NumHask.Space.Point

A 2-dimensional point.

Documentation

data Point a

A 2-dim point of a's

A Point is functorial over both arguments, and is a Num instance.

>>> let p = Point 1 1
>>> p + p
Point 2 2
>>> (2*) <$> p
Point 2 2

A major reason for this bespoke treatment of a point is that Points do not have maximums and minimums but they form a lattice, and this is useful for folding points to find out the (rectangular) Space they occupy.

>>> Point 0 1 /\ Point 1 0
Point 0 0
>>> Point 0 1 \/ Point 1 0
Point 1 1

Constructors

Point a a

Instances

Monad Point

Defined in NumHask.Space.Point

Methods

(>>=) :: Point a -> (a -> Point b) -> Point b

(>>) :: Point a -> Point b -> Point b

return :: a -> Point a

fail :: String -> Point a

Functor Point

Defined in NumHask.Space.Point

Methods

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

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

Applicative Point

Defined in NumHask.Space.Point

Methods

pure :: a -> Point a

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

liftA2 :: (a -> b -> c) -> Point a -> Point b -> Point c

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

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

Foldable Point

Defined in NumHask.Space.Point

Methods

fold :: Monoid m => Point m -> m

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

foldr :: (a -> b -> b) -> b -> Point a -> b

foldr' :: (a -> b -> b) -> b -> Point a -> b

foldl :: (b -> a -> b) -> b -> Point a -> b

foldl' :: (b -> a -> b) -> b -> Point a -> b

foldr1 :: (a -> a -> a) -> Point a -> a

foldl1 :: (a -> a -> a) -> Point a -> a

toList :: Point a -> [a]

null :: Point a -> Bool

length :: Point a -> Int

elem :: Eq a => a -> Point a -> Bool

maximum :: Ord a => Point a -> a

minimum :: Ord a => Point a -> a

sum :: Num a => Point a -> a

product :: Num a => Point a -> a

Traversable Point

Defined in NumHask.Space.Point

Methods

traverse :: Applicative f => (a -> f b) -> Point a -> f (Point b)

sequenceA :: Applicative f => Point (f a) -> f (Point a)

mapM :: Monad m => (a -> m b) -> Point a -> m (Point b)

sequence :: Monad m => Point (m a) -> m (Point a)

Distributive Point

Defined in NumHask.Space.Point

Methods

distribute :: Functor f => f (Point a) -> Point (f a)

collect :: Functor f => (a -> Point b) -> f a -> Point (f b)

distributeM :: Monad m => m (Point a) -> Point (m a)

collectM :: Monad m => (a -> Point b) -> m a -> Point (m b)

Representable Point

Defined in NumHask.Space.Point

Associated Types

type Rep Point :: Type

Methods

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

index :: Point a -> Rep Point -> a

Eq1 Point

Defined in NumHask.Space.Point

Methods

liftEq :: (a -> b -> Bool) -> Point a -> Point b -> Bool

Show1 Point

Defined in NumHask.Space.Point

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Point a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Point a] -> ShowS

Bounded a => Bounded (Point a)

Defined in NumHask.Space.Point

Methods

minBound :: Point a

maxBound :: Point a

Eq a => Eq (Point a)

Defined in NumHask.Space.Point

Methods

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

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

Fractional a => Fractional (Point a)

Defined in NumHask.Space.Point

Methods

(/) :: Point a -> Point a -> Point a

recip :: Point a -> Point a

fromRational :: Rational -> Point a

Num a => Num (Point a)

Defined in NumHask.Space.Point

Methods

(+) :: Point a -> Point a -> Point a

(-) :: Point a -> Point a -> Point a

(*) :: Point a -> Point a -> Point a

negate :: Point a -> Point a

abs :: Point a -> Point a

signum :: Point a -> Point a

fromInteger :: Integer -> Point a

Show a => Show (Point a)

Defined in NumHask.Space.Point

Methods

showsPrec :: Int -> Point a -> ShowS

show :: Point a -> String

showList :: [Point a] -> ShowS

Generic (Point a)

Defined in NumHask.Space.Point

Associated Types

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

Methods

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

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

Semigroup a => Semigroup (Point a)

Defined in NumHask.Space.Point

Methods

(<>) :: Point a -> Point a -> Point a

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

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

(Semigroup a, Monoid a) => Monoid (Point a)

Defined in NumHask.Space.Point

Methods

mempty :: Point a

mappend :: Point a -> Point a -> Point a

mconcat :: [Point a] -> Point a

Ord a => Lattice (Point a)

Defined in NumHask.Space.Point

Methods

(\/) :: Point a -> Point a -> Point a

(/\) :: Point a -> Point a -> Point a

type Rep Point

Defined in NumHask.Space.Point

type Rep Point = Bool

type Rep (Point a)

Defined in NumHask.Space.Point

type Rep (Point a) = D1 (MetaData "Point" "NumHask.Space.Point" "numhask-space-0.4.0-L0hnYZmJO1yAMyJV0BD725" False) (C1 (MetaCons "Point" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

rotate :: Floating a => a -> Point a -> Point a

rotate a point by x degrees relative to the origin

>>> rotate 90 (Point 0 1)
Point 1.0 6.123233995736766e-17

gridP :: (Ord a, Fractional a) => (a -> a) -> Range a -> Int -> [Point a]

Create Points for a formulae y = f(x) across an x range

>>> gridP (**2) (Range 0 4) 4
[Point 0.0 0.0,Point 1.0 1.0,Point 2.0 4.0,Point 3.0 9.0,Point 4.0 16.0]