linear-1.20.4: Linear Algebra

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 Source Source Source Source Source Source Source Source Source Source Source Source 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 Source Source 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.