linear-1.20.4: Linear Algebra

Linear.V4

Description

4-D Vectors

Synopsis

# Documentation

data V4 a Source

A 4-dimensional vector.

Constructors

 V4 !a !a !a !a

Instances

 Source Source Source Source Source Source Source Source Source Source Source Source Source Source Source Source Source Source Source Source Source Source Source Source Source Source 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 Source Source 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

 Source Source Source Source 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

 Source Source 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

 Source 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

 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