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)
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)
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 :: Functor f => (a -> f a) -> t a -> f (t a) Source

>>> V2 1 2 ^._y 2

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

_y :: Lens' (t a) a

_xy :: Functor f => (V2 a -> f (V2 a)) -> t a -> f (t a) Source

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

Instances

R2 V2
R2 V3
R2 V4
R2 f => R2 (Point f)

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 :: Functor f => (a -> f a) -> t a -> f (t a) Source

_z :: Lens' (t a) a

_xyz :: Functor f => (V3 a -> f (V3 a)) -> t a -> f (t a) Source

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

Instances

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

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 :: Functor f => (a -> f a) -> t a -> f (t a) Source

_w :: Lens' (t a) a

_xyzw :: Functor f => (V4 a -> f (V4 a)) -> t a -> f (t a) Source

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

Instances

R4 V4
R4 f => R4 (Point f)

ex :: R1 t => E t Source

ey :: R2 t => E t Source

ez :: R3 t => E t Source

ew :: R4 t => E t Source