Copyright	(c) 2011 diagrams-lib team (see LICENSE)
License	BSD-style (see LICENSE)
Maintainer	diagrams-discuss@googlegroups.com
Safe Haskell	None
Language	Haskell2010

Diagrams.TwoD.Types

Contents

2D Euclidean space
Orphan instances

Description

Basic types for two-dimensional Euclidean space.

Synopsis

2D Euclidean space

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

Monad V2
Methods (>>=) :: V2 a -> (a -> V2 b) -> V2 b # (>>) :: V2 a -> V2 b -> V2 b # return :: a -> V2 a # fail :: String -> V2 a #
Functor V2
Methods fmap :: (a -> b) -> V2 a -> V2 b # (<$) :: a -> V2 b -> V2 a #
MonadFix V2
Methods mfix :: (a -> V2 a) -> V2 a #
Applicative V2
Methods pure :: a -> V2 a # (<>) :: V2 (a -> b) -> V2 a -> V2 b # (>) :: V2 a -> V2 b -> V2 b # (<*) :: V2 a -> V2 b -> V2 a #
Foldable V2
Methods fold :: Monoid m => V2 m -> 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 #
Traversable 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) #
Generic1 V2
Associated Types type Rep1 (V2 :: * -> ) :: -> * # Methods from1 :: V2 a -> Rep1 V2 a # to1 :: Rep1 V2 a -> V2 a #
Apply V2
Methods (<.>) :: V2 (a -> b) -> V2 a -> V2 b # (.>) :: V2 a -> V2 b -> V2 b # (<.) :: V2 a -> V2 b -> V2 a #
Distributive 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) #
Representable V2
Associated Types type Rep (V2 :: * -> ) :: # Methods tabulate :: (Rep V2 -> a) -> V2 a # index :: V2 a -> Rep V2 -> a #
Eq1 V2
Methods liftEq :: (a -> b -> Bool) -> V2 a -> V2 b -> Bool #
Ord1 V2
Methods liftCompare :: (a -> b -> Ordering) -> V2 a -> V2 b -> Ordering #
Read1 V2
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V2 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V2 a] #
Show1 V2
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V2 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V2 a] -> ShowS #
MonadZip 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) #
Serial1 V2
Methods serializeWith :: MonadPut m => (a -> m ()) -> V2 a -> m () # deserializeWith :: MonadGet m => m a -> m (V2 a) #
Additive 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 #
Traversable1 V2
Methods traverse1 :: Apply f => (a -> f b) -> V2 a -> f (V2 b) # sequence1 :: Apply f => V2 (f b) -> f (V2 b) #
Affine V2
Associated Types type Diff (V2 :: * -> ) :: -> * # Methods (.-.) :: Num a => V2 a -> V2 a -> Diff V2 a # (.+^) :: Num a => V2 a -> Diff V2 a -> V2 a # (.-^) :: Num a => V2 a -> Diff V2 a -> V2 a #
R2 V2
Methods _y :: Functor f => (a -> f a) -> V2 a -> f (V2 a) # _xy :: Functor f => (V2 a -> f (V2 a)) -> V2 a -> f (V2 a) #
R1 V2
Methods _x :: Functor f => (a -> f a) -> V2 a -> f (V2 a) #
Finite V2
Associated Types type Size (V2 :: * -> *) :: Nat # Methods toV :: V2 a -> V Nat (Size V2) a # fromV :: V Nat (Size V2) a -> V2 a #
Metric 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 #
Bind V2
Methods (>>-) :: V2 a -> (a -> V2 b) -> V2 b # join :: V2 (V2 a) -> V2 a #
Foldable1 V2
Methods fold1 :: Semigroup m => V2 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V2 a -> m #
HasR V2 Source #
Methods _r :: RealFloat n => Lens' (V2 n) n Source #
Unbox a => Vector Vector (V2 a)
Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V2 a) -> m (Vector (V2 a)) # basicUnsafeThaw :: PrimMonad m => Vector (V2 a) -> m (Mutable Vector (PrimState m) (V2 a)) # basicLength :: Vector (V2 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V2 a) -> Vector (V2 a) # basicUnsafeIndexM :: Monad m => Vector (V2 a) -> Int -> m (V2 a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V2 a) -> Vector (V2 a) -> m () # elemseq :: Vector (V2 a) -> V2 a -> b -> b #
Unbox a => MVector MVector (V2 a)
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 :: PrimMonad m => Int -> m (MVector (PrimState m) (V2 a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V2 a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V2 a -> m (MVector (PrimState m) (V2 a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> m (V2 a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> V2 a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V2 a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V2 a) -> V2 a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V2 a) -> MVector (PrimState m) (V2 a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V2 a) -> MVector (PrimState m) (V2 a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> m (MVector (PrimState m) (V2 a)) #
Bounded a => Bounded (V2 a)
Methods minBound :: V2 a # maxBound :: V2 a #
Eq a => Eq (V2 a)
Methods (==) :: V2 a -> V2 a -> Bool # (/=) :: V2 a -> V2 a -> Bool #
Floating a => Floating (V2 a)
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 #
Fractional a => Fractional (V2 a)
Methods (/) :: V2 a -> V2 a -> V2 a # recip :: V2 a -> V2 a # fromRational :: Rational -> V2 a #
Data a => Data (V2 a)
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 :: (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) #
Num a => Num (V2 a)
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 #
Ord a => Ord (V2 a)
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 #
Read a => Read (V2 a)
Methods readsPrec :: Int -> ReadS (V2 a) # readList :: ReadS [V2 a] # readPrec :: ReadPrec (V2 a) # readListPrec :: ReadPrec [V2 a] #
Show a => Show (V2 a)
Methods showsPrec :: Int -> V2 a -> ShowS # show :: V2 a -> String # showList :: [V2 a] -> ShowS #
Ix a => Ix (V2 a)
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
Generic (V2 a)
Associated Types type Rep (V2 a) :: * -> * # Methods from :: V2 a -> Rep (V2 a) x # to :: Rep (V2 a) x -> V2 a #
Storable a => Storable (V2 a)
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 () #
Binary a => Binary (V2 a)
Methods put :: V2 a -> Put # get :: Get (V2 a) # putList :: [V2 a] -> Put #
Serial a => Serial (V2 a)
Methods serialize :: MonadPut m => V2 a -> m () # deserialize :: MonadGet m => m (V2 a) #
Serialize a => Serialize (V2 a)
Methods put :: Putter (V2 a) # get :: Get (V2 a) #
NFData a => NFData (V2 a)
Methods rnf :: V2 a -> () #
Hashable a => Hashable (V2 a)
Methods hashWithSalt :: Int -> V2 a -> Int # hash :: V2 a -> Int #
Unbox a => Unbox (V2 a)

Ixed (V2 a)
Methods ix :: Index (V2 a) -> Traversal' (V2 a) (IxValue (V2 a)) #
Epsilon a => Epsilon (V2 a)
Methods nearZero :: V2 a -> Bool #
Coordinates (V2 n) Source #
Associated Types type FinalCoord (V2 n) :: * Source # type PrevDim (V2 n) :: * Source # type Decomposition (V2 n) :: * Source # Methods (^&) :: PrevDim (V2 n) -> FinalCoord (V2 n) -> V2 n Source # pr :: PrevDim (V2 n) -> FinalCoord (V2 n) -> V2 n Source # coords :: V2 n -> Decomposition (V2 n) Source #
FunctorWithIndex (E V2) V2
Methods imap :: (E V2 -> a -> b) -> V2 a -> V2 b # imapped :: (Indexable (E V2) p, Settable f) => p a (f b) -> V2 a -> f (V2 b) #
FoldableWithIndex (E V2) V2
Methods ifoldMap :: Monoid m => (E V2 -> a -> m) -> V2 a -> m # ifolded :: (Indexable (E V2) p, Contravariant f, Applicative f) => p a (f a) -> V2 a -> f (V2 a) # 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 #
TraversableWithIndex (E V2) V2
Methods itraverse :: Applicative f => (E V2 -> a -> f b) -> V2 a -> f (V2 b) # itraversed :: (Indexable (E V2) p, Applicative f) => p a (f b) -> V2 a -> f (V2 b) #
Each (V2 a) (V2 b) a b
Methods each :: Traversal (V2 a) (V2 b) a b #
RealFloat n => Traced (BoundingBox V2 n) #
Methods getTrace :: BoundingBox V2 n -> Trace (V (BoundingBox V2 n)) (N (BoundingBox V2 n)) #
type Rep1 V2
type Rep1 V2 = D1 (MetaData "V2" "Linear.V2" "linear-1.20.6-BLaEvYulW0N9hH4LlOYSMv" False) (C1 (MetaCons "V2" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1)))
type Rep V2
type Rep V2 = E V2
type Diff V2
type Diff V2 = V2
type Size V2
type Size V2 = 2
data MVector s (V2 a)
data MVector s (V2 a) = MV_V2 ~Int ~(MVector s a)
type Rep (V2 a)
type Rep (V2 a) = D1 (MetaData "V2" "Linear.V2" "linear-1.20.6-BLaEvYulW0N9hH4LlOYSMv" False) (C1 (MetaCons "V2" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a))))
type V (V2 n) #
type V (V2 n) = V2
type N (V2 n) #
type N (V2 n) = n
data Vector (V2 a)
data Vector (V2 a) = V_V2 ~Int ~(Vector a)
type Index (V2 a)
type Index (V2 a) = E V2
type IxValue (V2 a)
type IxValue (V2 a) = a
type FinalCoord (V2 n) Source #
type FinalCoord (V2 n) = n
type PrevDim (V2 n) Source #
type PrevDim (V2 n) = n
type Decomposition (V2 n) Source #
type Decomposition (V2 n) = (:&) n n

class R1 t where #

A space that has at least 1 basis vector _x.

Methods

_x :: Functor f => (a -> f a) -> t a -> f (t a) #

>>> V1 2 ^._x
2

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

Instances

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

class R1 t => R2 t where #

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

Methods

_y :: Functor f => (a -> f a) -> t a -> f (t a) #

>>> V2 1 2 ^._y
2

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

_xy :: Functor f => (V2 a -> f (V2 a)) -> t a -> f (t a) #

Instances

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

type P2 = Point V2 Source #

type T2 = Transformation V2 Source #

r2 :: (n, n) -> V2 n Source #

Construct a 2D vector from a pair of components. See also &.

unr2 :: V2 n -> (n, n) Source #

Convert a 2D vector back into a pair of components. See also coords.

mkR2 :: n -> n -> V2 n Source #

Curried form of r2.

r2Iso :: Iso' (V2 n) (n, n) Source #

p2 :: (n, n) -> P2 n Source #

Construct a 2D point from a pair of coordinates. See also ^&.

mkP2 :: n -> n -> P2 n Source #

Curried form of p2.

unp2 :: P2 n -> (n, n) Source #

Convert a 2D point back into a pair of coordinates. See also coords.

p2Iso :: Iso' (Point V2 n) (n, n) Source #

r2PolarIso :: RealFloat n => Iso' (V2 n) (n, Angle n) Source #

class HasR t where Source #

A space which has magnitude _r that can be calculated numerically.

Methods

_r :: RealFloat n => Lens' (t n) n Source #

Instances

HasR V2 Source #
Methods _r :: RealFloat n => Lens' (V2 n) n Source #
HasR v => HasR (Point v) Source #
Methods _r :: RealFloat n => Lens' (Point v n) n Source #

Orphan instances

HasTheta V2 Source #
Methods _theta :: RealFloat n => Lens' (V2 n) (Angle n) Source #
Transformable (V2 n) Source #
Methods transform :: Transformation (V (V2 n)) (N (V2 n)) -> V2 n -> V2 n #