Linear.V2

2-D Vectors

Documentation

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

Distributive V2

Representable V2

MonadZip V2

Traversable1 V2

Foldable1 V2

Apply V2

Bind V2

Additive V2

Metric V2

R1 V2

R2 V2

Trace V2

Affine V2

Unbox a => Vector Vector (V2 a)

Unbox a => MVector MVector (V2 a)

Num r => Coalgebra r (E V2)

Eq a => Eq (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)

Hashable a => Hashable (V2 a)

Unbox a => Unbox (V2 a)

Ixed (V2 a)

Epsilon a => Epsilon (V2 a)

FunctorWithIndex (E V2) V2

FoldableWithIndex (E V2) V2

TraversableWithIndex (E V2) V2

Each (V2 a) (V2 b) a b

Typeable (* -> *) V2

type Rep1 V2

type Rep V2 = E V2

type Diff V2 = V2

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

type Rep (V2 a)

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

type Index (V2 a) = E V2

type IxValue (V2 a) = a

class R1 t where

A space that has at least 1 basis vector _x.

Minimal complete definition

Nothing

Methods

_x :: Lens' (t a) a

>>> V1 2 ^._x
2

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

Instances

R1 Identity

R1 V1

R1 V2

R1 V3

R1 V4

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

_y :: Lens' (t a) a

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

_xy :: Lens' (t a) (V2 a)

Instances

R2 V2

R2 V3

R2 V4

R2 f => R2 (Point f)

ex :: R1 t => E t

ey :: R2 t => E t

perp :: Num a => V2 a -> V2 a

the counter-clockwise perpendicular vector

>>> perp $ V2 10 20
V2 (-20) 10

angle :: Floating a => a -> V2 a