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
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
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
replicate :: Vector v a => a -> v a
imap :: (Vector v a, Vector v b) => (Int -> a -> b) -> v a -> v b
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

data C (n :: Nat) Source #

A proxy which can be used for the coordinates.

Constructors

C

Instances

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 #

Minimal complete definition

(.-.), (.+^)

Associated Types

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

Methods

(.-.) :: 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 #

Instances

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 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 #
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 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 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 #
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 #
(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 #
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 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 #

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 Source #

Test if v is a scalar multiple of u.

>>> Vector2 1 1 `isScalarMultipleOf` Vector2 10 10
True
>>> Vector2 1 1 `isScalarMultipleOf` Vector2 10 1
False
>>> 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

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

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

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

imap :: (Vector v a, Vector v b) => (Int -> a -> b) -> v a -> v b #

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

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

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

Orphan instances

(Arbitrary r, Arity d) => Arbitrary (Vector d r) Source #
Instance details Methods arbitrary :: Gen (Vector d r) shrink :: Vector d r -> [Vector d r]