Linear.Affine

Operations on affine spaces.

Documentation

class Additive (Diff p) => Affine p 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 :: * -> *

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

Affine []

Affine Complex

Affine ZipList

Affine Maybe

Affine Identity

Affine IntMap

Affine Vector

Affine V0

Affine V1

Affine V2

Affine V3

Affine V4

Affine Plucker

Affine Quaternion

Affine ((->) b)

Ord k => Affine (Map k)

(Eq k, Hashable k) => Affine (HashMap k)

Additive f => Affine (Point f)

Dim * n => Affine (V * n)

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

newtype Point f a

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

Constructors

P (f a)

Instances

Monad f => Monad (Point f)

Functor f => Functor (Point f)

Applicative f => Applicative (Point f)

Foldable f => Foldable (Point f)

Traversable f => Traversable (Point f)

Generic1 (Point f)

Distributive f => Distributive (Point f)

Representable f => Representable (Point f)

Apply f => Apply (Point f)

Bind f => Bind (Point f)

Additive f => Additive (Point f)

Metric f => Metric (Point f)

R1 f => R1 (Point f)

R2 f => R2 (Point f)

R3 f => R3 (Point f)

R4 f => R4 (Point f)

Additive f => Affine (Point f)

Eq (f a) => Eq (Point f a)

Fractional (f a) => Fractional (Point f a)

Num (f a) => Num (Point f a)

Ord (f a) => Ord (Point f a)

Read (f a) => Read (Point f a)

Show (f a) => Show (Point f a)

Ix (f a) => Ix (Point f a)

Generic (Point f a)

Storable (f a) => Storable (Point f a)

Hashable (f a) => Hashable (Point f a)

Ixed (f a) => Ixed (Point f a)

Wrapped (Point f a)

Epsilon (f a) => Epsilon (Point f a)

(~) * t (Point g b) => Rewrapped (Point f a) t

Traversable f => Each (Point f a) (Point f b) a b

type Rep1 (Point f)

type Rep (Point f) = Rep f

type Diff (Point f) = f

type Rep (Point f a)

type Index (Point f a) = Index (f a)

type IxValue (Point f a) = IxValue (f a)

type Unwrapped (Point f a) = f a

lensP :: Lens' (Point g a) (g a)

_Point :: Iso' (Point f a) (f a)

origin :: (Additive f, Num a) => Point f a

Vector spaces have origins.

relative :: (Additive f, Num a) => Point f a -> Iso' (Point f a) (f a)

An isomorphism between points and vectors, given a reference point.