License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

Linear.Affine

Description

Operations on affine spaces.

Synopsis

class Additive (Diff p) => Affine p where
- type Diff p :: Type -> Type
- (.-.) :: Num a => p a -> p a -> Diff p a
- (.+^) :: Num a => p a -> Diff p a -> p a
- (.-^) :: Num a => p a -> Diff p a -> p a
qdA :: (Affine p, Foldable (Diff p), Num a) => p a -> p a -> a
distanceA :: (Floating a, Foldable (Diff p), Affine p) => p a -> p a -> a
newtype Point f a = P (f a)
lensP :: Lens (Point f a) (Point g b) (f a) (g b)
_Point :: Iso (Point f a) (Point g b) (f a) (g b)
(.#) :: Coercible b a => (b -> c) -> (a -> b) -> a -> c
(#.) :: Coercible c b => (b -> c) -> (a -> b) -> a -> c
unP :: Point f a -> f a
origin :: (Additive f, Num a) => Point f a
relative :: (Additive f, Num a) => Point f a -> Iso' (Point f a) (f a)

Documentation

class Additive (Diff p) => Affine p where Source #

An affine space is roughly a vector space in which we have forgotten or at least pretend to have forgotten the origin.

a .+^ (b .-. a)  =  b@
(a .+^ u) .+^ v  =  a .+^ (u ^+^ v)@
(a .-. b) ^+^ v  =  (a .+^ v) .-. q@

Minimal complete definition

(.-.), (.+^)

Associated Types

type Diff p :: Type -> Type Source #

Methods

(.-.) :: Num a => p a -> p a -> Diff p a infixl 6 Source #

Get the difference between two points as a vector offset.

(.+^) :: Num a => p a -> Diff p a -> p a infixl 6 Source #

Add a vector offset to a point.

(.-^) :: Num a => p a -> Diff p a -> p a infixl 6 Source #

Subtract a vector offset from a point.

Instances

Instances details

Affine ZipList Source #
Instance details Defined in Linear.Affine Associated Types type Diff ZipList :: Type -> Type Source # Methods (.-.) :: Num a => ZipList a -> ZipList a -> Diff ZipList a Source # (.+^) :: Num a => ZipList a -> Diff ZipList a -> ZipList a Source # (.-^) :: Num a => ZipList a -> Diff ZipList a -> ZipList a Source #
Affine Complex Source #
Instance details Defined in Linear.Affine Associated Types type Diff Complex :: Type -> Type Source # Methods (.-.) :: Num a => Complex a -> Complex a -> Diff Complex a Source # (.+^) :: Num a => Complex a -> Diff Complex a -> Complex a Source # (.-^) :: Num a => Complex a -> Diff Complex a -> Complex a Source #
Affine Identity Source #
Instance details Defined in Linear.Affine Associated Types type Diff Identity :: Type -> Type Source # Methods (.-.) :: Num a => Identity a -> Identity a -> Diff Identity a Source # (.+^) :: Num a => Identity a -> Diff Identity a -> Identity a Source # (.-^) :: Num a => Identity a -> Diff Identity a -> Identity a Source #
Affine IntMap Source #
Instance details Defined in Linear.Affine Associated Types type Diff IntMap :: Type -> Type Source # Methods (.-.) :: Num a => IntMap a -> IntMap a -> Diff IntMap a Source # (.+^) :: Num a => IntMap a -> Diff IntMap a -> IntMap a Source # (.-^) :: Num a => IntMap a -> Diff IntMap a -> IntMap 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 #
Affine Quaternion Source #
Instance details Defined in Linear.Affine Associated Types type Diff Quaternion :: Type -> Type Source # Methods (.-.) :: Num a => Quaternion a -> Quaternion a -> Diff Quaternion a Source # (.+^) :: Num a => Quaternion a -> Diff Quaternion a -> Quaternion a Source # (.-^) :: Num a => Quaternion a -> Diff Quaternion a -> Quaternion a Source #
Affine V0 Source #
Instance details Defined in Linear.Affine Associated Types type Diff V0 :: Type -> Type Source # Methods (.-.) :: Num a => V0 a -> V0 a -> Diff V0 a Source # (.+^) :: Num a => V0 a -> Diff V0 a -> V0 a Source # (.-^) :: Num a => V0 a -> Diff V0 a -> V0 a Source #
Affine V1 Source #
Instance details Defined in Linear.Affine Associated Types type Diff V1 :: Type -> Type Source # Methods (.-.) :: Num a => V1 a -> V1 a -> Diff V1 a Source # (.+^) :: Num a => V1 a -> Diff V1 a -> V1 a Source # (.-^) :: Num a => V1 a -> Diff V1 a -> V1 a Source #
Affine V2 Source #
Instance details Defined in Linear.Affine Associated Types type Diff V2 :: Type -> Type Source # Methods (.-.) :: Num a => V2 a -> V2 a -> Diff V2 a Source # (.+^) :: Num a => V2 a -> Diff V2 a -> V2 a Source # (.-^) :: Num a => V2 a -> Diff V2 a -> V2 a Source #
Affine V3 Source #
Instance details Defined in Linear.Affine Associated Types type Diff V3 :: Type -> Type Source # Methods (.-.) :: Num a => V3 a -> V3 a -> Diff V3 a Source # (.+^) :: Num a => V3 a -> Diff V3 a -> V3 a Source # (.-^) :: Num a => V3 a -> Diff V3 a -> V3 a Source #
Affine V4 Source #
Instance details Defined in Linear.Affine Associated Types type Diff V4 :: Type -> Type Source # Methods (.-.) :: Num a => V4 a -> V4 a -> Diff V4 a Source # (.+^) :: Num a => V4 a -> Diff V4 a -> V4 a Source # (.-^) :: Num a => V4 a -> Diff V4 a -> V4 a Source #
Affine Vector Source #
Instance details Defined in Linear.Affine Associated Types type Diff Vector :: Type -> Type Source # Methods (.-.) :: Num a => Vector a -> Vector a -> Diff Vector a Source # (.+^) :: Num a => Vector a -> Diff Vector a -> Vector a Source # (.-^) :: Num a => Vector a -> Diff Vector a -> Vector a Source #
Affine Maybe Source #
Instance details Defined in Linear.Affine Associated Types type Diff Maybe :: Type -> Type Source # Methods (.-.) :: Num a => Maybe a -> Maybe a -> Diff Maybe a Source # (.+^) :: Num a => Maybe a -> Diff Maybe a -> Maybe a Source # (.-^) :: Num a => Maybe a -> Diff Maybe a -> Maybe a Source #
Affine List Source #
Instance details Defined in Linear.Affine Associated Types type Diff List :: Type -> Type Source # Methods (.-.) :: Num a => [a] -> [a] -> Diff List a Source # (.+^) :: Num a => [a] -> Diff List a -> [a] Source # (.-^) :: Num a => [a] -> Diff List a -> [a] Source #
Ord k => Affine (Map k) Source #
Instance details Defined in Linear.Affine Associated Types type Diff (Map k) :: Type -> Type Source # Methods (.-.) :: Num a => Map k a -> Map k a -> Diff (Map k) a Source # (.+^) :: Num a => Map k a -> Diff (Map k) a -> Map k a Source # (.-^) :: Num a => Map k a -> Diff (Map k) a -> Map k a Source #
Additive f => Affine (Point f) Source #
Instance details Defined in Linear.Affine Associated Types type Diff (Point f) :: Type -> Type Source # Methods (.-.) :: Num a => Point f a -> Point f a -> Diff (Point f) a Source # (.+^) :: Num a => Point f a -> Diff (Point f) a -> Point f a Source # (.-^) :: Num a => Point f a -> Diff (Point f) a -> Point f a Source #
(Eq k, Hashable k) => Affine (HashMap k) Source #
Instance details Defined in Linear.Affine Associated Types type Diff (HashMap k) :: Type -> Type Source # Methods (.-.) :: Num a => HashMap k a -> HashMap k a -> Diff (HashMap k) a Source # (.+^) :: Num a => HashMap k a -> Diff (HashMap k) a -> HashMap k a Source # (.-^) :: Num a => HashMap k a -> Diff (HashMap k) a -> HashMap k a Source #
Dim n => Affine (V n) Source #
Instance details Defined in Linear.Affine Associated Types type Diff (V n) :: Type -> Type Source # Methods (.-.) :: Num a => V n a -> V n a -> Diff (V n) a Source # (.+^) :: Num a => V n a -> Diff (V n) a -> V n a Source # (.-^) :: Num a => V n a -> Diff (V n) a -> V n a Source #
(Affine f, Affine g) => Affine (Product f g) Source #
Instance details Defined in Linear.Affine Associated Types type Diff (Product f g) :: Type -> Type Source # Methods (.-.) :: Num a => Product f g a -> Product f g a -> Diff (Product f g) a Source # (.+^) :: Num a => Product f g a -> Diff (Product f g) a -> Product f g a Source # (.-^) :: Num a => Product f g a -> Diff (Product f g) a -> Product f g a Source #
Affine ((->) b) Source #
Instance details Defined in Linear.Affine Associated Types type Diff ((->) b) :: Type -> Type Source # Methods (.-.) :: Num a => (b -> a) -> (b -> a) -> Diff ((->) b) a Source # (.+^) :: Num a => (b -> a) -> Diff ((->) b) a -> b -> a Source # (.-^) :: Num a => (b -> a) -> Diff ((->) b) a -> b -> a Source #

qdA :: (Affine p, Foldable (Diff p), Num a) => p a -> p a -> a Source #

Compute the quadrance of the difference (the square of the distance)

distanceA :: (Floating a, Foldable (Diff p), Affine p) => p a -> p a -> a Source #

Distance between two points in an affine space

newtype Point f a Source #

A handy wrapper to help distinguish points from vectors at the type level

Constructors

P (f a)

Instances

Instances details

Generic1 (Point f :: Type -> Type) Source #
Instance details Defined in Linear.Affine Associated Types type Rep1 (Point f) :: k -> Type Methods from1 :: forall (a :: k). Point f a -> Rep1 (Point f) a to1 :: forall (a :: k). Rep1 (Point f) a -> Point f a
Unbox (f a) => Vector Vector (Point f a) Source #
Instance details Defined in Linear.Affine Methods basicUnsafeFreeze :: Mutable Vector s (Point f a) -> ST s (Vector (Point f a)) basicUnsafeThaw :: Vector (Point f a) -> ST s (Mutable Vector s (Point f a)) basicLength :: Vector (Point f a) -> Int basicUnsafeSlice :: Int -> Int -> Vector (Point f a) -> Vector (Point f a) basicUnsafeIndexM :: Vector (Point f a) -> Int -> Box (Point f a) basicUnsafeCopy :: Mutable Vector s (Point f a) -> Vector (Point f a) -> ST s () elemseq :: Vector (Point f a) -> Point f a -> b -> b
Unbox (f a) => MVector MVector (Point f a) Source #
Instance details Defined in Linear.Affine Methods basicLength :: MVector s (Point f a) -> Int basicUnsafeSlice :: Int -> Int -> MVector s (Point f a) -> MVector s (Point f a) basicOverlaps :: MVector s (Point f a) -> MVector s (Point f a) -> Bool basicUnsafeNew :: Int -> ST s (MVector s (Point f a)) basicInitialize :: MVector s (Point f a) -> ST s () basicUnsafeReplicate :: Int -> Point f a -> ST s (MVector s (Point f a)) basicUnsafeRead :: MVector s (Point f a) -> Int -> ST s (Point f a) basicUnsafeWrite :: MVector s (Point f a) -> Int -> Point f a -> ST s () basicClear :: MVector s (Point f a) -> ST s () basicSet :: MVector s (Point f a) -> Point f a -> ST s () basicUnsafeCopy :: MVector s (Point f a) -> MVector s (Point f a) -> ST s () basicUnsafeMove :: MVector s (Point f a) -> MVector s (Point f a) -> ST s () basicUnsafeGrow :: MVector s (Point f a) -> Int -> ST s (MVector s (Point f a))
Representable f => Representable (Point f) Source #
Instance details Defined in Linear.Affine Associated Types type Rep (Point f) Methods tabulate :: (Rep (Point f) -> a) -> Point f a index :: Point f a -> Rep (Point f) -> a
Foldable f => Foldable (Point f) Source #
Instance details Defined in Linear.Affine Methods fold :: Monoid m => Point f m -> m foldMap :: Monoid m => (a -> m) -> Point f a -> m foldMap' :: Monoid m => (a -> m) -> Point f a -> m foldr :: (a -> b -> b) -> b -> Point f a -> b foldr' :: (a -> b -> b) -> b -> Point f a -> b foldl :: (b -> a -> b) -> b -> Point f a -> b foldl' :: (b -> a -> b) -> b -> Point f a -> b foldr1 :: (a -> a -> a) -> Point f a -> a foldl1 :: (a -> a -> a) -> Point f a -> a toList :: Point f a -> [a] null :: Point f a -> Bool length :: Point f a -> Int elem :: Eq a => a -> Point f a -> Bool maximum :: Ord a => Point f a -> a minimum :: Ord a => Point f a -> a sum :: Num a => Point f a -> a product :: Num a => Point f a -> a
Eq1 f => Eq1 (Point f) Source #
Instance details Defined in Linear.Affine Methods liftEq :: (a -> b -> Bool) -> Point f a -> Point f b -> Bool
Ord1 f => Ord1 (Point f) Source #
Instance details Defined in Linear.Affine Methods liftCompare :: (a -> b -> Ordering) -> Point f a -> Point f b -> Ordering
Read1 f => Read1 (Point f) Source #
Instance details Defined in Linear.Affine Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Point f a) liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Point f a] liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Point f a) liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Point f a]
Show1 f => Show1 (Point f) Source #
Instance details Defined in Linear.Affine Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Point f a -> ShowS liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Point f a] -> ShowS
Traversable f => Traversable (Point f) Source #
Instance details Defined in Linear.Affine Methods traverse :: Applicative f0 => (a -> f0 b) -> Point f a -> f0 (Point f b) sequenceA :: Applicative f0 => Point f (f0 a) -> f0 (Point f a) mapM :: Monad m => (a -> m b) -> Point f a -> m (Point f b) sequence :: Monad m => Point f (m a) -> m (Point f a)
Applicative f => Applicative (Point f) Source #
Instance details Defined in Linear.Affine Methods pure :: a -> Point f a (<>) :: Point f (a -> b) -> Point f a -> Point f b liftA2 :: (a -> b -> c) -> Point f a -> Point f b -> Point f c (>) :: Point f a -> Point f b -> Point f b (<*) :: Point f a -> Point f b -> Point f a
Functor f => Functor (Point f) Source #
Instance details Defined in Linear.Affine Methods fmap :: (a -> b) -> Point f a -> Point f b (<$) :: a -> Point f b -> Point f a
Monad f => Monad (Point f) Source #
Instance details Defined in Linear.Affine Methods (>>=) :: Point f a -> (a -> Point f b) -> Point f b (>>) :: Point f a -> Point f b -> Point f b return :: a -> Point f a
Serial1 f => Serial1 (Point f) Source #
Instance details Defined in Linear.Affine Methods serializeWith :: MonadPut m => (a -> m ()) -> Point f a -> m () deserializeWith :: MonadGet m => m a -> m (Point f a)
Distributive f => Distributive (Point f) Source #
Instance details Defined in Linear.Affine Methods distribute :: Functor f0 => f0 (Point f a) -> Point f (f0 a) collect :: Functor f0 => (a -> Point f b) -> f0 a -> Point f (f0 b) distributeM :: Monad m => m (Point f a) -> Point f (m a) collectM :: Monad m => (a -> Point f b) -> m a -> Point f (m b)
Hashable1 f => Hashable1 (Point f) Source #
Instance details Defined in Linear.Affine Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> Point f a -> Int
Additive f => Affine (Point f) Source #
Instance details Defined in Linear.Affine Associated Types type Diff (Point f) :: Type -> Type Source # Methods (.-.) :: Num a => Point f a -> Point f a -> Diff (Point f) a Source # (.+^) :: Num a => Point f a -> Diff (Point f) a -> Point f a Source # (.-^) :: Num a => Point f a -> Diff (Point f) a -> Point f a Source #
Metric f => Metric (Point f) Source #
Instance details Defined in Linear.Affine Methods dot :: Num a => Point f a -> Point f a -> a Source # quadrance :: Num a => Point f a -> a Source # qd :: Num a => Point f a -> Point f a -> a Source # distance :: Floating a => Point f a -> Point f a -> a Source # norm :: Floating a => Point f a -> a Source # signorm :: Floating a => Point f a -> Point f a Source #
Finite f => Finite (Point f) Source #
Instance details Defined in Linear.Affine Associated Types type Size (Point f) :: Nat Source # Methods toV :: Point f a -> V (Size (Point f)) a Source # fromV :: V (Size (Point f)) a -> Point f a Source #
R1 f => R1 (Point f) Source #
Instance details Defined in Linear.Affine Methods _x :: Lens' (Point f a) a Source #
R2 f => R2 (Point f) Source #
Instance details Defined in Linear.Affine Methods _y :: Lens' (Point f a) a Source # _xy :: Lens' (Point f a) (V2 a) Source #
R3 f => R3 (Point f) Source #
Instance details Defined in Linear.Affine Methods _z :: Lens' (Point f a) a Source # _xyz :: Lens' (Point f a) (V3 a) Source #
R4 f => R4 (Point f) Source #
Instance details Defined in Linear.Affine Methods _w :: Lens' (Point f a) a Source # _xyzw :: Lens' (Point f a) (V4 a) Source #
Additive f => Additive (Point f) Source #
Instance details Defined in Linear.Affine Methods zero :: Num a => Point f a Source # (^+^) :: Num a => Point f a -> Point f a -> Point f a Source # (^-^) :: Num a => Point f a -> Point f a -> Point f a Source # lerp :: Num a => a -> Point f a -> Point f a -> Point f a Source # liftU2 :: (a -> a -> a) -> Point f a -> Point f a -> Point f a Source # liftI2 :: (a -> b -> c) -> Point f a -> Point f b -> Point f c Source #
Apply f => Apply (Point f) Source #
Instance details Defined in Linear.Affine Methods (<.>) :: Point f (a -> b) -> Point f a -> Point f b (.>) :: Point f a -> Point f b -> Point f b (<.) :: Point f a -> Point f b -> Point f a liftF2 :: (a -> b -> c) -> Point f a -> Point f b -> Point f c
Bind f => Bind (Point f) Source #
Instance details Defined in Linear.Affine Methods (>>-) :: Point f a -> (a -> Point f b) -> Point f b join :: Point f (Point f a) -> Point f a
(Typeable f, Typeable a, Data (f a)) => Data (Point f a) Source #
Instance details Defined in Linear.Affine Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Point f a -> c (Point f a) gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Point f a) toConstr :: Point f a -> Constr dataTypeOf :: Point f a -> DataType dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Point f a)) dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Point f a)) gmapT :: (forall b. Data b => b -> b) -> Point f a -> Point f a gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Point f a -> r gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Point f a -> r gmapQ :: (forall d. Data d => d -> u) -> Point f a -> [u] gmapQi :: Int -> (forall d. Data d => d -> u) -> Point f a -> u gmapM :: Monad m => (forall d. Data d => d -> m d) -> Point f a -> m (Point f a) gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Point f a -> m (Point f a) gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Point f a -> m (Point f a)
Storable (f a) => Storable (Point f a) Source #
Instance details Defined in Linear.Affine Methods sizeOf :: Point f a -> Int alignment :: Point f a -> Int peekElemOff :: Ptr (Point f a) -> Int -> IO (Point f a) pokeElemOff :: Ptr (Point f a) -> Int -> Point f a -> IO () peekByteOff :: Ptr b -> Int -> IO (Point f a) pokeByteOff :: Ptr b -> Int -> Point f a -> IO () peek :: Ptr (Point f a) -> IO (Point f a) poke :: Ptr (Point f a) -> Point f a -> IO ()
Monoid (f a) => Monoid (Point f a) Source #
Instance details Defined in Linear.Affine Methods mempty :: Point f a mappend :: Point f a -> Point f a -> Point f a mconcat :: [Point f a] -> Point f a
Semigroup (f a) => Semigroup (Point f a) Source #
Instance details Defined in Linear.Affine Methods (<>) :: Point f a -> Point f a -> Point f a sconcat :: NonEmpty (Point f a) -> Point f a stimes :: Integral b => b -> Point f a -> Point f a
Generic (Point f a) Source #
Instance details Defined in Linear.Affine Associated Types type Rep (Point f a) :: Type -> Type Methods from :: Point f a -> Rep (Point f a) x to :: Rep (Point f a) x -> Point f a
Ix (f a) => Ix (Point f a) Source #
Instance details Defined in Linear.Affine Methods range :: (Point f a, Point f a) -> [Point f a] index :: (Point f a, Point f a) -> Point f a -> Int unsafeIndex :: (Point f a, Point f a) -> Point f a -> Int inRange :: (Point f a, Point f a) -> Point f a -> Bool rangeSize :: (Point f a, Point f a) -> Int unsafeRangeSize :: (Point f a, Point f a) -> Int
Num (f a) => Num (Point f a) Source #
Instance details Defined in Linear.Affine Methods (+) :: Point f a -> Point f a -> Point f a (-) :: Point f a -> Point f a -> Point f a (*) :: Point f a -> Point f a -> Point f a negate :: Point f a -> Point f a abs :: Point f a -> Point f a signum :: Point f a -> Point f a fromInteger :: Integer -> Point f a
Read (f a) => Read (Point f a) Source #
Instance details Defined in Linear.Affine Methods readsPrec :: Int -> ReadS (Point f a) readList :: ReadS [Point f a] readPrec :: ReadPrec (Point f a) readListPrec :: ReadPrec [Point f a]
Fractional (f a) => Fractional (Point f a) Source #
Instance details Defined in Linear.Affine Methods (/) :: Point f a -> Point f a -> Point f a recip :: Point f a -> Point f a fromRational :: Rational -> Point f a
Show (f a) => Show (Point f a) Source #
Instance details Defined in Linear.Affine Methods showsPrec :: Int -> Point f a -> ShowS show :: Point f a -> String showList :: [Point f a] -> ShowS
Binary (f a) => Binary (Point f a) Source #
Instance details Defined in Linear.Affine Methods put :: Point f a -> Put get :: Get (Point f a) putList :: [Point f a] -> Put
Serial (f a) => Serial (Point f a) Source #
Instance details Defined in Linear.Affine Methods serialize :: MonadPut m => Point f a -> m () deserialize :: MonadGet m => m (Point f a)
Serialize (f a) => Serialize (Point f a) Source #
Instance details Defined in Linear.Affine Methods put :: Putter (Point f a) get :: Get (Point f a)
NFData (f a) => NFData (Point f a) Source #
Instance details Defined in Linear.Affine Methods rnf :: Point f a -> ()
Eq (f a) => Eq (Point f a) Source #
Instance details Defined in Linear.Affine Methods (==) :: Point f a -> Point f a -> Bool (/=) :: Point f a -> Point f a -> Bool
Ord (f a) => Ord (Point f a) Source #
Instance details Defined in Linear.Affine Methods compare :: Point f a -> Point f a -> Ordering (<) :: Point f a -> Point f a -> Bool (<=) :: Point f a -> Point f a -> Bool (>) :: Point f a -> Point f a -> Bool (>=) :: Point f a -> Point f a -> Bool max :: Point f a -> Point f a -> Point f a min :: Point f a -> Point f a -> Point f a
Hashable (f a) => Hashable (Point f a) Source #
Instance details Defined in Linear.Affine Methods hashWithSalt :: Int -> Point f a -> Int hash :: Point f a -> Int
Ixed (f a) => Ixed (Point f a) Source #
Instance details Defined in Linear.Affine Methods ix :: Index (Point f a) -> Traversal' (Point f a) (IxValue (Point f a))
Wrapped (Point f a) Source #
Instance details Defined in Linear.Affine Associated Types type Unwrapped (Point f a) Methods _Wrapped' :: Iso' (Point f a) (Unwrapped (Point f a))
Epsilon (f a) => Epsilon (Point f a) Source #
Instance details Defined in Linear.Affine Methods nearZero :: Point f a -> Bool Source #
Random (f a) => Random (Point f a) Source #
Instance details Defined in Linear.Affine Methods randomR :: RandomGen g => (Point f a, Point f a) -> g -> (Point f a, g) random :: RandomGen g => g -> (Point f a, g) randomRs :: RandomGen g => (Point f a, Point f a) -> g -> [Point f a] randoms :: RandomGen g => g -> [Point f a]
Unbox (f a) => Unbox (Point f a) Source #
Instance details Defined in Linear.Affine
t ~ Point g b => Rewrapped (Point f a) t Source #
Instance details Defined in Linear.Affine
Traversable f => Each (Point f a) (Point f b) a b Source #
Instance details Defined in Linear.Affine Methods each :: Traversal (Point f a) (Point f b) a b
type Rep1 (Point f :: Type -> Type) Source #
Instance details Defined in Linear.Affine type Rep1 (Point f :: Type -> Type) = D1 ('MetaData "Point" "Linear.Affine" "linear-1.22-G4Vo2GnxAJbENICJAkz68L" 'True) (C1 ('MetaCons "P" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))
newtype MVector s (Point f a) Source #
Instance details Defined in Linear.Affine newtype MVector s (Point f a) = MV_P (MVector s (f a))
type Rep (Point f) Source #
Instance details Defined in Linear.Affine type Rep (Point f) = Rep f
type Diff (Point f) Source #
Instance details Defined in Linear.Affine type Diff (Point f) = f
type Size (Point f) Source #
Instance details Defined in Linear.Affine type Size (Point f) = Size f
type Rep (Point f a) Source #
Instance details Defined in Linear.Affine type Rep (Point f a) = D1 ('MetaData "Point" "Linear.Affine" "linear-1.22-G4Vo2GnxAJbENICJAkz68L" 'True) (C1 ('MetaCons "P" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))))
type Index (Point f a) Source #
Instance details Defined in Linear.Affine type Index (Point f a) = Index (f a)
type IxValue (Point f a) Source #
Instance details Defined in Linear.Affine type IxValue (Point f a) = IxValue (f a)
type Unwrapped (Point f a) Source #
Instance details Defined in Linear.Affine type Unwrapped (Point f a) = f a
newtype Vector (Point f a) Source #
Instance details Defined in Linear.Affine newtype Vector (Point f a) = V_P (Vector (f a))

lensP :: Lens (Point f a) (Point g b) (f a) (g b) Source #

_Point :: Iso (Point f a) (Point g b) (f a) (g b) Source #

(.#) :: Coercible b a => (b -> c) -> (a -> b) -> a -> c Source #

(#.) :: Coercible c b => (b -> c) -> (a -> b) -> a -> c Source #

unP :: Point f a -> f a Source #

origin :: (Additive f, Num a) => Point f a Source #

Vector spaces have origins.

relative :: (Additive f, Num a) => Point f a -> Iso' (Point f a) (f a) Source #

An isomorphism between points and vectors, given a reference point.