linear-0.6: Linear Algebra

Portability non-portable experimental Edward Kmett None

Linear.Plucker

Contents

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 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 -> 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

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)`.

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)`.

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)`.

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)`.

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)`.

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)`.

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)`.

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)`.

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)`.

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)`.

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)`.

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)`.