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.V3

Description

3-D Vectors

Synopsis

Documentation

data V3 a Source

A 3-dimensional vector

Constructors

V3 !a !a !a

Instances

Monad V3 Source
Methods (>>=) :: V3 a -> (a -> V3 b) -> V3 b (>>) :: V3 a -> V3 b -> V3 b return :: a -> V3 a fail :: String -> V3 a
Functor V3 Source
Methods fmap :: (a -> b) -> V3 a -> V3 b (<$) :: a -> V3 b -> V3 a
MonadFix V3 Source
Methods mfix :: (a -> V3 a) -> V3 a
Applicative V3 Source
Methods pure :: a -> V3 a (<>) :: V3 (a -> b) -> V3 a -> V3 b (>) :: V3 a -> V3 b -> V3 b (<*) :: V3 a -> V3 b -> V3 a
Foldable V3 Source
Methods fold :: Monoid m => V3 m -> m foldMap :: Monoid m => (a -> m) -> V3 a -> m foldr :: (a -> b -> b) -> b -> V3 a -> b foldr' :: (a -> b -> b) -> b -> V3 a -> b foldl :: (b -> a -> b) -> b -> V3 a -> b foldl' :: (b -> a -> b) -> b -> V3 a -> b foldr1 :: (a -> a -> a) -> V3 a -> a foldl1 :: (a -> a -> a) -> V3 a -> a toList :: V3 a -> [a] null :: V3 a -> Bool length :: V3 a -> Int elem :: Eq a => a -> V3 a -> Bool maximum :: Ord a => V3 a -> a minimum :: Ord a => V3 a -> a sum :: Num a => V3 a -> a product :: Num a => V3 a -> a
Traversable V3 Source
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)
Generic1 V3 Source
Associated Types type Rep1 (V3 :: * -> ) :: -> * Methods from1 :: V3 a -> Rep1 V3 a to1 :: Rep1 V3 a -> V3 a
Distributive V3 Source
Methods distribute :: Functor f => f (V3 a) -> V3 (f a) collect :: Functor f => (a -> V3 b) -> f a -> V3 (f b) distributeM :: Monad m => m (V3 a) -> V3 (m a) collectM :: Monad m => (a -> V3 b) -> m a -> V3 (m b)
Representable V3 Source
Associated Types type Rep (V3 :: * -> ) :: Methods tabulate :: (Rep V3 -> a) -> V3 a index :: V3 a -> Rep V3 -> a
MonadZip V3 Source
Methods mzip :: V3 a -> V3 b -> V3 (a, b) mzipWith :: (a -> b -> c) -> V3 a -> V3 b -> V3 c munzip :: V3 (a, b) -> (V3 a, V3 b)
Serial1 V3 Source
Methods serializeWith :: MonadPut m => (a -> m ()) -> V3 a -> m () deserializeWith :: MonadGet m => m a -> m (V3 a)
Traversable1 V3 Source
Methods traverse1 :: Apply f => (a -> f b) -> V3 a -> f (V3 b) sequence1 :: Apply f => V3 (f b) -> f (V3 b)
Apply V3 Source
Methods (<.>) :: V3 (a -> b) -> V3 a -> V3 b (.>) :: V3 a -> V3 b -> V3 b (<.) :: V3 a -> V3 b -> V3 a
Bind V3 Source
Methods (>>-) :: V3 a -> (a -> V3 b) -> V3 b join :: V3 (V3 a) -> V3 a
Foldable1 V3 Source
Methods fold1 :: Semigroup m => V3 m -> m foldMap1 :: Semigroup m => (a -> m) -> V3 a -> m
Eq1 V3 Source
Methods eq1 :: Eq a => V3 a -> V3 a -> Bool
Ord1 V3 Source
Methods compare1 :: Ord a => V3 a -> V3 a -> Ordering
Read1 V3 Source
Methods readsPrec1 :: Read a => Int -> ReadS (V3 a)
Show1 V3 Source
Methods showsPrec1 :: Show a => Int -> V3 a -> ShowS
Additive V3 Source
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
Metric V3 Source
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
R1 V3 Source
Methods _x :: Functor f => (a -> f a) -> V3 a -> f (V3 a) Source
R2 V3 Source
Methods _y :: Functor f => (a -> f a) -> V3 a -> f (V3 a) Source _xy :: Functor f => (V2 a -> f (V2 a)) -> V3 a -> f (V3 a) Source
R3 V3 Source
Methods _z :: Functor f => (a -> f a) -> V3 a -> f (V3 a) Source _xyz :: Functor f => (V3 a -> f (V3 a)) -> V3 a -> f (V3 a) Source
Trace V3 Source
Methods trace :: Num a => V3 (V3 a) -> a Source diagonal :: V3 (V3 a) -> V3 a Source
Affine V3 Source
Associated Types type Diff (V3 :: * -> ) :: -> * Source 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
Unbox a => Vector Vector (V3 a) Source
Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> m (Vector (V3 a)) basicUnsafeThaw :: PrimMonad m => Vector (V3 a) -> m (Mutable Vector (PrimState m) (V3 a)) basicLength :: Vector (V3 a) -> Int basicUnsafeSlice :: Int -> Int -> Vector (V3 a) -> Vector (V3 a) basicUnsafeIndexM :: Monad m => Vector (V3 a) -> Int -> m (V3 a) basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> Vector (V3 a) -> m () elemseq :: Vector (V3 a) -> V3 a -> b -> b
Unbox a => MVector MVector (V3 a) Source
Methods basicLength :: MVector s (V3 a) -> Int basicUnsafeSlice :: Int -> Int -> MVector s (V3 a) -> MVector s (V3 a) basicOverlaps :: MVector s (V3 a) -> MVector s (V3 a) -> Bool basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V3 a)) basicInitialize :: PrimMonad m => MVector (PrimState m) (V3 a) -> m () basicUnsafeReplicate :: PrimMonad m => Int -> V3 a -> m (MVector (PrimState m) (V3 a)) basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (V3 a) basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> V3 a -> m () basicClear :: PrimMonad m => MVector (PrimState m) (V3 a) -> m () basicSet :: PrimMonad m => MVector (PrimState m) (V3 a) -> V3 a -> m () basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m () basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m () basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (MVector (PrimState m) (V3 a))
Num r => Coalgebra r (E V3) Source
Methods comult :: (E V3 -> r) -> E V3 -> E V3 -> r Source counital :: (E V3 -> r) -> r Source
Bounded a => Bounded (V3 a) Source
Methods minBound :: V3 a maxBound :: V3 a
Eq a => Eq (V3 a) Source
Methods (==) :: V3 a -> V3 a -> Bool (/=) :: V3 a -> V3 a -> Bool
Floating a => Floating (V3 a) Source
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
Fractional a => Fractional (V3 a) Source
Methods (/) :: V3 a -> V3 a -> V3 a recip :: V3 a -> V3 a fromRational :: Rational -> V3 a
Data a => Data (V3 a) Source
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V3 a -> c (V3 a) gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V3 a) toConstr :: V3 a -> Constr dataTypeOf :: V3 a -> DataType dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (V3 a)) dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V3 a)) gmapT :: (forall b. Data b => b -> b) -> V3 a -> V3 a gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r gmapQ :: (forall d. Data d => d -> u) -> V3 a -> [u] gmapQi :: Int -> (forall d. Data d => d -> u) -> V3 a -> u gmapM :: Monad m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a)
Num a => Num (V3 a) Source
Methods (+) :: V3 a -> V3 a -> V3 a (-) :: V3 a -> V3 a -> V3 a (*) :: V3 a -> V3 a -> V3 a negate :: V3 a -> V3 a abs :: V3 a -> V3 a signum :: V3 a -> V3 a fromInteger :: Integer -> V3 a
Ord a => Ord (V3 a) Source
Methods compare :: V3 a -> V3 a -> Ordering (<) :: V3 a -> V3 a -> Bool (<=) :: V3 a -> V3 a -> Bool (>) :: V3 a -> V3 a -> Bool (>=) :: V3 a -> V3 a -> Bool max :: V3 a -> V3 a -> V3 a min :: V3 a -> V3 a -> V3 a
Read a => Read (V3 a) Source
Methods readsPrec :: Int -> ReadS (V3 a) readList :: ReadS [V3 a] readPrec :: ReadPrec (V3 a) readListPrec :: ReadPrec [V3 a]
Show a => Show (V3 a) Source
Methods showsPrec :: Int -> V3 a -> ShowS show :: V3 a -> String showList :: [V3 a] -> ShowS
Ix a => Ix (V3 a) Source
Methods range :: (V3 a, V3 a) -> [V3 a] index :: (V3 a, V3 a) -> V3 a -> Int unsafeIndex :: (V3 a, V3 a) -> V3 a -> Int inRange :: (V3 a, V3 a) -> V3 a -> Bool rangeSize :: (V3 a, V3 a) -> Int unsafeRangeSize :: (V3 a, V3 a) -> Int
Generic (V3 a) Source
Associated Types type Rep (V3 a) :: * -> * Methods from :: V3 a -> Rep (V3 a) x to :: Rep (V3 a) x -> V3 a
Storable a => Storable (V3 a) Source
Methods sizeOf :: V3 a -> Int alignment :: V3 a -> Int peekElemOff :: Ptr (V3 a) -> Int -> IO (V3 a) pokeElemOff :: Ptr (V3 a) -> Int -> V3 a -> IO () peekByteOff :: Ptr b -> Int -> IO (V3 a) pokeByteOff :: Ptr b -> Int -> V3 a -> IO () peek :: Ptr (V3 a) -> IO (V3 a) poke :: Ptr (V3 a) -> V3 a -> IO ()
Binary a => Binary (V3 a) Source
Methods put :: V3 a -> Put get :: Get (V3 a)
Serial a => Serial (V3 a) Source
Methods serialize :: MonadPut m => V3 a -> m () deserialize :: MonadGet m => m (V3 a)
Serialize a => Serialize (V3 a) Source
Methods put :: Putter (V3 a) get :: Get (V3 a)
NFData a => NFData (V3 a) Source
Methods rnf :: V3 a -> ()
Hashable a => Hashable (V3 a) Source
Methods hashWithSalt :: Int -> V3 a -> Int hash :: V3 a -> Int
Unbox a => Unbox (V3 a) Source

Ixed (V3 a) Source
Methods ix :: Index (V3 a) -> Traversal' (V3 a) (IxValue (V3 a))
Epsilon a => Epsilon (V3 a) Source
Methods nearZero :: V3 a -> Bool Source
FunctorWithIndex (E V3) V3 Source
Methods imap :: (E V3 -> a -> b) -> V3 a -> V3 b imapped :: (Indexable (E V3) p, Settable f) => p a (f b) -> V3 a -> f (V3 b)
FoldableWithIndex (E V3) V3 Source
Methods ifoldMap :: Monoid m => (E V3 -> a -> m) -> V3 a -> m ifolded :: (Indexable (E V3) p, Contravariant f, Applicative f) => p a (f a) -> V3 a -> f (V3 a) ifoldr :: (E V3 -> a -> b -> b) -> b -> V3 a -> b ifoldl :: (E V3 -> b -> a -> b) -> b -> V3 a -> b ifoldr' :: (E V3 -> a -> b -> b) -> b -> V3 a -> b ifoldl' :: (E V3 -> b -> a -> b) -> b -> V3 a -> b
TraversableWithIndex (E V3) V3 Source
Methods itraverse :: Applicative f => (E V3 -> a -> f b) -> V3 a -> f (V3 b) itraversed :: (Indexable (E V3) p, Applicative f) => p a (f b) -> V3 a -> f (V3 b)
Each (V3 a) (V3 b) a b Source
Methods each :: Traversal (V3 a) (V3 b) a b
type Rep1 V3 Source
type Rep V3 = E V3 Source
type Diff V3 = V3 Source
data MVector s (V3 a) = MV_V3 !Int !(MVector s a) Source
type Rep (V3 a) Source
data Vector (V3 a) = V_V3 !Int !(Vector a) Source
type Index (V3 a) = E V3 Source
type IxValue (V3 a) = a Source

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 where Source

A space that has at least 1 basis vector _x.

Minimal complete definition

Nothing

Methods

_x :: Lens' (t a) a Source

>>> V1 2 ^._x
2

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

Instances

R1 Identity Source
Methods _x :: Functor f => (a -> f a) -> Identity a -> f (Identity a) Source
R1 V1 Source
Methods _x :: Functor f => (a -> f a) -> V1 a -> f (V1 a) Source
R1 V2 Source
Methods _x :: Functor f => (a -> f a) -> V2 a -> f (V2 a) Source
R1 V3 Source
Methods _x :: Functor f => (a -> f a) -> V3 a -> f (V3 a) Source
R1 V4 Source
Methods _x :: Functor f => (a -> f a) -> V4 a -> f (V4 a) Source
R1 f => R1 (Point f) Source
Methods _x :: Functor b => (a -> b a) -> Point f a -> b (Point f 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

Nothing

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
Methods _y :: Functor f => (a -> f a) -> V2 a -> f (V2 a) Source _xy :: Functor f => (V2 a -> f (V2 a)) -> V2 a -> f (V2 a) Source
R2 V3 Source
Methods _y :: Functor f => (a -> f a) -> V3 a -> f (V3 a) Source _xy :: Functor f => (V2 a -> f (V2 a)) -> V3 a -> f (V3 a) Source
R2 V4 Source
Methods _y :: Functor f => (a -> f a) -> V4 a -> f (V4 a) Source _xy :: Functor f => (V2 a -> f (V2 a)) -> V4 a -> f (V4 a) Source
R2 f => R2 (Point f) Source
Methods _y :: Functor b => (a -> b a) -> Point f a -> b (Point f a) Source _xy :: Functor b => (V2 a -> b (V2 a)) -> Point f a -> b (Point f 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)

Minimal complete definition

Nothing

Methods

_z :: Lens' (t a) a Source

>>> V3 1 2 3 ^. _z
3

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

Instances

R3 V3 Source
Methods _z :: Functor f => (a -> f a) -> V3 a -> f (V3 a) Source _xyz :: Functor f => (V3 a -> f (V3 a)) -> V3 a -> f (V3 a) Source
R3 V4 Source
Methods _z :: Functor f => (a -> f a) -> V4 a -> f (V4 a) Source _xyz :: Functor f => (V3 a -> f (V3 a)) -> V4 a -> f (V4 a) Source
R3 f => R3 (Point f) Source
Methods _z :: Functor b => (a -> b a) -> Point f a -> b (Point f a) Source _xyz :: Functor b => (V3 a -> b (V3 a)) -> Point f a -> b (Point f 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

ex :: R1 t => E t Source

ey :: R2 t => E t Source

ez :: R3 t => E t Source