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

Stability | experimental |

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

Safe Haskell | None |

Plücker coordinates for lines in 3d homogeneous space.

- data Plucker a = Plucker !a !a !a !a !a !a
- squaredError :: (Eq a, Num a) => Plucker a -> a
- isotropic :: Epsilon a => Plucker a -> Bool
- (><) :: Num a => Plucker a -> Plucker a -> a
- plucker :: Num a => V4 a -> V4 a -> Plucker a
- intersects :: Epsilon a => Plucker a -> Plucker a -> Bool
- p01 :: Functor f => (a -> f a) -> Plucker a -> f (Plucker a)
- p02 :: Functor f => (a -> f a) -> Plucker a -> f (Plucker a)
- p03 :: Functor f => (a -> f a) -> Plucker a -> f (Plucker a)
- p10 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)
- p12 :: Functor f => (a -> f a) -> Plucker a -> f (Plucker a)
- p13 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)
- p20 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)
- p21 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)
- p23 :: Functor f => (a -> f a) -> Plucker a -> f (Plucker a)
- p30 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)
- p31 :: Functor f => (a -> f a) -> Plucker a -> f (Plucker a)
- p32 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)

# Documentation

Plücker coordinates for lines in a 3-dimensional space.

Plucker !a !a !a !a !a !a |

Monad Plucker | |

Functor Plucker | |

Applicative Plucker | |

Foldable Plucker | |

Traversable Plucker | |

Distributive Plucker | |

Traversable1 Plucker | |

Foldable1 Plucker | |

Apply Plucker | |

Bind Plucker | |

Additive Plucker | |

Metric Plucker | |

Core Plucker | |

Eq a => Eq (Plucker a) | |

Fractional a => Fractional (Plucker a) | |

Num a => Num (Plucker a) | |

Ord a => Ord (Plucker a) | |

Read a => Read (Plucker a) | |

Show a => Show (Plucker a) | |

Ix a => Ix (Plucker a) | |

Storable a => Storable (Plucker a) | |

Epsilon a => Epsilon (Plucker a) |

squaredError :: (Eq a, Num a) => Plucker a -> aSource

Valid Plücker coordinates `p`

will have `squaredError`

p `==`

0

That said, floating point makes a mockery of this claim, so you may want to use `nearZero`

.

isotropic :: Epsilon a => Plucker a -> BoolSource

Checks if the line is near-isotropic (isotropic vectors in this quadratic space represent lines in real 3d space)

(><) :: Num a => Plucker a -> Plucker a -> aSource

This isn't th actual metric because this bilinear form gives rise to an isotropic quadratic space

plucker :: Num a => V4 a -> V4 a -> Plucker aSource

Given a pair of points represented by homogeneous coordinates generate Plücker coordinates for the line through them.

intersects :: Epsilon a => Plucker a -> Plucker a -> BoolSource

Checks if the two vectors intersect (or nearly intersect)

# Basis elements

p10 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)Source

These elements form an alternate basis for the Plücker space, or the Grassmanian manifold `Gr(2,V4)`

.

`p10`

::`Num`

a => Lens' (`Plucker`

a) a`p20`

::`Num`

a => Lens' (`Plucker`

a) a`p30`

::`Num`

a => Lens' (`Plucker`

a) a`p32`

::`Num`

a => Lens' (`Plucker`

a) a`p13`

::`Num`

a => Lens' (`Plucker`

a) a`p21`

::`Num`

a => Lens' (`Plucker`

a) a

p13 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)Source

These elements form an alternate basis for the Plücker space, or the Grassmanian manifold `Gr(2,V4)`

.

`p10`

::`Num`

a => Lens' (`Plucker`

a) a`p20`

::`Num`

a => Lens' (`Plucker`

a) a`p30`

::`Num`

a => Lens' (`Plucker`

a) a`p32`

::`Num`

a => Lens' (`Plucker`

a) a`p13`

::`Num`

a => Lens' (`Plucker`

a) a`p21`

::`Num`

a => Lens' (`Plucker`

a) a

p20 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)Source

These elements form an alternate basis for the Plücker space, or the Grassmanian manifold `Gr(2,V4)`

.

`p10`

::`Num`

a => Lens' (`Plucker`

a) a`p20`

::`Num`

a => Lens' (`Plucker`

a) a`p30`

::`Num`

a => Lens' (`Plucker`

a) a`p32`

::`Num`

a => Lens' (`Plucker`

a) a`p13`

::`Num`

a => Lens' (`Plucker`

a) a`p21`

::`Num`

a => Lens' (`Plucker`

a) a

p21 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)Source

These elements form an alternate basis for the Plücker space, or the Grassmanian manifold `Gr(2,V4)`

.

`p10`

::`Num`

a => Lens' (`Plucker`

a) a`p20`

::`Num`

a => Lens' (`Plucker`

a) a`p30`

::`Num`

a => Lens' (`Plucker`

a) a`p32`

::`Num`

a => Lens' (`Plucker`

a) a`p13`

::`Num`

a => Lens' (`Plucker`

a) a`p21`

::`Num`

a => Lens' (`Plucker`

a) a

p30 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)Source

These elements form an alternate basis for the Plücker space, or the Grassmanian manifold `Gr(2,V4)`

.

`p10`

::`Num`

a => Lens' (`Plucker`

a) a`p20`

::`Num`

a => Lens' (`Plucker`

a) a`p30`

::`Num`

a => Lens' (`Plucker`

a) a`p32`

::`Num`

a => Lens' (`Plucker`

a) a`p13`

::`Num`

a => Lens' (`Plucker`

a) a`p21`

::`Num`

a => Lens' (`Plucker`

a) a

p32 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)Source

These elements form an alternate basis for the Plücker space, or the Grassmanian manifold `Gr(2,V4)`

.

`p10`

::`Num`

a => Lens' (`Plucker`

a) a`p20`

::`Num`

a => Lens' (`Plucker`

a) a`p30`

::`Num`

a => Lens' (`Plucker`

a) a`p32`

::`Num`

a => Lens' (`Plucker`

a) a`p13`

::`Num`

a => Lens' (`Plucker`

a) a`p21`

::`Num`

a => Lens' (`Plucker`

a) a