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.V4

Description

4-D Vectors

Synopsis

Documentation

data V4 a Source

A 4-dimensional vector.

Constructors

V4 !a !a !a !a

Instances

Monad V4 Source
Functor V4 Source
MonadFix V4 Source
Applicative V4 Source
Foldable V4 Source
Traversable V4 Source
Generic1 V4 Source
Distributive V4 Source
Representable V4 Source
MonadZip V4 Source
Serial1 V4 Source
Traversable1 V4 Source
Apply V4 Source
Bind V4 Source
Foldable1 V4 Source
Eq1 V4 Source
Ord1 V4 Source
Read1 V4 Source
Show1 V4 Source
Additive V4 Source
Metric V4 Source
R1 V4 Source
R2 V4 Source
R3 V4 Source
R4 V4 Source
Trace V4 Source
Affine V4 Source
Unbox a => Vector Vector (V4 a) Source
Unbox a => MVector MVector (V4 a) Source
Num r => Coalgebra r (E V4) Source
Bounded a => Bounded (V4 a) Source
Eq a => Eq (V4 a) Source
Floating a => Floating (V4 a) Source
Fractional a => Fractional (V4 a) Source
Data a => Data (V4 a) Source
Num a => Num (V4 a) Source
Ord a => Ord (V4 a) Source
Read a => Read (V4 a) Source
Show a => Show (V4 a) Source
Ix a => Ix (V4 a) Source
Generic (V4 a) Source
Storable a => Storable (V4 a) Source
Binary a => Binary (V4 a) Source
Serial a => Serial (V4 a) Source
Serialize a => Serialize (V4 a) Source
NFData a => NFData (V4 a) Source
Hashable a => Hashable (V4 a) Source
Unbox a => Unbox (V4 a) Source
Ixed (V4 a) Source
Epsilon a => Epsilon (V4 a) Source
FunctorWithIndex (E V4) V4 Source
FoldableWithIndex (E V4) V4 Source
TraversableWithIndex (E V4) V4 Source
Each (V4 a) (V4 b) a b Source
type Rep1 V4 Source
type Rep V4 = E V4 Source
type Diff V4 = V4 Source
data MVector s (V4 a) = MV_V4 !Int !(MVector s a) Source
type Rep (V4 a) Source
data Vector (V4 a) = V_V4 !Int !(Vector a) Source
type Index (V4 a) = E V4 Source
type IxValue (V4 a) = a Source

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

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

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

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

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

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 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

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

_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

class R3 t => R4 t where Source

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 Source

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

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

Instances

R4 V4 Source
R4 f => R4 (Point f) Source

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

ex :: R1 t => E t Source

ey :: R2 t => E t Source

ez :: R3 t => E t Source

ew :: R4 t => E t Source