Portability | portable |
---|---|

Stability | provisional |

Maintainer | Edward Kmett <ekmett@gmail.com> |

Safe Haskell | Trustworthy |

Operations on affine spaces.

# Documentation

class Additive (Diff p) => Affine p whereSource

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@

(.-.) :: Num a => p a -> p a -> Diff p aSource

Get the difference between two points as a vector offset.

(.+^) :: Num a => p a -> Diff p a -> p aSource

Add a vector offset to a point.

(.-^) :: Num a => p a -> Diff p a -> p aSource

Subtract a vector offset from a point.

Affine [] | |

Affine Complex | |

Affine ZipList | |

Affine Maybe | |

Affine IntMap | |

Affine Identity | |

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 -> aSource

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

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

Distance between two points in an affine space

A handy wrapper to help distinguish points from vectors at the type level

P (f a) |

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) | |

Apply f => Apply (Point f) | |

Bind f => Bind (Point f) | |

Additive f => Additive (Point f) | |

Metric f => Metric (Point f) | |

Core f => Core (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) | |

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) | |

Storable (f a) => Storable (Point f a) | |

Epsilon (f a) => Epsilon (Point f a) |