Data.Vec3

Vec3 class and implementations.

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 UVec3

Associated Types

data Matrix UVec3 :: *

Methods

origin :: UVec3

fromXYZ :: (Double, Double, Double) -> UVec3

toXYZ :: UVec3 -> (Double, Double, Double)

zipWith :: (Double -> Double -> Double) -> UVec3 -> UVec3 -> UVec3

(<+>) :: UVec3 -> UVec3 -> UVec3

(<->) :: UVec3 -> UVec3 -> UVec3

(><) :: UVec3 -> UVec3 -> UVec3

(.^) :: UVec3 -> Double -> UVec3

(.*) :: UVec3 -> UVec3 -> Double

norm :: UVec3 -> Double

normalize :: UVec3 -> UVec3

distance :: UVec3 -> UVec3 -> Double

invert :: UVec3 -> UVec3

fromRows :: (UVec3, UVec3, UVec3) -> Matrix UVec3

toRows :: Matrix UVec3 -> (UVec3, UVec3, UVec3)

dotM :: UVec3 -> UVec3 -> Matrix UVec3 -> Double

mxv :: Matrix UVec3 -> UVec3 -> UVec3

diag :: Double -> Matrix UVec3

vxv :: UVec3 -> UVec3 -> Matrix UVec3

addM :: Matrix UVec3 -> Matrix UVec3 -> Matrix UVec3

Vec3 UVec3

Associated Types

data Matrix UVec3 :: *

Methods

origin :: UVec3

fromXYZ :: (Double, Double, Double) -> UVec3

toXYZ :: UVec3 -> (Double, Double, Double)

zipWith :: (Double -> Double -> Double) -> UVec3 -> UVec3 -> UVec3

(<+>) :: UVec3 -> UVec3 -> UVec3

(<->) :: UVec3 -> UVec3 -> UVec3

(><) :: UVec3 -> UVec3 -> UVec3

(.^) :: UVec3 -> Double -> UVec3

(.*) :: UVec3 -> UVec3 -> Double

norm :: UVec3 -> Double

normalize :: UVec3 -> UVec3

distance :: UVec3 -> UVec3 -> Double

invert :: UVec3 -> UVec3

fromRows :: (UVec3, UVec3, UVec3) -> Matrix UVec3

toRows :: Matrix UVec3 -> (UVec3, UVec3, UVec3)

dotM :: UVec3 -> UVec3 -> Matrix UVec3 -> Double

mxv :: Matrix UVec3 -> UVec3 -> UVec3

diag :: Double -> Matrix UVec3

vxv :: UVec3 -> UVec3 -> Matrix UVec3

addM :: Matrix UVec3 -> Matrix UVec3 -> Matrix UVec3

Vec3 SVec3

Associated Types

data Matrix SVec3 :: *

Methods

origin :: SVec3

fromXYZ :: (Double, Double, Double) -> SVec3

toXYZ :: SVec3 -> (Double, Double, Double)

zipWith :: (Double -> Double -> Double) -> SVec3 -> SVec3 -> SVec3

(<+>) :: SVec3 -> SVec3 -> SVec3

(<->) :: SVec3 -> SVec3 -> SVec3

(><) :: SVec3 -> SVec3 -> SVec3

(.^) :: SVec3 -> Double -> SVec3

(.*) :: SVec3 -> SVec3 -> Double

norm :: SVec3 -> Double

normalize :: SVec3 -> SVec3

distance :: SVec3 -> SVec3 -> Double

invert :: SVec3 -> SVec3

fromRows :: (SVec3, SVec3, SVec3) -> Matrix SVec3

toRows :: Matrix SVec3 -> (SVec3, SVec3, SVec3)

dotM :: SVec3 -> SVec3 -> Matrix SVec3 -> Double

mxv :: Matrix SVec3 -> SVec3 -> SVec3

diag :: Double -> Matrix SVec3

vxv :: SVec3 -> SVec3 -> Matrix SVec3

addM :: Matrix SVec3 -> Matrix SVec3 -> Matrix SVec3

data SVec3

Vec3 implementation with Storable instance based on a single contiguous array storage scheme, suitable for use with Data.Vector.Storable.

Unbox instance provides the required index transformations.

interface: [d1 x   y   z  ; d2 x   y   z  ...], length = N = M / 3
               |   |   |       |   |   |
storage:   [  d1x d2y d2z ;   d2x d2y d2z ...], length = M

Constructors

SVec3 !CDouble !CDouble !CDouble

Instances

Eq SVec3

Methods

(==) :: SVec3 -> SVec3 -> Bool

(/=) :: SVec3 -> SVec3 -> Bool

Show SVec3

Methods

showsPrec :: Int -> SVec3 -> ShowS

show :: SVec3 -> String

showList :: [SVec3] -> ShowS

Arbitrary SVec3

Methods

arbitrary :: Gen SVec3

shrink :: SVec3 -> [SVec3]

Storable SVec3

Methods

sizeOf :: SVec3 -> Int

alignment :: SVec3 -> Int

peekElemOff :: Ptr SVec3 -> Int -> IO SVec3

pokeElemOff :: Ptr SVec3 -> Int -> SVec3 -> IO ()

peekByteOff :: Ptr b -> Int -> IO SVec3

pokeByteOff :: Ptr b -> Int -> SVec3 -> IO ()

peek :: Ptr SVec3 -> IO SVec3

poke :: Ptr SVec3 -> SVec3 -> IO ()

Vec3 SVec3

Associated Types

data Matrix SVec3 :: *

Methods

origin :: SVec3

fromXYZ :: (Double, Double, Double) -> SVec3

toXYZ :: SVec3 -> (Double, Double, Double)

zipWith :: (Double -> Double -> Double) -> SVec3 -> SVec3 -> SVec3

(<+>) :: SVec3 -> SVec3 -> SVec3

(<->) :: SVec3 -> SVec3 -> SVec3

(><) :: SVec3 -> SVec3 -> SVec3

(.^) :: SVec3 -> Double -> SVec3

(.*) :: SVec3 -> SVec3 -> Double

norm :: SVec3 -> Double

normalize :: SVec3 -> SVec3

distance :: SVec3 -> SVec3 -> Double

invert :: SVec3 -> SVec3

fromRows :: (SVec3, SVec3, SVec3) -> Matrix SVec3

toRows :: Matrix SVec3 -> (SVec3, SVec3, SVec3)

dotM :: SVec3 -> SVec3 -> Matrix SVec3 -> Double

mxv :: Matrix SVec3 -> SVec3 -> SVec3

diag :: Double -> Matrix SVec3

vxv :: SVec3 -> SVec3 -> Matrix SVec3

addM :: Matrix SVec3 -> Matrix SVec3 -> Matrix SVec3

Eq (Matrix SVec3)

Methods

(==) :: Matrix SVec3 -> Matrix SVec3 -> Bool

(/=) :: Matrix SVec3 -> Matrix SVec3 -> Bool

Show (Matrix SVec3)

Methods

showsPrec :: Int -> Matrix SVec3 -> ShowS

show :: Matrix SVec3 -> String

showList :: [Matrix SVec3] -> ShowS

data Matrix SVec3

data Matrix SVec3 = SMatrix (SVec3, SVec3, SVec3)

newtype UVec3

Vec3 implementation with Unbox instance based on tuples, suitable for use with Data.Vector.Unboxed.

This represents 3-vector as a triple of doubles, using the default Unbox instance for tuples as provided by Data.Vector.Unboxed, which wraps a vector of tuples as a tuple of vectors.

interface:  [d1 (x, y, z); d2 (x, y, z) ...], length = N
                 |  |  |       |  |  |
storage(x): [d1x-+  |  | ; d2x-+  |  |  ...], length = N
storage(y): [d1y----+  | ; d2y----+  |  ...], length = N
storage(z): [d1z-------+ ; d2z-------+  ...], length = N

Constructors

UVec3 (Double, Double, Double)

Instances

Eq UVec3

Methods

(==) :: UVec3 -> UVec3 -> Bool

(/=) :: UVec3 -> UVec3 -> Bool

Show UVec3

Methods

showsPrec :: Int -> UVec3 -> ShowS

show :: UVec3 -> String

showList :: [UVec3] -> ShowS

Unbox UVec3

Vec3 UVec3

Associated Types

data Matrix UVec3 :: *

Methods

origin :: UVec3

fromXYZ :: (Double, Double, Double) -> UVec3

toXYZ :: UVec3 -> (Double, Double, Double)

zipWith :: (Double -> Double -> Double) -> UVec3 -> UVec3 -> UVec3

(<+>) :: UVec3 -> UVec3 -> UVec3

(<->) :: UVec3 -> UVec3 -> UVec3

(><) :: UVec3 -> UVec3 -> UVec3

(.^) :: UVec3 -> Double -> UVec3

(.*) :: UVec3 -> UVec3 -> Double

norm :: UVec3 -> Double

normalize :: UVec3 -> UVec3

distance :: UVec3 -> UVec3 -> Double

invert :: UVec3 -> UVec3

fromRows :: (UVec3, UVec3, UVec3) -> Matrix UVec3

toRows :: Matrix UVec3 -> (UVec3, UVec3, UVec3)

dotM :: UVec3 -> UVec3 -> Matrix UVec3 -> Double

mxv :: Matrix UVec3 -> UVec3 -> UVec3

diag :: Double -> Matrix UVec3

vxv :: UVec3 -> UVec3 -> Matrix UVec3

addM :: Matrix UVec3 -> Matrix UVec3 -> Matrix UVec3

Vector Vector UVec3

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) UVec3 -> m (Vector UVec3)

basicUnsafeThaw :: PrimMonad m => Vector UVec3 -> m (Mutable Vector (PrimState m) UVec3)

basicLength :: Vector UVec3 -> Int

basicUnsafeSlice :: Int -> Int -> Vector UVec3 -> Vector UVec3

basicUnsafeIndexM :: Monad m => Vector UVec3 -> Int -> m UVec3

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) UVec3 -> Vector UVec3 -> m ()

elemseq :: Vector UVec3 -> UVec3 -> b -> b

MVector MVector UVec3

Methods

basicLength :: MVector s UVec3 -> Int

basicUnsafeSlice :: Int -> Int -> MVector s UVec3 -> MVector s UVec3

basicOverlaps :: MVector s UVec3 -> MVector s UVec3 -> Bool

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) UVec3)

basicInitialize :: PrimMonad m => MVector (PrimState m) UVec3 -> m ()

basicUnsafeReplicate :: PrimMonad m => Int -> UVec3 -> m (MVector (PrimState m) UVec3)

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) UVec3 -> Int -> m UVec3

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) UVec3 -> Int -> UVec3 -> m ()

basicClear :: PrimMonad m => MVector (PrimState m) UVec3 -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) UVec3 -> UVec3 -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) UVec3 -> MVector (PrimState m) UVec3 -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) UVec3 -> MVector (PrimState m) UVec3 -> m ()

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) UVec3 -> Int -> m (MVector (PrimState m) UVec3)

Vector Vector (Matrix UVec3)

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Matrix UVec3) -> m (Vector (Matrix UVec3))

basicUnsafeThaw :: PrimMonad m => Vector (Matrix UVec3) -> m (Mutable Vector (PrimState m) (Matrix UVec3))

basicLength :: Vector (Matrix UVec3) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Matrix UVec3) -> Vector (Matrix UVec3)

basicUnsafeIndexM :: Monad m => Vector (Matrix UVec3) -> Int -> m (Matrix UVec3)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Matrix UVec3) -> Vector (Matrix UVec3) -> m ()

elemseq :: Vector (Matrix UVec3) -> Matrix UVec3 -> b -> b

MVector MVector (Matrix UVec3)

Methods

basicLength :: MVector s (Matrix UVec3) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (Matrix UVec3) -> MVector s (Matrix UVec3)

basicOverlaps :: MVector s (Matrix UVec3) -> MVector s (Matrix UVec3) -> Bool

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Matrix UVec3))

basicInitialize :: PrimMonad m => MVector (PrimState m) (Matrix UVec3) -> m ()

basicUnsafeReplicate :: PrimMonad m => Int -> Matrix UVec3 -> m (MVector (PrimState m) (Matrix UVec3))

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Matrix UVec3) -> Int -> m (Matrix UVec3)

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Matrix UVec3) -> Int -> Matrix UVec3 -> m ()

basicClear :: PrimMonad m => MVector (PrimState m) (Matrix UVec3) -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) (Matrix UVec3) -> Matrix UVec3 -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Matrix UVec3) -> MVector (PrimState m) (Matrix UVec3) -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Matrix UVec3) -> MVector (PrimState m) (Matrix UVec3) -> m ()

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Matrix UVec3) -> Int -> m (MVector (PrimState m) (Matrix UVec3))

Eq (Matrix UVec3)

Methods

(==) :: Matrix UVec3 -> Matrix UVec3 -> Bool

(/=) :: Matrix UVec3 -> Matrix UVec3 -> Bool

Show (Matrix UVec3)

Methods

showsPrec :: Int -> Matrix UVec3 -> ShowS

show :: Matrix UVec3 -> String

showList :: [Matrix UVec3] -> ShowS

Unbox (Matrix UVec3)

data Vector UVec3

data Vector UVec3 = V_UVec3 (Vector (Double, Double, Double))

data Matrix UVec3

data Matrix UVec3 = UMatrix (UVec3, UVec3, UVec3)

data MVector s UVec3

data MVector s UVec3 = MV_UVec3 (MVector s (Double, Double, Double))

data MVector s (Matrix UVec3)

data MVector s (Matrix UVec3) = MV_UMatrix (MVector s (UVec3, UVec3, UVec3))

data Vector (Matrix UVec3)

data Vector (Matrix UVec3) = V_UMatrix (Vector (UVec3, UVec3, UVec3))