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.
- class Additive (Diff p) => Affine p where
- qdA :: (Affine p, Foldable (Diff p), Num a) => p a -> p a -> a
- distanceA :: (Floating a, Foldable (Diff p), Affine p) => p a -> p a -> a
- newtype Point f a = P (f a)
- lensP :: Lens' (Point g a) (g a)
- _Point :: Iso' (Point f a) (f a)
- origin :: (Additive f, Num a) => Point f a
- relative :: (Additive f, Num a) => Point f a -> Iso' (Point f a) (f a)
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@
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
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 | |
Eq1 f => Eq1 (Point f) Source | |
Ord1 f => Ord1 (Point f) Source | |
Read1 f => Read1 (Point f) Source | |
Show1 f => Show1 (Point f) Source | |
Bind f => Bind (Point f) Source | |
Apply f => Apply (Point f) Source | |
Additive f => Additive (Point f) Source | |
Metric f => Metric (Point f) Source | |
Serial1 f => Serial1 (Point f) Source | |
Representable f => Representable (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 | |
Serialize (f a) => Serialize (Point f a) Source | |
NFData (f a) => NFData (Point f a) Source | |
Unbox (f a) => Unbox (Point f a) Source | |
Hashable (f a) => Hashable (Point f a) Source | |
Wrapped (Point f a) Source | |
Ixed (f a) => Ixed (Point f a) Source | |
Epsilon (f a) => Epsilon (Point f a) Source | |
Serial (f a) => Serial (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 Unwrapped (Point f a) = f a Source | |
type IxValue (Point f a) = IxValue (f a) Source | |
type Index (Point f a) = Index (f a) Source |