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.V4

Description

4-D Vectors

Synopsis

Documentation

data V4 a Source

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
Traversable1 V4
Foldable1 V4
Apply V4
Bind 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)
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)
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
Typeable (* -> *) V4
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 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
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

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
R4 f => R4 (Point f)

_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