NumHask.Space.Rect

A (finite) two-dimensional plane, implemented as a composite of a Point of Ranges.

Documentation

newtype Rect a

a rectangular space often representing a finite 2-dimensional or XY plane.

>>> one :: Rect Double
Rect -0.5 0.5 -0.5 0.5

>>> zero :: Rect Double
Rect 0.0 0.0 0.0 0.0

>>> one + one :: Rect Double
Rect -1.0 1.0 -1.0 1.0

>>> let a = Rect (-1.0) 1.0 (-2.0) 4.0
>>> a
Rect -1.0 1.0 -2.0 4.0

>>> a * one
Rect -1.0 1.0 -2.0 4.0

>>> let (Ranges x y) = a
>>> x
Range -1.0 1.0
>>> y
Range -2.0 4.0
>>> fmap (+1) (Rect 1 2 3 4)
Rect 2 3 4 5

as a Space instance with Points as Elements

>>> project (Rect 0.0 1.0 (-1.0) 0.0) (Rect 1.0 4.0 10.0 0.0) (Point 0.5 1.0)
Point 2.5 -10.0
>>> gridSpace (Rect 0.0 10.0 0.0 1.0) (Point (2::Int) (2::Int))
[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 0.0 10.0 0.0 1.0) (Point (2::Int) (2::Int))
[Point 2.5 0.25,Point 2.5 0.75,Point 7.5 0.25,Point 7.5 0.75]

Constructors

Rect' (Compose Point Range a)

Instances

Functor Rect

Defined in NumHask.Space.Rect

Methods

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

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

Applicative Rect

Defined in NumHask.Space.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

Defined in NumHask.Space.Rect

Methods

fold :: Monoid m => Rect m -> m

foldMap :: Monoid m => (a -> m) -> Rect a -> 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

Defined in NumHask.Space.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

Defined in NumHask.Space.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

Defined in NumHask.Space.Rect

Associated Types

type Rep Rect

Methods

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

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

Eq a => Eq (Rect a)

Defined in NumHask.Space.Rect

Methods

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

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

Show a => Show (Rect a)

Defined in NumHask.Space.Rect

Methods

showsPrec :: Int -> Rect a -> ShowS

show :: Rect a -> String

showList :: [Rect a] -> ShowS

Generic (Rect a)

Defined in NumHask.Space.Rect

Associated Types

type Rep (Rect a) :: Type -> Type

Methods

from :: Rect a -> Rep (Rect a) x

to :: Rep (Rect a) x -> Rect a

Ord a => Semigroup (Rect a)

Defined in NumHask.Space.Rect

Methods

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

sconcat :: NonEmpty (Rect a) -> Rect a

stimes :: Integral b => b -> Rect a -> Rect a

(Ord a, Field a) => Signed (Rect a)

Defined in NumHask.Space.Rect

Methods

sign :: Rect a -> Rect a

abs :: Rect a -> Rect a

(Ord a, Field a) => Multiplicative (Rect a)

Defined in NumHask.Space.Rect

Methods

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

one :: Rect a

(Ord a, Field a) => Divisive (Rect a)

Defined in NumHask.Space.Rect

Methods

recip :: Rect a -> Rect a

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

Additive a => Additive (Rect a)

Numeric algebra based on interval arithmetioc for addition and unitRect and projection for multiplication >>> one + one :: Rect Double Rect -1.0 1.0 -1.0 1.0

Defined in NumHask.Space.Rect

Methods

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

zero :: Rect a

Subtractive a => Subtractive (Rect a)

Defined in NumHask.Space.Rect

Methods

negate :: Rect a -> Rect a

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

(FromIntegral a Int, Field a, Ord a) => FieldSpace (Rect a)

Defined in NumHask.Space.Rect

Associated Types

type Grid (Rect a)

Methods

grid :: Pos -> Rect a -> Grid (Rect a) -> [Element (Rect a)]

gridSpace :: Rect a -> Grid (Rect a) -> [Rect a]

Ord a => Space (Rect a)

Defined in NumHask.Space.Rect

Associated Types

type Element (Rect a)

Methods

lower :: Rect a -> Element (Rect a)

upper :: Rect a -> Element (Rect a)

singleton :: Element (Rect a) -> Rect a

intersection :: Rect a -> Rect a -> Rect a

union :: Rect a -> Rect a -> Rect a

normalise :: Rect a -> Rect a

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

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

(|.|) :: Element (Rect a) -> Rect a -> Bool

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

(|<|) :: Rect a -> Rect a -> Bool

type Rep Rect

Defined in NumHask.Space.Rect

type Rep Rect = (Bool, Bool)

type Rep (Rect a)

Defined in NumHask.Space.Rect

type Rep (Rect a) = D1 ('MetaData "Rect" "NumHask.Space.Rect" "numhask-space-0.10.0.0-7Vc0BQiwNPu4OVYJOuBT4u" 'True) (C1 ('MetaCons "Rect'" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Compose Point Range a))))

type Grid (Rect a)

Defined in NumHask.Space.Rect

type Grid (Rect a) = Point Int

type Element (Rect a)

Defined in NumHask.Space.Rect

type Element (Rect a) = Point a

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 :: Ord a => Rect a -> [Point a]

create a list of points representing the lower left and upper right corners of a rectangle.

>>> corners one
[Point -0.5 -0.5,Point 0.5 0.5]

corners4 :: Rect a -> [Point a]

the 4 corners

>>> corners4 one
[Point -0.5 -0.5,Point -0.5 0.5,Point 0.5 -0.5,Point 0.5 0.5]

projectRect :: (Field a, Ord a) => Rect a -> Rect a -> Rect a -> Rect a

project a Rect from an old Space (Rect) to a new one.

The Space instance of Rect uses Points as Elements, but a Rect can also be a Space over Rects.

>>> projectRect (Rect 0 1 (-1) 0) (Rect 0 4 0 8) (Rect 0.25 0.75 (-0.75) (-0.25))
Rect 1.0 3.0 2.0 6.0

foldRect :: Ord a => [Rect a] -> Maybe (Rect a)

convex hull union of Rect's

>>> foldRect [Rect 0 1 0 1, one]
Just Rect -0.5 1.0 -0.5 1.0

foldRectUnsafe :: (Foldable f, Ord a) => f (Rect a) -> Rect a

convex hull union of Rect's applied to a non-empty structure

>>> foldRectUnsafe [Rect 0 1 0 1, one]
Rect -0.5 1.0 -0.5 1.0

addPoint :: Additive a => Point a -> Rect a -> Rect a

add a Point to a Rect

>>> addPoint (Point 0 1) one
Rect -0.5 0.5 0.5 1.5

rotationBound :: (TrigField a, Ord a) => a -> Rect a -> Rect a

rotate the corners of a Rect by x degrees relative to the origin, and fold to a new Rect

>>> rotationBound (pi/4) one
Rect -0.7071067811865475 0.7071067811865475 -0.7071067811865475 0.7071067811865475

gridR :: (Field a, FromIntegral a Int, Ord a) => (a -> a) -> Range a -> Int -> [Rect a]

Create Rects for a formulae y = f(x) across an x range where the y range is Range 0 y

>>> gridR (^2) (Range 0 4) 4
[Rect 0.0 1.0 0.0 0.25,Rect 1.0 2.0 0.0 2.25,Rect 2.0 3.0 0.0 6.25,Rect 3.0 4.0 0.0 12.25]

gridF :: (Point Double -> b) -> Rect Double -> Grid (Rect Double) -> [(Rect Double, b)]

Create values c for Rects data for a formulae c = f(x,y)

>>> gridF (\(Point x y) -> x * y) (Rect 0 4 0 4) (Point 2 2)
[(Rect 0.0 2.0 0.0 2.0,1.0),(Rect 0.0 2.0 2.0 4.0,3.0),(Rect 2.0 4.0 0.0 2.0,3.0),(Rect 2.0 4.0 2.0 4.0,9.0)]

aspect :: Double -> Rect Double

convert a ratio (eg x:1) to a Rect with a height of one.

>>> aspect 2
Rect -1.0 1.0 -0.5 0.5

ratio :: Field a => Rect a -> a

convert a Rect to a ratio

>>> :set -XNegativeLiterals
>>> ratio (Rect -1 1 -0.5 0.5)
2.0

projectOnR :: Rect Double -> Rect Double -> Rect Double -> Rect Double

project a Rect from one Rect to another, preserving relative position, with guards for singleton Rects.

>>> projectOnR one (Rect 0 1 0 1) (Rect 0 0.5 0 0.5)
Rect -0.5 0.0 -0.5 0.0

projectOnP :: Rect Double -> Rect Double -> Point Double -> Point Double

project a Point from one Rect to another, preserving relative position, with guards for singleton Rects.

>>> projectOnP one (Rect 0 1 0 1) zero
Point -0.5 -0.5