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GHC 9.10.3 · lts/ghc-9.10.x · 248f8f0 · 2026-10-05

Modulesdl2-2.5.5.0Haskell2010

SDL.Vect

SDL's vector representation.

By default, re-exports the Linear and Linear.Affine modules from the linear package. With the no-linear Cabal flag, instead exports a duplicate implementation of the V2, V3, V4 and Point types from SDL.Internal.Vect, which provides as many instances as possible for those types while avoiding any additional dependencies.

  • 22 types
  • 15 classes
  • 168 values
  • Packagesdl2-2.5.5.0
  • Exports210
  • LanguageHaskell2010
  • LicenceBSD-3-Clause
  • SourceVect.hs
valuevector :: Num a => V3 a -> V4 a
#

Convert a 3-dimensional affine vector into a 4-dimensional homogeneous vector, i.e. sets the w coordinate to 0.

valueunit :: (Additive t, Num a) => ASetter' (t a) a -> t a
#

Create a unit vector.

Example1 expression
unit _x :: V2 IntV2 1 0
data familydata family Vector a
#
Instances133NFData1, IsList, Eq, Data, Ord, Read, …
newtypenewtype Point (f :: Type -> Type) a
#

A handy wrapper to help distinguish points from vectors at the type level

Constructors

  • P (f a)
Instances60Generic1, Monad, Functor, Applicative, Foldable, Traversable, …
datadata V2 a
#

A 2-dimensional vector

Example1 expression
pure 1 :: V2 IntV2 1 1
Example1 expression
V2 1 2 + V2 3 4V2 4 6
Example1 expression
V2 1 2 * V2 3 4V2 3 8
Example1 expression
sum (V2 1 2)3

Constructors

Instances69Monad, Functor, MonadFix, Applicative, Foldable, Traversable, …
datadata V3 a
#

A 3-dimensional vector

Constructors

  • V3 !a !a !a
Instances71Monad, Functor, MonadFix, Applicative, Foldable, Traversable, …
datadata V4 a
#

A 4-dimensional vector.

Constructors

  • V4 !a !a !a !a
Instances73Monad, Functor, MonadFix, Applicative, Foldable, Traversable, …
classclass Additive (Diff p) => Affine (p :: Type -> Type) where
#

An affine space is roughly a vector space in which we have forgotten or at least pretend to have forgotten the origin.

a .+^ (b .-. a)  =  b@
(a .+^ u) .+^ v  =  a .+^ (u ^+^ v)@
(a .-. b) ^+^ v  =  (a .+^ v) .-. q@

Associated types

Methods

  • (.-.) :: Num a => p a -> p a -> Diff p ainfixl 6

    Get the difference between two points as a vector offset.

  • (.+^) :: Num a => p a -> Diff p a -> p ainfixl 6

    Add a vector offset to a point.

  • (.-^) :: Num a => p a -> Diff p a -> p ainfixl 6

    Subtract a vector offset from a point.

Instances20Affine, …
data familydata family MVector s a
#
Instances112NFData1, NFData, MVector, …
classclass Num r => Algebra r m where
#

An associative unital algebra over a ring

Methods

  • mult :: (m -> m -> r) -> m -> r
  • unital :: r -> m -> r
Instances7Algebra, …
classclass Num r => Coalgebra r m where
#

A coassociative counital coalgebra over a ring

Methods

Instances10Coalgebra, …
classclass Num a => Conjugate a where
#

An involutive ring

Methods

  • conjugate :: a -> a

    Conjugate a value. This defaults to the trivial involution.

    Example1 expression
    conjugate (1 :+ 2)1.0 :+ (-2.0)
    Example1 expression
    conjugate 11
Instances17Conjugate, …
classclass Conjugate a => TrivialConjugate a
#

Requires and provides a default definition such that

conjugate = id
Instances15TrivialConjugate, …
newtypenewtype Covector r a
#

Linear functionals from elements of an (infinite) free module to a scalar

Constructors

Instances10Monad, Functor, Applicative, Alternative, MonadPlus, Alt, …
classclass Num a => Epsilon a where
#

Provides a fairly subjective test to see if a quantity is near zero.

Example1 expression
nearZero (1e-11 :: Double)False
Example1 expression
nearZero (1e-17 :: Double)True
Example1 expression
nearZero (1e-5 :: Float)False
Example1 expression
nearZero (1e-7 :: Float)True

Methods

Instances14Epsilon, …
value(!!*) :: (Functor m, Functor r, Num a) => m (r a) -> a -> m (r a)
#

Matrix-scalar product

Example1 expression
V2 (V2 1 2) (V2 3 4) !!* 5V2 (V2 5 10) (V2 15 20)
value(!*) :: (Functor m, Foldable r, Additive r, Num a) => m (r a) -> r a -> m a
#

Matrix * column vector

Example1 expression
V2 (V3 1 2 3) (V3 4 5 6) !* V3 7 8 9V2 50 122
value(!*!)
  1. :: (Functor m, Foldable t, Additive t, Additive n, Num a)
  2. => m (t a)
  3. -> t (n a)
  4. -> m (n a)
#

Matrix product. This can compute any combination of sparse and dense multiplication.

Example1 expression
V2 (V3 1 2 3) (V3 4 5 6) !*! V3 (V2 1 2) (V2 3 4) (V2 4 5)V2 (V2 19 25) (V2 43 58)
Example1 expression
V2 (IntMap.fromList [(1,2)]) (IntMap.fromList [(2,3)]) !*! IntMap.fromList [(1,V3 0 0 1), (2, V3 0 0 5)]V2 (V3 0 0 2) (V3 0 0 15)
value(!+!) :: (Additive m, Additive n, Num a) => m (n a) -> m (n a) -> m (n a)
#

Entry-wise matrix addition.

Example1 expression
V2 (V3 1 2 3) (V3 4 5 6) !+! V2 (V3 7 8 9) (V3 1 2 3)V2 (V3 8 10 12) (V3 5 7 9)
value(!-!) :: (Additive m, Additive n, Num a) => m (n a) -> m (n a) -> m (n a)
#

Entry-wise matrix subtraction.

Example1 expression
V2 (V3 1 2 3) (V3 4 5 6) !-! V2 (V3 7 8 9) (V3 1 2 3)V2 (V3 (-6) (-6) (-6)) (V3 3 3 3)
value(*!) :: (Num a, Foldable t, Additive f, Additive t) => t a -> t (f a) -> f a
#

Row vector * matrix

Example1 expression
V2 1 2 *! V2 (V3 3 4 5) (V3 6 7 8)V3 15 18 21
value(*!!) :: (Functor m, Functor r, Num a) => a -> m (r a) -> m (r a)
#

Scalar-matrix product

Example1 expression
5 *!! V2 (V2 1 2) (V2 3 4)V2 (V2 5 10) (V2 15 20)
typetype M22 a = V2 (V2 a)
#

A 2x2 matrix with row-major representation

typetype M23 a = V2 (V3 a)
#

A 2x3 matrix with row-major representation

typetype M24 a = V2 (V4 a)
#

A 2x4 matrix with row-major representation

typetype M32 a = V3 (V2 a)
#

A 3x2 matrix with row-major representation

typetype M33 a = V3 (V3 a)
#

A 3x3 matrix with row-major representation

typetype M34 a = V3 (V4 a)
#

A 3x4 matrix with row-major representation

typetype M42 a = V4 (V2 a)
#

A 4x2 matrix with row-major representation

typetype M43 a = V4 (V3 a)
#

A 4x3 matrix with row-major representation

typetype M44 a = V4 (V4 a)
#

A 4x4 matrix with row-major representation

value_m22 :: (Representable t, R2 t, R2 v) => Lens' (t (v a)) (M22 a)
#

Extract a 2x2 matrix from a matrix of higher dimensions by dropping excess rows and columns.

value_m23 :: (Representable t, R2 t, R3 v) => Lens' (t (v a)) (M23 a)
#

Extract a 2x3 matrix from a matrix of higher dimensions by dropping excess rows and columns.

value_m24 :: (Representable t, R2 t, R4 v) => Lens' (t (v a)) (M24 a)
#

Extract a 2x4 matrix from a matrix of higher dimensions by dropping excess rows and columns.

value_m32 :: (Representable t, R3 t, R2 v) => Lens' (t (v a)) (M32 a)
#

Extract a 3x2 matrix from a matrix of higher dimensions by dropping excess rows and columns.

value_m33 :: (Representable t, R3 t, R3 v) => Lens' (t (v a)) (M33 a)
#

Extract a 3x3 matrix from a matrix of higher dimensions by dropping excess rows and columns.

value_m34 :: (Representable t, R3 t, R4 v) => Lens' (t (v a)) (M34 a)
#

Extract a 3x4 matrix from a matrix of higher dimensions by dropping excess rows and columns.

value_m42 :: (Representable t, R4 t, R2 v) => Lens' (t (v a)) (M42 a)
#

Extract a 4x2 matrix from a matrix of higher dimensions by dropping excess rows and columns.

value_m43 :: (Representable t, R4 t, R3 v) => Lens' (t (v a)) (M43 a)
#

Extract a 4x3 matrix from a matrix of higher dimensions by dropping excess rows and columns.

value_m44 :: (Representable t, R4 t, R4 v) => Lens' (t (v a)) (M44 a)
#

Extract a 4x4 matrix from a matrix of higher dimensions by dropping excess rows and columns.

valueadjoint :: (Functor m, Distributive n, Conjugate a) => m (n a) -> n (m a)
#

Hermitian conjugate or conjugate transpose

Example1 expression
adjoint (V2 (V2 (1 :+ 2) (3 :+ 4)) (V2 (5 :+ 6) (7 :+ 8)))V2 (V2 (1.0 :+ (-2.0)) (5.0 :+ (-6.0))) (V2 (3.0 :+ (-4.0)) (7.0 :+ (-8.0)))
valuecolumn
  1. :: Representable f
  2. => LensLike (Context a b) s t a b
  3. -> Lens (f s) (f t) (f a) (f b)
#

This is a generalization of inside to work over any corepresentable Functor.

column :: Representable f => Lens s t a b -> Lens (f s) (f t) (f a) (f b)

In practice it is used to access a column of a matrix.

Example1 expression
V2 (V3 1 2 3) (V3 4 5 6) ^._xV3 1 2 3
Example1 expression
V2 (V3 1 2 3) (V3 4 5 6) ^.column _xV2 1 4
valuedet22 :: Num a => M22 a -> a
#

2x2 matrix determinant.

Example1 expression
det22 (V2 (V2 a b) (V2 c d))a * d - b * c
valuedet33 :: Num a => M33 a -> a
#

3x3 matrix determinant.

Example1 expression
det33 (V3 (V3 a b c) (V3 d e f) (V3 g h i))a * (e * i - f * h) - d * (b * i - c * h) + g * (b * f - c * e)
valuedet44 :: Num a => M44 a -> a
#

4x4 matrix determinant.

valueidentity :: (Num a, Traversable t, Applicative t) => t (t a)
#

The identity matrix for any dimension vector.

Example2 expressions
identity :: M44 IntV4 (V4 1 0 0 0) (V4 0 1 0 0) (V4 0 0 1 0) (V4 0 0 0 1)identity :: V3 (V3 Int)V3 (V3 1 0 0) (V3 0 1 0) (V3 0 0 1)
valueinv22 :: Fractional a => M22 a -> M22 a
#

2x2 matrix inverse.

Example1 expression
inv22 $ V2 (V2 1 2) (V2 3 4)V2 (V2 (-2.0) 1.0) (V2 1.5 (-0.5))
valueinv33 :: Fractional a => M33 a -> M33 a
#

3x3 matrix inverse.

Example1 expression
inv33 $ V3 (V3 1 2 4) (V3 4 2 2) (V3 1 1 1)V3 (V3 0.0 0.5 (-1.0)) (V3 (-0.5) (-0.75) 3.5) (V3 0.5 0.25 (-1.5))
valuem33_to_m44 :: Num a => M33 a -> M44 a
#

Convert a 3x3 matrix to a 4x4 matrix extending it with 0's in the new row and column.

valuem43_to_m44 :: Num a => M43 a -> M44 a
#

Convert from a 4x3 matrix to a 4x4 matrix, extending it with the [ 0 0 0 1 ] column vector

classclass Additive f => Metric (f :: Type -> Type) where
#

Free and sparse inner product/metric spaces.

Methods

  • dot :: Num a => f a -> f a -> a

    Compute the inner product of two vectors or (equivalently) convert a vector f a into a covector f a -> a.

    Example1 expression
    V2 1 2 `dot` V2 3 411
  • quadrance :: Num a => f a -> a

    Compute the squared norm. The name quadrance arises from Norman J. Wildberger's rational trigonometry.

  • qd :: Num a => f a -> f a -> a

    Compute the quadrance of the difference

  • distance :: Floating a => f a -> f a -> a

    Compute the distance between two vectors in a metric space

  • norm :: Floating a => f a -> a

    Compute the norm of a vector in a metric space

  • signorm :: Floating a => f a -> f a

    Convert a non-zero vector to unit vector.

Instances19Metric, …
valuefrustum
  1. :: Floating a
  2. => a

    Left

  3. -> a

    Right

  4. -> a

    Bottom

  5. -> a

    Top

  6. -> a

    Near

  7. -> a

    Far

  8. -> M44 a
#

Build a perspective matrix per the classic glFrustum arguments.

valueinfinitePerspective
  1. :: Floating a
  2. => a

    FOV (y direction, in radians)

  3. -> a

    Aspect Ratio

  4. -> a

    Near plane

  5. -> M44 a
#

Build a matrix for a symmetric perspective-view frustum with a far plane at infinite

valueinverseOrtho
  1. :: Fractional a
  2. => a

    Left

  3. -> a

    Right

  4. -> a

    Bottom

  5. -> a

    Top

  6. -> a

    Near

  7. -> a

    Far

  8. -> M44 a
#

Build an inverse orthographic perspective matrix from 6 clipping planes

valueinversePerspective
  1. :: Floating a
  2. => a

    FOV (y direction, in radians)

  3. -> a

    Aspect ratio

  4. -> a

    Near plane

  5. -> a

    Far plane

  6. -> M44 a
#

Build an inverse perspective matrix

valueortho
  1. :: Fractional a
  2. => a

    Left

  3. -> a

    Right

  4. -> a

    Bottom

  5. -> a

    Top

  6. -> a

    Near

  7. -> a

    Far

  8. -> M44 a
#

Build an orthographic perspective matrix from 6 clipping planes. This matrix takes the region delimited by these planes and maps it to normalized device coordinates between [-1,1]

This call is designed to mimic the parameters to the OpenGL glOrtho call, so it has a slightly strange convention: Notably: the near and far planes are negated.

Consequently:

ortho l r b t n f !* V4 l b (-n) 1 = V4 (-1) (-1) (-1) 1
ortho l r b t n f !* V4 r t (-f) 1 = V4 1 1 1 1

Examples:

Example1 expression
ortho 1 2 3 4 5 6 !* V4 1 3 (-5) 1V4 (-1.0) (-1.0) (-1.0) 1.0
Example1 expression
ortho 1 2 3 4 5 6 !* V4 2 4 (-6) 1V4 1.0 1.0 1.0 1.0
valueperspective
  1. :: Floating a
  2. => a

    FOV (y direction, in radians)

  3. -> a

    Aspect ratio

  4. -> a

    Near plane

  5. -> a

    Far plane

  6. -> M44 a
#

Build a matrix for a symmetric perspective-view frustum

datadata Quaternion a
#

Quaternions

Constructors

Instances74Monad, Functor, MonadFix, Applicative, Foldable, Traversable, …
classclass Functor m => Trace (m :: Type -> Type) where
#

Methods

  • trace :: Num a => m (m a) -> a

    Compute the trace of a matrix

    Example1 expression
    trace (V2 (V2 a b) (V2 c d))a + d
  • diagonal :: m (m a) -> m a

    Compute the diagonal of a matrix

    Example1 expression
    diagonal (V2 (V2 a b) (V2 c d))V2 a d
Instances14Trace, …
datadata V0 a
#

A 0-dimensional vector

Example1 expression
pure 1 :: V0 IntV0
Example1 expression
V0 + V0V0
V0
Instances65Monad, Functor, MonadFix, Applicative, Foldable, Traversable, …
  • Monad V0Defined in linear-1.22 · Linear.V0
  • Functor V0Defined in linear-1.22 · Linear.V0
  • MonadFix V0Defined in linear-1.22 · Linear.V0
  • Applicative V0Defined in linear-1.22 · Linear.V0
  • Foldable V0Defined in linear-1.22 · Linear.V0
  • Traversable V0Defined in linear-1.22 · Linear.V0
  • MonadZip V0Defined in linear-1.22 · Linear.V0
  • Eq1 V0Defined in linear-1.22 · Linear.V0
  • Ord1 V0Defined in linear-1.22 · Linear.V0
  • Read1 V0Defined in linear-1.22 · Linear.V0
  • Show1 V0Defined in linear-1.22 · Linear.V0
  • Hashable1 V0Defined in linear-1.22 · Linear.V0
  • Distributive V0Defined in linear-1.22 · Linear.V0
  • Apply V0Defined in linear-1.22 · Linear.V0
  • Bind V0Defined in linear-1.22 · Linear.V0
  • Representable V0Defined in linear-1.22 · Linear.V0
  • Serial1 V0Defined in linear-1.22 · Linear.V0
  • Metric V0Defined in linear-1.22 · Linear.V0
  • Trace V0Defined in linear-1.22 · Linear.Trace
  • Additive V0Defined in linear-1.22 · Linear.V0
  • Affine V0Defined in linear-1.22 · Linear.Affine
  • Finite V0Defined in linear-1.22 · Linear.V0
  • Generic1 V0Defined in linear-1.22 · Linear.V0
  • Lift (V0 a)Defined in linear-1.22 · Linear.V0
  • Vector Vector (V0 a)Defined in linear-1.22 · Linear.V0
  • MVector MVector (V0 a)Defined in linear-1.22 · Linear.V0
  • Num r => Algebra r (E V0)Defined in linear-1.22 · Linear.Algebra
  • Num r => Coalgebra r (E V0)Defined in linear-1.22 · Linear.Algebra
  • Bounded (V0 a)Defined in linear-1.22 · Linear.V0
  • Enum (V0 a)Defined in linear-1.22 · Linear.V0
  • Eq (V0 a)Defined in linear-1.22 · Linear.V0
  • Floating (V0 a)Defined in linear-1.22 · Linear.V0
  • Fractional (V0 a)Defined in linear-1.22 · Linear.V0
  • Data a => Data (V0 a)Defined in linear-1.22 · Linear.V0
  • Num (V0 a)Defined in linear-1.22 · Linear.V0
  • Ord (V0 a)Defined in linear-1.22 · Linear.V0
  • Read (V0 a)Defined in linear-1.22 · Linear.V0
  • Show (V0 a)Defined in linear-1.22 · Linear.V0
  • Ix (V0 a)Defined in linear-1.22 · Linear.V0
  • Generic (V0 a)Defined in linear-1.22 · Linear.V0
  • Semigroup (V0 a)Defined in linear-1.22 · Linear.V0
  • Monoid (V0 a)Defined in linear-1.22 · Linear.V0
  • Storable (V0 a)Defined in linear-1.22 · Linear.V0
  • NFData (V0 a)Defined in linear-1.22 · Linear.V0
  • Random (V0 a)Defined in linear-1.22 · Linear.V0
  • Binary (V0 a)Defined in linear-1.22 · Linear.V0
  • Hashable (V0 a)Defined in linear-1.22 · Linear.V0
  • Unbox (V0 a)Defined in linear-1.22 · Linear.V0
  • Serialize (V0 a)Defined in linear-1.22 · Linear.V0
  • Ixed (V0 a)Defined in linear-1.22 · Linear.V0
  • Serial (V0 a)Defined in linear-1.22 · Linear.V0
  • Epsilon (V0 a)Defined in linear-1.22 · Linear.V0
  • FoldableWithIndex (E V0) V0Defined in linear-1.22 · Linear.V0
  • FunctorWithIndex (E V0) V0Defined in linear-1.22 · Linear.V0
  • TraversableWithIndex (E V0) V0Defined in linear-1.22 · Linear.V0
  • Each (V0 a) (V0 b) a bDefined in linear-1.22 · Linear.V0
  • type Rep (V0 a) = D1 ('MetaData "V0" "Linear.V0" "linear-1.22-3d3RJcba25gDknnFKeY2an" 'False) (C1 ('MetaCons "V0" 'PrefixI 'False) U1)Defined in linear-1.22 · Linear.V0
  • type Rep1 V0 = D1 ('MetaData "V0" "Linear.V0" "linear-1.22-3d3RJcba25gDknnFKeY2an" 'False) (C1 ('MetaCons "V0" 'PrefixI 'False) U1)Defined in linear-1.22 · Linear.V0
  • data MVector s (V0 a)Defined in linear-1.22 · Linear.V0
  • data Vector (V0 a)Defined in linear-1.22 · Linear.V0
  • type Rep V0 = E V0Defined in linear-1.22 · Linear.V0
  • type Index (V0 a) = E V0Defined in linear-1.22 · Linear.V0
  • type IxValue (V0 a) = aDefined in linear-1.22 · Linear.V0
  • type Diff V0 = V0Defined in linear-1.22 · Linear.Affine
  • type Size V0 = 0Defined in linear-1.22 · Linear.V0
classclass R1 (t :: Type -> Type) where
#

A space that has at least 1 basis vector _x.

Methods

  • _x :: Lens' (t a) a
    Example1 expression
    V1 2 ^._x2
    Example1 expression
    V1 2 & _x .~ 3V1 3
Instances7R1, …
  • R1 IdentityDefined in linear-1.22 · Linear.V1
  • R1 QuaternionDefined in linear-1.22 · Linear.Quaternion
  • R1 V1Defined in linear-1.22 · Linear.V1
  • R1 V2Defined in linear-1.22 · Linear.V2
  • R1 V3Defined in linear-1.22 · Linear.V3
  • R1 V4Defined in linear-1.22 · Linear.V4
  • R1 f => R1 (Point f)Defined in linear-1.22 · Linear.Affine
newtypenewtype V1 a
#

A 1-dimensional vector

Example1 expression
pure 1 :: V1 IntV1 1
Example1 expression
V1 2 + V1 3V1 5
Example1 expression
V1 2 * V1 3V1 6
Example1 expression
sum (V1 2)2

Constructors

Instances68Monad, Functor, MonadFix, Applicative, Foldable, Traversable, …
classclass R1 t => R2 (t :: Type -> Type) where
#

A space that distinguishes 2 orthogonal basis vectors _x and _y, but may have more.

Methods

  • _y :: Lens' (t a) a
    Example1 expression
    V2 1 2 ^._y2
    Example1 expression
    V2 1 2 & _y .~ 3V2 1 3
  • _xy :: Lens' (t a) (V2 a)
Instances5R2
  • R2 QuaternionDefined in linear-1.22 · Linear.Quaternion
  • R2 V2Defined in linear-1.22 · Linear.V2
  • R2 V3Defined in linear-1.22 · Linear.V3
  • R2 V4Defined in linear-1.22 · Linear.V4
  • R2 f => R2 (Point f)Defined in linear-1.22 · Linear.Affine
value_yx :: R2 t => Lens' (t a) (V2 a)
#
Example1 expression
V2 1 2 ^. _yxV2 2 1
valuecrossZ :: Num a => V2 a -> V2 a -> a
#

The Z-component of the cross product of two vectors in the XY-plane.

Example1 expression
crossZ (V2 1 0) (V2 0 1)1
valueperp :: Num a => V2 a -> V2 a
#

the counter-clockwise perpendicular vector

Example1 expression
perp $ V2 10 20V2 (-20) 10
classclass R2 t => R3 (t :: Type -> Type) where
#

A space that distinguishes 3 orthogonal basis vectors: _x, _y, and _z. (It may have more)

Methods

Instances4R3
  • R3 QuaternionDefined in linear-1.22 · Linear.Quaternion
  • R3 V3Defined in linear-1.22 · Linear.V3
  • R3 V4Defined in linear-1.22 · Linear.V4
  • R3 f => R3 (Point f)Defined in linear-1.22 · Linear.Affine
classclass R3 t => R4 (t :: Type -> Type) where
#

A space that distinguishes orthogonal basis vectors _x, _y, _z, _w. (It may have more.)

Methods

Instances3R4
  • R4 QuaternionDefined in linear-1.22 · Linear.Quaternion
  • R4 V4Defined in linear-1.22 · Linear.V4
  • R4 f => R4 (Point f)Defined in linear-1.22 · Linear.Affine
valuenormalizePoint :: Fractional a => V4 a -> V3 a
#

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).

valuepoint :: Num a => V3 a -> V4 a
#

Convert a 3-dimensional affine point into a 4-dimensional homogeneous vector, i.e. sets the w coordinate to 1.

value(*^) :: (Functor f, Num a) => a -> f a -> f a
#

Compute the left scalar product

Example1 expression
2 *^ V2 3 4V2 6 8
classclass Functor f => Additive (f :: Type -> Type) where
#

A vector is an additive group with additional structure.

Methods

  • zero :: Num a => f a

    The zero vector

  • (^+^) :: Num a => f a -> f a -> f ainfixl 6

    Compute the sum of two vectors

    Example1 expression
    V2 1 2 ^+^ V2 3 4V2 4 6
  • (^-^) :: Num a => f a -> f a -> f ainfixl 6

    Compute the difference between two vectors

    Example1 expression
    V2 4 5 ^-^ V2 3 1V2 1 4
  • lerp :: Num a => a -> f a -> f a -> f a

    Linearly interpolate between two vectors.

  • liftU2 :: (a -> a -> a) -> f a -> f a -> f a

    Apply a function to merge the 'non-zero' components of two vectors, unioning the rest of the values.

    • For a dense vector this is equivalent to liftA2.

    • For a sparse vector this is equivalent to unionWith.

  • liftI2 :: (a -> b -> c) -> f a -> f b -> f c

    Apply a function to the components of two vectors.

Instances21Additive, …
newtypenewtype E (t :: Type -> Type)
#

Basis element

Constructors

Instances32Algebra, Coalgebra, FoldableWithIndex, FunctorWithIndex, TraversableWithIndex, …
value(^*) :: (Functor f, Num a) => f a -> a -> f a
#

Compute the right scalar product

Example1 expression
V2 3 4 ^* 2V2 6 8
value(^/) :: (Functor f, Fractional a) => f a -> a -> f a
#

Compute division by a scalar on the right.

valuebasis :: (Additive t, Traversable t, Num a) => [t a]
#

Produce a default basis for a vector space. If the dimensionality of the vector space is not statically known, see basisFor.

valuebasisFor :: (Traversable t, Num a) => t b -> [t a]
#

Produce a default basis for a vector space from which the argument is drawn.

valuenegated :: (Functor f, Num a) => f a -> f a
#

Compute the negation of a vector

Example1 expression
negated (V2 2 4)V2 (-2) (-4)
valuescaled :: (Traversable t, Num a) => t a -> t (t a)
#

Produce a diagonal (scale) matrix from a vector.

Example1 expression
scaled (V2 2 3)V2 (V2 2 0) (V2 0 3)
valuesumV :: (Foldable f, Additive v, Num a) => f (v a) -> v a
#

Sum over multiple vectors

Example1 expression
sumV [V2 1 1, V2 3 4]V2 4 5
familytype family Diff (p :: Type -> Type) :: Type -> Type
#
Instances20Diff, …
value(#.) :: Coercible c b => (b -> c) -> (a -> b) -> a -> c
#
value(.#) :: Coercible b a => (b -> c) -> (a -> b) -> a -> c
#
valueqdA :: (Affine p, Foldable (Diff p), Num a) => p a -> p a -> a
#

Compute the quadrance of the difference (the square of the distance)

Point

1 declaration
newtypenewtype Point (f :: Type -> Type) a
#

A handy wrapper to help distinguish points from vectors at the type level

Constructors

  • P (f a)
Instances60Generic1, Monad, Functor, Applicative, Foldable, Traversable, …

Vectors

3 declarations
datadata V2 a
#

A 2-dimensional vector

Example1 expression
pure 1 :: V2 IntV2 1 1
Example1 expression
V2 1 2 + V2 3 4V2 4 6
Example1 expression
V2 1 2 * V2 3 4V2 3 8
Example1 expression
sum (V2 1 2)3

Constructors

Instances69Monad, Functor, MonadFix, Applicative, Foldable, Traversable, …
datadata V3 a
#

A 3-dimensional vector

Constructors

  • V3 !a !a !a
Instances71Monad, Functor, MonadFix, Applicative, Foldable, Traversable, …
datadata V4 a
#

A 4-dimensional vector.

Constructors

  • V4 !a !a !a !a
Instances73Monad, Functor, MonadFix, Applicative, Foldable, Traversable, …