linear-1.2: Linear Algebra

Portability	non-portable
Stability	experimental
Maintainer	Edward Kmett <[email protected]>
Safe Haskell	Trustworthy

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
Trace Plucker
Affine 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 -> 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