Linear.Plucker

Plücker coordinates for lines in 3d homogeneous space.

Documentation

data Plucker a

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

Representable Plucker

Metric 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)

(Num (Plucker a), Epsilon a) => Epsilon (Plucker a)

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

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

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 -> a

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 a

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

Checks if the two vectors intersect (or nearly intersect)