b -> V2 a -> b

FunctorWithIndex (E V2) V2

Defined in Linear.V2

Methods

imap :: (E V2 -> a -> b) -> V2 a -> V2 b

TraversableWithIndex (E V2) V2

Defined in Linear.V2

Methods

itraverse :: Applicative f => (E V2 -> a -> f b) -> V2 a -> f (V2 b)

Lift a => Lift (V2 a :: Type)

Defined in Linear.V2

Methods

lift :: Quote m => V2 a -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => V2 a -> Code m (V2 a)

Each (V2 a) (V2 b) a b

Defined in Linear.V2

Methods

each :: Traversal (V2 a) (V2 b) a b

Field1 (V2 a) (V2 a) a a

Defined in Linear.V2

Methods

_1 :: Lens (V2 a) (V2 a) a a

Field2 (V2 a) (V2 a) a a

Defined in Linear.V2

Methods

_2 :: Lens (V2 a) (V2 a) a a

type Rep V2

Defined in Linear.V2

type Rep V2 = E V2

type Size V2

Defined in Linear.V2

type Size V2 = 2

type Rep1 V2

Defined in Linear.V2

type Rep1 V2 = D1 ('MetaData "V2" "Linear.V2" "linear-1.22-ANafbhSdznBKD15zEySBd9" 'False) (C1 ('MetaCons "V2" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1))

data MVector s (V2 a)

Defined in Linear.V2

data MVector s (V2 a) = MV_V2 !Int !(MVector s a)

type Rep (V2 a)

Defined in Linear.V2

type Rep (V2 a) = D1 ('MetaData "V2" "Linear.V2" "linear-1.22-ANafbhSdznBKD15zEySBd9" '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)

Defined in Linear.V2

type Index (V2 a) = E V2

type IxValue (V2 a)

Defined in Linear.V2

type IxValue (V2 a) = a

data Vector (V2 a)

Defined in Linear.V2

data Vector (V2 a) = V_V2 !Int !(Vector a)

data V4 a

A 4-dimensional vector.

Constructors

V4 !a !a !a !a

Instances

Representable V4

Defined in Linear.V4

Associated Types

type Rep V4

Methods

tabulate :: (Rep V4 -> a) -> V4 a

index :: V4 a -> Rep V4 -> a

MonadFix V4

Defined in Linear.V4

Methods

mfix :: (a -> V4 a) -> V4 a

MonadZip V4

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)

Foldable V4

Defined in Linear.V4

Methods

fold :: Monoid m => V4 m -> m

foldMap :: Monoid m => (a -> m) -> V4 a -> 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

Eq1 V4

Defined in Linear.V4

Methods

liftEq :: (a -> b -> Bool) -> V4 a -> V4 b -> Bool

Ord1 V4

Defined in Linear.V4

Methods

liftCompare :: (a -> b -> Ordering) -> V4 a -> V4 b -> Ordering

Read1 V4

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

Defined in Linear.V4

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V4 a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V4 a] -> ShowS

Traversable V4

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)

Applicative V4

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

Functor V4

Defined in Linear.V4

Methods

fmap :: (a -> b) -> V4 a -> V4 b

(<$) :: a -> V4 b -> V4 a

Monad V4

Defined in Linear.V4

Methods

(>>=) :: V4 a -> (a -> V4 b) -> V4 b

(>>) :: V4 a -> V4 b -> V4 b

return :: a -> V4 a

Serial1 V4

Defined in Linear.V4

Methods

serializeWith :: MonadPut m => (a -> m ()) -> V4 a -> m ()

deserializeWith :: MonadGet m => m a -> m (V4 a)

Distributive V4

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)

Foldable1 V4

Defined in Linear.V4

Methods

fold1 :: Semigroup m => V4 m -> m

foldMap1 :: Semigroup m => (a -> m) -> V4 a -> m

foldMap1' :: Semigroup m => (a -> m) -> V4 a -> m

toNonEmpty :: V4 a -> NonEmpty a

maximum :: Ord a => V4 a -> a

minimum :: Ord a => V4 a -> a

head :: V4 a -> a

last :: V4 a -> a

foldrMap1 :: (a -> b) -> (a -> b -> b) -> V4 a -> b

foldlMap1' :: (a -> b) -> (b -> a -> b) -> V4 a -> b

foldlMap1 :: (a -> b) -> (b -> a -> b) -> V4 a -> b

foldrMap1' :: (a -> b) -> (a -> b -> b) -> V4 a -> b

Hashable1 V4

Defined in Linear.V4

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> V4 a -> Int

Metric V4

Defined in Linear.V4

Methods

dot :: Num a => V4 a -> V4 a -> a

quadrance :: Num a => V4 a -> a

qd :: Num a => V4 a -> V4 a -> a

distance :: Floating a => V4 a -> V4 a -> a

norm :: Floating a => V4 a -> a

signorm :: Floating a => V4 a -> V4 a

Finite V4

Defined in Linear.V4

Associated Types

type Size V4 :: Nat

Methods

toV :: V4 a -> V (Size V4) a

fromV :: V (Size V4) a -> V4 a

R1 V4

Defined in Linear.V4

Methods

_x :: Lens' (V4 a) a

R2 V4

Defined in Linear.V4

Methods

_y :: Lens' (V4 a) a

_xy :: Lens' (V4 a) (V2 a)

R3 V4

Defined in Linear.V4

Methods

_z :: Lens' (V4 a) a

_xyz :: Lens' (V4 a) (V3 a)

R4 V4

Defined in Linear.V4

Methods

_w :: Lens' (V4 a) a

_xyzw :: Lens' (V4 a) (V4 a)

Additive V4

Defined in Linear.V4

Methods

zero :: Num a => V4 a

(^+^) :: Num a => V4 a -> V4 a -> V4 a

(^-^) :: Num a => V4 a -> V4 a -> V4 a

lerp :: Num a => a -> V4 a -> V4 a -> V4 a

liftU2 :: (a -> a -> a) -> V4 a -> V4 a -> V4 a

liftI2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c

Apply V4

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

Bind V4

Defined in Linear.V4

Methods

(>>-) :: V4 a -> (a -> V4 b) -> V4 b

join :: V4 (V4 a) -> V4 a

Traversable1 V4

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)

Generic1 V4

Defined in Linear.V4

Associated Types

type Rep1 V4 :: k -> Type

Methods

from1 :: forall (a :: k). V4 a -> Rep1 V4 a

to1 :: forall (a :: k). Rep1 V4 a -> V4 a

Unbox a => Vector Vector (V4 a)

Defined in Linear.V4

Methods

basicUnsafeFreeze :: Mutable Vector s (V4 a) -> ST s (Vector (V4 a))

basicUnsafeThaw :: Vector (V4 a) -> ST s (Mutable Vector s (V4 a))

basicLength :: Vector (V4 a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (V4 a) -> Vector (V4 a)

basicUnsafeIndexM :: Vector (V4 a) -> Int -> Box (V4 a)

basicUnsafeCopy :: Mutable Vector s (V4 a) -> Vector (V4 a) -> ST s ()

elemseq :: Vector (V4 a) -> V4 a -> b -> b

Unbox a => MVector MVector (V4 a)

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 :: Int -> ST s (MVector s (V4 a))

basicInitialize :: MVector s (V4 a) -> ST s ()

basicUnsafeReplicate :: Int -> V4 a -> ST s (MVector s (V4 a))

basicUnsafeRead :: MVector s (V4 a) -> Int -> ST s (V4 a)

basicUnsafeWrite :: MVector s (V4 a) -> Int -> V4 a -> ST s ()

basicClear :: MVector s (V4 a) -> ST s ()

basicSet :: MVector s (V4 a) -> V4 a -> ST s ()

basicUnsafeCopy :: MVector s (V4 a) -> MVector s (V4 a) -> ST s ()

basicUnsafeMove :: MVector s (V4 a) -> MVector s (V4 a) -> ST s ()

basicUnsafeGrow :: MVector s (V4 a) -> Int -> ST s (MVector s (V4 a))

Data a => Data (V4 a)

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 :: forall r r'. (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)

Storable a => Storable (V4 a)

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 ()

Monoid a => Monoid (V4 a)

Defined in Linear.V4

Methods

mempty :: V4 a

mappend :: V4 a -> V4 a -> V4 a

mconcat :: [V4 a] -> V4 a

Semigroup a => Semigroup (V4 a)

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

Bounded a => Bounded (V4 a)

Defined in Linear.V4

Methods

minBound :: V4 a

maxBound :: V4 a

Floating a => Floating (V4 a)

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

Generic (V4 a)

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

Ix a => Ix (V4 a)

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

Num a => Num (V4 a)

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

Read a => Read (V4 a)

Defined in Linear.V4

Methods

readsPrec :: Int -> ReadS (V4 a)

readList :: ReadS [V4 a]

readPrec :: ReadPrec (V4 a)

readListPrec :: ReadPrec [V4 a]

Fractional a => Fractional (V4 a)

Defined in Linear.V4

Methods

(/) :: V4 a -> V4 a -> V4 a

recip :: V4 a -> V4 a

fromRational :: Rational -> V4 a

Show a => Show (V4 a)

Defined in Linear.V4

Methods

showsPrec :: Int -> V4 a -> ShowS

show :: V4 a -> String

showList :: [V4 a] -> ShowS

Binary a => Binary (V4 a)

Defined in Linear.V4

Methods

put :: V4 a -> Put

get :: Get (V4 a)

putList :: [V4 a] -> Put

Serial a => Serial (V4 a)

Defined in Linear.V4

Methods

serialize :: MonadPut m => V4 a -> m ()

deserialize :: MonadGet m => m (V4 a)

Serialize a => Serialize (V4 a)

Defined in Linear.V4

Methods

put :: Putter (V4 a)

get :: Get (V4 a)

NFData a => NFData (V4 a)

Defined in Linear.V4

Methods

rnf :: V4 a -> ()

Eq a => Eq (V4 a)

Defined in Linear.V4

Methods

(==) :: V4 a -> V4 a -> Bool

(/=) :: V4 a -> V4 a -> Bool

Ord a => Ord (V4 a)

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

Hashable a => Hashable (V4 a)

Defined in Linear.V4

Methods

hashWithSalt :: Int -> V4 a -> Int

hash :: V4 a -> Int

Ixed (V4 a)

Defined in Linear.V4

Methods

ix :: Index (V4 a) -> Traversal' (V4 a) (IxValue (V4 a))

Epsilon a => Epsilon (V4 a)

Defined in Linear.V4

Methods

nearZero :: V4 a -> Bool

Random a => Random (V4 a)

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]

Unbox a => Unbox (V4 a)

Defined in Linear.V4

FoldableWithIndex (E V4) V4

Defined in Linear.V4

Methods

ifoldMap :: Monoid m => (E V4 -> a -> m) -> V4 a -> m

ifoldMap' :: Monoid m => (E V4 -> a -> m) -> V4 a -> m

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

FunctorWithIndex (E V4) V4

Defined in Linear.V4

Methods

imap :: (E V4 -> a -> b) -> V4 a -> V4 b

TraversableWithIndex (E V4) V4

Defined in Linear.V4

Methods

itraverse :: Applicative f => (E V4 -> a -> f b) -> V4 a -> f (V4 b)

Lift a => Lift (V4 a :: Type)

Defined in Linear.V4

Methods

lift :: Quote m => V4 a -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => V4 a -> Code m (V4 a)

Each (V4 a) (V4 b) a b

Defined in Linear.V4

Methods

each :: Traversal (V4 a) (V4 b) a b

Field1 (V4 a) (V4 a) a a

Defined in Linear.V4

Methods

_1 :: Lens (V4 a) (V4 a) a a

Field2 (V4 a) (V4 a) a a

Defined in Linear.V4

Methods

_2 :: Lens (V4 a) (V4 a) a a

Field3 (V4 a) (V4 a) a a

Defined in Linear.V4

Methods

_3 :: Lens (V4 a) (V4 a) a a

Field4 (V4 a) (V4 a) a a

Defined in Linear.V4

Methods

_4 :: Lens (V4 a) (V4 a) a a

type Rep V4

Defined in Linear.V4

type Rep V4 = E V4

type Size V4

Defined in Linear.V4

type Size V4 = 4

type Rep1 V4

Defined in Linear.V4

type Rep1 V4 = D1 ('MetaData "V4" "Linear.V4" "linear-1.22-ANafbhSdznBKD15zEySBd9" '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)))

data MVector s (V4 a)

Defined in Linear.V4

data MVector s (V4 a) = MV_V4 !Int !(MVector s a)

type Rep (V4 a)

Defined in Linear.V4

type Rep (V4 a) = D1 ('MetaData "V4" "Linear.V4" "linear-1.22-ANafbhSdznBKD15zEySBd9" '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))))

type Index (V4 a)

Defined in Linear.V4

type Index (V4 a) = E V4

type IxValue (V4 a)

Defined in Linear.V4

type IxValue (V4 a) = a

data Vector (V4 a)

Defined in Linear.V4

data Vector (V4 a) = V_V4 !Int !(Vector a)