NumHask.Rect

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

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

Methods

fmap :: (a -> b) -> Rect a -> Rect b

(<$) :: a -> Rect b -> Rect a

Applicative Rect

Methods

pure :: a -> Rect a

(<*>) :: Rect (a -> b) -> Rect a -> Rect b

(*>) :: Rect a -> Rect b -> Rect b

(<*) :: Rect a -> Rect b -> Rect a

Foldable 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

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

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

Associated Types

type Rep (Rect :: * -> *) :: *

Methods

tabulate :: (Rep Rect -> a) -> Rect a

index :: Rect a -> Rep Rect -> a

Traversable1 Rect

Methods

traverse1 :: Apply f => (a -> f b) -> Rect a -> f (Rect b)

sequence1 :: Apply f => Rect (f b) -> f (Rect b)

Apply Rect

Methods

(<.>) :: Rect (a -> b) -> Rect a -> Rect b

(.>) :: Rect a -> Rect b -> Rect b

(<.) :: Rect a -> Rect b -> Rect a

Foldable1 Rect

Methods

fold1 :: Semigroup m => Rect m -> m

foldMap1 :: Semigroup m => (a -> m) -> Rect a -> m

toNonEmpty :: Rect a -> NonEmpty a

Eq a => Eq (Rect a)

Methods

(==) :: Rect a -> Rect a -> Bool

(/=) :: Rect a -> Rect a -> Bool

Show a => Show (Rect a)

Methods

showsPrec :: Int -> Rect a -> ShowS

show :: Rect a -> String

showList :: [Rect a] -> ShowS

(Signed a, Ord a, BoundedField a, FromInteger a) => Monoid (Rect a)

Methods

mempty :: Rect a

mappend :: Rect a -> Rect a -> Rect a

mconcat :: [Rect a] -> Rect a

Arbitrary a => Arbitrary (Rect a)

Methods

arbitrary :: Gen (Rect a)

shrink :: Rect a -> [Rect a]

NFData a => NFData (Rect a)

Methods

rnf :: Rect a -> ()

(AdditiveInvertible a, BoundedField a, Ord a, FromInteger a) => Signed (Rect a)

Methods

sign :: Rect a -> Rect a

abs :: Rect a -> Rect a

(BoundedField a, Ord a, FromInteger a, Epsilon a) => Epsilon (Rect a)

Methods

nearZero :: Rect a -> Bool

aboutEqual :: Rect a -> Rect a -> Bool

positive :: Rect a -> Bool

veryPositive :: Rect a -> Bool

veryNegative :: Rect a -> Bool

(Ord a, BoundedField a, FromInteger a) => MultiplicativeMagma (Rect a)

Methods

times :: Rect a -> Rect a -> Rect a

(Ord a, BoundedField a, FromInteger a) => MultiplicativeUnital (Rect a)

Methods

one :: Rect a

(Ord a, FromInteger a, BoundedField a) => MultiplicativeAssociative (Rect a)

(Ord a, BoundedField a, FromInteger a) => MultiplicativeCommutative (Rect a)

(Ord a, FromInteger a, BoundedField a) => MultiplicativeInvertible (Rect a)

Methods

recip :: Rect a -> Rect a

(Ord a, BoundedField a, FromInteger a) => Multiplicative (Rect a)

Methods

(*) :: Rect a -> Rect a -> Rect a

(Ord a, BoundedField a, FromInteger a) => MultiplicativeGroup (Rect a)

Methods

(/) :: Rect a -> Rect a -> Rect a

(Ord a, BoundedField a, FromInteger a) => AdditiveMagma (Rect a)

Methods

plus :: Rect a -> Rect a -> Rect a

(Ord a, BoundedField a, FromInteger a) => AdditiveUnital (Rect a)

Methods

zero :: Rect a

(Ord a, FromInteger a, BoundedField a) => AdditiveAssociative (Rect a)

(Ord a, BoundedField a, FromInteger a) => AdditiveCommutative (Rect a)

(Ord a, FromInteger a, BoundedField a) => AdditiveInvertible (Rect a)

Methods

negate :: Rect a -> Rect a

(Ord a, FromInteger a, BoundedField a) => AdditiveIdempotent (Rect a)

(Ord a, BoundedField a, FromInteger a) => Additive (Rect a)

Methods

(+) :: Rect a -> Rect a -> Rect a

(Ord a, BoundedField a, FromInteger a) => AdditiveGroup (Rect a)

Methods

(-) :: Rect a -> Rect a -> Rect a

(Signed a, FromInteger a, Ord a, BoundedField a) => Space (Rect a)

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

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)

Methods

size :: Rect a -> Pair a

type Rep Rect

type Rep Rect = (Bool, Bool)

type Element (Rect a)

type Element (Rect a) = Pair a

type Grid (Rect a)

type Grid (Rect a) = Pair Int

pattern Rect :: forall a. a -> a -> a -> a -> Rect a

pattern of Rect lowerx upperx lowery uppery

pattern Ranges :: forall a. Range a -> Range a -> Rect a

pattern of Ranges xrange yrange

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

project a Rect from an old range to a new one