Data.Vec3.Class

Documentation

class Vec3 v where

Three-dimensional vector, with an associated matrix type.

Minimal complete definition

fromXYZ, toXYZ, fromRows, toRows

Associated Types

data Matrix v

Associated type for 3×3 matrix.

Methods

origin :: v

Origin point (0, 0, 0).

fromXYZ :: (Double, Double, Double) -> v

Construct a new vector from components.

toXYZ :: v -> (Double, Double, Double)

Deconstruct a vector into components.

zipWith :: (Double -> Double -> Double) -> v -> v -> v

Zip two vectors elementwise.

(<+>) :: v -> v -> v

Add two vectors.

(<->) :: v -> v -> v

Subtract two vectors.

(><) :: v -> v -> v

Cross product.

(.^) :: v -> Double -> v

Scale a vector.

(.*) :: v -> v -> Double

Dot product.

norm :: v -> Double

Euclidean norm of a vector.

normalize :: v -> v

Produce unit vector with the same direction as the original one.

distance :: v -> v -> Double

Distance between two points.

invert :: v -> v

Invert the direction of a vector.

fromRows :: (v, v, v) -> Matrix v

Construct a new matrix from rows.

toRows :: Matrix v -> (v, v, v)

Deconstruct a matrix into rows.

dotM :: v -> v -> Matrix v -> Double

Generic vector dot product.

Multiply the transpose of the first vector by the given matrix, then multiply the result by the second vector.

                    [ a11  a12  a13 ]   [ v2x ]
                    [               ]   [     ]
[ v1x  v1y  v1z ] . [ a21  a22  a23 ] . [ v2y ] = s
                    [               ]   [     ]
                    [ a31  a32  a33 ]   [ v2z ]

mxv :: Matrix v -> v -> v

Multiply a matrix and a vector.

[ a11  a12  a13 ]   [ v2x ]   [ rx ]
[               ]   [     ]   [    ]
[ a21  a22  a23 ] . [ v2y ] = [ ry ]
[               ]   [     ]   [    ]
[ a31  a32  a33 ]   [ v2z ]   [ rz ]

diag :: Double -> Matrix v

Build a diagonal matrix from a number d.

[ d  0  0 ]
[         ]
[ 0  d  0 ]
[         ]
[ 0  0  d ]

vxv :: v -> v -> Matrix v

Transpose a vector and multiply it by another vector, producing a matrix.

[ v1x ]                       [ r11  r12  r13 ]
[     ]                       [               ]
[ v1y ] . [ v2x  v2y  v2z ] = [ r21  r22  r23 ]
[     ]                       [               ]
[ v1z ]                       [ r31  r32  r33 ]

addM :: Matrix v -> Matrix v -> Matrix v

Add two matrices.

Instances

Vec3 TVec3

Associated Types

data Matrix TVec3 :: *

Methods

origin :: TVec3

fromXYZ :: (Double, Double, Double) -> TVec3

toXYZ :: TVec3 -> (Double, Double, Double)

zipWith :: (Double -> Double -> Double) -> TVec3 -> TVec3 -> TVec3

(<+>) :: TVec3 -> TVec3 -> TVec3

(<->) :: TVec3 -> TVec3 -> TVec3

(><) :: TVec3 -> TVec3 -> TVec3

(.^) :: TVec3 -> Double -> TVec3

(.*) :: TVec3 -> TVec3 -> Double

norm :: TVec3 -> Double

normalize :: TVec3 -> TVec3

distance :: TVec3 -> TVec3 -> Double

invert :: TVec3 -> TVec3

fromRows :: (TVec3, TVec3, TVec3) -> Matrix TVec3

toRows :: Matrix TVec3 -> (TVec3, TVec3, TVec3)

dotM :: TVec3 -> TVec3 -> Matrix TVec3 -> Double

mxv :: Matrix TVec3 -> TVec3 -> TVec3

diag :: Double -> Matrix TVec3

vxv :: TVec3 -> TVec3 -> Matrix TVec3

addM :: Matrix TVec3 -> Matrix TVec3 -> Matrix TVec3

Vec3 CVec3

Associated Types

data Matrix CVec3 :: *

Methods

origin :: CVec3

fromXYZ :: (Double, Double, Double) -> CVec3

toXYZ :: CVec3 -> (Double, Double, Double)

zipWith :: (Double -> Double -> Double) -> CVec3 -> CVec3 -> CVec3

(<+>) :: CVec3 -> CVec3 -> CVec3

(<->) :: CVec3 -> CVec3 -> CVec3

(><) :: CVec3 -> CVec3 -> CVec3

(.^) :: CVec3 -> Double -> CVec3

(.*) :: CVec3 -> CVec3 -> Double

norm :: CVec3 -> Double

normalize :: CVec3 -> CVec3

distance :: CVec3 -> CVec3 -> Double

invert :: CVec3 -> CVec3

fromRows :: (CVec3, CVec3, CVec3) -> Matrix CVec3

toRows :: Matrix CVec3 -> (CVec3, CVec3, CVec3)

dotM :: CVec3 -> CVec3 -> Matrix CVec3 -> Double

mxv :: Matrix CVec3 -> CVec3 -> CVec3

diag :: Double -> Matrix CVec3

vxv :: CVec3 -> CVec3 -> Matrix CVec3

addM :: Matrix CVec3 -> Matrix CVec3 -> Matrix CVec3

type TVec3 = (Double, Double, Double)

Vec3 implementation with Unbox instance based on default Unbox instance for tuples of arrays, which wraps a vector of tuples as a tuple of vectors.

interface:  [v1 (x, y, z); v2 (x, y, z) ...], length = N
                 |  |  |       |  |  |
storage(x): [v1x-+  |  | ; v2x-+  |  |  ...], length = N
storage(y): [v1y----+  | ; v2y----+  |  ...], length = N
storage(z): [v1z-------+ ; v2z-------+  ...], length = N

You almost definitely want to use CVec3 instead as it has better performance.