Diagrams.TwoD.Types

Basic types for two-dimensional Euclidean space.

2D Euclidean space

data V2 a :: * -> *

A 2-dimensional vector

>>> pure 1 :: V2 Int
V2 1 1

>>> V2 1 2 + V2 3 4
V2 4 6

>>> V2 1 2 * V2 3 4
V2 3 8

>>> sum (V2 1 2)
3

Constructors

V2 !a !a

Instances

Monad V2

Functor V2

MonadFix V2

Applicative V2

Foldable V2

Traversable V2

Generic1 V2

Apply V2

Distributive V2

Representable V2

MonadZip V2

Serial1 V2

Additive V2

Traversable1 V2

Affine V2

R2 V2

R1 V2

Metric V2

Bind V2

Foldable1 V2

Eq1 V2

Ord1 V2

Read1 V2

Show1 V2

HasR V2

Unbox a => Vector Vector (V2 a)

Unbox a => MVector MVector (V2 a)

Bounded a => Bounded (V2 a)

Eq a => Eq (V2 a)

Floating a => Floating (V2 a)

Fractional a => Fractional (V2 a)

Data a => Data (V2 a)

Num a => Num (V2 a)

Ord a => Ord (V2 a)

Read a => Read (V2 a)

Show a => Show (V2 a)

Ix a => Ix (V2 a)

Generic (V2 a)

Storable a => Storable (V2 a)

Binary a => Binary (V2 a)

Serial a => Serial (V2 a)

Serialize a => Serialize (V2 a)

NFData a => NFData (V2 a)

Hashable a => Hashable (V2 a)

Unbox a => Unbox (V2 a)

Ixed (V2 a)

Epsilon a => Epsilon (V2 a)

Coordinates (V2 n)

FunctorWithIndex (E V2) V2

FoldableWithIndex (E V2) V2

TraversableWithIndex (E V2) V2

Each (V2 a) (V2 b) a b

RealFloat n => Traced (BoundingBox V2 n)

type Rep1 V2 = D1 D1V2 (C1 C1_0V2 ((:*:) (S1 NoSelector Par1) (S1 NoSelector Par1)))

type Rep V2 = E V2

type Diff V2 = V2

data MVector s (V2 a) = MV_V2 !Int !(MVector s a)

type Rep (V2 a) = D1 D1V2 (C1 C1_0V2 ((:*:) (S1 NoSelector (Rec0 a)) (S1 NoSelector (Rec0 a))))

type V (V2 n) = V2

type N (V2 n) = n

data Vector (V2 a) = V_V2 !Int !(Vector a)

type Index (V2 a) = E V2

type IxValue (V2 a) = a

type FinalCoord (V2 n) = n

type PrevDim (V2 n) = n

type Decomposition (V2 n) = (:&) n n

class R1 t where

A space that has at least 1 basis vector _x.

Minimal complete definition

Nothing

Methods

_x :: Functor f => (a -> f a) -> t a -> f (t a)

>>> V1 2 ^._x
2

>>> V1 2 & _x .~ 3
V1 3

Instances

R1 Identity

R1 V4

R1 V3

R1 V2

R1 V1

R1 f => R1 (Point f)

class R1 t => R2 t where

A space that distinguishes 2 orthogonal basis vectors _x and _y, but may have more.

Minimal complete definition

Nothing

Methods

_y :: Functor f => (a -> f a) -> t a -> f (t a)

>>> V2 1 2 ^._y
2

>>> V2 1 2 & _y .~ 3
V2 1 3

_xy :: Functor f => (V2 a -> f (V2 a)) -> t a -> f (t a)

Instances

R2 V4

R2 V3

R2 V2

R2 f => R2 (Point f)

type P2 = Point V2

type T2 = Transformation V2

r2 :: (n, n) -> V2 n

Construct a 2D vector from a pair of components. See also &.

unr2 :: V2 n -> (n, n)

Convert a 2D vector back into a pair of components. See also coords.

mkR2 :: n -> n -> V2 n

Curried form of r2.

r2Iso :: Iso' (V2 n) (n, n)

p2 :: (n, n) -> P2 n

Construct a 2D point from a pair of coordinates. See also ^&.

mkP2 :: n -> n -> P2 n

Curried form of p2.

unp2 :: P2 n -> (n, n)

Convert a 2D point back into a pair of coordinates. See also coords.

p2Iso :: Iso' (Point V2 n) (n, n)

r2PolarIso :: RealFloat n => Iso' (V2 n) (n, Angle n)

class HasR t where

A space which has magnitude _r that can be calculated numerically.

Minimal complete definition

Nothing

Methods

_r :: RealFloat n => Lens' (t n) n

Instances

HasR V2

HasR v => HasR (Point v)