diagrams-lib-1.4: Embedded domain-specific language for declarative graphics

Diagrams.Points

Contents

Description

Points in space. For more tools for working with points and vectors, see Linear.Affine.

Synopsis

# Points

newtype Point f 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) MethodsbasicUnsafeFreeze :: 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) MethodsbasicLength :: 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) 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) Methodsfmap :: (a -> b) -> Point f a -> Point f b #(<\$) :: a -> Point f b -> Point f a # Applicative f => Applicative (Point f) Methodspure :: a -> Point f a #(<*>) :: 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 # Foldable f => Foldable (Point f) Methodsfold :: 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) Methodstraverse :: Applicative f => (a -> f b) -> Point f a -> f (Point f b) #sequenceA :: Applicative f => Point f (f a) -> f (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) # Associated Typestype Rep1 (Point f :: * -> *) :: * -> * # Methodsfrom1 :: Point f a -> Rep1 (Point f) a #to1 :: Rep1 (Point f) a -> Point f a # Apply f => Apply (Point f) 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 # Methodsdistribute :: Functor f => f (Point f a) -> Point f (f a) #collect :: Functor f => (a -> Point f b) -> f a -> Point f (f 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) # Associated Typestype Rep (Point f :: * -> *) :: * # Methodstabulate :: (Rep (Point f) -> a) -> Point f a #index :: Point f a -> Rep (Point f) -> a # Eq1 f => Eq1 (Point f) MethodsliftEq :: (a -> b -> Bool) -> Point f a -> Point f b -> Bool # Ord1 f => Ord1 (Point f) MethodsliftCompare :: (a -> b -> Ordering) -> Point f a -> Point f b -> Ordering # Read1 f => Read1 (Point f) MethodsliftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Point f a) #liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Point f a] # Show1 f => Show1 (Point f) MethodsliftShowsPrec :: (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) MethodsserializeWith :: MonadPut m => (a -> m ()) -> Point f a -> m () #deserializeWith :: MonadGet m => m a -> m (Point f a) # Additive f => Additive (Point f) Methodszero :: 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 # Additive f => Affine (Point f) Associated Typestype Diff (Point 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 # R4 f => R4 (Point f) Methods_w :: Functor f => (a -> f a) -> Point f a -> f (Point f a) #_xyzw :: Functor f => (V4 a -> f (V4 a)) -> Point f a -> f (Point f a) # R3 f => R3 (Point f) Methods_z :: Functor f => (a -> f a) -> Point f a -> f (Point f a) #_xyz :: Functor f => (V3 a -> f (V3 a)) -> Point f a -> f (Point f 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) # R1 f => R1 (Point f) Methods_x :: Functor f => (a -> f a) -> Point f a -> f (Point f a) # Metric f => Metric (Point f) Methodsdot :: 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 # Bind f => Bind (Point f) Methods(>>-) :: Point f a -> (a -> Point f b) -> Point f b #join :: Point f (Point f a) -> Point f a # HasPhi v => HasPhi (Point v) Source # Methods_phi :: RealFloat n => Lens' (Point v n) (Angle n) Source # HasTheta v => HasTheta (Point v) Source # Methods_theta :: RealFloat n => Lens' (Point v n) (Angle n) Source # HasR v => HasR (Point v) Source # Methods_r :: RealFloat n => Lens' (Point v n) n Source # (Metric v, OrderedField n) => TrailLike [Point v n] Source # A list of points is trail-like; this instance simply computes the vertices of the trail, using trailPoints. MethodstrailLike :: Located (Trail (V [Point v n]) (N [Point v n])) -> [Point v n] Source # Functor v => Cosieve (Query v) (Point v) Methodscosieve :: Query v a b -> Point v a -> b # Eq (f a) => Eq (Point f a) Methods(==) :: Point f a -> Point f a -> Bool #(/=) :: Point f a -> Point f a -> Bool # Fractional (f a) => Fractional (Point f a) Methods(/) :: Point f a -> Point f a -> Point f a #recip :: Point f a -> Point f a #fromRational :: Rational -> Point f a # (Data (f a), Typeable * a, Typeable (* -> *) f) => Data (Point f a) Methodsgfoldl :: (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) 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) Methodscompare :: 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) MethodsreadsPrec :: 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) MethodsshowsPrec :: Int -> Point f a -> ShowS #show :: Point f a -> String #showList :: [Point f a] -> ShowS # Ix (f a) => Ix (Point f a) Methodsrange :: (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 -> IntinRange :: (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) Associated Typestype Rep (Point f a) :: * -> * # Methodsfrom :: Point f a -> Rep (Point f a) x #to :: Rep (Point f a) x -> Point f a # Storable (f a) => Storable (Point f a) MethodssizeOf :: 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) Methodsput :: Point f a -> Put #get :: Get (Point f a) #putList :: [Point f a] -> Put # Serial (f a) => Serial (Point f a) Methodsserialize :: MonadPut m => Point f a -> m () #deserialize :: MonadGet m => m (Point f a) # Serialize (f a) => Serialize (Point f a) Methodsput :: Putter (Point f a) #get :: Get (Point f a) # NFData (f a) => NFData (Point f a) Methodsrnf :: Point f a -> () # (OrderedField n, Metric v) => Enveloped (Point v n) MethodsgetEnvelope :: Point v n -> Envelope (V (Point v n)) (N (Point v n)) # (Additive v, Ord n) => Traced (Point v n) 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). MethodsgetTrace :: Point v n -> Trace (V (Point v n)) (N (Point v n)) # (Additive v, Num n) => Transformable (Point v n) Methodstransform :: Transformation (V (Point v n)) (N (Point v n)) -> Point v n -> Point v n # (Additive v, Num n) => HasOrigin (Point v n) MethodsmoveOriginTo :: Point (V (Point v n)) (N (Point v n)) -> Point v n -> Point v n # Hashable (f a) => Hashable (Point f a) MethodshashWithSalt :: Int -> Point f a -> Int #hash :: Point f a -> Int # Unbox (f a) => Unbox (Point f a) Ixed (f a) => Ixed (Point f a) Methodsix :: Index (Point f a) -> Traversal' (Point f a) (IxValue (Point f a)) # Wrapped (Point f a) Associated Typestype Unwrapped (Point f a) :: * # Methods_Wrapped' :: Iso' (Point f a) (Unwrapped (Point f a)) # Epsilon (f a) => Epsilon (Point f a) MethodsnearZero :: Point f a -> Bool # Coordinates (v n) => Coordinates (Point v n) Source # Associated Typestype FinalCoord (Point v n) :: * Source #type PrevDim (Point v n) :: * Source #type Decomposition (Point v n) :: * Source # Methods(^&) :: PrevDim (Point v n) -> FinalCoord (Point v n) -> Point v n Source #pr :: PrevDim (Point v n) -> FinalCoord (Point v n) -> Point v n Source #coords :: Point v n -> Decomposition (Point v n) Source # (~) * t (Point g b) => Rewrapped (Point f a) t (~) * r (Point u n) => Deformable (Point v n) r Source # Methodsdeform' :: N (Point v n) -> Deformation (V (Point v n)) (V r) (N (Point v n)) -> Point v n -> r Source #deform :: Deformation (V (Point v n)) (V r) (N (Point v n)) -> Point v n -> r Source # (Additive v, Num n, (~) * r (Point u n)) => AffineMappable (Point v n) r Source # Methodsamap :: AffineMap (V (Point v n)) (V r) (N r) -> Point v n -> r Source # LinearMappable (Point v n) (Point u m) Source # Methodsvmap :: (Vn (Point v n) -> Vn (Point u m)) -> Point v n -> Point u m Source # Traversable f => Each (Point f a) (Point f b) a b Methodseach :: Traversal (Point f a) (Point f b) a b # Each (FixedSegment v n) (FixedSegment v' n') (Point v n) (Point v' n') # Methodseach :: Traversal (FixedSegment v n) (FixedSegment v' n') (Point v n) (Point v' n') # (Additive v', Foldable v', Ord n') => Each (BoundingBox v n) (BoundingBox v' n') (Point v n) (Point v' n') # Only valid if the second point is not smaller than the first. Methodseach :: Traversal (BoundingBox v n) (BoundingBox v' n') (Point v n) (Point v' n') # data MVector s (Point f a) data MVector s (Point f a) = MV_P ~(MVector s (f a)) type Rep1 (Point f) type Rep1 (Point f) = D1 (MetaData "Point" "Linear.Affine" "linear-1.20.5-ALqHTYew01KD1PdDd6TYmz" True) (C1 (MetaCons "P" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f))) type Rep (Point f) type Rep (Point f) = Rep f type Diff (Point f) type Diff (Point f) = f type Rep (Point f a) type Rep (Point f a) = D1 (MetaData "Point" "Linear.Affine" "linear-1.20.5-ALqHTYew01KD1PdDd6TYmz" True) (C1 (MetaCons "P" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f a)))) type V (Point v n) type V (Point v n) = v type N (Point v n) type N (Point v n) = n data Vector (Point f a) data Vector (Point f a) = V_P ~(Vector (f a)) type Index (Point f a) type Index (Point f a) = Index (f a) type IxValue (Point f a) type IxValue (Point f a) = IxValue (f a) type Unwrapped (Point f a) type Unwrapped (Point f a) = f a type FinalCoord (Point v n) Source # type FinalCoord (Point v n) = FinalCoord (v n) type PrevDim (Point v n) Source # type PrevDim (Point v n) = PrevDim (v n) type Decomposition (Point v n) Source # type Decomposition (Point v n) = Decomposition (v n)

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

Vector spaces have origins.

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

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

# Point-related utilities

centroid :: (Additive v, Fractional n) => [Point v n] -> Point v n Source #

The centroid of a set of n points is their sum divided by n.

pointDiagram :: (Metric v, Fractional n) => Point v n -> QDiagram b v n m #

Create a "point diagram", which has no content, no trace, an empty query, and a point envelope.

_Point :: (Profunctor p, Functor f) => p (f a) (f (f a)) -> p (Point f a) (f (Point f a)) #

lensP :: Functor f => (g a -> f (g a)) -> Point g a -> f (Point g a) #