Copyright	(c) 2011 diagrams-core team (see LICENSE)
License	BSD-style (see LICENSE)
Maintainer	[email protected]
Safe Haskell	Safe-Inferred
Language	Haskell2010

Diagrams.Core.Points

Contents

Points

Description

A type for points (as distinct from vectors).

Synopsis

newtype Point (f :: Type -> Type) a = P (f a)
origin :: forall (f :: Type -> Type) a. (Additive f, Num a) => Point f a
(*.) :: forall (v :: Type -> Type) n. (Functor v, Num n) => n -> Point v n -> Point v n
relative :: forall (f :: Type -> Type) a. (Additive f, Num a) => Point f a -> Iso' (Point f a) (f a)
_Point :: forall f1 a g b p f2. (Profunctor p, Functor f2) => p (f1 a) (f2 (g b)) -> p (Point f1 a) (f2 (Point g b))
reflectThrough :: forall (v :: Type -> Type) n. (Additive v, Num n) => Point v n -> Point v n -> Point v n
mirror :: forall (v :: Type -> Type) n. (Additive v, Num n) => Point v n -> Point v n
relative2 :: (Additive v, Num n) => Point v n -> (v n -> v n -> v n) -> Point v n -> Point v n -> Point v n
relative3 :: (Additive v, Num n) => Point v n -> (v n -> v n -> v n -> v n) -> Point v n -> Point v n -> Point v n -> Point v n

Points

newtype Point (f :: Type -> Type) a #

A handy wrapper to help distinguish points from vectors at the type level

Constructors

P (f a)

Instances

Instances details

Generic1 (Point f :: Type -> Type)

Instance details

Defined in Linear.Affine

Associated Types

type Rep1 (Point f :: Type -> Type)
Instance details Defined in Linear.Affine type Rep1 (Point f :: Type -> Type) = D1 ('MetaData "Point" "Linear.Affine" "linear-1.23.1-5yZd8EJ9W0rJMbCzL1ttMf" 'True) (C1 ('MetaCons "P" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))

Methods

from1 :: Point f a -> Rep1 (Point f) a #

to1 :: Rep1 (Point f) a -> Point f a #

Unbox (f a) => Vector Vector (Point f a)

Instance details

Defined in Linear.Affine

Methods

basicUnsafeFreeze :: Mutable Vector s (Point f a) -> ST s (Vector (Point f a))

basicUnsafeThaw :: Vector (Point f a) -> ST s (Mutable Vector s (Point f a))

basicLength :: Vector (Point f a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Point f a) -> Vector (Point f a)

basicUnsafeIndexM :: Vector (Point f a) -> Int -> Box (Point f a)

basicUnsafeCopy :: Mutable Vector s (Point f a) -> Vector (Point f a) -> ST s ()

elemseq :: Vector (Point f a) -> Point f a -> b -> b

Unbox (f a) => MVector MVector (Point f a)

Instance details

Defined in Linear.Affine

Methods

basicLength :: MVector s (Point f a) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (Point f a) -> MVector s (Point f a)

basicOverlaps :: MVector s (Point f a) -> MVector s (Point f a) -> Bool

basicUnsafeNew :: Int -> ST s (MVector s (Point f a))

basicInitialize :: MVector s (Point f a) -> ST s ()

basicUnsafeReplicate :: Int -> Point f a -> ST s (MVector s (Point f a))

basicUnsafeRead :: MVector s (Point f a) -> Int -> ST s (Point f a)

basicUnsafeWrite :: MVector s (Point f a) -> Int -> Point f a -> ST s ()

basicClear :: MVector s (Point f a) -> ST s ()

basicSet :: MVector s (Point f a) -> Point f a -> ST s ()

basicUnsafeCopy :: MVector s (Point f a) -> MVector s (Point f a) -> ST s ()

basicUnsafeMove :: MVector s (Point f a) -> MVector s (Point f a) -> ST s ()

basicUnsafeGrow :: MVector s (Point f a) -> Int -> ST s (MVector s (Point f a))

Representable f => Representable (Point f)

Instance details

Defined in Linear.Affine

Associated Types

type Rep (Point f)
Instance details Defined in Linear.Affine type Rep (Point f) = Rep f

Methods

tabulate :: (Rep (Point f) -> a) -> Point f a #

index :: Point f a -> Rep (Point f) -> a #

Foldable f => Foldable (Point f)

Instance details

Defined in Linear.Affine

Methods

fold :: Monoid m => Point f m -> m #

foldMap :: Monoid m => (a -> m) -> Point f a -> m #

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

foldr :: (a -> b -> b) -> b -> Point f a -> b #

foldr' :: (a -> b -> b) -> b -> Point f a -> b #

foldl :: (b -> a -> b) -> b -> Point f a -> b #

foldl' :: (b -> a -> b) -> b -> Point f a -> b #

foldr1 :: (a -> a -> a) -> Point f a -> a #

foldl1 :: (a -> a -> a) -> Point f a -> a #

toList :: Point f a -> [a] #

null :: Point f a -> Bool #

length :: Point f a -> Int #

elem :: Eq a => a -> Point f a -> Bool #

maximum :: Ord a => Point f a -> a #

minimum :: Ord a => Point f a -> a #

sum :: Num a => Point f a -> a #

product :: Num a => Point f a -> a #

Eq1 f => Eq1 (Point f)

Instance details

Defined in Linear.Affine

Methods

liftEq :: (a -> b -> Bool) -> Point f a -> Point f b -> Bool #

Ord1 f => Ord1 (Point f)

Instance details

Defined in Linear.Affine

Methods

liftCompare :: (a -> b -> Ordering) -> Point f a -> Point f b -> Ordering #

Read1 f => Read1 (Point f)

Instance details

Defined in Linear.Affine

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Point f a) #

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Point f a] #

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Point f a) #

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Point f a] #

Show1 f => Show1 (Point f)

Instance details

Defined in Linear.Affine

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Point f a -> ShowS #

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Point f a] -> ShowS #

Traversable f => Traversable (Point f)

Instance details

Defined in Linear.Affine

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Point f a -> f0 (Point f b) #

sequenceA :: Applicative f0 => Point f (f0 a) -> f0 (Point f a) #

mapM :: Monad m => (a -> m b) -> Point f a -> m (Point f b) #

sequence :: Monad m => Point f (m a) -> m (Point f a) #

Applicative f => Applicative (Point f)

Instance details

Defined in Linear.Affine

Methods

pure :: a -> Point f a #

(<*>) :: Point f (a -> b) -> Point f a -> Point f b #

liftA2 :: (a -> b -> c) -> Point f a -> Point f b -> Point f c #

(*>) :: Point f a -> Point f b -> Point f b #

(<*) :: Point f a -> Point f b -> Point f a #

Functor f => Functor (Point f)

Instance details

Defined in Linear.Affine

Methods

fmap :: (a -> b) -> Point f a -> Point f b #

(<$) :: a -> Point f b -> Point f a #

Monad f => Monad (Point f)

Instance details

Defined in Linear.Affine

Methods

(>>=) :: Point f a -> (a -> Point f b) -> Point f b #

(>>) :: Point f a -> Point f b -> Point f b #

return :: a -> Point f a #

Serial1 f => Serial1 (Point f)

Instance details

Defined in Linear.Affine

Methods

serializeWith :: MonadPut m => (a -> m ()) -> Point f a -> m () #

deserializeWith :: MonadGet m => m a -> m (Point f a) #

Distributive f => Distributive (Point f)

Instance details

Defined in Linear.Affine

Methods

distribute :: Functor f0 => f0 (Point f a) -> Point f (f0 a) #

collect :: Functor f0 => (a -> Point f b) -> f0 a -> Point f (f0 b) #

distributeM :: Monad m => m (Point f a) -> Point f (m a) #

collectM :: Monad m => (a -> Point f b) -> m a -> Point f (m b) #

Hashable1 f => Hashable1 (Point f)

Instance details

Defined in Linear.Affine

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> Point f a -> Int #

Additive f => Affine (Point f)

Instance details

Defined in Linear.Affine

Associated Types

type Diff (Point f)
Instance details Defined in Linear.Affine type Diff (Point f) = f

Methods

(.-.) :: Num a => Point f a -> Point f a -> Diff (Point f) a #

(.+^) :: Num a => Point f a -> Diff (Point f) a -> Point f a #

(.-^) :: Num a => Point f a -> Diff (Point f) a -> Point f a #

Metric f => Metric (Point f)

Instance details

Defined in Linear.Affine

Methods

dot :: Num a => Point f a -> Point f a -> a #

quadrance :: Num a => Point f a -> a #

qd :: Num a => Point f a -> Point f a -> a #

distance :: Floating a => Point f a -> Point f a -> a #

norm :: Floating a => Point f a -> a #

signorm :: Floating a => Point f a -> Point f a #

Finite f => Finite (Point f)

Instance details

Defined in Linear.Affine

Associated Types

type Size (Point f)
Instance details Defined in Linear.Affine type Size (Point f) = Size f

Methods

toV :: Point f a -> V (Size (Point f)) a #

fromV :: V (Size (Point f)) a -> Point f a #

R1 f => R1 (Point f)

Instance details

Defined in Linear.Affine

Methods

_x :: Lens' (Point f a) a #

R2 f => R2 (Point f)

Instance details

Defined in Linear.Affine

Methods

_y :: Lens' (Point f a) a #

_xy :: Lens' (Point f a) (V2 a) #

R3 f => R3 (Point f)

Instance details

Defined in Linear.Affine

Methods

_z :: Lens' (Point f a) a #

_xyz :: Lens' (Point f a) (V3 a) #

R4 f => R4 (Point f)

Instance details

Defined in Linear.Affine

Methods

_w :: Lens' (Point f a) a #

_xyzw :: Lens' (Point f a) (V4 a) #

Additive f => Additive (Point f)

Instance details

Defined in Linear.Affine

Methods

zero :: Num a => Point f a #

(^+^) :: Num a => Point f a -> Point f a -> Point f a #

(^-^) :: Num a => Point f a -> Point f a -> Point f a #

lerp :: Num a => a -> Point f a -> Point f a -> Point f a #

liftU2 :: (a -> a -> a) -> Point f a -> Point f a -> Point f a #

liftI2 :: (a -> b -> c) -> Point f a -> Point f b -> Point f c #

Apply f => Apply (Point f)

Instance details

Defined in Linear.Affine

Methods

(<.>) :: Point f (a -> b) -> Point f a -> Point f b #

(.>) :: Point f a -> Point f b -> Point f b #

(<.) :: Point f a -> Point f b -> Point f a #

liftF2 :: (a -> b -> c) -> Point f a -> Point f b -> Point f c #

Bind f => Bind (Point f)

Instance details

Defined in Linear.Affine

Methods

(>>-) :: Point f a -> (a -> Point f b) -> Point f b #

join :: Point f (Point f a) -> Point f a #

Functor v => Cosieve (Query v) (Point v) Source #

Instance details

Defined in Diagrams.Core.Query

Methods

cosieve :: Query v a b -> Point v a -> b #

(Typeable f, Typeable a, Data (f a)) => Data (Point f a)

Instance details

Defined in Linear.Affine

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Point f a -> c (Point f a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Point f a) #

toConstr :: Point f a -> Constr #

dataTypeOf :: Point f a -> DataType #

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

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

gmapT :: (forall b. Data b => b -> b) -> Point f a -> Point f a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Point f a -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Point f a -> r #

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

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

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

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

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

Storable (f a) => Storable (Point f a)

Instance details

Defined in Linear.Affine

Methods

sizeOf :: Point f a -> Int #

alignment :: Point f a -> Int #

peekElemOff :: Ptr (Point f a) -> Int -> IO (Point f a) #

pokeElemOff :: Ptr (Point f a) -> Int -> Point f a -> IO () #

peekByteOff :: Ptr b -> Int -> IO (Point f a) #

pokeByteOff :: Ptr b -> Int -> Point f a -> IO () #

peek :: Ptr (Point f a) -> IO (Point f a) #

poke :: Ptr (Point f a) -> Point f a -> IO () #

Monoid (f a) => Monoid (Point f a)

Instance details

Defined in Linear.Affine

Methods

mempty :: Point f a #

mappend :: Point f a -> Point f a -> Point f a #

mconcat :: [Point f a] -> Point f a #

Semigroup (f a) => Semigroup (Point f a)

Instance details

Defined in Linear.Affine

Methods

(<>) :: Point f a -> Point f a -> Point f a #

sconcat :: NonEmpty (Point f a) -> Point f a #

stimes :: Integral b => b -> Point f a -> Point f a #

Generic (Point f a)

Instance details

Defined in Linear.Affine

Associated Types

type Rep (Point f a)
Instance details Defined in Linear.Affine type Rep (Point f a) = D1 ('MetaData "Point" "Linear.Affine" "linear-1.23.1-5yZd8EJ9W0rJMbCzL1ttMf" 'True) (C1 ('MetaCons "P" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))))

Methods

from :: Point f a -> Rep (Point f a) x #

to :: Rep (Point f a) x -> Point f a #

Ix (f a) => Ix (Point f a)

Instance details

Defined in Linear.Affine

Methods

range :: (Point f a, Point f a) -> [Point f a] #

index :: (Point f a, Point f a) -> Point f a -> Int #

unsafeIndex :: (Point f a, Point f a) -> Point f a -> Int #

inRange :: (Point f a, Point f a) -> Point f a -> Bool #

rangeSize :: (Point f a, Point f a) -> Int #

unsafeRangeSize :: (Point f a, Point f a) -> Int #

Num (f a) => Num (Point f a)

Instance details

Defined in Linear.Affine

Methods

(+) :: Point f a -> Point f a -> Point f a #

(-) :: Point f a -> Point f a -> Point f a #

(*) :: Point f a -> Point f a -> Point f a #

negate :: Point f a -> Point f a #

abs :: Point f a -> Point f a #

signum :: Point f a -> Point f a #

fromInteger :: Integer -> Point f a #

Read (f a) => Read (Point f a)

Instance details

Defined in Linear.Affine

Methods

readsPrec :: Int -> ReadS (Point f a) #

readList :: ReadS [Point f a] #

readPrec :: ReadPrec (Point f a) #

readListPrec :: ReadPrec [Point f a] #

Fractional (f a) => Fractional (Point f a)

Instance details

Defined in Linear.Affine

Methods

(/) :: Point f a -> Point f a -> Point f a #

recip :: Point f a -> Point f a #

fromRational :: Rational -> Point f a #

Show (f a) => Show (Point f a)

Instance details

Defined in Linear.Affine

Methods

showsPrec :: Int -> Point f a -> ShowS #

show :: Point f a -> String #

showList :: [Point f a] -> ShowS #

Binary (f a) => Binary (Point f a)

Instance details

Defined in Linear.Affine

Methods

put :: Point f a -> Put #

get :: Get (Point f a) #

putList :: [Point f a] -> Put #

Serial (f a) => Serial (Point f a)

Instance details

Defined in Linear.Affine

Methods

serialize :: MonadPut m => Point f a -> m () #

deserialize :: MonadGet m => m (Point f a) #

Serialize (f a) => Serialize (Point f a)

Instance details

Defined in Linear.Affine

Methods

put :: Putter (Point f a) #

get :: Get (Point f a) #

NFData (f a) => NFData (Point f a)

Instance details

Defined in Linear.Affine

Methods

rnf :: Point f a -> () #

(OrderedField n, Metric v) => Enveloped (Point v n) Source #

Instance details

Defined in Diagrams.Core.Envelope

Methods

getEnvelope :: Point v n -> Envelope (V (Point v n)) (N (Point v n)) Source #

(Additive v, Num n) => HasOrigin (Point v n) Source #

Instance details

Defined in Diagrams.Core.HasOrigin

Methods

moveOriginTo :: Point (V (Point v n)) (N (Point v n)) -> Point v n -> Point v n Source #

(Additive v, Ord n) => Traced (Point v n) Source #

The trace of a single point is the empty trace, i.e. the one which returns no intersection points for every query. Arguably it should return a single finite distance for vectors aimed directly at the given point, but due to floating-point inaccuracy this is problematic. Note that the envelope for a single point is not the empty envelope (see Diagrams.Core.Envelope).

Instance details

Defined in Diagrams.Core.Trace

Methods

getTrace :: Point v n -> Trace (V (Point v n)) (N (Point v n)) Source #