linear-1.21.1: Linear Algebra
Copyright(C) 2012-2015 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityexperimental
Portabilitynon-portable
Safe HaskellTrustworthy
LanguageHaskell2010

Linear.Plucker

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

Instances details
Monad Plucker Source # 
Instance details

Defined in Linear.Plucker

Methods

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

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

return :: a -> Plucker a

Functor Plucker Source # 
Instance details

Defined in Linear.Plucker

Methods

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

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

MonadFix Plucker Source # 
Instance details

Defined in Linear.Plucker

Methods

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

Applicative Plucker Source # 
Instance details

Defined in Linear.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 Source # 
Instance details

Defined in Linear.Plucker

Methods

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

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

Defined in Linear.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)

Show1 Plucker Source # 
Instance details

Defined in Linear.Plucker

Methods

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

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

Read1 Plucker Source # 
Instance details

Defined in Linear.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]

Ord1 Plucker Source # 
Instance details

Defined in Linear.Plucker

Methods

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

Eq1 Plucker Source # 
Instance details

Defined in Linear.Plucker

Methods

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

MonadZip Plucker Source # 
Instance details

Defined in Linear.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)

Traversable1 Plucker Source # 
Instance details

Defined in Linear.Plucker

Methods

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

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

Additive Plucker Source # 
Instance details

Defined in Linear.Plucker

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 #

Apply Plucker Source # 
Instance details

Defined in Linear.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

Distributive Plucker Source # 
Instance details

Defined in Linear.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)

Bind Plucker Source # 
Instance details

Defined in Linear.Plucker

Methods

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

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

Metric Plucker Source # 
Instance details

Defined in Linear.Plucker

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 #

Serial1 Plucker Source # 
Instance details

Defined in Linear.Plucker

Methods

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

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

Representable Plucker Source # 
Instance details

Defined in Linear.Plucker

Associated Types

type Rep Plucker

Methods

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

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

Foldable1 Plucker Source # 
Instance details

Defined in Linear.Plucker

Methods

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

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

toNonEmpty :: Plucker a -> NonEmpty a

Finite Plucker Source # 
Instance details

Defined in Linear.Plucker

Associated Types

type Size Plucker :: Nat Source #

Methods

toV :: Plucker a -> V (Size Plucker) a Source #

fromV :: V (Size Plucker) a -> Plucker a Source #

Trace Plucker Source # 
Instance details

Defined in Linear.Trace

Methods

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

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

Affine Plucker Source # 
Instance details

Defined in Linear.Affine

Associated Types

type Diff Plucker :: Type -> Type 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 # 
Instance details

Defined in Linear.Plucker

Methods

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

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

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

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

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

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

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

Unbox a => MVector MVector (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

Methods

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

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

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

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

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

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

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

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

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

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

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

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

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

Eq a => Eq (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

Methods

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

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

Floating a => Floating (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

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 # 
Instance details

Defined in Linear.Plucker

Methods

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

recip :: Plucker a -> Plucker a

fromRational :: Rational -> Plucker a

Num a => Num (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

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 # 
Instance details

Defined in Linear.Plucker

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 # 
Instance details

Defined in Linear.Plucker

Methods

readsPrec :: Int -> ReadS (Plucker a)

readList :: ReadS [Plucker a]

readPrec :: ReadPrec (Plucker a)

readListPrec :: ReadPrec [Plucker a]

Show a => Show (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

Methods

showsPrec :: Int -> Plucker a -> ShowS

show :: Plucker a -> String

showList :: [Plucker a] -> ShowS

Ix a => Ix (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

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 # 
Instance details

Defined in Linear.Plucker

Associated Types

type Rep (Plucker a) :: Type -> Type

Methods

from :: Plucker a -> Rep (Plucker a) x

to :: Rep (Plucker a) x -> Plucker a

Semigroup a => Semigroup (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

Methods

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

sconcat :: NonEmpty (Plucker a) -> Plucker a

stimes :: Integral b => b -> Plucker a -> Plucker a

Monoid a => Monoid (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

Methods

mempty :: Plucker a

mappend :: Plucker a -> Plucker a -> Plucker a

mconcat :: [Plucker a] -> Plucker a

Lift a => Lift (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

Methods

lift :: Plucker a -> Q Exp

Storable a => Storable (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

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 ()

Unbox a => Unbox (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

Random a => Random (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

Methods

randomR :: RandomGen g => (Plucker a, Plucker a) -> g -> (Plucker a, g) Source #

random :: RandomGen g => g -> (Plucker a, g) Source #

randomRs :: RandomGen g => (Plucker a, Plucker a) -> g -> [Plucker a] Source #

randoms :: RandomGen g => g -> [Plucker a] Source #

randomRIO :: (Plucker a, Plucker a) -> IO (Plucker a) Source #

randomIO :: IO (Plucker a) Source #

Binary a => Binary (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

Methods

put :: Plucker a -> Put

get :: Get (Plucker a)

putList :: [Plucker a] -> Put

NFData a => NFData (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

Methods

rnf :: Plucker a -> ()

Epsilon a => Epsilon (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

Methods

nearZero :: Plucker a -> Bool Source #

Ixed (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

Methods

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

Hashable a => Hashable (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

Methods

hashWithSalt :: Int -> Plucker a -> Int

hash :: Plucker a -> Int

Serial a => Serial (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

Methods

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

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

Serialize a => Serialize (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

Methods

put :: Putter (Plucker a)

get :: Get (Plucker a)

Generic1 Plucker Source # 
Instance details

Defined in Linear.Plucker

Associated Types

type Rep1 Plucker :: k -> Type

Methods

from1 :: forall (a :: k). Plucker a -> Rep1 Plucker a

to1 :: forall (a :: k). Rep1 Plucker a -> Plucker a

FoldableWithIndex (E Plucker) Plucker Source # 
Instance details

Defined in Linear.Plucker

Methods

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

ifolded :: IndexedFold (E Plucker) (Plucker a) 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

FunctorWithIndex (E Plucker) Plucker Source # 
Instance details

Defined in Linear.Plucker

Methods

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

imapped :: IndexedSetter (E Plucker) (Plucker a) (Plucker b) a b

TraversableWithIndex (E Plucker) Plucker Source # 
Instance details

Defined in Linear.Plucker

Methods

itraverse :: Applicative f => (E Plucker -> a -> f b) -> Plucker a -> f (Plucker b)

itraversed :: IndexedTraversal (E Plucker) (Plucker a) (Plucker b) a b

Each (Plucker a) (Plucker b) a b Source # 
Instance details

Defined in Linear.Plucker

Methods

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

Field1 (Plucker a) (Plucker a) a a Source # 
Instance details

Defined in Linear.Plucker

Methods

_1 :: Lens (Plucker a) (Plucker a) a a

Field2 (Plucker a) (Plucker a) a a Source # 
Instance details

Defined in Linear.Plucker

Methods

_2 :: Lens (Plucker a) (Plucker a) a a

Field3 (Plucker a) (Plucker a) a a Source # 
Instance details

Defined in Linear.Plucker

Methods

_3 :: Lens (Plucker a) (Plucker a) a a

Field4 (Plucker a) (Plucker a) a a Source # 
Instance details

Defined in Linear.Plucker

Methods

_4 :: Lens (Plucker a) (Plucker a) a a

Field5 (Plucker a) (Plucker a) a a Source # 
Instance details

Defined in Linear.Plucker

Methods

_5 :: Lens (Plucker a) (Plucker a) a a

Field6 (Plucker a) (Plucker a) a a Source # 
Instance details

Defined in Linear.Plucker

Methods

_6 :: Lens (Plucker a) (Plucker a) a a

type Rep Plucker Source # 
Instance details

Defined in Linear.Plucker

type Rep Plucker = E Plucker
type Size Plucker Source # 
Instance details

Defined in Linear.Plucker

type Size Plucker = 6
type Diff Plucker Source # 
Instance details

Defined in Linear.Affine

data MVector s (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

data MVector s (Plucker a) = MV_Plucker !Int (MVector s a)
type Rep (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

type Rep (Plucker a) = D1 ('MetaData "Plucker" "Linear.Plucker" "linear-1.21.1-ILvJ7ath0ShCdBBZlFlbTo" 'False) (C1 ('MetaCons "Plucker" 'PrefixI 'False) ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a))) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)))))
data Vector (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

data Vector (Plucker a) = V_Plucker !Int (Vector a)
type Index (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

type Index (Plucker a) = E Plucker
type IxValue (Plucker a) Source # 
Instance details

Defined in Linear.Plucker

type IxValue (Plucker a) = a
type Rep1 Plucker Source # 
Instance details

Defined in Linear.Plucker

type Rep1 Plucker = D1 ('MetaData "Plucker" "Linear.Plucker" "linear-1.21.1-ILvJ7ath0ShCdBBZlFlbTo" 'False) (C1 ('MetaCons "Plucker" 'PrefixI 'False) ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1))))

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

Instances details
Eq LinePass Source # 
Instance details

Defined in Linear.Plucker

Methods

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

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

Show LinePass Source # 
Instance details

Defined in Linear.Plucker

Methods

showsPrec :: Int -> LinePass -> ShowS

show :: LinePass -> String

showList :: [LinePass] -> ShowS

Generic LinePass Source # 
Instance details

Defined in Linear.Plucker

Associated Types

type Rep LinePass :: Type -> Type

Methods

from :: LinePass -> Rep LinePass x

to :: Rep LinePass x -> LinePass

type Rep LinePass Source # 
Instance details

Defined in Linear.Plucker

type Rep LinePass = D1 ('MetaData "LinePass" "Linear.Plucker" "linear-1.21.1-ILvJ7ath0ShCdBBZlFlbTo" 'False) (C1 ('MetaCons "Coplanar" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "Clockwise" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Counterclockwise" 'PrefixI 'False) (U1 :: Type -> Type)))

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