Copyright	(c) 2011 diagrams-core team (see LICENSE)
License	BSD-style (see LICENSE)
Maintainer	diagrams-discuss@googlegroups.com
Safe Haskell	None
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 :: (Additive f, Num a) => Point f a
(*.) :: (Functor v, Num n) => n -> Point v n -> Point v n
relative :: (Additive f, Num a) => Point f a -> Iso' (Point f a) (f a)
_Point :: Iso' (Point f a) (f a)
reflectThrough :: (Additive v, Num n) => Point v n -> Point v n -> Point v n
mirror :: (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

Unbox (f a) => Vector Vector (Point f a)
Instance details Defined in Linear.Affine Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Point f a) -> m (Vector (Point f a)) # basicUnsafeThaw :: PrimMonad m => Vector (Point f a) -> m (Mutable Vector (PrimState m) (Point f a)) # basicLength :: Vector (Point f a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Point f a) -> Vector (Point f a) # basicUnsafeIndexM :: Monad m => Vector (Point f a) -> Int -> m (Point f a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Point f a) -> Vector (Point f a) -> m () # 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 :: PrimMonad m => Int -> m (MVector (PrimState m) (Point f a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (Point f a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Point f a -> m (MVector (PrimState m) (Point f a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Point f a) -> Int -> m (Point f a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Point f a) -> Int -> Point f a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (Point f a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (Point f a) -> Point f a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Point f a) -> MVector (PrimState m) (Point f a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Point f a) -> MVector (PrimState m) (Point f a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Point f a) -> Int -> m (MVector (PrimState m) (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 # fail :: String -> 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 #
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 #
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 # 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 #
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) #
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) #
Representable f => Representable (Point f)
Instance details Defined in Linear.Affine Associated Types type Rep (Point f) :: Type # Methods tabulate :: (Rep (Point f) -> a) -> Point f a # index :: Point f a -> Rep (Point f) -> 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 #
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) #
Hashable1 f => Hashable1 (Point f)
Instance details Defined in Linear.Affine Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> Point f a -> Int #
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 #
Additive f => Affine (Point f)
Instance details Defined in Linear.Affine Associated Types type Diff (Point f) :: Type -> Type # 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 #
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) #
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) #
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) #
R1 f => R1 (Point f)
Instance details Defined in Linear.Affine Methods _x :: Lens' (Point f a) a #
Finite f => Finite (Point f)
Instance details Defined in Linear.Affine Associated Types type Size (Point f) :: Nat # Methods toV :: Point f a -> V (Size (Point f)) a # fromV :: V (Size (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 #
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 #
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 #
Generic1 (Point f :: Type -> Type)
Instance details Defined in Linear.Affine Associated Types type Rep1 (Point f) :: k -> Type # Methods from1 :: Point f a -> Rep1 (Point f) a # to1 :: Rep1 (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 #
Eq (f a) => Eq (Point f a)
Instance details Defined in Linear.Affine Methods (==) :: Point f a -> Point f a -> Bool # (/=) :: Point f a -> Point f a -> Bool #
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 #
(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 :: (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) #
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 #
Ord (f a) => Ord (Point f a)
Instance details Defined in Linear.Affine Methods compare :: Point f a -> Point f a -> Ordering # (<) :: Point f a -> Point f a -> Bool # (<=) :: Point f a -> Point f a -> Bool # (>) :: Point f a -> Point f a -> Bool # (>=) :: Point f a -> Point f a -> Bool # max :: Point f a -> Point f a -> Point f a # min :: Point f a -> Point f a -> 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] #
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 #
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
Generic (Point f a)
Instance details Defined in Linear.Affine Associated Types type Rep (Point f a) :: Type -> Type # Methods from :: Point f a -> Rep (Point f a) x # to :: Rep (Point f a) x -> 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 () #
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 -> () #
Hashable (f a) => Hashable (Point f a)
Instance details Defined in Linear.Affine Methods hashWithSalt :: Int -> Point f a -> Int # hash :: Point f a -> Int #
Unbox (f a) => Unbox (Point f a)
Instance details Defined in Linear.Affine
Ixed (f a) => Ixed (Point f a)
Instance details Defined in Linear.Affine Methods ix :: Index (Point f a) -> Traversal' (Point f a) (IxValue (Point f a)) #
Wrapped (Point f a)
Instance details Defined in Linear.Affine Associated Types type Unwrapped (Point f a) :: Type # Methods _Wrapped' :: Iso' (Point f a) (Unwrapped (Point f a)) #
Epsilon (f a) => Epsilon (Point f a)
Instance details Defined in Linear.Affine Methods nearZero :: Point f a -> Bool #
(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, Num n) => Transformable (Point v n) Source #
Instance details Defined in Diagrams.Core.Transform Methods transform :: Transformation (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 #
(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 #
t ~ Point g b => Rewrapped (Point f a) t
Instance details Defined in Linear.Affine
Traversable f => Each (Point f a) (Point f b) a b
Instance details Defined in Linear.Affine Methods each :: Traversal (Point f a) (Point f b) a b #
newtype MVector s (Point f a)
Instance details Defined in Linear.Affine newtype MVector s (Point f a) = MV_P (MVector s (f a))
type Rep (Point f)
Instance details Defined in Linear.Affine type Rep (Point f) = Rep f
type Diff (Point f)
Instance details Defined in Linear.Affine type Diff (Point f) = f
type Size (Point f)
Instance details Defined in Linear.Affine type Size (Point f) = Size f
type Rep1 (Point f :: Type -> Type)
Instance details Defined in Linear.Affine type Rep1 (Point f :: Type -> Type) = D1 (MetaData "Point" "Linear.Affine" "linear-1.20.9-FQ1kq2xAlAxC2ls6AC0YzF" True) (C1 (MetaCons "P" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f)))
type Rep (Point f a)
Instance details Defined in Linear.Affine type Rep (Point f a) = D1 (MetaData "Point" "Linear.Affine" "linear-1.20.9-FQ1kq2xAlAxC2ls6AC0YzF" True) (C1 (MetaCons "P" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f a))))
newtype Vector (Point f a)
Instance details Defined in Linear.Affine newtype Vector (Point f a) = V_P (Vector (f a))
type Index (Point f a)
Instance details Defined in Linear.Affine type Index (Point f a) = Index (f a)
type IxValue (Point f a)
Instance details Defined in Linear.Affine type IxValue (Point f a) = IxValue (f a)
type Unwrapped (Point f a)
Instance details Defined in Linear.Affine type Unwrapped (Point f a) = f a
type N (Point v n) Source #
Instance details Defined in Diagrams.Core.Points type N (Point v n) = n
type V (Point v n) Source #
Instance details Defined in Diagrams.Core.Points type V (Point v n) = v

origin :: (Additive f, Num a) => Point f a #

Vector spaces have origins.

(*.) :: (Functor v, Num n) => n -> Point v n -> Point v n Source #

Scale a point by a scalar. Specialized version of '(*^)'.

relative :: (Additive f, Num a) => Point f a -> Iso' (Point f a) (f a) #

An isomorphism between points and vectors, given a reference point.

_Point :: Iso' (Point f a) (f a) #

reflectThrough :: (Additive v, Num n) => Point v n -> Point v n -> Point v n Source #

Mirror a point through a given point.

mirror :: (Additive v, Num n) => Point v n -> Point v n Source #

Reflect a point across the origin.

relative2 :: (Additive v, Num n) => Point v n -> (v n -> v n -> v n) -> Point v n -> Point v n -> Point v n Source #

Apply a transformation relative to the given point.

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 Source #

Apply a transformation relative to the given point.