Copyright	(C) 2012-2013 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.V3

Description

3-D Vectors

Synopsis

Documentation

data V3 a Source

A 3-dimensional vector

Constructors

V3 !a !a !a

Instances

Monad V3
Functor V3
MonadFix V3
Applicative V3
Foldable V3
Traversable V3
Generic1 V3
Distributive V3
Representable V3
MonadZip V3
Traversable1 V3
Foldable1 V3
Apply V3
Bind V3
Additive V3
Metric V3
R1 V3
R2 V3
R3 V3
Trace V3
Affine V3
Unbox a => Vector Vector (V3 a)
Unbox a => MVector MVector (V3 a)
Num r => Coalgebra r (E V3)
Bounded a => Bounded (V3 a)
Eq a => Eq (V3 a)
Floating a => Floating (V3 a)
Fractional a => Fractional (V3 a)
Data a => Data (V3 a)
Num a => Num (V3 a)
Ord a => Ord (V3 a)
Read a => Read (V3 a)
Show a => Show (V3 a)
Ix a => Ix (V3 a)
Generic (V3 a)
Storable a => Storable (V3 a)
NFData a => NFData (V3 a)
Hashable a => Hashable (V3 a)
Unbox a => Unbox (V3 a)
Ixed (V3 a)
Epsilon a => Epsilon (V3 a)
FunctorWithIndex (E V3) V3
FoldableWithIndex (E V3) V3
TraversableWithIndex (E V3) V3
Each (V3 a) (V3 b) a b
Typeable (* -> *) V3
type Rep1 V3
type Rep V3 = E V3
type Diff V3 = V3
data MVector s (V3 a) = MV_V3 !Int (MVector s a)
type Rep (V3 a)
data Vector (V3 a) = V_V3 !Int (Vector a)
type Index (V3 a) = E V3
type IxValue (V3 a) = a

cross :: Num a => V3 a -> V3 a -> V3 a Source

cross product

triple :: Num a => V3 a -> V3 a -> V3 a -> a Source

scalar triple product

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

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

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

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

class R2 t => R3 t where Source

A space that distinguishes 3 orthogonal basis vectors: _x, _y, and _z. (It may have more)

Minimal complete definition

Nothing

Methods

_z :: Lens' (t a) a Source

>>> V3 1 2 3 ^. _z
3

_xyz :: Lens' (t a) (V3 a) Source

Instances

R3 V3
R3 V4
R3 f => R3 (Point f)

_xz :: R3 t => Lens' (t a) (V2 a) Source

_yz :: R3 t => Lens' (t a) (V2 a) Source

_zx :: R3 t => Lens' (t a) (V2 a) Source

_zy :: R3 t => Lens' (t a) (V2 a) Source

_xzy :: R3 t => Lens' (t a) (V3 a) Source

_yxz :: R3 t => Lens' (t a) (V3 a) Source

_yzx :: R3 t => Lens' (t a) (V3 a) Source

_zxy :: R3 t => Lens' (t a) (V3 a) Source

_zyx :: R3 t => Lens' (t a) (V3 a) Source

ex :: R1 t => E t Source

ey :: R2 t => E t Source

ez :: R3 t => E t Source