Data.Geometry.Vector

\(d\)-dimensional vectors.

Documentation

module Data.Geometry.Vector.VectorFamily

data C (n :: Nat)

A proxy which can be used for the coordinates.

Constructors

C

Instances

Eq (C n)

Defined in Data.Geometry.Vector.VectorFixed

Methods

(==) :: C n -> C n -> Bool

(/=) :: C n -> C n -> Bool

Ord (C n)

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)

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)

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 []

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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

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

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

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

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

Orphan instances

(Arbitrary r, Arity d) => Arbitrary (Vector d r)

Methods

arbitrary :: Gen (Vector d r)

shrink :: Vector d r -> [Vector d r]