Safe Haskell	None
Language	Haskell2010

NumHask.Rect

Description

a two-dimensional plane, implemented as a composite of a Pair of Ranges.

Synopsis

newtype Rect a = Rect' (Compose Pair Range a)
pattern Rect :: a -> a -> a -> a -> Rect a
pattern Ranges :: Range a -> Range a -> Rect a
corners :: (FromInteger a, Signed a, BoundedField a, Ord a) => Rect a -> [Pair a]
projectRect :: (FromInteger a, Signed a, Ord a, BoundedField a) => Rect a -> Rect a -> Rect a -> Rect a

Documentation

newtype Rect a #

a Pair of Ranges that form a rectangle in what is often thought of as the XY plane.

>>> let a = Rect (-1) 1 (-2) 4
>>> a
Rect -1 1 -2 4
>>> let (Ranges x y) = a
>>> x
Range -1 1
>>> y
Range -2 4
>>> fmap (+1) (Rect 1 2 3 4)
Rect 2 3 4 5
>>> one :: Rect Double
Rect -0.5 0.5 -0.5 0.5
>>> zero :: Rect Double
Rect Infinity -Infinity Infinity -Infinity

as a Field instance

>>> Rect 0 1 2 3 + zero
Rect 0.0 1.0 2.0 3.0
>>> Rect 0 1 (-2) (-1) + Rect 2 3 (-5) 3
Rect 0.0 3.0 -5.0 3.0
>>> Rect 1 1 1 1 - one
Rect 0.5 1.0 0.5 1.0
>>> Rect 0 1 0 1 * one
Rect 0.0 1.0 0.0 1.0
>>> Rect 0 1 0 1 / one
Rect 0.0 1.0 0.0 1.0
>>> singleton (Pair 1.0 2.0) :: Rect Double
Rect 1.0 1.0 2.0 2.0
>>> abs (Rect 1 0 1 0)
Rect 0.0 1.0 0.0 1.0
>>> sign (Rect 1 0 1 0) == negate one
True

as a Space instance

>>> project (Rect 0 1 (-1) 0) (Rect 1 4 10 0) (Pair 0.5 1)
Pair 2.5 -10.0
>>> gridSpace (Rect 0 10 0 1) (Pair 2 2)
[Rect 0.0 5.0 0.0 0.5,Rect 0.0 5.0 0.5 1.0,Rect 5.0 10.0 0.0 0.5,Rect 5.0 10.0 0.5 1.0]
>>> grid MidPos (Rect 0 10 0 1) (Pair 2 2)
[Pair 2.5 0.25,Pair 2.5 0.75,Pair 7.5 0.25,Pair 7.5 0.75]

Constructors

Rect' (Compose Pair Range a)

Instances

Functor Rect #
Instance details Defined in NumHask.Rect Methods fmap :: (a -> b) -> Rect a -> Rect b # (<$) :: a -> Rect b -> Rect a #
Applicative Rect #
Instance details Defined in NumHask.Rect Methods pure :: a -> Rect a # (<>) :: Rect (a -> b) -> Rect a -> Rect b # liftA2 :: (a -> b -> c) -> Rect a -> Rect b -> Rect c # (>) :: Rect a -> Rect b -> Rect b # (<*) :: Rect a -> Rect b -> Rect a #
Foldable Rect #
Instance details Defined in NumHask.Rect Methods fold :: Monoid m => Rect m -> m # foldMap :: Monoid m => (a -> m) -> Rect a -> m # foldr :: (a -> b -> b) -> b -> Rect a -> b # foldr' :: (a -> b -> b) -> b -> Rect a -> b # foldl :: (b -> a -> b) -> b -> Rect a -> b # foldl' :: (b -> a -> b) -> b -> Rect a -> b # foldr1 :: (a -> a -> a) -> Rect a -> a # foldl1 :: (a -> a -> a) -> Rect a -> a # toList :: Rect a -> [a] # null :: Rect a -> Bool # length :: Rect a -> Int # elem :: Eq a => a -> Rect a -> Bool # maximum :: Ord a => Rect a -> a # minimum :: Ord a => Rect a -> a # sum :: Num a => Rect a -> a # product :: Num a => Rect a -> a #
Traversable Rect #
Instance details Defined in NumHask.Rect Methods traverse :: Applicative f => (a -> f b) -> Rect a -> f (Rect b) # sequenceA :: Applicative f => Rect (f a) -> f (Rect a) # mapM :: Monad m => (a -> m b) -> Rect a -> m (Rect b) # sequence :: Monad m => Rect (m a) -> m (Rect a) #
Distributive Rect #
Instance details Defined in NumHask.Rect Methods distribute :: Functor f => f (Rect a) -> Rect (f a) # collect :: Functor f => (a -> Rect b) -> f a -> Rect (f b) # distributeM :: Monad m => m (Rect a) -> Rect (m a) # collectM :: Monad m => (a -> Rect b) -> m a -> Rect (m b) #
Representable Rect #
Instance details Defined in NumHask.Rect Associated Types type Rep Rect :: * # Methods tabulate :: (Rep Rect -> a) -> Rect a # index :: Rect a -> Rep Rect -> a #
Singleton Rect #	fixme: this is a deeply flawed hack
Instance details Defined in NumHask.Rect Methods singleton :: a -> Rect a #
Traversable1 Rect #
Instance details Defined in NumHask.Rect Methods traverse1 :: Apply f => (a -> f b) -> Rect a -> f (Rect b) # sequence1 :: Apply f => Rect (f b) -> f (Rect b) #
Foldable1 Rect #
Instance details Defined in NumHask.Rect Methods fold1 :: Semigroup m => Rect m -> m # foldMap1 :: Semigroup m => (a -> m) -> Rect a -> m # toNonEmpty :: Rect a -> NonEmpty a #
Apply Rect #
Instance details Defined in NumHask.Rect Methods (<.>) :: Rect (a -> b) -> Rect a -> Rect b # (.>) :: Rect a -> Rect b -> Rect b # (<.) :: Rect a -> Rect b -> Rect a # liftF2 :: (a -> b -> c) -> Rect a -> Rect b -> Rect c #
Additive a => AdditiveModule Rect a #
Instance details Defined in NumHask.Rect Methods (.+) :: Rect a -> a -> Rect a # (+.) :: a -> Rect a -> Rect a #
AdditiveGroup a => AdditiveGroupModule Rect a #
Instance details Defined in NumHask.Rect Methods (.-) :: Rect a -> a -> Rect a # (-.) :: a -> Rect a -> Rect a #
Multiplicative a => MultiplicativeModule Rect a #
Instance details Defined in NumHask.Rect Methods (.) :: Rect a -> a -> Rect a # (.) :: a -> Rect a -> Rect a #
MultiplicativeGroup a => MultiplicativeGroupModule Rect a #
Instance details Defined in NumHask.Rect Methods (./) :: Rect a -> a -> Rect a # (/.) :: a -> Rect a -> Rect a #
Additive a => AdditiveBasis Rect a #
Instance details Defined in NumHask.Rect Methods (.+.) :: Rect a -> Rect a -> Rect a #
AdditiveGroup a => AdditiveGroupBasis Rect a #
Instance details Defined in NumHask.Rect Methods (.-.) :: Rect a -> Rect a -> Rect a #
Multiplicative a => MultiplicativeBasis Rect a #
Instance details Defined in NumHask.Rect Methods (.*.) :: Rect a -> Rect a -> Rect a #
MultiplicativeGroup a => MultiplicativeGroupBasis Rect a #
Instance details Defined in NumHask.Rect Methods (./.) :: Rect a -> Rect a -> Rect a #
Eq a => Eq (Rect a) #
Instance details Defined in NumHask.Rect Methods (==) :: Rect a -> Rect a -> Bool # (/=) :: Rect a -> Rect a -> Bool #
Show a => Show (Rect a) #
Instance details Defined in NumHask.Rect Methods showsPrec :: Int -> Rect a -> ShowS # show :: Rect a -> String # showList :: [Rect a] -> ShowS #
Generic (Rect a) #
Instance details Defined in NumHask.Rect Associated Types type Rep (Rect a) :: * -> * # Methods from :: Rect a -> Rep (Rect a) x # to :: Rep (Rect a) x -> Rect a #
(FromInteger a, Signed a, Ord a, BoundedField a) => Semigroup (Rect a) #
Instance details Defined in NumHask.Rect Methods (<>) :: Rect a -> Rect a -> Rect a # sconcat :: NonEmpty (Rect a) -> Rect a # stimes :: Integral b => b -> Rect a -> Rect a #
(FromInteger a, Signed a, Ord a, BoundedField a) => Monoid (Rect a) #
Instance details Defined in NumHask.Rect Methods mempty :: Rect a # mappend :: Rect a -> Rect a -> Rect a # mconcat :: [Rect a] -> Rect a #
Arbitrary a => Arbitrary (Rect a) #
Instance details Defined in NumHask.Rect Methods arbitrary :: Gen (Rect a) # shrink :: Rect a -> [Rect a] #
NFData a => NFData (Rect a) #
Instance details Defined in NumHask.Rect Methods rnf :: Rect a -> () #
(FromInteger a, AdditiveInvertible a, BoundedField a, Ord a) => Signed (Rect a) #
Instance details Defined in NumHask.Rect Methods sign :: Rect a -> Rect a # abs :: Rect a -> Rect a #
(BoundedField a, Ord a, Epsilon a) => Epsilon (Rect a) #
Instance details Defined in NumHask.Rect Methods nearZero :: Rect a -> Bool # aboutEqual :: Rect a -> Rect a -> Bool # positive :: Rect a -> Bool # veryPositive :: Rect a -> Bool # veryNegative :: Rect a -> Bool #
(FromInteger a, Ord a, BoundedField a) => MultiplicativeMagma (Rect a) #
Instance details Defined in NumHask.Rect Methods times :: Rect a -> Rect a -> Rect a #
(FromInteger a, Ord a, BoundedField a) => MultiplicativeUnital (Rect a) #
Instance details Defined in NumHask.Rect Methods one :: Rect a #
(FromInteger a, Ord a, BoundedField a) => MultiplicativeAssociative (Rect a) #
Instance details Defined in NumHask.Rect
(FromInteger a, Ord a, BoundedField a) => MultiplicativeCommutative (Rect a) #
Instance details Defined in NumHask.Rect
(FromInteger a, Ord a, BoundedField a) => MultiplicativeInvertible (Rect a) #
Instance details Defined in NumHask.Rect Methods recip :: Rect a -> Rect a #
(FromInteger a, Ord a, BoundedField a) => Multiplicative (Rect a) #
Instance details Defined in NumHask.Rect Methods (*) :: Rect a -> Rect a -> Rect a #
(FromInteger a, Ord a, BoundedField a) => MultiplicativeGroup (Rect a) #
Instance details Defined in NumHask.Rect Methods (/) :: Rect a -> Rect a -> Rect a #
Ord a => AdditiveMagma (Rect a) #
Instance details Defined in NumHask.Rect Methods plus :: Rect a -> Rect a -> Rect a #
(Ord a, BoundedField a) => AdditiveUnital (Rect a) #
Instance details Defined in NumHask.Rect Methods zero :: Rect a #
Ord a => AdditiveAssociative (Rect a) #
Instance details Defined in NumHask.Rect
Ord a => AdditiveCommutative (Rect a) #
Instance details Defined in NumHask.Rect
Ord a => AdditiveInvertible (Rect a) #
Instance details Defined in NumHask.Rect Methods negate :: Rect a -> Rect a #
Ord a => AdditiveIdempotent (Rect a) #
Instance details Defined in NumHask.Rect
(Ord a, BoundedField a) => Additive (Rect a) #
Instance details Defined in NumHask.Rect Methods (+) :: Rect a -> Rect a -> Rect a #
(Ord a, BoundedField a) => AdditiveGroup (Rect a) #
Instance details Defined in NumHask.Rect Methods (-) :: Rect a -> Rect a -> Rect a #
(FromInteger a, Signed a, Ord a, BoundedField a) => Space (Rect a) #
Instance details Defined in NumHask.Rect Associated Types type Element (Rect a) :: * # type Grid (Rect a) :: * # Methods lower :: Rect a -> Element (Rect a) # upper :: Rect a -> Element (Rect a) # mid :: Rect a -> Element (Rect a) # width :: Rect a -> Element (Rect a) # singleton :: Element (Rect a) -> Rect a # singular :: Rect a -> Bool # element :: Element (Rect a) -> Rect a -> Bool # contains :: Rect a -> Rect a -> Bool # disjoint :: Rect a -> Rect a -> Bool # intersects :: Rect a -> Rect a -> Bool # union :: Rect a -> Rect a -> Rect a # nul :: Rect a # space :: Foldable f => f (Element (Rect a)) -> Rect a # project :: Rect a -> Rect a -> Element (Rect a) -> Element (Rect a) # grid :: Pos -> Rect a -> Grid (Rect a) -> [Element (Rect a)] # gridSpace :: Rect a -> Grid (Rect a) -> [Rect a] #
AdditiveGroup a => Normed (Rect a) (Pair a) #
Instance details Defined in NumHask.Rect Methods normL1 :: Rect a -> Pair a # normL2 :: Rect a -> Pair a # normLp :: Pair a -> Rect a -> Pair a #
type Rep Rect #
Instance details Defined in NumHask.Rect type Rep Rect = (Bool, Bool)
type Rep (Rect a) #
Instance details Defined in NumHask.Rect type Rep (Rect a) = D1 (MetaData "Rect" "NumHask.Rect" "numhask-range-0.2.3.1-J89sQYUYBLeKCiE9B8m0BR" True) (C1 (MetaCons "Rect'" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Compose Pair Range a))))
type Element (Rect a) #
Instance details Defined in NumHask.Rect type Element (Rect a) = Pair a
type Grid (Rect a) #
Instance details Defined in NumHask.Rect type Grid (Rect a) = Pair Int

pattern Rect :: a -> a -> a -> a -> Rect a #

pattern of Rect lowerx upperx lowery uppery

pattern Ranges :: Range a -> Range a -> Rect a #

pattern of Ranges xrange yrange

corners :: (FromInteger a, Signed a, BoundedField a, Ord a) => Rect a -> [Pair a] #

create a list of pairs representing the lower left and upper right cormners of a rectangle.

projectRect :: (FromInteger a, Signed a, Ord a, BoundedField a) => Rect a -> Rect a -> Rect a -> Rect a #

project a Rect from an old range to a new one