Linear.Plucker

Pl

Documentation

data Plucker a

Pl

Constructors

Plucker !a !a !a !a !a !a

Instances

Monad Plucker

Functor Plucker

MonadFix Plucker

Applicative Plucker

Foldable Plucker

Traversable Plucker

Generic1 Plucker

Distributive Plucker

Representable Plucker

Traversable1 Plucker

Foldable1 Plucker

Apply Plucker

Bind Plucker

MonadZip Plucker

Additive Plucker

Metric Plucker

Trace Plucker

Affine Plucker

Unbox a => Vector Vector (Plucker a)

Unbox a => MVector MVector (Plucker a)

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)

Generic (Plucker a)

Hashable a => Hashable (Plucker a)

Storable a => Storable (Plucker a)

Unbox a => Unbox (Plucker a)

Ixed (Plucker a)

Epsilon a => Epsilon (Plucker a)

FunctorWithIndex (E Plucker) Plucker

FoldableWithIndex (E Plucker) Plucker

TraversableWithIndex (E Plucker) Plucker

Each (Plucker a) (Plucker b) a b

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

Valid Pl

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 Pl

plucker3D :: Num a => V3 a -> V3 a -> Plucker a

Given a pair of 3D points, generate Pl

Operations on lines

parallel :: Epsilon a => Plucker a -> Plucker a -> Bool

Checks if two lines are parallel.

intersects :: (Epsilon a, Ord a) => Plucker a -> Plucker a -> Bool

Checks if two lines intersect (or nearly intersect).

data LinePass

Describe how two lines pass each other.

Constructors

Coplanar

The lines are coplanar (parallel or intersecting).

Clockwise

The lines pass each other clockwise (right-handed screw)

Counterclockwise

The lines pass each other counterclockwise (left-handed screw).

Instances

Eq LinePass

Show LinePass

Generic LinePass

passes :: (Epsilon a, Num a, Ord a) => Plucker a -> Plucker a -> LinePass

Check how two lines pass each other. passes l1 l2 describes l2 when looking down l1.

quadranceToOrigin :: Fractional a => Plucker a -> a

The minimum squared distance of a line from the origin.

closestToOrigin :: Fractional a => Plucker a -> V3 a

The point where a line is closest to the origin.

isLine :: Epsilon a => Plucker a -> Bool

Not all 6-dimensional points correspond to a line in 3D. This predicate tests that a Pl

data Coincides a where

When lines are represented as Pl

Constructors

Line :: (Epsilon a, Fractional a) => Plucker a -> Coincides a

Ray :: (Epsilon a, Fractional a, Ord a) => Plucker a -> Coincides a

Instances

Eq (Coincides a)

Basis elements

p01 :: Lens' (Plucker a) a

These elements form a basis for the Pl

p02 :: Lens' (Plucker a) a

These elements form a basis for the Pl

p03 :: Lens' (Plucker a) a

These elements form a basis for the Pl

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

These elements form an alternate basis for the Pl

p12 :: Lens' (Plucker a) a

These elements form a basis for the Pl

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

These elements form an alternate basis for the Pl

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

These elements form an alternate basis for the Pl

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

These elements form an alternate basis for the Pl

p23 :: Lens' (Plucker a) a

These elements form a basis for the Pl

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

These elements form an alternate basis for the Pl

p31 :: Lens' (Plucker a) a

These elements form a basis for the Pl

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

These elements form an alternate basis for the Pl

e01 :: E Plucker

e02 :: E Plucker

e03 :: E Plucker

e12 :: E Plucker

e31 :: E Plucker

e23 :: E Plucker