Linear.V4

4-D Vectors

Documentation

data V4 a

A 4-dimensional vector.

Constructors

V4 !a !a !a !a

Instances

Monad V4

Functor V4

MonadFix V4

Applicative V4

Foldable V4

Traversable V4

Generic1 V4

Distributive V4

Representable V4

MonadZip V4

Serial1 V4

Traversable1 V4

Apply V4

Bind V4

Foldable1 V4

Eq1 V4

Ord1 V4

Read1 V4

Show1 V4

Additive V4

Metric V4

R1 V4

R2 V4

R3 V4

R4 V4

Trace V4

Affine V4

Unbox a => Vector Vector (V4 a)

Unbox a => MVector MVector (V4 a)

Num r => Coalgebra r (E V4)

Bounded a => Bounded (V4 a)

Eq a => Eq (V4 a)

Floating a => Floating (V4 a)

Fractional a => Fractional (V4 a)

Data a => Data (V4 a)

Num a => Num (V4 a)

Ord a => Ord (V4 a)

Read a => Read (V4 a)

Show a => Show (V4 a)

Ix a => Ix (V4 a)

Generic (V4 a)

Storable a => Storable (V4 a)

Binary a => Binary (V4 a)

Serial a => Serial (V4 a)

Serialize a => Serialize (V4 a)

NFData a => NFData (V4 a)

Hashable a => Hashable (V4 a)

Unbox a => Unbox (V4 a)

Ixed (V4 a)

Epsilon a => Epsilon (V4 a)

FunctorWithIndex (E V4) V4

FoldableWithIndex (E V4) V4

TraversableWithIndex (E V4) V4

Each (V4 a) (V4 b) a b

type Rep1 V4

type Rep V4 = E V4

type Diff V4 = V4

data MVector s (V4 a) = MV_V4 !Int !(MVector s a)

type Rep (V4 a)

data Vector (V4 a) = V_V4 !Int !(Vector a)

type Index (V4 a) = E V4

type IxValue (V4 a) = a

vector :: Num a => V3 a -> V4 a

Convert a 3-dimensional affine vector into a 4-dimensional homogeneous vector.

point :: Num a => V3 a -> V4 a

Convert a 3-dimensional affine point into a 4-dimensional homogeneous vector.

normalizePoint :: Fractional a => V4 a -> V3 a

Convert 4-dimensional projective coordinates to a 3-dimensional point. This operation may be denoted, euclidean [x:y:z:w] = (x/w, y/w, z/w) where the projective, homogenous, coordinate [x:y:z:w] is one of many associated with a single point (x/w, y/w, z/w).

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)

class R3 t => R4 t where

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

Minimal complete definition

Nothing

Methods

_w :: Lens' (t a) a

>>> V4 1 2 3 4 ^._w
4

_xyzw :: Lens' (t a) (V4 a)

Instances

R4 V4

R4 f => R4 (Point f)

_xw :: R4 t => Lens' (t a) (V2 a)

_yw :: R4 t => Lens' (t a) (V2 a)

_zw :: R4 t => Lens' (t a) (V2 a)

_wx :: R4 t => Lens' (t a) (V2 a)

_wy :: R4 t => Lens' (t a) (V2 a)

_wz :: R4 t => Lens' (t a) (V2 a)

_xyw :: R4 t => Lens' (t a) (V3 a)

_xzw :: R4 t => Lens' (t a) (V3 a)

_xwy :: R4 t => Lens' (t a) (V3 a)

_xwz :: R4 t => Lens' (t a) (V3 a)

_yxw :: R4 t => Lens' (t a) (V3 a)

_yzw :: R4 t => Lens' (t a) (V3 a)

_ywx :: R4 t => Lens' (t a) (V3 a)

_ywz :: R4 t => Lens' (t a) (V3 a)

_zxw :: R4 t => Lens' (t a) (V3 a)

_zyw :: R4 t => Lens' (t a) (V3 a)

_zwx :: R4 t => Lens' (t a) (V3 a)

_zwy :: R4 t => Lens' (t a) (V3 a)

_wxy :: R4 t => Lens' (t a) (V3 a)

_wxz :: R4 t => Lens' (t a) (V3 a)

_wyx :: R4 t => Lens' (t a) (V3 a)

_wyz :: R4 t => Lens' (t a) (V3 a)

_wzx :: R4 t => Lens' (t a) (V3 a)

_wzy :: R4 t => Lens' (t a) (V3 a)

_xywz :: R4 t => Lens' (t a) (V4 a)

_xzyw :: R4 t => Lens' (t a) (V4 a)

_xzwy :: R4 t => Lens' (t a) (V4 a)

_xwyz :: R4 t => Lens' (t a) (V4 a)

_xwzy :: R4 t => Lens' (t a) (V4 a)

_yxzw :: R4 t => Lens' (t a) (V4 a)

_yxwz :: R4 t => Lens' (t a) (V4 a)

_yzxw :: R4 t => Lens' (t a) (V4 a)

_yzwx :: R4 t => Lens' (t a) (V4 a)

_ywxz :: R4 t => Lens' (t a) (V4 a)

_ywzx :: R4 t => Lens' (t a) (V4 a)

_zxyw :: R4 t => Lens' (t a) (V4 a)

_zxwy :: R4 t => Lens' (t a) (V4 a)

_zyxw :: R4 t => Lens' (t a) (V4 a)

_zywx :: R4 t => Lens' (t a) (V4 a)

_zwxy :: R4 t => Lens' (t a) (V4 a)

_zwyx :: R4 t => Lens' (t a) (V4 a)

_wxyz :: R4 t => Lens' (t a) (V4 a)

_wxzy :: R4 t => Lens' (t a) (V4 a)

_wyxz :: R4 t => Lens' (t a) (V4 a)

_wyzx :: R4 t => Lens' (t a) (V4 a)

_wzxy :: R4 t => Lens' (t a) (V4 a)

_wzyx :: R4 t => Lens' (t a) (V4 a)

ex :: R1 t => E t

ey :: R2 t => E t

ez :: R3 t => E t

ew :: R4 t => E t