linear-1.20.1: Linear Algebra

License BSD-style (see the file LICENSE) Edward Kmett provisional portable Trustworthy 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.