linear-1.20.7: Linear Algebra

Copyright | (C) 2012-2015 Edward Kmett
License | BSD-style (see the file LICENSE)
Maintainer | Edward Kmett <ekmett@gmail.com>
Stability | experimental
Portability | non-portable
Safe Haskell | Trustworthy
Language | Haskell98

Linear.Plucker

Contents

- Operations on lines
- Basis elements

Description

Plücker coordinates for lines in 3d homogeneous space.

Synopsis

- data Plucker a = Plucker !a !a !a !a !a !a
- squaredError :: Num a => Plucker a -> a
- isotropic :: Epsilon a => Plucker a -> Bool
- (><) :: Num a => Plucker a -> Plucker a -> a
- plucker :: Num a => V4 a -> V4 a -> Plucker a
- plucker3D :: Num a => V3 a -> V3 a -> Plucker a
- parallel :: Epsilon a => Plucker a -> Plucker a -> Bool
- intersects :: (Epsilon a, Ord a) => Plucker a -> Plucker a -> Bool
- data LinePass
  - = Coplanar
  - | Clockwise
  - | Counterclockwise
- passes :: (Epsilon a, Ord a) => Plucker a -> Plucker a -> LinePass
- quadranceToOrigin :: Fractional a => Plucker a -> a
- closestToOrigin :: Fractional a => Plucker a -> V3 a
- isLine :: Epsilon a => Plucker a -> Bool
- coincides :: (Epsilon a, Fractional a) => Plucker a -> Plucker a -> Bool
- coincides' :: (Epsilon a, Fractional a, Ord a) => Plucker a -> Plucker a -> Bool
- p01 :: Lens' (Plucker a) a
- p02 :: Lens' (Plucker a) a
- p03 :: Lens' (Plucker a) a
- p10 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)
- p12 :: Lens' (Plucker a) a
- p13 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)
- p20 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)
- p21 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)
- p23 :: Lens' (Plucker a) a
- p30 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)
- p31 :: Lens' (Plucker a) a
- p32 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)
- e01 :: E Plucker
- e02 :: E Plucker
- e03 :: E Plucker
- e12 :: E Plucker
- e31 :: E Plucker
- e23 :: E Plucker

# 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 Source # |
Methods (>>=) :: Plucker a -> (a -> Plucker b) -> Plucker b # (>>) :: Plucker a -> Plucker b -> Plucker b # return :: a -> Plucker a # fail :: String -> Plucker a #
Functor Plucker Source # |
Methods fmap :: (a -> b) -> Plucker a -> Plucker b # (<$) :: a -> Plucker b -> Plucker a #
MonadFix Plucker Source # |
Methods mfix :: (a -> Plucker a) -> Plucker a #
Applicative Plucker Source # |
Methods pure :: a -> Plucker a # (<*>) :: Plucker (a -> b) -> Plucker a -> Plucker b # (*>) :: Plucker a -> Plucker b -> Plucker b # (<*) :: Plucker a -> Plucker b -> Plucker a #
Foldable Plucker Source # |

Methods

fold :: Monoid m => Plucker m -> m #

foldMap :: Monoid m => (a -> m) -> Plucker a -> m #

foldr :: (a -> b -> b) -> b -> Plucker a -> b #

foldr' :: (a -> b -> b) -> b -> Plucker a -> b #

foldl :: (b -> a -> b) -> b -> Plucker a -> b #

foldl' :: (b -> a -> b) -> b -> Plucker a -> b #

foldr1 :: (a -> a -> a) -> Plucker a -> a #

foldl1 :: (a -> a -> a) -> Plucker a -> a #

toList :: Plucker a -> [a] #

null :: Plucker a -> Bool #

length :: Plucker a -> Int #

elem :: Eq a => a -> Plucker a -> Bool #

maximum :: Ord a => Plucker a -> a #

minimum :: Ord a => Plucker a -> a #

sum :: Num a => Plucker a -> a #

product :: Num a => Plucker a -> a #

Traversable Plucker Source # |
Methods traverse :: Applicative f => (a -> f b) -> Plucker a -> f (Plucker b) # sequenceA :: Applicative f => Plucker (f a) -> f (Plucker a) # mapM :: Monad m => (a -> m b) -> Plucker a -> m (Plucker b) # sequence :: Monad m => Plucker (m a) -> m (Plucker a) #
Generic1 Plucker Source # |
Associated Types type Rep1 (Plucker :: * -> *) :: * -> * # Methods from1 :: Plucker a -> Rep1 Plucker a # to1 :: Rep1 Plucker a -> Plucker a #
Distributive Plucker Source # |
Methods distribute :: Functor f => f (Plucker a) -> Plucker (f a) # collect :: Functor f => (a -> Plucker b) -> f a -> Plucker (f b) # distributeM :: Monad m => m (Plucker a) -> Plucker (m a) # collectM :: Monad m => (a -> Plucker b) -> m a -> Plucker (m b) #
Representable Plucker Source # |
Associated Types type Rep (Plucker :: * -> *) :: * # Methods tabulate :: (Rep Plucker -> a) -> Plucker a # index :: Plucker a -> Rep Plucker -> a #
Eq1 Plucker Source # |
Methods liftEq :: (a -> b -> Bool) -> Plucker a -> Plucker b -> Bool #
Ord1 Plucker Source # |
Methods liftCompare :: (a -> b -> Ordering) -> Plucker a -> Plucker b -> Ordering #
Read1 Plucker Source # |
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Plucker a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Plucker a] #
Show1 Plucker Source # |
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Plucker a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Plucker a] -> ShowS #
MonadZip Plucker Source # |
Methods mzip :: Plucker a -> Plucker b -> Plucker (a, b) # mzipWith :: (a -> b -> c) -> Plucker a -> Plucker b -> Plucker c # munzip :: Plucker (a, b) -> (Plucker a, Plucker b) #
Serial1 Plucker Source # |
Methods serializeWith :: MonadPut m => (a -> m ()) -> Plucker a -> m () # deserializeWith :: MonadGet m => m a -> m (Plucker a) #
Traversable1 Plucker Source # |
Methods traverse1 :: Apply f => (a -> f b) -> Plucker a -> f (Plucker b) # sequence1 :: Apply f => Plucker (f b) -> f (Plucker b) #
Apply Plucker Source # |
Methods (<.>) :: Plucker (a -> b) -> Plucker a -> Plucker b # (.>) :: Plucker a -> Plucker b -> Plucker b # (<.) :: Plucker a -> Plucker b -> Plucker a #
Bind Plucker Source # |
Methods (>>-) :: Plucker a -> (a -> Plucker b) -> Plucker b # join :: Plucker (Plucker a) -> Plucker a #
Foldable1 Plucker Source # |
Methods fold1 :: Semigroup m => Plucker m -> m # foldMap1 :: Semigroup m => (a -> m) -> Plucker a -> m # toNonEmpty :: Plucker a -> NonEmpty a #
Additive Plucker Source # |
Methods zero :: Num a => Plucker a Source # (^+^) :: Num a => Plucker a -> Plucker a -> Plucker a Source # (^-^) :: Num a => Plucker a -> Plucker a -> Plucker a Source # lerp :: Num a => a -> Plucker a -> Plucker a -> Plucker a Source # liftU2 :: (a -> a -> a) -> Plucker a -> Plucker a -> Plucker a Source # liftI2 :: (a -> b -> c) -> Plucker a -> Plucker b -> Plucker c Source #
Metric Plucker Source # |
Methods dot :: Num a => Plucker a -> Plucker a -> a Source # quadrance :: Num a => Plucker a -> a Source # qd :: Num a => Plucker a -> Plucker a -> a Source # distance :: Floating a => Plucker a -> Plucker a -> a Source # norm :: Floating a => Plucker a -> a Source # signorm :: Floating a => Plucker a -> Plucker a Source #
Finite Plucker Source # |
Associated Types type Size (Plucker :: * -> *) :: Nat Source # Methods toV :: Plucker a -> V Nat (Size Plucker) a Source # fromV :: V Nat (Size Plucker) a -> Plucker a Source #
Trace Plucker Source # |
Methods trace :: Num a => Plucker (Plucker a) -> a Source # diagonal :: Plucker (Plucker a) -> Plucker a Source #
Affine Plucker Source # |
Associated Types type Diff (Plucker :: * -> *) :: * -> * Source # Methods (.-.) :: Num a => Plucker a -> Plucker a -> Diff Plucker a Source # (.+^) :: Num a => Plucker a -> Diff Plucker a -> Plucker a Source # (.-^) :: Num a => Plucker a -> Diff Plucker a -> Plucker a Source #
Unbox a => Vector Vector (Plucker a) Source # |

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Plucker a) -> m (Vector (Plucker a)) #

basicUnsafeThaw :: PrimMonad m => Vector (Plucker a) -> m (Mutable Vector (PrimState m) (Plucker a)) #

basicLength :: Vector (Plucker a) -> Int #

basicUnsafeSlice :: Int -> Int -> Vector (Plucker a) -> Vector (Plucker a) #

basicUnsafeIndexM :: Monad m => Vector (Plucker a) -> Int -> m (Plucker a) #

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Plucker a) -> Vector (Plucker a) -> m () #

elemseq :: Vector (Plucker a) -> Plucker a -> b -> b #

Unbox a => MVector MVector (Plucker a) Source # |

Methods

basicLength :: MVector s (Plucker a) -> Int #

basicUnsafeSlice :: Int -> Int -> MVector s (Plucker a) -> MVector s (Plucker a) #

basicOverlaps :: MVector s (Plucker a) -> MVector s (Plucker a) -> Bool #

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Plucker a)) #

basicInitialize :: PrimMonad m => MVector (PrimState m) (Plucker a) -> m () #

basicUnsafeReplicate :: PrimMonad m => Int -> Plucker a -> m (MVector (PrimState m) (Plucker a)) #

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Plucker a) -> Int -> m (Plucker a) #

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Plucker a) -> Int -> Plucker a -> m () #

basicClear :: PrimMonad m => MVector (PrimState m) (Plucker a) -> m () #

basicSet :: PrimMonad m => MVector (PrimState m) (Plucker a) -> Plucker a -> m () #

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Plucker a) -> MVector (PrimState m) (Plucker a) -> m () #

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Plucker a) -> MVector (PrimState m) (Plucker a) -> m () #

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Plucker a) -> Int -> m (MVector (PrimState m) (Plucker a)) #

Eq a => Eq (Plucker a) Source # |
Methods (==) :: Plucker a -> Plucker a -> Bool # (/=) :: Plucker a -> Plucker a -> Bool #
Floating a => Floating (Plucker a) Source # |

Methods

pi :: Plucker a #

exp :: Plucker a -> Plucker a #

log :: Plucker a -> Plucker a #

sqrt :: Plucker a -> Plucker a #

(**) :: Plucker a -> Plucker a -> Plucker a #

logBase :: Plucker a -> Plucker a -> Plucker a #

sin :: Plucker a -> Plucker a #

cos :: Plucker a -> Plucker a #

tan :: Plucker a -> Plucker a #

asin :: Plucker a -> Plucker a #

acos :: Plucker a -> Plucker a #

atan :: Plucker a -> Plucker a #

sinh :: Plucker a -> Plucker a #

cosh :: Plucker a -> Plucker a #

tanh :: Plucker a -> Plucker a #

asinh :: Plucker a -> Plucker a #

acosh :: Plucker a -> Plucker a #

atanh :: Plucker a -> Plucker a #

log1p :: Plucker a -> Plucker a #

expm1 :: Plucker a -> Plucker a #

log1pexp :: Plucker a -> Plucker a #

log1mexp :: Plucker a -> Plucker a #

Fractional a => Fractional (Plucker a) Source # |
Methods (/) :: Plucker a -> Plucker a -> Plucker a # recip :: Plucker a -> Plucker a # fromRational :: Rational -> Plucker a #
Num a => Num (Plucker a) Source # |
Methods (+) :: Plucker a -> Plucker a -> Plucker a # (-) :: Plucker a -> Plucker a -> Plucker a # (*) :: Plucker a -> Plucker a -> Plucker a # negate :: Plucker a -> Plucker a # abs :: Plucker a -> Plucker a # signum :: Plucker a -> Plucker a # fromInteger :: Integer -> Plucker a #
Ord a => Ord (Plucker a) Source # |
Methods compare :: Plucker a -> Plucker a -> Ordering # (<) :: Plucker a -> Plucker a -> Bool # (<=) :: Plucker a -> Plucker a -> Bool # (>) :: Plucker a -> Plucker a -> Bool # (>=) :: Plucker a -> Plucker a -> Bool # max :: Plucker a -> Plucker a -> Plucker a # min :: Plucker a -> Plucker a -> Plucker a #
Read a => Read (Plucker a) Source # |
Methods readsPrec :: Int -> ReadS (Plucker a) # readList :: ReadS [Plucker a] # readPrec :: ReadPrec (Plucker a) # readListPrec :: ReadPrec [Plucker a] #
Show a => Show (Plucker a) Source # |
Methods showsPrec :: Int -> Plucker a -> ShowS # show :: Plucker a -> String # showList :: [Plucker a] -> ShowS #
Ix a => Ix (Plucker a) Source # |
Methods range :: (Plucker a, Plucker a) -> [Plucker a] # index :: (Plucker a, Plucker a) -> Plucker a -> Int # unsafeIndex :: (Plucker a, Plucker a) -> Plucker a -> Int inRange :: (Plucker a, Plucker a) -> Plucker a -> Bool # rangeSize :: (Plucker a, Plucker a) -> Int # unsafeRangeSize :: (Plucker a, Plucker a) -> Int
Generic (Plucker a) Source # |
Associated Types type Rep (Plucker a) :: * -> * # Methods from :: Plucker a -> Rep (Plucker a) x # to :: Rep (Plucker a) x -> Plucker a #
Storable a => Storable (Plucker a) Source # |
Methods sizeOf :: Plucker a -> Int # alignment :: Plucker a -> Int # peekElemOff :: Ptr (Plucker a) -> Int -> IO (Plucker a) # pokeElemOff :: Ptr (Plucker a) -> Int -> Plucker a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Plucker a) # pokeByteOff :: Ptr b -> Int -> Plucker a -> IO () # peek :: Ptr (Plucker a) -> IO (Plucker a) # poke :: Ptr (Plucker a) -> Plucker a -> IO () #
Binary a => Binary (Plucker a) Source # |
Methods put :: Plucker a -> Put # get :: Get (Plucker a) # putList :: [Plucker a] -> Put #
Serial a => Serial (Plucker a) Source # |
Methods serialize :: MonadPut m => Plucker a -> m () # deserialize :: MonadGet m => m (Plucker a) #
Serialize a => Serialize (Plucker a) Source # |
Methods put :: Putter (Plucker a) # get :: Get (Plucker a) #
NFData a => NFData (Plucker a) Source # |
Methods rnf :: Plucker a -> () #
Hashable a => Hashable (Plucker a) Source # |
Methods hashWithSalt :: Int -> Plucker a -> Int # hash :: Plucker a -> Int #
Unbox a => Unbox (Plucker a) Source # |
Ixed (Plucker a) Source # |
Methods ix :: Index (Plucker a) -> Traversal' (Plucker a) (IxValue (Plucker a)) #
Epsilon a => Epsilon (Plucker a) Source # |
Methods nearZero :: Plucker a -> Bool Source #
FunctorWithIndex (E Plucker) Plucker Source # |
Methods imap :: (E Plucker -> a -> b) -> Plucker a -> Plucker b # imapped :: (Indexable (E Plucker) p, Settable f) => p a (f b) -> Plucker a -> f (Plucker b) #
FoldableWithIndex (E Plucker) Plucker Source # |

Methods

ifoldMap :: Monoid m => (E Plucker -> a -> m) -> Plucker a -> m #

ifolded :: (Indexable (E Plucker) p, Contravariant f, Applicative f) => p a (f a) -> Plucker a -> f (Plucker a) #

ifoldr :: (E Plucker -> a -> b -> b) -> b -> Plucker a -> b #

ifoldl :: (E Plucker -> b -> a -> b) -> b -> Plucker a -> b #

ifoldr' :: (E Plucker -> a -> b -> b) -> b -> Plucker a -> b #

ifoldl' :: (E Plucker -> b -> a -> b) -> b -> Plucker a -> b #

TraversableWithIndex (E Plucker) Plucker Source # |
Methods itraverse :: Applicative f => (E Plucker -> a -> f b) -> Plucker a -> f (Plucker b) # itraversed :: (Indexable (E Plucker) p, Applicative f) => p a (f b) -> Plucker a -> f (Plucker b) #
Each (Plucker a) (Plucker b) a b Source # |
Methods each :: Traversal (Plucker a) (Plucker b) a b #
type Rep1 Plucker Source # |

type Rep1 Plucker = D1 (MetaData "Plucker" "Linear.Plucker" "linear-1.20.7-CvaXC2ebC1zHQ7FJwFrAk8" False) (C1 (MetaCons "Plucker" PrefixI False) ((:*:) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1))) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1)))))

type Rep Plucker Source # |
type Rep Plucker = E Plucker
type Size Plucker Source # |
type Size Plucker = 6
type Diff Plucker Source # |
type Diff Plucker = Plucker
data MVector s (Plucker a) Source # |
data MVector s (Plucker a) = MV_Plucker !Int (MVector s a)
type Rep (Plucker a) Source # |

type Rep (Plucker a) = D1 (MetaData "Plucker" "Linear.Plucker" "linear-1.20.7-CvaXC2ebC1zHQ7FJwFrAk8" False) (C1 (MetaCons "Plucker" PrefixI False) ((:*:) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)))) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a))))))

data Vector (Plucker a) Source # |
data Vector (Plucker a) = V_Plucker !Int (Vector a)
type Index (Plucker a) Source # |
type Index (Plucker a) = E Plucker
type IxValue (Plucker a) Source # |
type IxValue (Plucker a) = a

squaredError :: Num a => Plucker a -> a Source #

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 -> a infixl 5 Source #

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 Source #

Given a pair of points represented by homogeneous coordinates generate Plücker coordinates for the line through them, directed from the second towards the first.

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

Given a pair of 3D points, generate Plücker coordinates for the line through them, directed from the second towards the first.

# Operations on lines

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

Checks if two lines are parallel.

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

Checks if two lines intersect (or nearly intersect).

data LinePass Source #

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 Source # |
Methods (==) :: LinePass -> LinePass -> Bool # (/=) :: LinePass -> LinePass -> Bool #
Show LinePass Source # |
Methods showsPrec :: Int -> LinePass -> ShowS # show :: LinePass -> String # showList :: [LinePass] -> ShowS #
Generic LinePass Source # |
Associated Types type Rep LinePass :: * -> * # Methods from :: LinePass -> Rep LinePass x # to :: Rep LinePass x -> LinePass #
type Rep LinePass Source # |
type Rep LinePass = D1 (MetaData "LinePass" "Linear.Plucker" "linear-1.20.7-CvaXC2ebC1zHQ7FJwFrAk8" False) ((:+:) (C1 (MetaCons "Coplanar" PrefixI False) U1) ((:+:) (C1 (MetaCons "Clockwise" PrefixI False) U1) (C1 (MetaCons "Counterclockwise" PrefixI False) U1)))

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

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

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

The minimum squared distance of a line from the origin.

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

The point where a line is closest to the origin.

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

Not all 6-dimensional points correspond to a line in 3D. This predicate tests that a Plücker coordinate lies on the Grassmann manifold, and does indeed represent a 3D line.

coincides :: (Epsilon a, Fractional a) => Plucker a -> Plucker a -> Bool Source #

Checks if two lines coincide in space. In other words, undirected equality.

coincides' :: (Epsilon a, Fractional a, Ord a) => Plucker a -> Plucker a -> Bool Source #

Checks if two lines coincide in space, and have the same orientation.

# Basis elements

p01 :: Lens' (Plucker a) 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 :: Lens' (Plucker a) 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 :: Lens' (Plucker a) 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 :: Lens' (Plucker a) 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 :: Lens' (Plucker a) 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 :: Lens' (Plucker a) 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

e01 :: E Plucker Source #

e02 :: E Plucker Source #

e03 :: E Plucker Source #

e12 :: E Plucker Source #

e31 :: E Plucker Source #

e23 :: E Plucker Source #