Data.Vec3

Vec3 class and implementations.

The package provides two different implementations for Vec3 type class, which differ in storage scheme. Benchmarks are included for both. You most likely want to use CVec3 which is based on contiguous storage scheme and offers the best performance.

Examples

>>> let v1 = (-1, 0.0,  0.2) :: TVec3
>>> let v2 = ( 1, 2.3,  5.0) :: TVec3
>>> let v3 = ( 1,   1, -0.2) :: TVec3

Add two vectors:

>>> v1 <+> v2
(0.0,2.3,5.2)

Dot product:

>>> v1 .* v2
0.0

Multiply by a scalar:

>>> v1 .^ 5
(-5.0,0.0,1.0)

Cross product:

>>> v1 >< v3
(-0.2,0.0,-1.0)

Matrix-vector product:

>>> diag 2 `mxv` v2
(2.0,4.6,10.0)

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

Implementations

data CVec3

Vec3 implementation with Unbox and Storable instances based on a single contiguous array storage scheme, suitable for use with Data.Vector.Unboxed and Data.Vector.Storable.

interface: [v1 x   y   z  ; v2 x   y   z  ...], length = N = M / 3
               |   |   |       |   |   |
storage:   [  v1x v2y v2z ;   v2x v2y v2z ...], length = M

This implementation has the best performance.

Constructors

CVec3 !Double !Double !Double

Instances

Eq CVec3

Methods

(==) :: CVec3 -> CVec3 -> Bool

(/=) :: CVec3 -> CVec3 -> Bool

Show CVec3

Methods

showsPrec :: Int -> CVec3 -> ShowS

show :: CVec3 -> String

showList :: [CVec3] -> ShowS

Arbitrary CVec3

Methods

arbitrary :: Gen CVec3

shrink :: CVec3 -> [CVec3]

Storable CVec3

Methods

sizeOf :: CVec3 -> Int

alignment :: CVec3 -> Int

peekElemOff :: Ptr CVec3 -> Int -> IO CVec3

pokeElemOff :: Ptr CVec3 -> Int -> CVec3 -> IO ()

peekByteOff :: Ptr b -> Int -> IO CVec3

pokeByteOff :: Ptr b -> Int -> CVec3 -> IO ()

peek :: Ptr CVec3 -> IO CVec3

poke :: Ptr CVec3 -> CVec3 -> IO ()

Unbox CVec3

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

Vector Vector CVec3

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) CVec3 -> m (Vector CVec3)

basicUnsafeThaw :: PrimMonad m => Vector CVec3 -> m (Mutable Vector (PrimState m) CVec3)

basicLength :: Vector CVec3 -> Int

basicUnsafeSlice :: Int -> Int -> Vector CVec3 -> Vector CVec3

basicUnsafeIndexM :: Monad m => Vector CVec3 -> Int -> m CVec3

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) CVec3 -> Vector CVec3 -> m ()

elemseq :: Vector CVec3 -> CVec3 -> b -> b

MVector MVector CVec3

Methods

basicLength :: MVector s CVec3 -> Int

basicUnsafeSlice :: Int -> Int -> MVector s CVec3 -> MVector s CVec3

basicOverlaps :: MVector s CVec3 -> MVector s CVec3 -> Bool

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) CVec3)

basicInitialize :: PrimMonad m => MVector (PrimState m) CVec3 -> m ()

basicUnsafeReplicate :: PrimMonad m => Int -> CVec3 -> m (MVector (PrimState m) CVec3)

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) CVec3 -> Int -> m CVec3

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) CVec3 -> Int -> CVec3 -> m ()

basicClear :: PrimMonad m => MVector (PrimState m) CVec3 -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) CVec3 -> CVec3 -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) CVec3 -> MVector (PrimState m) CVec3 -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) CVec3 -> MVector (PrimState m) CVec3 -> m ()

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) CVec3 -> Int -> m (MVector (PrimState m) CVec3)

Eq (Matrix CVec3)

Methods

(==) :: Matrix CVec3 -> Matrix CVec3 -> Bool

(/=) :: Matrix CVec3 -> Matrix CVec3 -> Bool

Show (Matrix CVec3)

Methods

showsPrec :: Int -> Matrix CVec3 -> ShowS

show :: Matrix CVec3 -> String

showList :: [Matrix CVec3] -> ShowS

Arbitrary (Matrix CVec3)

Methods

arbitrary :: Gen (Matrix CVec3)

shrink :: Matrix CVec3 -> [Matrix CVec3]

data Vector CVec3

data Vector CVec3 = V_CVec3 (Vector Double)

data Matrix CVec3

data Matrix CVec3 = CMatrix (CVec3, CVec3, CVec3)

data MVector s CVec3

data MVector s CVec3 = MV_CVec3 (MVector s Double)

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.