Copyright	(C) Frank Staals
License	see the LICENSE file
Maintainer	Frank Staals
Safe Haskell	None
Language	Haskell2010

Data.Geometry.Vector

Contents

Orphan instances

Description

\(d\)-dimensional vectors.

Synopsis

module Data.Geometry.Vector.VectorFamily
outer :: (Functor f, Functor g, Num a) => f a -> g a -> f (g a)
unit :: (Additive t, Num a) => ASetter' (t a) a -> t a
scaled :: (Traversable t, Num a) => t a -> t (t a)
basisFor :: (Traversable t, Num a) => t b -> [t a]
basis :: (Additive t, Traversable t, Num a) => [t a]
(^/) :: (Functor f, Fractional a) => f a -> a -> f a
(^*) :: (Functor f, Num a) => f a -> a -> f a
(*^) :: (Functor f, Num a) => a -> f a -> f a
sumV :: (Foldable f, Additive v, Num a) => f (v a) -> v a
negated :: (Functor f, Num a) => f a -> f a
class Functor f => Additive (f :: Type -> Type) where
- zero :: Num a => f a
- (^+^) :: Num a => f a -> f a -> f a
- (^-^) :: Num a => f a -> f a -> f a
- lerp :: Num a => a -> f a -> f a -> f a
- liftU2 :: (a -> a -> a) -> f a -> f a -> f a
- liftI2 :: (a -> b -> c) -> f a -> f b -> f c
data C (n :: Nat) = C
class Additive (Diff p) => Affine (p :: Type -> Type) where
- type Diff (p :: Type -> Type) :: Type -> Type
- (.-.) :: Num a => p a -> p a -> Diff p a
- (.+^) :: Num a => p a -> Diff p a -> p a
- (.-^) :: Num a => p a -> Diff p a -> p a
quadrance :: (Metric f, Num a) => f a -> a
qdA :: (Affine p, Foldable (Diff p), Num a) => p a -> p a -> a
distanceA :: (Floating a, Foldable (Diff p), Affine p) => p a -> p a -> a
dot :: (Metric f, Num a) => f a -> f a -> a
norm :: (Metric f, Floating a) => f a -> a
signorm :: (Metric f, Floating a) => f a -> f a
isScalarMultipleOf :: (Eq r, Fractional r, Arity d) => Vector d r -> Vector d r -> Bool
scalarMultiple :: (Eq r, Fractional r, Arity d) => Vector d r -> Vector d r -> Maybe r
sameDirection :: (Eq r, Num r, Arity d) => Vector d r -> Vector d r -> Bool
replicate :: Vector v a => a -> v a
xComponent :: (1 <= d, Arity d) => Lens' (Vector d r) r
yComponent :: (2 <= d, Arity d) => Lens' (Vector d r) r
zComponent :: (3 <= d, Arity d) => Lens' (Vector d r) r

Documentation

module Data.Geometry.Vector.VectorFamily

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

Outer (tensor) product of two vectors

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

Create a unit vector.

>>> unit _x :: V2 Int
V2 1 0

scaled :: (Traversable t, Num a) => t a -> t (t a) #

Produce a diagonal (scale) matrix from a vector.

>>> scaled (V2 2 3)
V2 (V2 2 0) (V2 0 3)

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

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

basis :: (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.

(^/) :: (Functor f, Fractional a) => f a -> a -> f a infixl 7 #

Compute division by a scalar on the right.

(^*) :: (Functor f, Num a) => f a -> a -> f a infixl 7 #

Compute the right scalar product

>>> V2 3 4 ^* 2
V2 6 8

(*^) :: (Functor f, Num a) => a -> f a -> f a infixl 7 #

Compute the left scalar product

>>> 2 *^ V2 3 4
V2 6 8

sumV :: (Foldable f, Additive v, Num a) => f (v a) -> v a #

Sum over multiple vectors

>>> sumV [V2 1 1, V2 3 4]
V2 4 5

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

Compute the negation of a vector

>>> negated (V2 2 4)
V2 (-2) (-4)

class Functor f => Additive (f :: Type -> Type) where #

A vector is an additive group with additional structure.

Minimal complete definition

Nothing

Methods

zero :: Num a => f a #

The zero vector

(^+^) :: Num a => f a -> f a -> f a infixl 6 #

Compute the sum of two vectors

>>> V2 1 2 ^+^ V2 3 4
V2 4 6

(^-^) :: Num a => f a -> f a -> f a infixl 6 #

Compute the difference between two vectors

>>> V2 4 5 ^-^ V2 3 1
V2 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.

For a dense vector this is equivalent to liftA2.
For a sparse vector this is equivalent to intersectionWith.

Instances

Instances details

Additive []
Instance details Defined in Linear.Vector Methods zero :: Num a => [a] # (^+^) :: Num a => [a] -> [a] -> [a] # (^-^) :: Num a => [a] -> [a] -> [a] # lerp :: Num a => a -> [a] -> [a] -> [a] # liftU2 :: (a -> a -> a) -> [a] -> [a] -> [a] # liftI2 :: (a -> b -> c) -> [a] -> [b] -> [c] #
Additive Maybe
Instance details Defined in Linear.Vector Methods zero :: Num a => Maybe a # (^+^) :: Num a => Maybe a -> Maybe a -> Maybe a # (^-^) :: Num a => Maybe a -> Maybe a -> Maybe a # lerp :: Num a => a -> Maybe a -> Maybe a -> Maybe a # liftU2 :: (a -> a -> a) -> Maybe a -> Maybe a -> Maybe a # liftI2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c #
Additive Complex
Instance details Defined in Linear.Vector Methods zero :: Num a => Complex a # (^+^) :: Num a => Complex a -> Complex a -> Complex a # (^-^) :: Num a => Complex a -> Complex a -> Complex a # lerp :: Num a => a -> Complex a -> Complex a -> Complex a # liftU2 :: (a -> a -> a) -> Complex a -> Complex a -> Complex a # liftI2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c #
Additive ZipList
Instance details Defined in Linear.Vector Methods zero :: Num a => ZipList a # (^+^) :: Num a => ZipList a -> ZipList a -> ZipList a # (^-^) :: Num a => ZipList a -> ZipList a -> ZipList a # lerp :: Num a => a -> ZipList a -> ZipList a -> ZipList a # liftU2 :: (a -> a -> a) -> ZipList a -> ZipList a -> ZipList a # liftI2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c #
Additive Identity
Instance details Defined in Linear.Vector Methods zero :: Num a => Identity a # (^+^) :: Num a => Identity a -> Identity a -> Identity a # (^-^) :: Num a => Identity a -> Identity a -> Identity a # lerp :: Num a => a -> Identity a -> Identity a -> Identity a # liftU2 :: (a -> a -> a) -> Identity a -> Identity a -> Identity a # liftI2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c #
Additive IntMap
Instance details Defined in Linear.Vector Methods zero :: Num a => IntMap a # (^+^) :: Num a => IntMap a -> IntMap a -> IntMap a # (^-^) :: Num a => IntMap a -> IntMap a -> IntMap a # lerp :: Num a => a -> IntMap a -> IntMap a -> IntMap a # liftU2 :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a # liftI2 :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c #
Additive Vector
Instance details Defined in Linear.Vector Methods zero :: Num a => Vector a # (^+^) :: Num a => Vector a -> Vector a -> Vector a # (^-^) :: Num a => Vector a -> Vector a -> Vector a # lerp :: Num a => a -> Vector a -> Vector a -> Vector a # liftU2 :: (a -> a -> a) -> Vector a -> Vector a -> Vector a # liftI2 :: (a -> b -> c) -> Vector a -> Vector b -> Vector c #
Additive Plucker
Instance details Defined in Linear.Plucker Methods zero :: Num a => Plucker a # (^+^) :: Num a => Plucker a -> Plucker a -> Plucker a # (^-^) :: Num a => Plucker a -> Plucker a -> Plucker a # lerp :: Num a => a -> Plucker a -> Plucker a -> Plucker a # liftU2 :: (a -> a -> a) -> Plucker a -> Plucker a -> Plucker a # liftI2 :: (a -> b -> c) -> Plucker a -> Plucker b -> Plucker c #
Additive Quaternion
Instance details Defined in Linear.Quaternion Methods zero :: Num a => Quaternion a # (^+^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a # (^-^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a # lerp :: Num a => a -> Quaternion a -> Quaternion a -> Quaternion a # liftU2 :: (a -> a -> a) -> Quaternion a -> Quaternion a -> Quaternion a # liftI2 :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c #
Additive V0
Instance details Defined in Linear.V0 Methods zero :: Num a => V0 a # (^+^) :: Num a => V0 a -> V0 a -> V0 a # (^-^) :: Num a => V0 a -> V0 a -> V0 a # lerp :: Num a => a -> V0 a -> V0 a -> V0 a # liftU2 :: (a -> a -> a) -> V0 a -> V0 a -> V0 a # liftI2 :: (a -> b -> c) -> V0 a -> V0 b -> V0 c #
Additive V4
Instance details Defined in Linear.V4 Methods zero :: Num a => V4 a # (^+^) :: Num a => V4 a -> V4 a -> V4 a # (^-^) :: Num a => V4 a -> V4 a -> V4 a # lerp :: Num a => a -> V4 a -> V4 a -> V4 a # liftU2 :: (a -> a -> a) -> V4 a -> V4 a -> V4 a # liftI2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c #
Additive V3
Instance details Defined in Linear.V3 Methods zero :: Num a => V3 a # (^+^) :: Num a => V3 a -> V3 a -> V3 a # (^-^) :: Num a => V3 a -> V3 a -> V3 a # lerp :: Num a => a -> V3 a -> V3 a -> V3 a # liftU2 :: (a -> a -> a) -> V3 a -> V3 a -> V3 a # liftI2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c #
Additive V2
Instance details Defined in Linear.V2 Methods zero :: Num a => V2 a # (^+^) :: Num a => V2 a -> V2 a -> V2 a # (^-^) :: Num a => V2 a -> V2 a -> V2 a # lerp :: Num a => a -> V2 a -> V2 a -> V2 a # liftU2 :: (a -> a -> a) -> V2 a -> V2 a -> V2 a # liftI2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c #
Additive V1
Instance details Defined in Linear.V1 Methods zero :: Num a => V1 a # (^+^) :: Num a => V1 a -> V1 a -> V1 a # (^-^) :: Num a => V1 a -> V1 a -> V1 a # lerp :: Num a => a -> V1 a -> V1 a -> V1 a # liftU2 :: (a -> a -> a) -> V1 a -> V1 a -> V1 a # liftI2 :: (a -> b -> c) -> V1 a -> V1 b -> V1 c #
(Eq k, Hashable k) => Additive (HashMap k)
Instance details Defined in Linear.Vector Methods zero :: Num a => HashMap k a # (^+^) :: Num a => HashMap k a -> HashMap k a -> HashMap k a # (^-^) :: Num a => HashMap k a -> HashMap k a -> HashMap k a # lerp :: Num a => a -> HashMap k a -> HashMap k a -> HashMap k a # liftU2 :: (a -> a -> a) -> HashMap k a -> HashMap k a -> HashMap k a # liftI2 :: (a -> b -> c) -> HashMap k a -> HashMap k b -> HashMap k c #
Ord k => Additive (Map k)
Instance details Defined in Linear.Vector Methods zero :: Num a => Map k a # (^+^) :: Num a => Map k a -> Map k a -> Map k a # (^-^) :: Num a => Map k a -> Map k a -> Map k a # lerp :: Num a => a -> Map k a -> Map k a -> Map k a # liftU2 :: (a -> a -> a) -> Map k a -> Map k a -> Map k a # liftI2 :: (a -> b -> c) -> Map k a -> Map k b -> Map k c #
Additive f => Additive (Point f)
Instance details Defined in Linear.Affine Methods zero :: Num a => Point f a # (^+^) :: Num a => Point f a -> Point f a -> Point f a # (^-^) :: Num a => Point f a -> Point f a -> Point f a # lerp :: Num a => a -> Point f a -> Point f a -> Point f a # liftU2 :: (a -> a -> a) -> Point f a -> Point f a -> Point f a # liftI2 :: (a -> b -> c) -> Point f a -> Point f b -> Point f c #
Arity d => Additive (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFixed Methods zero :: Num a => Vector d a # (^+^) :: Num a => Vector d a -> Vector d a -> Vector d a # (^-^) :: Num a => Vector d a -> Vector d a -> Vector d a # lerp :: Num a => a -> Vector d a -> Vector d a -> Vector d a # liftU2 :: (a -> a -> a) -> Vector d a -> Vector d a -> Vector d a # liftI2 :: (a -> b -> c) -> Vector d a -> Vector d b -> Vector d c #
ImplicitArity d => Additive (VectorFamily d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamilyPeano Methods zero :: Num a => VectorFamily d a # (^+^) :: Num a => VectorFamily d a -> VectorFamily d a -> VectorFamily d a # (^-^) :: Num a => VectorFamily d a -> VectorFamily d a -> VectorFamily d a # lerp :: Num a => a -> VectorFamily d a -> VectorFamily d a -> VectorFamily d a # liftU2 :: (a -> a -> a) -> VectorFamily d a -> VectorFamily d a -> VectorFamily d a # liftI2 :: (a -> b -> c) -> VectorFamily d a -> VectorFamily d b -> VectorFamily d c #
Arity d => Additive (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods zero :: Num a => Vector d a # (^+^) :: Num a => Vector d a -> Vector d a -> Vector d a # (^-^) :: Num a => Vector d a -> Vector d a -> Vector d a # lerp :: Num a => a -> Vector d a -> Vector d a -> Vector d a # liftU2 :: (a -> a -> a) -> Vector d a -> Vector d a -> Vector d a # liftI2 :: (a -> b -> c) -> Vector d a -> Vector d b -> Vector d c #
Dim n => Additive (V n)
Instance details Defined in Linear.V Methods zero :: Num a => V n a # (^+^) :: Num a => V n a -> V n a -> V n a # (^-^) :: Num a => V n a -> V n a -> V n a # lerp :: Num a => a -> V n a -> V n a -> V n a # liftU2 :: (a -> a -> a) -> V n a -> V n a -> V n a # liftI2 :: (a -> b -> c) -> V n a -> V n b -> V n c #
Additive ((->) b :: Type -> Type)
Instance details Defined in Linear.Vector Methods zero :: Num a => b -> a # (^+^) :: Num a => (b -> a) -> (b -> a) -> b -> a # (^-^) :: Num a => (b -> a) -> (b -> a) -> b -> a # lerp :: Num a => a -> (b -> a) -> (b -> a) -> b -> a # liftU2 :: (a -> a -> a) -> (b -> a) -> (b -> a) -> b -> a # liftI2 :: (a -> b0 -> c) -> (b -> a) -> (b -> b0) -> b -> c #
(Additive f, Additive g) => Additive (Product f g)
Instance details Defined in Linear.Vector Methods zero :: Num a => Product f g a # (^+^) :: Num a => Product f g a -> Product f g a -> Product f g a # (^-^) :: Num a => Product f g a -> Product f g a -> Product f g a # lerp :: Num a => a -> Product f g a -> Product f g a -> Product f g a # liftU2 :: (a -> a -> a) -> Product f g a -> Product f g a -> Product f g a # liftI2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c #
(Additive f, Additive g) => Additive (Compose f g)
Instance details Defined in Linear.Vector Methods zero :: Num a => Compose f g a # (^+^) :: Num a => Compose f g a -> Compose f g a -> Compose f g a # (^-^) :: Num a => Compose f g a -> Compose f g a -> Compose f g a # lerp :: Num a => a -> Compose f g a -> Compose f g a -> Compose f g a # liftU2 :: (a -> a -> a) -> Compose f g a -> Compose f g a -> Compose f g a # liftI2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c #

data C (n :: Nat) Source #

A proxy which can be used for the coordinates.

Constructors

C

Instances

Instances details

Eq (C n) Source #
Instance details Defined in Data.Geometry.Vector.VectorFixed Methods (==) :: C n -> C n -> Bool # (/=) :: C n -> C n -> Bool #
Ord (C n) Source #
Instance details Defined in Data.Geometry.Vector.VectorFixed Methods compare :: C n -> C n -> Ordering # (<) :: C n -> C n -> Bool # (<=) :: C n -> C n -> Bool # (>) :: C n -> C n -> Bool # (>=) :: C n -> C n -> Bool # max :: C n -> C n -> C n # min :: C n -> C n -> C n #
Read (C n) Source #
Instance details Defined in Data.Geometry.Vector.VectorFixed Methods readsPrec :: Int -> ReadS (C n) # readList :: ReadS [C n] # readPrec :: ReadPrec (C n) # readListPrec :: ReadPrec [C n] #
Show (C n) Source #
Instance details Defined in Data.Geometry.Vector.VectorFixed Methods showsPrec :: Int -> C n -> ShowS # show :: C n -> String # showList :: [C n] -> ShowS #

class 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@

Minimal complete definition

(.-.), (.+^)

Associated Types

type Diff (p :: Type -> Type) :: Type -> Type #

Methods

(.-.) :: Num a => p a -> p a -> Diff p a infixl 6 #

Get the difference between two points as a vector offset.

(.+^) :: Num a => p a -> Diff p a -> p a infixl 6 #

Add a vector offset to a point.

(.-^) :: Num a => p a -> Diff p a -> p a infixl 6 #

Subtract a vector offset from a point.

Instances

Instances details

Affine []
Instance details Defined in Linear.Affine Associated Types type Diff [] :: Type -> Type # Methods (.-.) :: Num a => [a] -> [a] -> Diff [] a # (.+^) :: Num a => [a] -> Diff [] a -> [a] # (.-^) :: Num a => [a] -> Diff [] a -> [a] #
Affine Maybe
Instance details Defined in Linear.Affine Associated Types type Diff Maybe :: Type -> Type # Methods (.-.) :: Num a => Maybe a -> Maybe a -> Diff Maybe a # (.+^) :: Num a => Maybe a -> Diff Maybe a -> Maybe a # (.-^) :: Num a => Maybe a -> Diff Maybe a -> Maybe a #
Affine Complex
Instance details Defined in Linear.Affine Associated Types type Diff Complex :: Type -> Type # Methods (.-.) :: Num a => Complex a -> Complex a -> Diff Complex a # (.+^) :: Num a => Complex a -> Diff Complex a -> Complex a # (.-^) :: Num a => Complex a -> Diff Complex a -> Complex a #
Affine ZipList
Instance details Defined in Linear.Affine Associated Types type Diff ZipList :: Type -> Type # Methods (.-.) :: Num a => ZipList a -> ZipList a -> Diff ZipList a # (.+^) :: Num a => ZipList a -> Diff ZipList a -> ZipList a # (.-^) :: Num a => ZipList a -> Diff ZipList a -> ZipList a #
Affine Identity
Instance details Defined in Linear.Affine Associated Types type Diff Identity :: Type -> Type # Methods (.-.) :: Num a => Identity a -> Identity a -> Diff Identity a # (.+^) :: Num a => Identity a -> Diff Identity a -> Identity a # (.-^) :: Num a => Identity a -> Diff Identity a -> Identity a #
Affine IntMap
Instance details Defined in Linear.Affine Associated Types type Diff IntMap :: Type -> Type # Methods (.-.) :: Num a => IntMap a -> IntMap a -> Diff IntMap a # (.+^) :: Num a => IntMap a -> Diff IntMap a -> IntMap a # (.-^) :: Num a => IntMap a -> Diff IntMap a -> IntMap a #
Affine Vector
Instance details Defined in Linear.Affine Associated Types type Diff Vector :: Type -> Type # Methods (.-.) :: Num a => Vector a -> Vector a -> Diff Vector a # (.+^) :: Num a => Vector a -> Diff Vector a -> Vector a # (.-^) :: Num a => Vector a -> Diff Vector a -> Vector a #
Affine Plucker
Instance details Defined in Linear.Affine Associated Types type Diff Plucker :: Type -> Type # Methods (.-.) :: Num a => Plucker a -> Plucker a -> Diff Plucker a # (.+^) :: Num a => Plucker a -> Diff Plucker a -> Plucker a # (.-^) :: Num a => Plucker a -> Diff Plucker a -> Plucker a #
Affine Quaternion
Instance details Defined in Linear.Affine Associated Types type Diff Quaternion :: Type -> Type # Methods (.-.) :: Num a => Quaternion a -> Quaternion a -> Diff Quaternion a # (.+^) :: Num a => Quaternion a -> Diff Quaternion a -> Quaternion a # (.-^) :: Num a => Quaternion a -> Diff Quaternion a -> Quaternion a #
Affine V0
Instance details Defined in Linear.Affine Associated Types type Diff V0 :: Type -> Type # Methods (.-.) :: Num a => V0 a -> V0 a -> Diff V0 a # (.+^) :: Num a => V0 a -> Diff V0 a -> V0 a # (.-^) :: Num a => V0 a -> Diff V0 a -> V0 a #
Affine V4
Instance details Defined in Linear.Affine Associated Types type Diff V4 :: Type -> Type # Methods (.-.) :: Num a => V4 a -> V4 a -> Diff V4 a # (.+^) :: Num a => V4 a -> Diff V4 a -> V4 a # (.-^) :: Num a => V4 a -> Diff V4 a -> V4 a #
Affine V3
Instance details Defined in Linear.Affine Associated Types type Diff V3 :: Type -> Type # Methods (.-.) :: Num a => V3 a -> V3 a -> Diff V3 a # (.+^) :: Num a => V3 a -> Diff V3 a -> V3 a # (.-^) :: Num a => V3 a -> Diff V3 a -> V3 a #
Affine V2
Instance details Defined in Linear.Affine Associated Types type Diff V2 :: Type -> Type # Methods (.-.) :: Num a => V2 a -> V2 a -> Diff V2 a # (.+^) :: Num a => V2 a -> Diff V2 a -> V2 a # (.-^) :: Num a => V2 a -> Diff V2 a -> V2 a #
Affine V1
Instance details Defined in Linear.Affine Associated Types type Diff V1 :: Type -> Type # Methods (.-.) :: Num a => V1 a -> V1 a -> Diff V1 a # (.+^) :: Num a => V1 a -> Diff V1 a -> V1 a # (.-^) :: Num a => V1 a -> Diff V1 a -> V1 a #
(Eq k, Hashable k) => Affine (HashMap k)
Instance details Defined in Linear.Affine Associated Types type Diff (HashMap k) :: Type -> Type # Methods (.-.) :: Num a => HashMap k a -> HashMap k a -> Diff (HashMap k) a # (.+^) :: Num a => HashMap k a -> Diff (HashMap k) a -> HashMap k a # (.-^) :: Num a => HashMap k a -> Diff (HashMap k) a -> HashMap k a #
Ord k => Affine (Map k)
Instance details Defined in Linear.Affine Associated Types type Diff (Map k) :: Type -> Type # Methods (.-.) :: Num a => Map k a -> Map k a -> Diff (Map k) a # (.+^) :: Num a => Map k a -> Diff (Map k) a -> Map k a # (.-^) :: Num a => Map k a -> Diff (Map k) a -> Map k a #
Additive f => Affine (Point f)
Instance details Defined in Linear.Affine Associated Types type Diff (Point f) :: Type -> Type # Methods (.-.) :: Num a => Point f a -> Point f a -> Diff (Point f) a # (.+^) :: Num a => Point f a -> Diff (Point f) a -> Point f a # (.-^) :: Num a => Point f a -> Diff (Point f) a -> Point f a #
Arity d => Affine (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFixed Associated Types type Diff (Vector d) :: Type -> Type # Methods (.-.) :: Num a => Vector d a -> Vector d a -> Diff (Vector d) a # (.+^) :: Num a => Vector d a -> Diff (Vector d) a -> Vector d a # (.-^) :: Num a => Vector d a -> Diff (Vector d) a -> Vector d a #
ImplicitArity d => Affine (VectorFamily d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamilyPeano Associated Types type Diff (VectorFamily d) :: Type -> Type # Methods (.-.) :: Num a => VectorFamily d a -> VectorFamily d a -> Diff (VectorFamily d) a # (.+^) :: Num a => VectorFamily d a -> Diff (VectorFamily d) a -> VectorFamily d a # (.-^) :: Num a => VectorFamily d a -> Diff (VectorFamily d) a -> VectorFamily d a #
Arity d => Affine (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Associated Types type Diff (Vector d) :: Type -> Type # Methods (.-.) :: Num a => Vector d a -> Vector d a -> Diff (Vector d) a # (.+^) :: Num a => Vector d a -> Diff (Vector d) a -> Vector d a # (.-^) :: Num a => Vector d a -> Diff (Vector d) a -> Vector d a #
Arity d => Affine (Point d) Source #
Instance details Defined in Data.Geometry.Point.Internal Associated Types type Diff (Point d) :: Type -> Type # Methods (.-.) :: Num a => Point d a -> Point d a -> Diff (Point d) a # (.+^) :: Num a => Point d a -> Diff (Point d) a -> Point d a # (.-^) :: Num a => Point d a -> Diff (Point d) a -> Point d a #
Dim n => Affine (V n)
Instance details Defined in Linear.Affine Associated Types type Diff (V n) :: Type -> Type # Methods (.-.) :: Num a => V n a -> V n a -> Diff (V n) a # (.+^) :: Num a => V n a -> Diff (V n) a -> V n a # (.-^) :: Num a => V n a -> Diff (V n) a -> V n a #
Affine ((->) b :: Type -> Type)
Instance details Defined in Linear.Affine Associated Types type Diff ((->) b) :: Type -> Type # Methods (.-.) :: Num a => (b -> a) -> (b -> a) -> Diff ((->) b) a # (.+^) :: Num a => (b -> a) -> Diff ((->) b) a -> b -> a # (.-^) :: Num a => (b -> a) -> Diff ((->) b) a -> b -> a #
(Affine f, Affine g) => Affine (Product f g)
Instance details Defined in Linear.Affine Associated Types type Diff (Product f g) :: Type -> Type # Methods (.-.) :: Num a => Product f g a -> Product f g a -> Diff (Product f g) a # (.+^) :: Num a => Product f g a -> Diff (Product f g) a -> Product f g a # (.-^) :: Num a => Product f g a -> Diff (Product f g) a -> Product f g a #

quadrance :: (Metric f, Num a) => f a -> a #

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

qdA :: (Affine p, Foldable (Diff p), Num a) => p a -> p a -> a #

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

distanceA :: (Floating a, Foldable (Diff p), Affine p) => p a -> p a -> a #

Distance between two points in an affine space

dot :: (Metric f, 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.

>>> V2 1 2 `dot` V2 3 4
11

norm :: (Metric f, Floating a) => f a -> a #

Compute the norm of a vector in a metric space

signorm :: (Metric f, Floating a) => f a -> f a #

Convert a non-zero vector to unit vector.

isScalarMultipleOf :: (Eq r, Fractional r, Arity d) => Vector d r -> Vector d r -> Bool Source #

'isScalarmultipleof u v' test if v is a scalar multiple of u.

>>> Vector2 1 1 `isScalarMultipleOf` Vector2 10 10
True
>>> Vector3 1 1 2 `isScalarMultipleOf` Vector3 10 10 20
True
>>> Vector2 1 1 `isScalarMultipleOf` Vector2 10 1
False
>>> Vector2 1 1 `isScalarMultipleOf` Vector2 (-1) (-1)
True
>>> Vector2 1 1 `isScalarMultipleOf` Vector2 11.1 11.1
True
>>> Vector2 1 1 `isScalarMultipleOf` Vector2 11.1 11.2
False
>>> Vector2 2 1 `isScalarMultipleOf` Vector2 11.1 11.2
False
>>> Vector2 2 1 `isScalarMultipleOf` Vector2 4 2
True
>>> Vector2 2 1 `isScalarMultipleOf` Vector2 4 0
False
>>> Vector3 2 1 0 `isScalarMultipleOf` Vector3 4 0 5
False
>>> Vector3 0 0 0 `isScalarMultipleOf` Vector3 4 0 5
True

scalarMultiple :: (Eq r, Fractional r, Arity d) => Vector d r -> Vector d r -> Maybe r Source #

scalarMultiple u v computes the scalar labmda s.t. v = lambda * u (if it exists)

sameDirection :: (Eq r, Num r, Arity d) => Vector d r -> Vector d r -> Bool Source #

Given two colinar vectors, u and v, test if they point in the same direction, i.e. iff scalarMultiple' u v == Just lambda, with lambda > 0

pre: u and v are colinear, u and v are non-zero

replicate :: Vector v a => a -> v a #

Replicate value n times.

Examples:

>>> import Data.Vector.Fixed.Boxed (Vec2)
>>> replicate 1 :: Vec2 Int
fromList [1,1]

>>> replicate 2 :: (Double,Double,Double)
(2.0,2.0,2.0)

>>> import Data.Vector.Fixed.Boxed (Vec4)
>>> replicate "foo" :: Vec4 String
fromList ["foo","foo","foo","foo"]

xComponent :: (1 <= d, Arity d) => Lens' (Vector d r) r Source #

Shorthand to access the first component

>>> Vector3 1 2 3 ^. xComponent
1
>>> Vector2 1 2 & xComponent .~ 10
Vector2 10 2

yComponent :: (2 <= d, Arity d) => Lens' (Vector d r) r Source #

Shorthand to access the second component

>>> Vector3 1 2 3 ^. yComponent
2
>>> Vector2 1 2 & yComponent .~ 10
Vector2 1 10

zComponent :: (3 <= d, Arity d) => Lens' (Vector d r) r Source #

Shorthand to access the third component

>>> Vector3 1 2 3 ^. zComponent
3
>>> Vector3 1 2 3 & zComponent .~ 10
Vector3 1 2 10

Orphan instances

Arity d => Arbitrary1 (Vector d) Source #
Instance details Methods liftArbitrary :: Gen a -> Gen (Vector d a) # liftShrink :: (a -> [a]) -> Vector d a -> [Vector d a] #
(Random r, Arity d) => Random (Vector d r) Source #
Instance details Methods randomR :: RandomGen g => (Vector d r, Vector d r) -> g -> (Vector d r, g) # random :: RandomGen g => g -> (Vector d r, g) # randomRs :: RandomGen g => (Vector d r, Vector d r) -> g -> [Vector d r] # randoms :: RandomGen g => g -> [Vector d r] #
(Arbitrary r, Arity d) => Arbitrary (Vector d r) Source #
Instance details Methods arbitrary :: Gen (Vector d r) # shrink :: Vector d r -> [Vector d r] #