Data.Vect.Floating.Base

Documentation

class AbelianGroup g where

Methods

(&+) :: g -> g -> g

(&-) :: g -> g -> g

neg :: g -> g

zero :: g

Instances

Floating a => AbelianGroup (Mat4 a)

Floating a => AbelianGroup (Mat3 a)

Floating a => AbelianGroup (Mat2 a)

Floating a => AbelianGroup (Vec4 a)

Floating a => AbelianGroup (Vec3 a)

Floating a => AbelianGroup (Vec2 a)

Floating a => AbelianGroup (Quaternion a)

vecSum :: AbelianGroup g => [g] -> g

class MultSemiGroup r where

Methods

(.*.) :: r -> r -> r

one :: r

Instances

Floating a => MultSemiGroup (Proj4 a)

Floating a => MultSemiGroup (Proj3 a)

Floating a => MultSemiGroup (Ortho4 a)

Floating a => MultSemiGroup (Ortho3 a)

Floating a => MultSemiGroup (Ortho2 a)

Floating a => MultSemiGroup (Mat4 a)

Floating a => MultSemiGroup (Mat3 a)

Floating a => MultSemiGroup (Mat2 a)

Floating a => MultSemiGroup (UnitQuaternion a)

Num a => MultSemiGroup (Quaternion a)

class (AbelianGroup r, MultSemiGroup r) => Ring r

Instances

Floating a => Ring (Mat4 a)

Floating a => Ring (Mat3 a)

Floating a => Ring (Mat2 a)

semigroupProduct :: MultSemiGroup r => [r] -> r

class LeftModule r m where

Methods

lmul :: r -> m -> m

(*.) :: r -> m -> m

Instances

Floating a => LeftModule (Mat4 a) (Vec4 a)

Floating a => LeftModule (Mat3 a) (Vec3 a)

Floating a => LeftModule (Mat2 a) (Vec2 a)

Num a => LeftModule (UnitQuaternion a) (Vec3 a)

class RightModule m r | m -> r, r -> m where

Methods

rmul :: m -> r -> m

(.*) :: m -> r -> m

Instances

Floating a => RightModule (Vec4 a) (Mat4 a)

Floating a => RightModule (Vec3 a) (Mat3 a)

Floating a => RightModule (Vec2 a) (Mat2 a)

class AbelianGroup (v a) => Vector a v where

Methods

mapVec :: (a -> a) -> v a -> v a

scalarMul :: a -> v a -> v a

(*&) :: a -> v a -> v a

(&*) :: v a -> a -> v a

Instances

Floating a => Vector a Mat4

Floating a => Vector a Vec4

Floating a => Vector a Mat3

Floating a => Vector a Vec3

Floating a => Vector a Mat2

Floating a => Vector a Vec2

Floating a => Vector a Quaternion

class Floating a => DotProd a v where

Methods

(&.) :: v a -> v a -> a

norm :: v a -> a

normsqr :: v a -> a

len :: v a -> a

lensqr :: v a -> a

dotprod :: v a -> v a -> a

Instances

Floating a => DotProd a Vec4

Floating a => DotProd a Vec3

Floating a => DotProd a Vec2

Floating a => DotProd a Normal4

Floating a => DotProd a Normal3

Floating a => DotProd a Normal2

Floating a => DotProd a UnitQuaternion

Floating a => DotProd a Quaternion

class CrossProd v where

Cross product

Methods

crossprod :: v -> v -> v

(&^) :: v -> v -> v

Instances

Floating a => CrossProd (Normal3 a)

Floating a => CrossProd (Vec3 a)

normalize :: (Vector a v, DotProd a v) => v a -> v a

distance :: (Vector a v, DotProd a v) => v a -> v a -> a

angle :: (Vector a v, DotProd a v) => v a -> v a -> a

the angle between two vectors

angle' :: (Vector a v, UnitVector a v u, DotProd a v) => u a -> u a -> a

the angle between two unit vectors

class (Vector a v, DotProd a v) => UnitVector a v u | u -> v, v -> u where

Methods

mkNormal

Arguments

:: v a

-> u a

normalizes the input

toNormalUnsafe

Arguments

:: v a

-> u a

does not normalize the input!

fromNormal :: u a -> v a

fromNormalRadius :: a -> u a -> v a

Instances

Floating a => UnitVector a Vec4 Normal4

Floating a => UnitVector a Vec3 Normal3

Floating a => UnitVector a Vec2 Normal2

Floating a => UnitVector a Quaternion UnitQuaternion

class Pointwise v where

Pointwise multiplication

Methods

pointwise :: v -> v -> v

(&!) :: v -> v -> v

Instances

Floating a => Pointwise (Mat4 a)

Floating a => Pointwise (Mat3 a)

Floating a => Pointwise (Mat2 a)

Num a => Pointwise (Vec4 a)

Num a => Pointwise (Vec3 a)

Floating a => Pointwise (Vec2 a)

class Extend a u v where

conversion between vectors (and matrices) of different dimensions

Methods

extendZero

Arguments

:: u a

-> v a

example: extendZero (Vec2 5 6) = Vec4 5 6 0 0

extendWith

Arguments

:: a

-> u a

-> v a

example: extendWith 1 (Vec2 5 6) = Vec4 5 6 1 1

trim

Arguments

:: v a

-> u a

example: trim (Vec4 5 6 7 8) = Vec2 5 6

Instances

Floating a => Extend a Mat3 Mat4

Floating a => Extend a Mat2 Mat4

Floating a => Extend a Mat2 Mat3

Floating a => Extend a Vec3 Vec4

Floating a => Extend a Vec2 Vec4

Floating a => Extend a Vec2 Vec3

class HasCoordinates v x | v -> x where

Methods

_1 :: v -> x

_2 :: v -> x

_3 :: v -> x

_4 :: v -> x

Instances

Floating a => HasCoordinates (Vec4 a) a

Floating a => HasCoordinates (Vec3 a) a

Floating a => HasCoordinates (Vec2 a) a

Floating a => HasCoordinates (Mat4 a) (Vec4 a)

Floating a => HasCoordinates (Mat3 a) (Vec3 a)

Floating a => HasCoordinates (Mat2 a) (Vec2 a)

class Dimension a where

Methods

dim :: a -> Int

Instances

Floating a => Dimension (Ortho4 a)

Floating a => Dimension (Ortho3 a)

Floating a => Dimension (Ortho2 a)

Floating a => Dimension (Normal4 a)

Floating a => Dimension (Normal3 a)

Floating a => Dimension (Normal2 a)

Floating a => Dimension (Mat4 a)

Floating a => Dimension (Mat3 a)

Floating a => Dimension (Mat2 a)

Floating a => Dimension (Vec4 a)

Floating a => Dimension (Vec3 a)

Floating a => Dimension (Vec2 a)

class Matrix m where

Methods

transpose :: m -> m

inverse :: m -> m

idmtx :: m

Instances

Floating a => Matrix (Proj4 a)

Floating a => Matrix (Proj3 a)

Floating a => Matrix (Ortho4 a)

Floating a => Matrix (Ortho3 a)

Floating a => Matrix (Ortho2 a)

Floating a => Matrix (Mat4 a)

Floating a => Matrix (Mat3 a)

Floating a => Matrix (Mat2 a)

class Tensor t v | t -> v where

Outer product (could be unified with Diagonal?)

Methods

outer :: v -> v -> t

Instances

Floating a => Tensor (Mat4 a) (Vec4 a)

Floating a => Tensor (Mat3 a) (Vec3 a)

Floating a => Tensor (Mat2 a) (Vec2 a)

class Diagonal s t | t -> s where

makes a diagonal matrix from a vector

Methods

diag :: s -> t

Instances

Floating a => Diagonal (Vec4 a) (Mat4 a)

Floating a => Diagonal (Vec3 a) (Mat3 a)

Floating a => Diagonal (Vec2 a) (Mat2 a)

class Determinant a m where

Methods

det :: m -> a

Instances

Floating a => Determinant a (Ortho4 a)

Floating a => Determinant a (Ortho3 a)

Floating a => Determinant a (Ortho2 a)

Floating a => Determinant a (Mat4 a)

Floating a => Determinant a (Mat3 a)

Floating a => Determinant a (Mat2 a)

Floating a => Determinant a (Vec2 a, Vec2 a)

Floating a => Determinant a (Vec3 a, Vec3 a, Vec3 a)

class Matrix (m a) => Orthogonal a m o | m -> o, o -> m where

Methods

fromOrtho :: o a -> m a

toOrthoUnsafe :: m a -> o a

Instances

Floating a => Orthogonal a Mat4 Ortho4

Floating a => Orthogonal a Mat3 Ortho3

Floating a => Orthogonal a Mat2 Ortho2

class (Vector a v, Orthogonal a n o, Diagonal (v a) (n a)) => Projective a v n o m p | m -> p, p -> m, p -> o, o -> p, p -> n, n -> p, p -> v, v -> p, n -> o, n -> v, v -> n where

"Projective" matrices have the following form: the top left corner is an any matrix, the bottom right corner is 1, and the top-right column is zero. These describe the affine orthogonal transformation of the space one dimension less.

Methods

fromProjective :: p a -> m a

toProjectiveUnsafe :: m a -> p a

orthogonal :: o a -> p a

linear :: n a -> p a

translation :: v a -> p a

scaling :: v a -> p a

Instances

Floating a => Projective a Vec3 Mat3 Ortho3 Mat4 Proj4

Floating a => Projective a Vec2 Mat2 Ortho2 Mat3 Proj3

class (AbelianGroup m, Matrix m) => MatrixNorms a m where

Methods

frobeniusNorm

Arguments

:: m

-> a

the frobenius norm (= euclidean norm in the space of matrices)

matrixDistance

Arguments

:: m

-> m

-> a

euclidean distance in the space of matrices

operatorNorm

Arguments

:: m

-> a

(euclidean) operator norm (not implemented yet)

Instances

Floating a => MatrixNorms a (Mat4 a)

Floating a => MatrixNorms a (Mat3 a)

Floating a => MatrixNorms a (Mat2 a)

data Vec2 a

Constructors

Vec2 !a !a

Instances

Typeable1 Vec2

Floating a => DotProd a Vec2

Floating a => Vector a Vec2

Floating a => Extend a Vec2 Vec4

Floating a => Extend a Vec2 Vec3

Floating a => UnitVector a Vec2 Normal2

Floating a => Projective a Vec2 Mat2 Ortho2 Mat3 Proj3

Floating a => Interpolate a (Vec2 a)

Floating a => Determinant a (Vec2 a, Vec2 a)

Read a => Read (Vec2 a)

Show a => Show (Vec2 a)

(Floating a, Random a) => Random (Vec2 a)

(Floating a, Storable a) => Storable (Vec2 a)

Floating a => Dimension (Vec2 a)

Floating a => Pointwise (Vec2 a)

Floating a => AbelianGroup (Vec2 a)

Floating a => HasCoordinates (Vec2 a) a

Floating a => Tensor (Mat2 a) (Vec2 a)

Floating a => Diagonal (Vec2 a) (Mat2 a)

Floating a => HasCoordinates (Mat2 a) (Vec2 a)

Floating a => RightModule (Vec2 a) (Mat2 a)

Floating a => LeftModule (Mat2 a) (Vec2 a)

Floating a => GramSchmidt (Vec2 a, Vec2 a)

data Vec3 a

Constructors

Vec3 !a !a !a

Instances

Typeable1 Vec3

Floating a => DotProd a Vec3

Floating a => Vector a Vec3

Floating a => Extend a Vec3 Vec4

Floating a => Extend a Vec2 Vec3

Floating a => UnitVector a Vec3 Normal3

Floating a => Projective a Vec3 Mat3 Ortho3 Mat4 Proj4

Floating a => Interpolate a (Vec3 a)

Floating a => Determinant a (Vec3 a, Vec3 a, Vec3 a)

Read a => Read (Vec3 a)

Show a => Show (Vec3 a)

(Floating a, Random a) => Random (Vec3 a)

(Floating a, Storable a) => Storable (Vec3 a)

Floating a => Dimension (Vec3 a)

Num a => Pointwise (Vec3 a)

Floating a => CrossProd (Vec3 a)

Floating a => AbelianGroup (Vec3 a)

Floating a => HasCoordinates (Vec3 a) a

Floating a => Tensor (Mat3 a) (Vec3 a)

Floating a => Diagonal (Vec3 a) (Mat3 a)

Floating a => HasCoordinates (Mat3 a) (Vec3 a)

Floating a => RightModule (Vec3 a) (Mat3 a)

Floating a => LeftModule (Mat3 a) (Vec3 a)

Num a => LeftModule (UnitQuaternion a) (Vec3 a)

Floating a => GramSchmidt (Vec3 a, Vec3 a)

Floating a => GramSchmidt (Vec3 a, Vec3 a, Vec3 a)

data Vec4 a

Constructors

Vec4 !a !a !a !a

Instances

Typeable1 Vec4

Floating a => DotProd a Vec4

Floating a => Vector a Vec4

Floating a => Extend a Vec3 Vec4

Floating a => Extend a Vec2 Vec4

Floating a => UnitVector a Vec4 Normal4

Floating a => Interpolate a (Vec4 a)

Read a => Read (Vec4 a)

Show a => Show (Vec4 a)

(Floating a, Random a) => Random (Vec4 a)

(Floating a, Storable a) => Storable (Vec4 a)

Floating a => Dimension (Vec4 a)

Num a => Pointwise (Vec4 a)

Floating a => AbelianGroup (Vec4 a)

Floating a => HasCoordinates (Vec4 a) a

Floating a => Tensor (Mat4 a) (Vec4 a)

Floating a => Diagonal (Vec4 a) (Mat4 a)

Floating a => HasCoordinates (Mat4 a) (Vec4 a)

Floating a => RightModule (Vec4 a) (Mat4 a)

Floating a => LeftModule (Mat4 a) (Vec4 a)

Floating a => GramSchmidt (Vec4 a, Vec4 a)

Floating a => GramSchmidt (Vec4 a, Vec4 a, Vec4 a)

Floating a => GramSchmidt (Vec4 a, Vec4 a, Vec4 a, Vec4 a)

data Mat2 a

The components are row vectors

Constructors

Mat2 !(Vec2 a) !(Vec2 a)

Instances

Floating a => Vector a Mat2

Floating a => Orthogonal a Mat2 Ortho2

Floating a => Extend a Mat2 Mat4

Floating a => Extend a Mat2 Mat3

Floating a => Projective a Vec2 Mat2 Ortho2 Mat3 Proj3

Floating a => Determinant a (Mat2 a)

Floating a => MatrixNorms a (Mat2 a)

Read a => Read (Mat2 a)

Show a => Show (Mat2 a)

(Floating a, Random a) => Random (Mat2 a)

(Floating a, Storable a) => Storable (Mat2 a)

Floating a => Dimension (Mat2 a)

Floating a => Matrix (Mat2 a)

Floating a => Pointwise (Mat2 a)

Floating a => Ring (Mat2 a)

Floating a => MultSemiGroup (Mat2 a)

Floating a => AbelianGroup (Mat2 a)

Floating a => Tensor (Mat2 a) (Vec2 a)

Floating a => Diagonal (Vec2 a) (Mat2 a)

Floating a => HasCoordinates (Mat2 a) (Vec2 a)

Floating a => RightModule (Vec2 a) (Mat2 a)

Floating a => LeftModule (Mat2 a) (Vec2 a)

data Mat3 a

Constructors

Mat3 !(Vec3 a) !(Vec3 a) !(Vec3 a)

Instances

Floating a => Vector a Mat3

Floating a => Orthogonal a Mat3 Ortho3

Floating a => Extend a Mat3 Mat4

Floating a => Extend a Mat2 Mat3

Floating a => Projective a Vec3 Mat3 Ortho3 Mat4 Proj4

Floating a => Projective a Vec2 Mat2 Ortho2 Mat3 Proj3

Floating a => Determinant a (Mat3 a)

Floating a => MatrixNorms a (Mat3 a)

Read a => Read (Mat3 a)

Show a => Show (Mat3 a)

(Floating a, Random a) => Random (Mat3 a)

(Floating a, Storable a) => Storable (Mat3 a)

Floating a => Dimension (Mat3 a)

Floating a => Matrix (Mat3 a)

Floating a => Pointwise (Mat3 a)

Floating a => Ring (Mat3 a)

Floating a => MultSemiGroup (Mat3 a)

Floating a => AbelianGroup (Mat3 a)

Floating a => Tensor (Mat3 a) (Vec3 a)

Floating a => Diagonal (Vec3 a) (Mat3 a)

Floating a => HasCoordinates (Mat3 a) (Vec3 a)

Floating a => RightModule (Vec3 a) (Mat3 a)

Floating a => LeftModule (Mat3 a) (Vec3 a)

data Mat4 a

Constructors

Mat4 !(Vec4 a) !(Vec4 a) !(Vec4 a) !(Vec4 a)

Instances

Floating a => Vector a Mat4

Floating a => Orthogonal a Mat4 Ortho4

Floating a => Extend a Mat3 Mat4

Floating a => Extend a Mat2 Mat4

Floating a => Projective a Vec3 Mat3 Ortho3 Mat4 Proj4

Floating a => Determinant a (Mat4 a)

Floating a => MatrixNorms a (Mat4 a)

Read a => Read (Mat4 a)

Show a => Show (Mat4 a)

(Floating a, Random a) => Random (Mat4 a)

(Floating a, Storable a) => Storable (Mat4 a)

Floating a => Dimension (Mat4 a)

Floating a => Matrix (Mat4 a)

Floating a => Pointwise (Mat4 a)

Floating a => Ring (Mat4 a)

Floating a => MultSemiGroup (Mat4 a)

Floating a => AbelianGroup (Mat4 a)

Floating a => Tensor (Mat4 a) (Vec4 a)

Floating a => Diagonal (Vec4 a) (Mat4 a)

Floating a => HasCoordinates (Mat4 a) (Vec4 a)

Floating a => RightModule (Vec4 a) (Mat4 a)

Floating a => LeftModule (Mat4 a) (Vec4 a)

data Ortho2 a

Orthogonal matrices.

Note: the Random instances generates orthogonal matrices with determinant 1 (that is, orientation-preserving orthogonal transformations)!

Instances

Floating a => Orthogonal a Mat2 Ortho2

Floating a => Projective a Vec2 Mat2 Ortho2 Mat3 Proj3

Floating a => Determinant a (Ortho2 a)

Read a => Read (Ortho2 a)

Show a => Show (Ortho2 a)

(Floating a, Ord a, Random a) => Random (Ortho2 a)

(Floating a, Storable a) => Storable (Ortho2 a)

Floating a => Dimension (Ortho2 a)

Floating a => Matrix (Ortho2 a)

Floating a => MultSemiGroup (Ortho2 a)

data Ortho3 a

Instances

Floating a => Orthogonal a Mat3 Ortho3

Floating a => Projective a Vec3 Mat3 Ortho3 Mat4 Proj4

Floating a => Determinant a (Ortho3 a)

Read a => Read (Ortho3 a)

Show a => Show (Ortho3 a)

(Floating a, Ord a, Random a) => Random (Ortho3 a)

(Floating a, Storable a) => Storable (Ortho3 a)

Floating a => Dimension (Ortho3 a)

Floating a => Matrix (Ortho3 a)

Floating a => MultSemiGroup (Ortho3 a)

data Ortho4 a

Instances

Floating a => Orthogonal a Mat4 Ortho4

Floating a => Determinant a (Ortho4 a)

Read a => Read (Ortho4 a)

Show a => Show (Ortho4 a)

(Floating a, Ord a, Random a) => Random (Ortho4 a)

(Floating a, Storable a) => Storable (Ortho4 a)

Floating a => Dimension (Ortho4 a)

Floating a => Matrix (Ortho4 a)

Floating a => MultSemiGroup (Ortho4 a)

data Normal2 a

The assumption when dealing with these is always that they are of unit length. Also, interpolation works differently.

Instances

Typeable1 Normal2

Floating a => DotProd a Normal2

Floating a => UnitVector a Vec2 Normal2

Floating a => Interpolate a (Normal2 a)

Read a => Read (Normal2 a)

Show a => Show (Normal2 a)

(Floating a, Random a, Ord a) => Random (Normal2 a)

(Floating a, Storable a) => Storable (Normal2 a)

Floating a => Dimension (Normal2 a)

Floating a => GramSchmidt (Normal2 a, Normal2 a)

data Normal3 a

Instances

Typeable1 Normal3

Floating a => DotProd a Normal3

Floating a => UnitVector a Vec3 Normal3

Floating a => Interpolate a (Normal3 a)

Read a => Read (Normal3 a)

Show a => Show (Normal3 a)

(Floating a, Random a, Ord a) => Random (Normal3 a)

(Floating a, Storable a) => Storable (Normal3 a)

Floating a => Dimension (Normal3 a)

Floating a => CrossProd (Normal3 a)

Floating a => GramSchmidt (Normal3 a, Normal3 a)

Floating a => GramSchmidt (Normal3 a, Normal3 a, Normal3 a)

data Normal4 a

Instances

Typeable1 Normal4

Floating a => DotProd a Normal4

Floating a => UnitVector a Vec4 Normal4

Floating a => Interpolate a (Normal4 a)

Read a => Read (Normal4 a)

Show a => Show (Normal4 a)

(Floating a, Random a, Ord a) => Random (Normal4 a)

(Floating a, Storable a) => Storable (Normal4 a)

Floating a => Dimension (Normal4 a)

Floating a => GramSchmidt (Normal4 a, Normal4 a)

Floating a => GramSchmidt (Normal4 a, Normal4 a, Normal4 a)

Floating a => GramSchmidt (Normal4 a, Normal4 a, Normal4 a, Normal4 a)

data Proj3 a

Projective matrices, encoding affine transformations in dimension one less.

Instances

Floating a => Projective a Vec2 Mat2 Ortho2 Mat3 Proj3

Read a => Read (Proj3 a)

Show a => Show (Proj3 a)

(Floating a, Storable a) => Storable (Proj3 a)

Floating a => Matrix (Proj3 a)

Floating a => MultSemiGroup (Proj3 a)

data Proj4 a

Instances

Floating a => Projective a Vec3 Mat3 Ortho3 Mat4 Proj4

Read a => Read (Proj4 a)

Show a => Show (Proj4 a)

(Floating a, Storable a) => Storable (Proj4 a)

Floating a => Matrix (Proj4 a)

Floating a => MultSemiGroup (Proj4 a)

mkVec2 :: (a, a) -> Vec2 a

mkVec3 :: (a, a, a) -> Vec3 a

mkVec4 :: (a, a, a, a) -> Vec4 a

project :: (Vector a v, DotProd a v) => v a -> v a -> v a

project' :: (Vector a v, UnitVector a v u, DotProd a v) => v a -> u a -> v a

Projects the first vector down to the hyperplane orthogonal to the second (unit) vector

projectUnsafe :: (Vector a v, DotProd a v) => v a -> v a -> v a

Direction (second argument) is assumed to be a unit vector!

flipNormal :: UnitVector a v n => n a -> n a

Since unit vectors are not a group, we need a separate function.

householder :: (Vector a v, UnitVector a v u, Matrix (m a), Vector a m, Tensor (m a) (v a)) => u a -> m a

Householder matrix, see http://en.wikipedia.org/wiki/Householder_transformation. In plain words, it is the reflection to the hyperplane orthogonal to the input vector.

householderOrtho :: (Vector a v, UnitVector a v u, Matrix (m a), Vector a m, Tensor (m a) (v a), Orthogonal a m o) => u a -> o a