Data.Array.Accelerate.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

Methods

(>>=) :: Plucker a -> (a -> Plucker b) -> Plucker b

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

return :: a -> Plucker a

fail :: String -> Plucker a

Functor Plucker

Methods

fmap :: (a -> b) -> Plucker a -> Plucker b

(<$) :: a -> Plucker b -> Plucker a

MonadFix Plucker

Methods

mfix :: (a -> Plucker a) -> Plucker a

Applicative Plucker

Methods

pure :: a -> Plucker a

(<*>) :: Plucker (a -> b) -> Plucker a -> Plucker b

liftA2 :: (a -> b -> c) -> Plucker a -> Plucker b -> Plucker c

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

(<*) :: Plucker a -> Plucker b -> Plucker a

Foldable Plucker

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

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)

Distributive Plucker

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

Associated Types

type Rep (Plucker :: * -> *) :: *

Methods

tabulate :: (Rep Plucker -> a) -> Plucker a

index :: Plucker a -> Rep Plucker -> a

Eq1 Plucker

Methods

liftEq :: (a -> b -> Bool) -> Plucker a -> Plucker b -> Bool

Ord1 Plucker

Methods

liftCompare :: (a -> b -> Ordering) -> Plucker a -> Plucker b -> Ordering

Read1 Plucker

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Plucker a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Plucker a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Plucker a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Plucker a]

Show1 Plucker

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Plucker a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Plucker a] -> ShowS

MonadZip Plucker

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

Methods

serializeWith :: MonadPut m => (a -> m ()) -> Plucker a -> m ()

deserializeWith :: MonadGet m => m a -> m (Plucker a)

Apply Plucker

Methods

(<.>) :: Plucker (a -> b) -> Plucker a -> Plucker b

(.>) :: Plucker a -> Plucker b -> Plucker b

(<.) :: Plucker a -> Plucker b -> Plucker a

liftF2 :: (a -> b -> c) -> Plucker a -> Plucker b -> Plucker c

Traversable1 Plucker

Methods

traverse1 :: Apply f => (a -> f b) -> Plucker a -> f (Plucker b)

sequence1 :: Apply f => Plucker (f b) -> f (Plucker b)

Trace Plucker

Methods

trace :: Num a => Plucker (Plucker a) -> a

diagonal :: Plucker (Plucker a) -> Plucker a

Finite Plucker

Associated Types

type Size (Plucker :: * -> *) :: Nat

Methods

toV :: Plucker a -> V Nat (Size Plucker) a

fromV :: V Nat (Size Plucker) a -> Plucker a

Metric Plucker

Methods

dot :: Num a => Plucker a -> Plucker a -> a

quadrance :: Num a => Plucker a -> a

qd :: Num a => Plucker a -> Plucker a -> a

distance :: Floating a => Plucker a -> Plucker a -> a

norm :: Floating a => Plucker a -> a

signorm :: Floating a => Plucker a -> Plucker a

Additive Plucker

Methods

zero :: Num a => Plucker a

(^+^) :: Num a => Plucker a -> Plucker a -> Plucker a

(^-^) :: Num a => Plucker a -> Plucker a -> Plucker a

lerp :: Num a => a -> Plucker a -> Plucker a -> Plucker a

liftU2 :: (a -> a -> a) -> Plucker a -> Plucker a -> Plucker a

liftI2 :: (a -> b -> c) -> Plucker a -> Plucker b -> Plucker c

Foldable1 Plucker

Methods

fold1 :: Semigroup m => Plucker m -> m

foldMap1 :: Semigroup m => (a -> m) -> Plucker a -> m

toNonEmpty :: Plucker a -> NonEmpty a

Bind Plucker

Methods

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

join :: Plucker (Plucker a) -> Plucker a

Trace Plucker

Methods

trace :: (Num a, Box2 Plucker Plucker a) => Exp (Plucker (Plucker a)) -> Exp a

diagonal :: Box2 Plucker Plucker a => Exp (Plucker (Plucker a)) -> Exp (Plucker a)

Unbox a => Vector Vector (Plucker a)

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)

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)

Methods

(==) :: Plucker a -> Plucker a -> Bool

(/=) :: Plucker a -> Plucker a -> Bool

Floating a => Floating (Plucker a)

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)

Methods

(/) :: Plucker a -> Plucker a -> Plucker a

recip :: Plucker a -> Plucker a

fromRational :: Rational -> Plucker a

Num a => Num (Plucker a)

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)

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)

Methods

readsPrec :: Int -> ReadS (Plucker a)

readList :: ReadS [Plucker a]

readPrec :: ReadPrec (Plucker a)

readListPrec :: ReadPrec [Plucker a]

Show a => Show (Plucker a)

Methods

showsPrec :: Int -> Plucker a -> ShowS

show :: Plucker a -> String

showList :: [Plucker a] -> ShowS

Ix a => Ix (Plucker a)

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)

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)

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)

Methods

put :: Plucker a -> Put

get :: Get (Plucker a)

putList :: [Plucker a] -> Put

Serial a => Serial (Plucker a)

Methods

serialize :: MonadPut m => Plucker a -> m ()

deserialize :: MonadGet m => m (Plucker a)

Serialize a => Serialize (Plucker a)

Methods

put :: Putter (Plucker a)

get :: Get (Plucker a)

NFData a => NFData (Plucker a)

Methods

rnf :: Plucker a -> ()

Hashable a => Hashable (Plucker a)

Methods

hashWithSalt :: Int -> Plucker a -> Int

hash :: Plucker a -> Int

Unbox a => Unbox (Plucker a)

Ixed (Plucker a)

Methods

ix :: Index (Plucker a) -> Traversal' (Plucker a) (IxValue (Plucker a))

Epsilon a => Epsilon (Plucker a)

Methods

nearZero :: Plucker a -> Bool

Generic1 * Plucker

Associated Types

type Rep1 Plucker (f :: Plucker -> *) :: k -> *

Methods

from1 :: f a -> Rep1 Plucker f a

to1 :: Rep1 Plucker f a -> f a

FunctorWithIndex (E Plucker) Plucker

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

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

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

Methods

each :: Traversal (Plucker a) (Plucker b) a b

type Rep Plucker

type Rep Plucker = E Plucker

type Size Plucker

type Size Plucker = 6

data MVector s (Plucker a)

data MVector s (Plucker a) = MV_Plucker !Int (MVector s a)

type Rep (Plucker a)

type Rep (Plucker a) = D1 * (MetaData "Plucker" "Linear.Plucker" "linear-1.20.7-A94GAJeQ1UJ94Gh1xcTI1S" 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))))))

type EltRepr (Plucker a)

type EltRepr (Plucker a) = EltRepr (a, a, a, a, a, a)

type ProdRepr (Plucker a)

type ProdRepr (Plucker a) = ProdRepr (a, a, a, a, a, a)

type Plain (Plucker a)

type Plain (Plucker a) = Plucker (Plain a)

data Vector (Plucker a)

data Vector (Plucker a) = V_Plucker !Int (Vector a)

type Index (Plucker a)

type Index (Plucker a) = E Plucker

type IxValue (Plucker a)

type IxValue (Plucker a) = a

type Rep1 * Plucker

type Rep1 * Plucker = D1 * (MetaData "Plucker" "Linear.Plucker" "linear-1.20.7-A94GAJeQ1UJ94Gh1xcTI1S" 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)))))

squaredError :: forall a. Num a => Exp (Plucker a) -> Exp 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 => Exp (Plucker a) -> Exp Bool

Checks if the line is near-isotropic (isotropic vectors in this quadratic space represent lines in real 3D space).

(><) :: forall a. Num a => Exp (Plucker a) -> Exp (Plucker a) -> Exp a infixl 5

This isn't the actual metric because this bilinear form gives rise to an isotropic quadratic space.

plucker :: forall a. Num a => Exp (V4 a) -> Exp (V4 a) -> Exp (Plucker a)

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 :: forall a. Num a => Exp (V3 a) -> Exp (V3 a) -> Exp (Plucker a)

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

operations on lines

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

Methods

(==) :: LinePass -> LinePass -> Bool

(/=) :: LinePass -> LinePass -> Bool

Show LinePass

Methods

showsPrec :: Int -> LinePass -> ShowS

show :: LinePass -> String

showList :: [LinePass] -> ShowS

Generic LinePass

Associated Types

type Rep LinePass :: * -> *

Methods

from :: LinePass -> Rep LinePass x

to :: Rep LinePass x -> LinePass

type Rep LinePass

type Rep LinePass = D1 * (MetaData "LinePass" "Linear.Plucker" "linear-1.20.7-A94GAJeQ1UJ94Gh1xcTI1S" False) ((:+:) * (C1 * (MetaCons "Coplanar" PrefixI False) (U1 *)) ((:+:) * (C1 * (MetaCons "Clockwise" PrefixI False) (U1 *)) (C1 * (MetaCons "Counterclockwise" PrefixI False) (U1 *))))

type EltRepr LinePass

type EltRepr LinePass = Int8

parallel :: Epsilon a => Exp (Plucker a) -> Exp (Plucker a) -> Exp Bool

Checks if two lines are parallel.

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

Checks if two lines intersect (or nearly intersect).

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

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

quadranceToOrigin :: Fractional a => Exp (Plucker a) -> Exp a

The minimum squared distance of a line from the origin.

closestToOrigin :: Fractional a => Exp (Plucker a) -> Exp (V3 a)

The point where a line is closest to the origin.

isLine :: Epsilon a => Exp (Plucker a) -> Exp Bool

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.

Basis elements

p01 :: Elt a => Lens' (Exp (Plucker a)) (Exp a)

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 :: Elt a => Lens' (Exp (Plucker a)) (Exp a)

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 :: Elt a => Lens' (Exp (Plucker a)) (Exp a)

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 :: Num a => Lens' (Exp (Plucker a)) (Exp a)

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 :: Elt a => Lens' (Exp (Plucker a)) (Exp a)

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 :: Num a => Lens' (Exp (Plucker a)) (Exp a)

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 :: Num a => Lens' (Exp (Plucker a)) (Exp a)

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 :: Num a => Lens' (Exp (Plucker a)) (Exp a)

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 :: Elt a => Lens' (Exp (Plucker a)) (Exp a)

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 :: Num a => Lens' (Exp (Plucker a)) (Exp a)

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 :: Elt a => Lens' (Exp (Plucker a)) (Exp a)

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 :: Num a => Lens' (Exp (Plucker a)) (Exp a)

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

Orphan instances

Eq LinePass

Methods

(==) :: Exp LinePass -> Exp LinePass -> Exp Bool

(/=) :: Exp LinePass -> Exp LinePass -> Exp Bool

Functor Plucker

Methods

fmap :: (Elt a, Elt b, Elt (Plucker a), Elt (Plucker b)) => (Exp a -> Exp b) -> Exp (Plucker a) -> Exp (Plucker b)

(<$) :: (Elt a, Elt b, Elt (Plucker a), Elt (Plucker b)) => Exp a -> Exp (Plucker b) -> Exp (Plucker a)

Elt LinePass

Methods

eltType :: LinePass -> TupleType (EltRepr LinePass)

fromElt :: LinePass -> EltRepr LinePass

toElt :: EltRepr LinePass -> LinePass

Additive Plucker

Methods

zero :: (Elt (Plucker a), Num a) => Exp (Plucker a)

(^+^) :: (Num a, Box Plucker a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp (Plucker a)

(^-^) :: (Num a, Box Plucker a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp (Plucker a)

lerp :: (Num a, Box Plucker a) => Exp a -> Exp (Plucker a) -> Exp (Plucker a) -> Exp (Plucker a)

Metric Plucker

Methods

dot :: (Num a, Box Plucker a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp a

quadrance :: (Num a, Box Plucker a) => Exp (Plucker a) -> Exp a

qd :: (Num a, Box Plucker a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp a

distance :: (Floating a, Box Plucker a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp a

norm :: (Floating a, Box Plucker a) => Exp (Plucker a) -> Exp a

signorm :: (Floating a, Box Plucker a) => Exp (Plucker a) -> Exp (Plucker a)

cst a => IsProduct cst (Plucker a)

Associated Types

type ProdRepr (Plucker a) :: *

Methods

fromProd :: proxy cst -> Plucker a -> ProdRepr (Plucker a)

toProd :: proxy cst -> ProdRepr (Plucker a) -> Plucker a

prod :: proxy cst -> Plucker a -> ProdR cst (ProdRepr (Plucker a))

(Lift Exp a, Elt (Plain a)) => Lift Exp (Plucker a)

Associated Types

type Plain (Plucker a) :: *

Methods

lift :: Plucker a -> Exp (Plain (Plucker a))

Elt a => Unlift Exp (Plucker (Exp a))

Methods

unlift :: Exp (Plain (Plucker (Exp a))) -> Plucker (Exp a)

Floating a => Floating (Exp (Plucker a))

Methods

pi :: Exp (Plucker a)

exp :: Exp (Plucker a) -> Exp (Plucker a)

log :: Exp (Plucker a) -> Exp (Plucker a)

sqrt :: Exp (Plucker a) -> Exp (Plucker a)

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

logBase :: Exp (Plucker a) -> Exp (Plucker a) -> Exp (Plucker a)

sin :: Exp (Plucker a) -> Exp (Plucker a)

cos :: Exp (Plucker a) -> Exp (Plucker a)

tan :: Exp (Plucker a) -> Exp (Plucker a)

asin :: Exp (Plucker a) -> Exp (Plucker a)

acos :: Exp (Plucker a) -> Exp (Plucker a)

atan :: Exp (Plucker a) -> Exp (Plucker a)

sinh :: Exp (Plucker a) -> Exp (Plucker a)

cosh :: Exp (Plucker a) -> Exp (Plucker a)

tanh :: Exp (Plucker a) -> Exp (Plucker a)

asinh :: Exp (Plucker a) -> Exp (Plucker a)

acosh :: Exp (Plucker a) -> Exp (Plucker a)

atanh :: Exp (Plucker a) -> Exp (Plucker a)

log1p :: Exp (Plucker a) -> Exp (Plucker a)

expm1 :: Exp (Plucker a) -> Exp (Plucker a)

log1pexp :: Exp (Plucker a) -> Exp (Plucker a)

log1mexp :: Exp (Plucker a) -> Exp (Plucker a)

Fractional a => Fractional (Exp (Plucker a))

Methods

(/) :: Exp (Plucker a) -> Exp (Plucker a) -> Exp (Plucker a)

recip :: Exp (Plucker a) -> Exp (Plucker a)

fromRational :: Rational -> Exp (Plucker a)

Num a => Num (Exp (Plucker a))

Methods

(+) :: Exp (Plucker a) -> Exp (Plucker a) -> Exp (Plucker a)

(-) :: Exp (Plucker a) -> Exp (Plucker a) -> Exp (Plucker a)

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

negate :: Exp (Plucker a) -> Exp (Plucker a)

abs :: Exp (Plucker a) -> Exp (Plucker a)

signum :: Exp (Plucker a) -> Exp (Plucker a)

fromInteger :: Integer -> Exp (Plucker a)

Ord a => Ord (Plucker a)

Methods

(<) :: Exp (Plucker a) -> Exp (Plucker a) -> Exp Bool

(>) :: Exp (Plucker a) -> Exp (Plucker a) -> Exp Bool

(<=) :: Exp (Plucker a) -> Exp (Plucker a) -> Exp Bool

(>=) :: Exp (Plucker a) -> Exp (Plucker a) -> Exp Bool

min :: Exp (Plucker a) -> Exp (Plucker a) -> Exp (Plucker a)

max :: Exp (Plucker a) -> Exp (Plucker a) -> Exp (Plucker a)

compare :: Exp (Plucker a) -> Exp (Plucker a) -> Exp Ordering

Eq a => Eq (Plucker a)

Methods

(==) :: Exp (Plucker a) -> Exp (Plucker a) -> Exp Bool

(/=) :: Exp (Plucker a) -> Exp (Plucker a) -> Exp Bool

Elt a => Elt (Plucker a)

Methods

eltType :: Plucker a -> TupleType (EltRepr (Plucker a))

fromElt :: Plucker a -> EltRepr (Plucker a)

toElt :: EltRepr (Plucker a) -> Plucker a

Epsilon a => Epsilon (Plucker a)

Methods

nearZero :: Exp (Plucker a) -> Exp Bool

(Elt a, Elt b) => Each (Exp (Plucker a)) (Exp (Plucker b)) (Exp a) (Exp b)

Methods

each :: Traversal (Exp (Plucker a)) (Exp (Plucker b)) (Exp a) (Exp b)