Linear.V3

3-D Vectors

Documentation

data V3 a

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)

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

cross product

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

scalar triple product

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 :: Lens' (t a) a

>>> V2 1 2 ^._y
2

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

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

Instances

R2 V2

R2 V3

R2 V4

R2 f => R2 (Point f)

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

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

class R2 t => R3 t where

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

>>> V3 1 2 3 ^. _z
3

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

Instances

R3 V3

R3 V4

R3 f => R3 (Point f)

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

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

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

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

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

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

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

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

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

ex :: R1 t => E t

ey :: R2 t => E t

ez :: R3 t => E t