Copyright	(C) 2012-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	non-portable
Safe Haskell	Trustworthy
Language	Haskell98

Linear.V2

Description

2-D Vectors

Synopsis

Documentation

data V2 a Source

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 Source
Functor V2 Source
MonadFix V2 Source
Applicative V2 Source
Foldable V2 Source
Traversable V2 Source
Generic1 V2 Source
Distributive V2 Source
Representable V2 Source
MonadZip V2 Source
Serial1 V2 Source
Traversable1 V2 Source
Apply V2 Source
Bind V2 Source
Foldable1 V2 Source
Eq1 V2 Source
Ord1 V2 Source
Read1 V2 Source
Show1 V2 Source
Additive V2 Source
Metric V2 Source
R1 V2 Source
R2 V2 Source
Trace V2 Source
Affine V2 Source
Unbox a => Vector Vector (V2 a) Source
Unbox a => MVector MVector (V2 a) Source
Num r => Coalgebra r (E V2) Source
Bounded a => Bounded (V2 a) Source
Eq a => Eq (V2 a) Source
Floating a => Floating (V2 a) Source
Fractional a => Fractional (V2 a) Source
Data a => Data (V2 a) Source
Num a => Num (V2 a) Source
Ord a => Ord (V2 a) Source
Read a => Read (V2 a) Source
Show a => Show (V2 a) Source
Ix a => Ix (V2 a) Source
Generic (V2 a) Source
Storable a => Storable (V2 a) Source
Binary a => Binary (V2 a) Source
Serial a => Serial (V2 a) Source
Serialize a => Serialize (V2 a) Source
NFData a => NFData (V2 a) Source
Hashable a => Hashable (V2 a) Source
Unbox a => Unbox (V2 a) Source
Ixed (V2 a) Source
Epsilon a => Epsilon (V2 a) Source
FunctorWithIndex (E V2) V2 Source
FoldableWithIndex (E V2) V2 Source
TraversableWithIndex (E V2) V2 Source
Each (V2 a) (V2 b) a b Source
type Rep1 V2 Source
type Rep V2 = E V2 Source
type Diff V2 = V2 Source
data MVector s (V2 a) = MV_V2 !Int !(MVector s a) Source
type Rep (V2 a) Source
data Vector (V2 a) = V_V2 !Int !(Vector a) Source
type Index (V2 a) = E V2 Source
type IxValue (V2 a) = a Source

class R1 t where Source

A space that has at least 1 basis vector _x.

Minimal complete definition

Nothing

Methods

_x :: Lens' (t a) a Source

>>> V1 2 ^._x
2

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

Instances

R1 Identity Source
R1 V1 Source
R1 V2 Source
R1 V3 Source
R1 V4 Source
R1 f => R1 (Point f) Source

class R1 t => R2 t where Source

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

Minimal complete definition

Nothing

Methods

_y :: Lens' (t a) a Source

>>> V2 1 2 ^._y
2

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

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

Instances

R2 V2 Source
R2 V3 Source
R2 V4 Source
R2 f => R2 (Point f) Source

_yx :: R2 t => Lens' (t a) (V2 a) Source

>>> V2 1 2 ^. _yx
V2 2 1

ex :: R1 t => E t Source

ey :: R2 t => E t Source

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

the counter-clockwise perpendicular vector

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

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