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	Haskell2010

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

Instances details

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 #
MonadFix Plucker Source #
Instance details Defined in Linear.Plucker Methods mfix :: (a -> Plucker a) -> Plucker a #
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) #
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 #
Eq1 Plucker Source #
Instance details Defined in Linear.Plucker Methods liftEq :: (a -> b -> Bool) -> Plucker a -> Plucker b -> Bool #
Ord1 Plucker Source #
Instance details Defined in Linear.Plucker Methods liftCompare :: (a -> b -> Ordering) -> Plucker a -> Plucker b -> Ordering #
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] #
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 #
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) #
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 #
Functor Plucker Source #
Instance details Defined in Linear.Plucker Methods fmap :: (a -> b) -> Plucker a -> Plucker b # (<$) :: a -> Plucker b -> Plucker a #
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 #
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) #
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) #
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 #
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 #
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 #
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 #
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 #
Bind Plucker Source #
Instance details Defined in Linear.Plucker Methods (>>-) :: Plucker a -> (a -> Plucker b) -> Plucker b # join :: Plucker (Plucker a) -> 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 #
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) #
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 #
Unbox a => Vector Vector (Plucker a) Source #
Instance details Defined in Linear.Plucker Methods basicUnsafeFreeze :: Mutable Vector s (Plucker a) -> ST s (Vector (Plucker a)) # basicUnsafeThaw :: Vector (Plucker a) -> ST s (Mutable Vector s (Plucker a)) # basicLength :: Vector (Plucker a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Plucker a) -> Vector (Plucker a) # basicUnsafeIndexM :: Vector (Plucker a) -> Int -> Box (Plucker a) # basicUnsafeCopy :: Mutable Vector s (Plucker a) -> Vector (Plucker a) -> ST s () # elemseq :: Vector (Plucker a) -> Plucker a -> b -> b #
Unbox a => MVector MVector (Plucker a) Source #
Instance details Defined in Linear.Plucker 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 :: Int -> ST s (MVector s (Plucker a)) # basicInitialize :: MVector s (Plucker a) -> ST s () # basicUnsafeReplicate :: Int -> Plucker a -> ST s (MVector s (Plucker a)) # basicUnsafeRead :: MVector s (Plucker a) -> Int -> ST s (Plucker a) # basicUnsafeWrite :: MVector s (Plucker a) -> Int -> Plucker a -> ST s () # basicClear :: MVector s (Plucker a) -> ST s () # basicSet :: MVector s (Plucker a) -> Plucker a -> ST s () # basicUnsafeCopy :: MVector s (Plucker a) -> MVector s (Plucker a) -> ST s () # basicUnsafeMove :: MVector s (Plucker a) -> MVector s (Plucker a) -> ST s () # basicUnsafeGrow :: MVector s (Plucker a) -> Int -> ST s (MVector s (Plucker a)) #
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 () #
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 #
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 #
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 #
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 #
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 #
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 #
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] #
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 #
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 #
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 #
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) #
NFData a => NFData (Plucker a) Source #
Instance details Defined in Linear.Plucker Methods rnf :: Plucker a -> () #
Eq a => Eq (Plucker a) Source #
Instance details Defined in Linear.Plucker Methods (==) :: Plucker a -> Plucker a -> Bool # (/=) :: Plucker a -> Plucker a -> Bool #
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 #
Hashable a => Hashable (Plucker a) Source #
Instance details Defined in Linear.Plucker Methods hashWithSalt :: Int -> Plucker a -> Int # hash :: Plucker a -> Int #
Ixed (Plucker a) Source #
Instance details Defined in Linear.Plucker Methods ix :: Index (Plucker a) -> Traversal' (Plucker a) (IxValue (Plucker a)) #
Epsilon a => Epsilon (Plucker a) Source #
Instance details Defined in Linear.Plucker Methods nearZero :: Plucker a -> Bool Source #
Random a => Random (Plucker a) Source #
Instance details Defined in Linear.Plucker Methods randomR :: RandomGen g => (Plucker a, Plucker a) -> g -> (Plucker a, g) # random :: RandomGen g => g -> (Plucker a, g) # randomRs :: RandomGen g => (Plucker a, Plucker a) -> g -> [Plucker a] # randoms :: RandomGen g => g -> [Plucker a] #
Unbox a => Unbox (Plucker a) Source #
Instance details Defined in Linear.Plucker
FoldableWithIndex (E Plucker) Plucker Source #
Instance details Defined in Linear.Plucker Methods ifoldMap :: Monoid m => (E Plucker -> a -> m) -> Plucker a -> m # ifoldMap' :: Monoid m => (E Plucker -> a -> m) -> Plucker a -> m # 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 #
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) #
Lift a => Lift (Plucker a :: Type) Source #
Instance details Defined in Linear.Plucker Methods lift :: Quote m => Plucker a -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Plucker a -> Code m (Plucker a) #
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 Diff Plucker Source #
Instance details Defined in Linear.Affine type Diff Plucker = Plucker
type Size Plucker Source #
Instance details Defined in Linear.Plucker type Size Plucker = 6
type Rep1 Plucker Source #
Instance details Defined in Linear.Plucker type Rep1 Plucker = D1 ('MetaData "Plucker" "Linear.Plucker" "linear-1.22-azR7kz4en7IbThf75KgP8" '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))))
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-1.22-azR7kz4en7IbThf75KgP8" '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)))))
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
data Vector (Plucker a) Source #
Instance details Defined in Linear.Plucker data Vector (Plucker a) = V_Plucker !Int (Vector 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

Instances details

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 #
Show LinePass Source #
Instance details Defined in Linear.Plucker Methods showsPrec :: Int -> LinePass -> ShowS # show :: LinePass -> String # showList :: [LinePass] -> ShowS #
Eq LinePass Source #
Instance details Defined in Linear.Plucker Methods (==) :: LinePass -> LinePass -> Bool # (/=) :: LinePass -> LinePass -> Bool #
type Rep LinePass Source #
Instance details Defined in Linear.Plucker type Rep LinePass = D1 ('MetaData "LinePass" "Linear.Plucker" "linear-1.22-azR7kz4en7IbThf75KgP8" '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 #