License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell98

Linear.Affine

Description

Operations on affine spaces.

Synopsis

Documentation

class Additive (Diff p) => Affine p where Source

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 :: * -> * Source

Methods

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

Get the difference between two points as a vector offset.

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

Add a vector offset to a point.

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

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 Source

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

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

Distance between two points in an affine space

newtype Point f a Source

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)
Serial1 f => Serial1 (Point f)
Apply f => Apply (Point f)
Bind f => Bind (Point f)
Eq1 f => Eq1 (Point f)
Ord1 f => Ord1 (Point f)
Read1 f => Read1 (Point f)
Show1 f => Show1 (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)
(Data (f a), Typeable (* -> ) f, Typeable a) => Data (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)
Binary (f a) => Binary (Point f a)
Serial (f a) => Serial (Point f a)
Serialize (f a) => Serialize (Point f a)
NFData (f a) => NFData (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)
Typeable ((* -> ) -> -> *) Point
(~) * 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) Source

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

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

Vector spaces have origins.

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

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