linear-0.9.2: Linear Algebra

Portability	non-portable
Stability	experimental
Maintainer	Edward Kmett <ekmett@gmail.com>
Safe Haskell	None

Linear.Plucker

Contents

Basis elements

Description

Plücker coordinates for lines in 3d homogeneous space.

Synopsis

Documentation

data Plucker a Source

Plücker coordinates for lines in a 3-dimensional space.

Constructors

Plucker a a a a a a

Instances

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)
(Num (Plucker a), Fractional a) => Fractional (Plucker a)
Num a => Num (Plucker a)
(Eq (Plucker a), Ord a) => Ord (Plucker a)
Read a => Read (Plucker a)
Show a => Show (Plucker a)
(Ord (Plucker a), Ix a) => Ix (Plucker a)
Storable a => Storable (Plucker a)
(Num (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 -> Bool Source

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 -> Bool Source

Checks if the two vectors intersect (or nearly intersect)

Basis elements

p01 :: Functor f => (a -> f a) -> Plucker a -> f (Plucker a)Source

These elements form a basis for the Plücker space, or the Grassmanian manifold Gr(2,V4).

 p01 :: Lens' (Plucker a) a
 p02 :: Lens' (Plucker a) a
 p03 :: Lens' (Plucker a) a
 p23 :: Lens' (Plucker a) a
 p31 :: Lens' (Plucker a) a
 p12 :: Lens' (Plucker a) a

p02 :: Functor f => (a -> f a) -> Plucker a -> f (Plucker a)Source

These elements form a basis for the Plücker space, or the Grassmanian manifold Gr(2,V4).

 p01 :: Lens' (Plucker a) a
 p02 :: Lens' (Plucker a) a
 p03 :: Lens' (Plucker a) a
 p23 :: Lens' (Plucker a) a
 p31 :: Lens' (Plucker a) a
 p12 :: Lens' (Plucker a) a

p03 :: Functor f => (a -> f a) -> Plucker a -> f (Plucker a)Source

These elements form a basis for the Plücker space, or the Grassmanian manifold Gr(2,V4).

 p01 :: Lens' (Plucker a) a
 p02 :: Lens' (Plucker a) a
 p03 :: Lens' (Plucker a) a
 p23 :: Lens' (Plucker a) a
 p31 :: Lens' (Plucker a) a
 p12 :: Lens' (Plucker a) a

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

p12 :: Functor f => (a -> f a) -> Plucker a -> f (Plucker a)Source

These elements form a basis for the Plücker space, or the Grassmanian manifold Gr(2,V4).

 p01 :: Lens' (Plucker a) a
 p02 :: Lens' (Plucker a) a
 p03 :: Lens' (Plucker a) a
 p23 :: Lens' (Plucker a) a
 p31 :: Lens' (Plucker a) a
 p12 :: 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

p23 :: Functor f => (a -> f a) -> Plucker a -> f (Plucker a)Source

These elements form a basis for the Plücker space, or the Grassmanian manifold Gr(2,V4).

 p01 :: Lens' (Plucker a) a
 p02 :: Lens' (Plucker a) a
 p03 :: Lens' (Plucker a) a
 p23 :: Lens' (Plucker a) a
 p31 :: Lens' (Plucker a) a
 p12 :: 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

p31 :: Functor f => (a -> f a) -> Plucker a -> f (Plucker a)Source

These elements form a basis for the Plücker space, or the Grassmanian manifold Gr(2,V4).

 p01 :: Lens' (Plucker a) a
 p02 :: Lens' (Plucker a) a
 p03 :: Lens' (Plucker a) a
 p23 :: Lens' (Plucker a) a
 p31 :: Lens' (Plucker a) a
 p12 :: 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