Copyright	2014 Edward Kmett Charles Durham [2015..2020] Trevor L. McDonell
License	BSD-style (see the file LICENSE)
Maintainer	Trevor L. McDonell <trevor.mcdonell@gmail.com>
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Array.Accelerate.Linear.Plucker

Contents

operations on lines
Basis elements
Orphan instances

Description

Plücker coordinates for lines in 3d homogeneous space.

Synopsis

data Plucker a = Plucker !a !a !a !a !a !a
pattern Plucker_ :: Elt a => Exp a -> Exp a -> Exp a -> Exp a -> Exp a -> Exp a -> Exp (Plucker a)
squaredError :: forall a. Num a => Exp (Plucker a) -> Exp a
isotropic :: Epsilon a => Exp (Plucker a) -> Exp Bool
(><) :: forall a. Num a => Exp (Plucker a) -> Exp (Plucker a) -> Exp a
plucker :: forall a. Num a => Exp (V4 a) -> Exp (V4 a) -> Exp (Plucker a)
plucker3D :: forall a. Num a => Exp (V3 a) -> Exp (V3 a) -> Exp (Plucker a)
data LinePass
- = Coplanar
- | Clockwise
- | Counterclockwise
pattern Clockwise_ :: HasCallStack => Exp LinePass
pattern Counterclockwise_ :: HasCallStack => Exp LinePass
pattern Coplanar_ :: HasCallStack => Exp LinePass
parallel :: Epsilon a => Exp (Plucker a) -> Exp (Plucker a) -> Exp Bool
intersects :: (Epsilon a, Ord a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp Bool
passes :: (Epsilon a, Ord a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp LinePass
quadranceToOrigin :: Fractional a => Exp (Plucker a) -> Exp a
closestToOrigin :: Fractional a => Exp (Plucker a) -> Exp (V3 a)
isLine :: Epsilon a => Exp (Plucker a) -> Exp Bool
p01 :: Elt a => Lens' (Exp (Plucker a)) (Exp a)
p02 :: Elt a => Lens' (Exp (Plucker a)) (Exp a)
p03 :: Elt a => Lens' (Exp (Plucker a)) (Exp a)
p10 :: Num a => Lens' (Exp (Plucker a)) (Exp a)
p12 :: Elt a => Lens' (Exp (Plucker a)) (Exp a)
p13 :: Num a => Lens' (Exp (Plucker a)) (Exp a)
p20 :: Num a => Lens' (Exp (Plucker a)) (Exp a)
p21 :: Num a => Lens' (Exp (Plucker a)) (Exp a)
p23 :: Elt a => Lens' (Exp (Plucker a)) (Exp a)
p30 :: Num a => Lens' (Exp (Plucker a)) (Exp a)
p31 :: Elt a => Lens' (Exp (Plucker a)) (Exp a)
p32 :: Num a => Lens' (Exp (Plucker a)) (Exp a)

Documentation

data Plucker a #

Plücker coordinates for lines in a 3-dimensional space.

Constructors

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

Instances

Monad Plucker
Instance details Defined in Linear.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
Instance details Defined in Linear.Plucker Methods fmap :: (a -> b) -> Plucker a -> Plucker b # (<$) :: a -> Plucker b -> Plucker a #
MonadFix Plucker
Instance details Defined in Linear.Plucker Methods mfix :: (a -> Plucker a) -> Plucker a #
Applicative Plucker
Instance details Defined in Linear.Plucker Methods pure :: a -> Plucker a # (<>) :: Plucker (a -> b) -> Plucker a -> Plucker b # liftA2 :: (a -> b -> c) -> Plucker a -> Plucker b -> Plucker c # (>) :: Plucker a -> Plucker b -> Plucker b # (<*) :: Plucker a -> Plucker b -> Plucker a #
Foldable Plucker
Instance details Defined in Linear.Plucker Methods fold :: Monoid m => Plucker m -> m # foldMap :: Monoid m => (a -> m) -> Plucker a -> m # foldr :: (a -> b -> b) -> b -> Plucker a -> b # foldr' :: (a -> b -> b) -> b -> Plucker a -> b # foldl :: (b -> a -> b) -> b -> Plucker a -> b # foldl' :: (b -> a -> b) -> b -> Plucker a -> b # foldr1 :: (a -> a -> a) -> Plucker a -> a # foldl1 :: (a -> a -> a) -> Plucker a -> a # toList :: Plucker a -> [a] # null :: Plucker a -> Bool # length :: Plucker a -> Int # elem :: Eq a => a -> Plucker a -> Bool # maximum :: Ord a => Plucker a -> a # minimum :: Ord a => Plucker a -> a # sum :: Num a => Plucker a -> a # product :: Num a => Plucker a -> a #
Traversable Plucker
Instance details Defined in Linear.Plucker Methods traverse :: Applicative f => (a -> f b) -> Plucker a -> f (Plucker b) # sequenceA :: Applicative f => Plucker (f a) -> f (Plucker a) # mapM :: Monad m => (a -> m b) -> Plucker a -> m (Plucker b) # sequence :: Monad m => Plucker (m a) -> m (Plucker a) #
Functor Plucker Source #
Instance details Defined in Data.Array.Accelerate.Linear.Plucker Methods fmap :: (Elt a, Elt b, Elt (Plucker a), Elt (Plucker b)) => (Exp a -> Exp b) -> Exp (Plucker a) -> Exp (Plucker b) # (<$) :: (Elt a, Elt b, Elt (Plucker a), Elt (Plucker b)) => Exp a -> Exp (Plucker b) -> Exp (Plucker a) #
Distributive Plucker
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) #
Representable Plucker
Instance details Defined in Linear.Plucker Associated Types type Rep Plucker :: Type # Methods tabulate :: (Rep Plucker -> a) -> Plucker a # index :: Plucker a -> Rep Plucker -> a #
Eq1 Plucker
Instance details Defined in Linear.Plucker Methods liftEq :: (a -> b -> Bool) -> Plucker a -> Plucker b -> Bool #
Ord1 Plucker
Instance details Defined in Linear.Plucker Methods liftCompare :: (a -> b -> Ordering) -> Plucker a -> Plucker b -> Ordering #
Read1 Plucker
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
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 #
MonadZip Plucker
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) #
Serial1 Plucker
Instance details Defined in Linear.Plucker Methods serializeWith :: MonadPut m => (a -> m ()) -> Plucker a -> m () # deserializeWith :: MonadGet m => m a -> m (Plucker a) #
Apply Plucker
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 #
Traversable1 Plucker
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) #
Trace Plucker
Instance details Defined in Linear.Trace Methods trace :: Num a => Plucker (Plucker a) -> a # diagonal :: Plucker (Plucker a) -> Plucker a #
Finite Plucker
Instance details Defined in Linear.Plucker Associated Types type Size Plucker :: Nat # Methods toV :: Plucker a -> V (Size Plucker) a # fromV :: V (Size Plucker) a -> Plucker a #
Metric Plucker
Instance details Defined in Linear.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
Instance details Defined in Linear.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
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 #
Bind Plucker
Instance details Defined in Linear.Plucker Methods (>>-) :: Plucker a -> (a -> Plucker b) -> Plucker b # join :: Plucker (Plucker a) -> Plucker a #
Additive Plucker Source #
Instance details Defined in Data.Array.Accelerate.Linear.Plucker Methods zero :: (Elt (Plucker a), Num a) => Exp (Plucker a) Source # (^+^) :: (Num a, Box Plucker a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp (Plucker a) Source # (^-^) :: (Num a, Box Plucker a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp (Plucker a) Source # lerp :: (Num a, Box Plucker a) => Exp a -> Exp (Plucker a) -> Exp (Plucker a) -> Exp (Plucker a) Source #
Metric Plucker Source #
Instance details Defined in Data.Array.Accelerate.Linear.Plucker Methods dot :: (Num a, Box Plucker a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp a Source # quadrance :: (Num a, Box Plucker a) => Exp (Plucker a) -> Exp a Source # qd :: (Num a, Box Plucker a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp a Source # distance :: (Floating a, Box Plucker a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp a Source # norm :: (Floating a, Box Plucker a) => Exp (Plucker a) -> Exp a Source # signorm :: (Floating a, Box Plucker a) => Exp (Plucker a) -> Exp (Plucker a) Source #
Trace Plucker Source #
Instance details Defined in Data.Array.Accelerate.Linear.Trace Methods trace :: (Num a, Box2 Plucker Plucker a) => Exp (Plucker (Plucker a)) -> Exp a Source # diagonal :: Box2 Plucker Plucker a => Exp (Plucker (Plucker a)) -> Exp (Plucker a) Source #
(Lift Exp a, Elt (Plain a)) => Lift Exp (Plucker a) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Plucker Associated Types type Plain (Plucker a) :: Type # Methods lift :: Plucker a -> Exp (Plain (Plucker a)) #
Elt a => Unlift Exp (Plucker (Exp a)) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Plucker Methods unlift :: Exp (Plain (Plucker (Exp a))) -> Plucker (Exp a) #
Unbox a => Vector Vector (Plucker a)
Instance details Defined in Linear.Plucker 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)
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 :: 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)
Instance details Defined in Linear.Plucker Methods (==) :: Plucker a -> Plucker a -> Bool # (/=) :: Plucker a -> Plucker a -> Bool #
Floating a => Floating (Exp (Plucker a)) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Plucker 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) #
Floating a => Floating (Plucker a)
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 (Exp (Plucker a)) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Plucker Methods (/) :: Exp (Plucker a) -> Exp (Plucker a) -> Exp (Plucker a) # recip :: Exp (Plucker a) -> Exp (Plucker a) # fromRational :: Rational -> Exp (Plucker a) #
Fractional a => Fractional (Plucker a)
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 (Exp (Plucker a)) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Plucker 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) #
Num a => Num (Plucker a)
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)
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)
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)
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)
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)
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)
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)
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)
Instance details Defined in Linear.Plucker Methods lift :: Plucker a -> Q Exp #
Ord a => Ord (Plucker a) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Plucker 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) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Plucker Methods (==) :: Exp (Plucker a) -> Exp (Plucker a) -> Exp Bool # (/=) :: Exp (Plucker a) -> Exp (Plucker a) -> Exp Bool #
Elt a => Elt (Plucker a) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Plucker Associated Types type EltR (Plucker a) :: Type Methods eltR :: TypeR (EltR (Plucker a)) tagsR :: [TagR (EltR (Plucker a))] fromElt :: Plucker a -> EltR (Plucker a) toElt :: EltR (Plucker a) -> Plucker a
Storable a => Storable (Plucker a)
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 () #
Binary a => Binary (Plucker a)
Instance details Defined in Linear.Plucker Methods put :: Plucker a -> Put # get :: Get (Plucker a) # putList :: [Plucker a] -> Put #
Serial a => Serial (Plucker a)
Instance details Defined in Linear.Plucker Methods serialize :: MonadPut m => Plucker a -> m () # deserialize :: MonadGet m => m (Plucker a) #
Serialize a => Serialize (Plucker a)
Instance details Defined in Linear.Plucker Methods put :: Putter (Plucker a) # get :: Get (Plucker a) #
NFData a => NFData (Plucker a)
Instance details Defined in Linear.Plucker Methods rnf :: Plucker a -> () #
Hashable a => Hashable (Plucker a)
Instance details Defined in Linear.Plucker Methods hashWithSalt :: Int -> Plucker a -> Int # hash :: Plucker a -> Int #
Unbox a => Unbox (Plucker a)
Instance details Defined in Linear.Plucker
Ixed (Plucker a)
Instance details Defined in Linear.Plucker Methods ix :: Index (Plucker a) -> Traversal' (Plucker a) (IxValue (Plucker a)) #
Epsilon a => Epsilon (Plucker a)
Instance details Defined in Linear.Plucker Methods nearZero :: Plucker a -> Bool #
Random a => Random (Plucker a)
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] # randomRIO :: (Plucker a, Plucker a) -> IO (Plucker a) # randomIO :: IO (Plucker a) #
Epsilon a => Epsilon (Plucker a) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Plucker Methods nearZero :: Exp (Plucker a) -> Exp Bool Source #
Generic1 Plucker
Instance details Defined in Linear.Plucker Associated Types type Rep1 Plucker :: k -> Type # Methods from1 :: Plucker a -> Rep1 Plucker a # to1 :: Rep1 Plucker a -> Plucker a #
FunctorWithIndex (E Plucker) Plucker
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 #
FoldableWithIndex (E Plucker) Plucker
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 #
TraversableWithIndex (E Plucker) Plucker
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
Instance details Defined in Linear.Plucker Methods each :: Traversal (Plucker a) (Plucker b) a b #
Field1 (Plucker a) (Plucker a) a a
Instance details Defined in Linear.Plucker Methods _1 :: Lens (Plucker a) (Plucker a) a a #
Field2 (Plucker a) (Plucker a) a a
Instance details Defined in Linear.Plucker Methods _2 :: Lens (Plucker a) (Plucker a) a a #
Field3 (Plucker a) (Plucker a) a a
Instance details Defined in Linear.Plucker Methods _3 :: Lens (Plucker a) (Plucker a) a a #
Field4 (Plucker a) (Plucker a) a a
Instance details Defined in Linear.Plucker Methods _4 :: Lens (Plucker a) (Plucker a) a a #
Field5 (Plucker a) (Plucker a) a a
Instance details Defined in Linear.Plucker Methods _5 :: Lens (Plucker a) (Plucker a) a a #
Field6 (Plucker a) (Plucker a) a a
Instance details Defined in Linear.Plucker Methods _6 :: Lens (Plucker a) (Plucker a) a a #
(Elt a, Elt b) => Each (Exp (Plucker a)) (Exp (Plucker b)) (Exp a) (Exp b) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Plucker Methods each :: Traversal (Exp (Plucker a)) (Exp (Plucker b)) (Exp a) (Exp b) #
type Rep Plucker
Instance details Defined in Linear.Plucker type Rep Plucker = E Plucker
type Size Plucker
Instance details Defined in Linear.Plucker type Size Plucker = 6
data MVector s (Plucker a)
Instance details Defined in Linear.Plucker data MVector s (Plucker a) = MV_Plucker !Int (MVector s a)
type Rep (Plucker a)
Instance details Defined in Linear.Plucker type Rep (Plucker a) = D1 (MetaData "Plucker" "Linear.Plucker" "linear-1.21.1-GSRtap511Ww6RirKx1xviJ" 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 EltR (Plucker a)
Instance details Defined in Data.Array.Accelerate.Linear.Plucker type EltR (Plucker a) = GEltR () (Rep (Plucker a))
type Plain (Plucker a) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Plucker type Plain (Plucker a) = Plucker (Plain a)
data Vector (Plucker a)
Instance details Defined in Linear.Plucker data Vector (Plucker a) = V_Plucker !Int (Vector a)
type Index (Plucker a)
Instance details Defined in Linear.Plucker type Index (Plucker a) = E Plucker
type IxValue (Plucker a)
Instance details Defined in Linear.Plucker type IxValue (Plucker a) = a
type Rep1 Plucker
Instance details Defined in Linear.Plucker type Rep1 Plucker = D1 (MetaData "Plucker" "Linear.Plucker" "linear-1.21.1-GSRtap511Ww6RirKx1xviJ" 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))))

pattern Plucker_ :: Elt a => Exp a -> Exp a -> Exp a -> Exp a -> Exp a -> Exp a -> Exp (Plucker a) Source #

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

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 Source #

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

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
Instance details Defined in Linear.Plucker Methods (==) :: LinePass -> LinePass -> Bool # (/=) :: LinePass -> LinePass -> Bool #
Show LinePass
Instance details Defined in Linear.Plucker Methods showsPrec :: Int -> LinePass -> ShowS # show :: LinePass -> String # showList :: [LinePass] -> ShowS #
Generic LinePass
Instance details Defined in Linear.Plucker Associated Types type Rep LinePass :: Type -> Type # Methods from :: LinePass -> Rep LinePass x # to :: Rep LinePass x -> LinePass #
Eq LinePass Source #
Instance details Defined in Data.Array.Accelerate.Linear.Plucker Methods (==) :: Exp LinePass -> Exp LinePass -> Exp Bool # (/=) :: Exp LinePass -> Exp LinePass -> Exp Bool #
Elt LinePass Source #
Instance details Defined in Data.Array.Accelerate.Linear.Plucker Associated Types type EltR LinePass :: Type Methods eltR :: TypeR (EltR LinePass) tagsR :: [TagR (EltR LinePass)] fromElt :: LinePass -> EltR LinePass toElt :: EltR LinePass -> LinePass
type Rep LinePass
Instance details Defined in Linear.Plucker type Rep LinePass = D1 (MetaData "LinePass" "Linear.Plucker" "linear-1.21.1-GSRtap511Ww6RirKx1xviJ" 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)))
type EltR LinePass
Instance details Defined in Data.Array.Accelerate.Linear.Plucker type EltR LinePass = GEltR () (Rep LinePass)

pattern Clockwise_ :: HasCallStack => Exp LinePass Source #

pattern Counterclockwise_ :: HasCallStack => Exp LinePass Source #

pattern Coplanar_ :: HasCallStack => Exp LinePass Source #

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

Checks if two lines are parallel.

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

Checks if two lines intersect (or nearly intersect).

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

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

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

The minimum squared distance of a line from the origin.

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

The point where a line is closest to the origin.

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

Basis elements

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