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 [] Source
Affine Identity Source
Affine Complex Source
Affine ZipList Source
Affine Maybe Source
Affine IntMap Source
Affine Vector Source
Affine V0 Source
Affine V1 Source
Affine V2 Source
Affine V3 Source
Affine V4 Source
Affine Plucker Source
Affine Quaternion Source
Affine ((->) b) Source
Ord k => Affine (Map k) Source
(Eq k, Hashable k) => Affine (HashMap k) Source
Additive f => Affine (Point f) Source
Dim * n => Affine (V * n) Source

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

Unbox (f a) => Vector Vector (Point f a) Source
Unbox (f a) => MVector MVector (Point f a) Source
Monad f => Monad (Point f) Source
Functor f => Functor (Point f) Source
Applicative f => Applicative (Point f) Source
Foldable f => Foldable (Point f) Source
Traversable f => Traversable (Point f) Source
Generic1 (Point f) Source
Distributive f => Distributive (Point f) Source
Representable f => Representable (Point f) Source
Serial1 f => Serial1 (Point f) Source
Apply f => Apply (Point f) Source
Bind f => Bind (Point f) Source
Eq1 f => Eq1 (Point f) Source
Ord1 f => Ord1 (Point f) Source
Read1 f => Read1 (Point f) Source
Show1 f => Show1 (Point f) Source
Additive f => Additive (Point f) Source
Metric f => Metric (Point f) Source
R1 f => R1 (Point f) Source
R2 f => R2 (Point f) Source
R3 f => R3 (Point f) Source
R4 f => R4 (Point f) Source
Additive f => Affine (Point f) Source
Eq (f a) => Eq (Point f a) Source
Fractional (f a) => Fractional (Point f a) Source
(Data (f a), Typeable (* -> ) f, Typeable a) => Data (Point f a) Source
Num (f a) => Num (Point f a) Source
Ord (f a) => Ord (Point f a) Source
Read (f a) => Read (Point f a) Source
Show (f a) => Show (Point f a) Source
Ix (f a) => Ix (Point f a) Source
Generic (Point f a) Source
Storable (f a) => Storable (Point f a) Source
Binary (f a) => Binary (Point f a) Source
Serial (f a) => Serial (Point f a) Source
Serialize (f a) => Serialize (Point f a) Source
NFData (f a) => NFData (Point f a) Source
Hashable (f a) => Hashable (Point f a) Source
Unbox (f a) => Unbox (Point f a) Source
Ixed (f a) => Ixed (Point f a) Source
Wrapped (Point f a) Source
Epsilon (f a) => Epsilon (Point f a) Source
(~) * t (Point g b) => Rewrapped (Point f a) t Source
Traversable f => Each (Point f a) (Point f b) a b Source
data MVector s (Point f a) = MV_P !(MVector s (f a)) Source
type Rep1 (Point f) Source
type Rep (Point f) = Rep f Source
type Diff (Point f) = f Source
type Rep (Point f a) Source
data Vector (Point f a) = V_P !(Vector (f a)) Source
type Index (Point f a) = Index (f a) Source
type IxValue (Point f a) = IxValue (f a) Source
type Unwrapped (Point f a) = f a Source

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.