Copyright	(c) 2011 diagrams-lib team (see LICENSE)
License	BSD-style (see LICENSE)
Maintainer	diagrams-discuss@googlegroups.com
Safe Haskell	None
Language	Haskell2010

Diagrams.ThreeD.Types

Contents

3D Euclidean space
Orphan instances

Description

Basic types for three-dimensional Euclidean space.

Synopsis

r3 :: (n, n, n) -> V3 n
unr3 :: V3 n -> (n, n, n)
mkR3 :: n -> n -> n -> V3 n
p3 :: (n, n, n) -> P3 n
unp3 :: P3 n -> (n, n, n)
mkP3 :: n -> n -> n -> P3 n
r3Iso :: Iso' (V3 n) (n, n, n)
p3Iso :: Iso' (P3 n) (n, n, n)
project :: (Metric v, Fractional a) => v a -> v a -> v a
r3SphericalIso :: RealFloat n => Iso' (V3 n) (n, Angle n, Angle n)
r3CylindricalIso :: RealFloat n => Iso' (V3 n) (n, Angle n, n)
data V3 a = V3 !a !a !a
type P3 = Point V3
type T3 = Transformation V3
class R1 (t :: Type -> Type) where
- _x :: Lens' (t a) a
class R1 t => R2 (t :: Type -> Type) where
- _y :: Lens' (t a) a
- _xy :: Lens' (t a) (V2 a)
class R2 t => R3 (t :: Type -> Type) where
- _z :: Lens' (t a) a
- _xyz :: Lens' (t a) (V3 a)

3D Euclidean space

r3 :: (n, n, n) -> V3 n Source #

Construct a 3D vector from a triple of components.

unr3 :: V3 n -> (n, n, n) Source #

Convert a 3D vector back into a triple of components.

mkR3 :: n -> n -> n -> V3 n Source #

Curried version of r3.

p3 :: (n, n, n) -> P3 n Source #

Construct a 3D point from a triple of coordinates.

unp3 :: P3 n -> (n, n, n) Source #

Convert a 3D point back into a triple of coordinates.

mkP3 :: n -> n -> n -> P3 n Source #

Curried version of r3.

r3Iso :: Iso' (V3 n) (n, n, n) Source #

p3Iso :: Iso' (P3 n) (n, n, n) Source #

project :: (Metric v, Fractional a) => v a -> v a -> v a #

project u v computes the projection of v onto u.

r3SphericalIso :: RealFloat n => Iso' (V3 n) (n, Angle n, Angle n) Source #

r3CylindricalIso :: RealFloat n => Iso' (V3 n) (n, Angle n, n) Source #

data V3 a #

A 3-dimensional vector

Constructors

V3 !a !a !a

Instances

Instances details

Monad V3
Instance details Defined in Linear.V3 Methods (>>=) :: V3 a -> (a -> V3 b) -> V3 b # (>>) :: V3 a -> V3 b -> V3 b # return :: a -> V3 a #
Functor V3
Instance details Defined in Linear.V3 Methods fmap :: (a -> b) -> V3 a -> V3 b # (<$) :: a -> V3 b -> V3 a #
MonadFix V3
Instance details Defined in Linear.V3 Methods mfix :: (a -> V3 a) -> V3 a #
Applicative V3
Instance details Defined in Linear.V3 Methods pure :: a -> V3 a # (<>) :: V3 (a -> b) -> V3 a -> V3 b # liftA2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c # (>) :: V3 a -> V3 b -> V3 b # (<*) :: V3 a -> V3 b -> V3 a #
Foldable V3
Instance details Defined in Linear.V3 Methods fold :: Monoid m => V3 m -> m # foldMap :: Monoid m => (a -> m) -> V3 a -> m # foldMap' :: Monoid m => (a -> m) -> V3 a -> m # foldr :: (a -> b -> b) -> b -> V3 a -> b # foldr' :: (a -> b -> b) -> b -> V3 a -> b # foldl :: (b -> a -> b) -> b -> V3 a -> b # foldl' :: (b -> a -> b) -> b -> V3 a -> b # foldr1 :: (a -> a -> a) -> V3 a -> a # foldl1 :: (a -> a -> a) -> V3 a -> a # toList :: V3 a -> [a] # null :: V3 a -> Bool # length :: V3 a -> Int # elem :: Eq a => a -> V3 a -> Bool # maximum :: Ord a => V3 a -> a # minimum :: Ord a => V3 a -> a # sum :: Num a => V3 a -> a # product :: Num a => V3 a -> a #
Traversable V3
Instance details Defined in Linear.V3 Methods traverse :: Applicative f => (a -> f b) -> V3 a -> f (V3 b) # sequenceA :: Applicative f => V3 (f a) -> f (V3 a) # mapM :: Monad m => (a -> m b) -> V3 a -> m (V3 b) # sequence :: Monad m => V3 (m a) -> m (V3 a) #
Apply V3
Instance details Defined in Linear.V3 Methods (<.>) :: V3 (a -> b) -> V3 a -> V3 b # (.>) :: V3 a -> V3 b -> V3 b # (<.) :: V3 a -> V3 b -> V3 a # liftF2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c #
Distributive V3
Instance details Defined in Linear.V3 Methods distribute :: Functor f => f (V3 a) -> V3 (f a) # collect :: Functor f => (a -> V3 b) -> f a -> V3 (f b) # distributeM :: Monad m => m (V3 a) -> V3 (m a) # collectM :: Monad m => (a -> V3 b) -> m a -> V3 (m b) #
Representable V3
Instance details Defined in Linear.V3 Associated Types type Rep V3 # Methods tabulate :: (Rep V3 -> a) -> V3 a # index :: V3 a -> Rep V3 -> a #
Eq1 V3
Instance details Defined in Linear.V3 Methods liftEq :: (a -> b -> Bool) -> V3 a -> V3 b -> Bool #
Ord1 V3
Instance details Defined in Linear.V3 Methods liftCompare :: (a -> b -> Ordering) -> V3 a -> V3 b -> Ordering #
Read1 V3
Instance details Defined in Linear.V3 Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V3 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V3 a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V3 a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V3 a] #
Show1 V3
Instance details Defined in Linear.V3 Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V3 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V3 a] -> ShowS #
MonadZip V3
Instance details Defined in Linear.V3 Methods mzip :: V3 a -> V3 b -> V3 (a, b) # mzipWith :: (a -> b -> c) -> V3 a -> V3 b -> V3 c # munzip :: V3 (a, b) -> (V3 a, V3 b) #
Serial1 V3
Instance details Defined in Linear.V3 Methods serializeWith :: MonadPut m => (a -> m ()) -> V3 a -> m () # deserializeWith :: MonadGet m => m a -> m (V3 a) #
Additive V3
Instance details Defined in Linear.V3 Methods zero :: Num a => V3 a # (^+^) :: Num a => V3 a -> V3 a -> V3 a # (^-^) :: Num a => V3 a -> V3 a -> V3 a # lerp :: Num a => a -> V3 a -> V3 a -> V3 a # liftU2 :: (a -> a -> a) -> V3 a -> V3 a -> V3 a # liftI2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c #
Hashable1 V3
Instance details Defined in Linear.V3 Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> V3 a -> Int #
Traversable1 V3
Instance details Defined in Linear.V3 Methods traverse1 :: Apply f => (a -> f b) -> V3 a -> f (V3 b) # sequence1 :: Apply f => V3 (f b) -> f (V3 b) #
Affine V3
Instance details Defined in Linear.Affine Associated Types type Diff V3 :: Type -> Type # Methods (.-.) :: Num a => V3 a -> V3 a -> Diff V3 a # (.+^) :: Num a => V3 a -> Diff V3 a -> V3 a # (.-^) :: Num a => V3 a -> Diff V3 a -> V3 a #
Trace V3
Instance details Defined in Linear.Trace Methods trace :: Num a => V3 (V3 a) -> a # diagonal :: V3 (V3 a) -> V3 a #
R3 V3
Instance details Defined in Linear.V3 Methods _z :: Lens' (V3 a) a # _xyz :: Lens' (V3 a) (V3 a) #
R2 V3
Instance details Defined in Linear.V3 Methods _y :: Lens' (V3 a) a # _xy :: Lens' (V3 a) (V2 a) #
R1 V3
Instance details Defined in Linear.V3 Methods _x :: Lens' (V3 a) a #
Finite V3
Instance details Defined in Linear.V3 Associated Types type Size V3 :: Nat # Methods toV :: V3 a -> V (Size V3) a # fromV :: V (Size V3) a -> V3 a #
Metric V3
Instance details Defined in Linear.V3 Methods dot :: Num a => V3 a -> V3 a -> a # quadrance :: Num a => V3 a -> a # qd :: Num a => V3 a -> V3 a -> a # distance :: Floating a => V3 a -> V3 a -> a # norm :: Floating a => V3 a -> a # signorm :: Floating a => V3 a -> V3 a #
Bind V3
Instance details Defined in Linear.V3 Methods (>>-) :: V3 a -> (a -> V3 b) -> V3 b # join :: V3 (V3 a) -> V3 a #
Foldable1 V3
Instance details Defined in Linear.V3 Methods fold1 :: Semigroup m => V3 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V3 a -> m # toNonEmpty :: V3 a -> NonEmpty a #
HasPhi V3 Source #
Instance details Defined in Diagrams.ThreeD.Types Methods _phi :: RealFloat n => Lens' (V3 n) (Angle n) Source #
HasTheta V3 Source #
Instance details Defined in Diagrams.ThreeD.Types Methods _theta :: RealFloat n => Lens' (V3 n) (Angle n) Source #
HasR V3 Source #
Instance details Defined in Diagrams.ThreeD.Types Methods _r :: RealFloat n => Lens' (V3 n) n Source #
Lift a => Lift (V3 a :: Type)
Instance details Defined in Linear.V3 Methods lift :: V3 a -> Q Exp # liftTyped :: V3 a -> Q (TExp (V3 a)) #
Unbox a => Vector Vector (V3 a)
Instance details Defined in Linear.V3 Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> m (Vector (V3 a)) # basicUnsafeThaw :: PrimMonad m => Vector (V3 a) -> m (Mutable Vector (PrimState m) (V3 a)) # basicLength :: Vector (V3 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V3 a) -> Vector (V3 a) # basicUnsafeIndexM :: Monad m => Vector (V3 a) -> Int -> m (V3 a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> Vector (V3 a) -> m () # elemseq :: Vector (V3 a) -> V3 a -> b -> b #
Num r => Coalgebra r (E V3)
Instance details Defined in Linear.Algebra Methods comult :: (E V3 -> r) -> E V3 -> E V3 -> r # counital :: (E V3 -> r) -> r #
Unbox a => MVector MVector (V3 a)
Instance details Defined in Linear.V3 Methods basicLength :: MVector s (V3 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V3 a) -> MVector s (V3 a) # basicOverlaps :: MVector s (V3 a) -> MVector s (V3 a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V3 a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V3 a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V3 a -> m (MVector (PrimState m) (V3 a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (V3 a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> V3 a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V3 a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V3 a) -> V3 a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (MVector (PrimState m) (V3 a)) #
Bounded a => Bounded (V3 a)
Instance details Defined in Linear.V3 Methods minBound :: V3 a # maxBound :: V3 a #
Eq a => Eq (V3 a)
Instance details Defined in Linear.V3 Methods (==) :: V3 a -> V3 a -> Bool # (/=) :: V3 a -> V3 a -> Bool #
Floating a => Floating (V3 a)
Instance details Defined in Linear.V3 Methods pi :: V3 a # exp :: V3 a -> V3 a # log :: V3 a -> V3 a # sqrt :: V3 a -> V3 a # (**) :: V3 a -> V3 a -> V3 a # logBase :: V3 a -> V3 a -> V3 a # sin :: V3 a -> V3 a # cos :: V3 a -> V3 a # tan :: V3 a -> V3 a # asin :: V3 a -> V3 a # acos :: V3 a -> V3 a # atan :: V3 a -> V3 a # sinh :: V3 a -> V3 a # cosh :: V3 a -> V3 a # tanh :: V3 a -> V3 a # asinh :: V3 a -> V3 a # acosh :: V3 a -> V3 a # atanh :: V3 a -> V3 a # log1p :: V3 a -> V3 a # expm1 :: V3 a -> V3 a # log1pexp :: V3 a -> V3 a # log1mexp :: V3 a -> V3 a #
Fractional a => Fractional (V3 a)
Instance details Defined in Linear.V3 Methods (/) :: V3 a -> V3 a -> V3 a # recip :: V3 a -> V3 a # fromRational :: Rational -> V3 a #
Data a => Data (V3 a)
Instance details Defined in Linear.V3 Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V3 a -> c (V3 a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V3 a) # toConstr :: V3 a -> Constr # dataTypeOf :: V3 a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (V3 a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V3 a)) # gmapT :: (forall b. Data b => b -> b) -> V3 a -> V3 a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r # gmapQ :: (forall d. Data d => d -> u) -> V3 a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> V3 a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) #
Num a => Num (V3 a)
Instance details Defined in Linear.V3 Methods (+) :: V3 a -> V3 a -> V3 a # (-) :: V3 a -> V3 a -> V3 a # (*) :: V3 a -> V3 a -> V3 a # negate :: V3 a -> V3 a # abs :: V3 a -> V3 a # signum :: V3 a -> V3 a # fromInteger :: Integer -> V3 a #
Ord a => Ord (V3 a)
Instance details Defined in Linear.V3 Methods compare :: V3 a -> V3 a -> Ordering # (<) :: V3 a -> V3 a -> Bool # (<=) :: V3 a -> V3 a -> Bool # (>) :: V3 a -> V3 a -> Bool # (>=) :: V3 a -> V3 a -> Bool # max :: V3 a -> V3 a -> V3 a # min :: V3 a -> V3 a -> V3 a #
Read a => Read (V3 a)
Instance details Defined in Linear.V3 Methods readsPrec :: Int -> ReadS (V3 a) # readList :: ReadS [V3 a] # readPrec :: ReadPrec (V3 a) # readListPrec :: ReadPrec [V3 a] #
Show a => Show (V3 a)
Instance details Defined in Linear.V3 Methods showsPrec :: Int -> V3 a -> ShowS # show :: V3 a -> String # showList :: [V3 a] -> ShowS #
Ix a => Ix (V3 a)
Instance details Defined in Linear.V3 Methods range :: (V3 a, V3 a) -> [V3 a] # index :: (V3 a, V3 a) -> V3 a -> Int # unsafeIndex :: (V3 a, V3 a) -> V3 a -> Int # inRange :: (V3 a, V3 a) -> V3 a -> Bool # rangeSize :: (V3 a, V3 a) -> Int # unsafeRangeSize :: (V3 a, V3 a) -> Int #
Generic (V3 a)
Instance details Defined in Linear.V3 Associated Types type Rep (V3 a) :: Type -> Type # Methods from :: V3 a -> Rep (V3 a) x # to :: Rep (V3 a) x -> V3 a #
Semigroup a => Semigroup (V3 a)
Instance details Defined in Linear.V3 Methods (<>) :: V3 a -> V3 a -> V3 a # sconcat :: NonEmpty (V3 a) -> V3 a # stimes :: Integral b => b -> V3 a -> V3 a #
Monoid a => Monoid (V3 a)
Instance details Defined in Linear.V3 Methods mempty :: V3 a # mappend :: V3 a -> V3 a -> V3 a # mconcat :: [V3 a] -> V3 a #
Storable a => Storable (V3 a)
Instance details Defined in Linear.V3 Methods sizeOf :: V3 a -> Int # alignment :: V3 a -> Int # peekElemOff :: Ptr (V3 a) -> Int -> IO (V3 a) # pokeElemOff :: Ptr (V3 a) -> Int -> V3 a -> IO () # peekByteOff :: Ptr b -> Int -> IO (V3 a) # pokeByteOff :: Ptr b -> Int -> V3 a -> IO () # peek :: Ptr (V3 a) -> IO (V3 a) # poke :: Ptr (V3 a) -> V3 a -> IO () #
Binary a => Binary (V3 a)
Instance details Defined in Linear.V3 Methods put :: V3 a -> Put # get :: Get (V3 a) # putList :: [V3 a] -> Put #
Serial a => Serial (V3 a)
Instance details Defined in Linear.V3 Methods serialize :: MonadPut m => V3 a -> m () # deserialize :: MonadGet m => m (V3 a) #
Serialize a => Serialize (V3 a)
Instance details Defined in Linear.V3 Methods put :: Putter (V3 a) # get :: Get (V3 a) #
NFData a => NFData (V3 a)
Instance details Defined in Linear.V3 Methods rnf :: V3 a -> () #
Transformable (V3 n) Source #
Instance details Defined in Diagrams.ThreeD.Types Methods transform :: Transformation (V (V3 n)) (N (V3 n)) -> V3 n -> V3 n #
Hashable a => Hashable (V3 a)
Instance details Defined in Linear.V3 Methods hashWithSalt :: Int -> V3 a -> Int # hash :: V3 a -> Int #
Unbox a => Unbox (V3 a)
Instance details Defined in Linear.V3
Ixed (V3 a)
Instance details Defined in Linear.V3 Methods ix :: Index (V3 a) -> Traversal' (V3 a) (IxValue (V3 a)) #
Epsilon a => Epsilon (V3 a)
Instance details Defined in Linear.V3 Methods nearZero :: V3 a -> Bool #
Random a => Random (V3 a)
Instance details Defined in Linear.V3 Methods randomR :: RandomGen g => (V3 a, V3 a) -> g -> (V3 a, g) # random :: RandomGen g => g -> (V3 a, g) # randomRs :: RandomGen g => (V3 a, V3 a) -> g -> [V3 a] # randoms :: RandomGen g => g -> [V3 a] #
Coordinates (V3 n) Source #
Instance details Defined in Diagrams.Coordinates Associated Types type FinalCoord (V3 n) Source # type PrevDim (V3 n) Source # type Decomposition (V3 n) Source # Methods (^&) :: PrevDim (V3 n) -> FinalCoord (V3 n) -> V3 n Source # pr :: PrevDim (V3 n) -> FinalCoord (V3 n) -> V3 n Source # coords :: V3 n -> Decomposition (V3 n) Source #
Generic1 V3
Instance details Defined in Linear.V3 Associated Types type Rep1 V3 :: k -> Type # Methods from1 :: forall (a :: k). V3 a -> Rep1 V3 a # to1 :: forall (a :: k). Rep1 V3 a -> V3 a #
FunctorWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods imap :: (E V3 -> a -> b) -> V3 a -> V3 b #
FoldableWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods ifoldMap :: Monoid m => (E V3 -> a -> m) -> V3 a -> m # ifoldMap' :: Monoid m => (E V3 -> a -> m) -> V3 a -> m # ifoldr :: (E V3 -> a -> b -> b) -> b -> V3 a -> b # ifoldl :: (E V3 -> b -> a -> b) -> b -> V3 a -> b # ifoldr' :: (E V3 -> a -> b -> b) -> b -> V3 a -> b # ifoldl' :: (E V3 -> b -> a -> b) -> b -> V3 a -> b #
TraversableWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods itraverse :: Applicative f => (E V3 -> a -> f b) -> V3 a -> f (V3 b) #
Each (V3 a) (V3 b) a b
Instance details Defined in Linear.V3 Methods each :: Traversal (V3 a) (V3 b) a b #
Field1 (V3 a) (V3 a) a a
Instance details Defined in Linear.V3 Methods _1 :: Lens (V3 a) (V3 a) a a #
Field2 (V3 a) (V3 a) a a
Instance details Defined in Linear.V3 Methods _2 :: Lens (V3 a) (V3 a) a a #
Field3 (V3 a) (V3 a) a a
Instance details Defined in Linear.V3 Methods _3 :: Lens (V3 a) (V3 a) a a #
TypeableFloat n => Traced (BoundingBox V3 n) Source #
Instance details Defined in Diagrams.BoundingBox Methods getTrace :: BoundingBox V3 n -> Trace (V (BoundingBox V3 n)) (N (BoundingBox V3 n)) #
type Rep V3
Instance details Defined in Linear.V3 type Rep V3 = E V3
type Diff V3
Instance details Defined in Linear.Affine type Diff V3 = V3
type Size V3
Instance details Defined in Linear.V3 type Size V3 = 3
data MVector s (V3 a)
Instance details Defined in Linear.V3 data MVector s (V3 a) = MV_V3 !Int !(MVector s a)
type Rep (V3 a)
Instance details Defined in Linear.V3 type Rep (V3 a) = D1 ('MetaData "V3" "Linear.V3" "linear-1.21.8-EtxeJWQbh7CIGwzUT72syQ" 'False) (C1 ('MetaCons "V3" '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))))
type V (V3 n) Source #
Instance details Defined in Diagrams.ThreeD.Types type V (V3 n) = V3
type N (V3 n) Source #
Instance details Defined in Diagrams.ThreeD.Types type N (V3 n) = n
data Vector (V3 a)
Instance details Defined in Linear.V3 data Vector (V3 a) = V_V3 !Int !(Vector a)
type Index (V3 a)
Instance details Defined in Linear.V3 type Index (V3 a) = E V3
type IxValue (V3 a)
Instance details Defined in Linear.V3 type IxValue (V3 a) = a
type FinalCoord (V3 n) Source #
Instance details Defined in Diagrams.Coordinates type FinalCoord (V3 n) = n
type PrevDim (V3 n) Source #
Instance details Defined in Diagrams.Coordinates type PrevDim (V3 n) = V2 n
type Decomposition (V3 n) Source #
Instance details Defined in Diagrams.Coordinates type Decomposition (V3 n) = (n :& n) :& n
type Rep1 V3
Instance details Defined in Linear.V3 type Rep1 V3 = D1 ('MetaData "V3" "Linear.V3" "linear-1.21.8-EtxeJWQbh7CIGwzUT72syQ" 'False) (C1 ('MetaCons "V3" '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)))

type P3 = Point V3 Source #

type T3 = Transformation V3 Source #

class R1 (t :: Type -> Type) where #

A space that has at least 1 basis vector _x.

Methods

_x :: Lens' (t a) a #

>>> V1 2 ^._x
2

>>> V1 2 & _x .~ 3
V1 3

Instances

Instances details

R1 Identity
Instance details Defined in Linear.V1 Methods _x :: Lens' (Identity a) a #
R1 Quaternion
Instance details Defined in Linear.Quaternion Methods _x :: Lens' (Quaternion a) a #
R1 V4
Instance details Defined in Linear.V4 Methods _x :: Lens' (V4 a) a #
R1 V3
Instance details Defined in Linear.V3 Methods _x :: Lens' (V3 a) a #
R1 V2
Instance details Defined in Linear.V2 Methods _x :: Lens' (V2 a) a #
R1 V1
Instance details Defined in Linear.V1 Methods _x :: Lens' (V1 a) a #
R1 f => R1 (Point f)
Instance details Defined in Linear.Affine Methods _x :: Lens' (Point f a) a #

class R1 t => R2 (t :: Type -> Type) where #

A space that distinguishes 2 orthogonal basis vectors _x and _y, but may have more.

Minimal complete definition

_xy

Methods

_y :: Lens' (t a) a #

>>> V2 1 2 ^._y
2

>>> V2 1 2 & _y .~ 3
V2 1 3

_xy :: Lens' (t a) (V2 a) #

Instances

Instances details

R2 Quaternion
Instance details Defined in Linear.Quaternion Methods _y :: Lens' (Quaternion a) a # _xy :: Lens' (Quaternion a) (V2 a) #
R2 V4
Instance details Defined in Linear.V4 Methods _y :: Lens' (V4 a) a # _xy :: Lens' (V4 a) (V2 a) #
R2 V3
Instance details Defined in Linear.V3 Methods _y :: Lens' (V3 a) a # _xy :: Lens' (V3 a) (V2 a) #
R2 V2
Instance details Defined in Linear.V2 Methods _y :: Lens' (V2 a) a # _xy :: Lens' (V2 a) (V2 a) #
R2 f => R2 (Point f)
Instance details Defined in Linear.Affine Methods _y :: Lens' (Point f a) a # _xy :: Lens' (Point f a) (V2 a) #

class R2 t => R3 (t :: Type -> Type) where #

A space that distinguishes 3 orthogonal basis vectors: _x, _y, and _z. (It may have more)

Methods

_z :: Lens' (t a) a #

>>> V3 1 2 3 ^. _z
3

_xyz :: Lens' (t a) (V3 a) #

Instances

Instances details

R3 Quaternion
Instance details Defined in Linear.Quaternion Methods _z :: Lens' (Quaternion a) a # _xyz :: Lens' (Quaternion a) (V3 a) #
R3 V4
Instance details Defined in Linear.V4 Methods _z :: Lens' (V4 a) a # _xyz :: Lens' (V4 a) (V3 a) #
R3 V3
Instance details Defined in Linear.V3 Methods _z :: Lens' (V3 a) a # _xyz :: Lens' (V3 a) (V3 a) #
R3 f => R3 (Point f)
Instance details Defined in Linear.Affine Methods _z :: Lens' (Point f a) a # _xyz :: Lens' (Point f a) (V3 a) #

Orphan instances

HasPhi V3 Source #
Instance details Methods _phi :: RealFloat n => Lens' (V3 n) (Angle n) Source #
HasTheta V3 Source #
Instance details Methods _theta :: RealFloat n => Lens' (V3 n) (Angle n) Source #
HasR V3 Source #
Instance details Methods _r :: RealFloat n => Lens' (V3 n) n Source #
Transformable (V3 n) Source #
Instance details Methods transform :: Transformation (V (V3 n)) (N (V3 n)) -> V3 n -> V3 n #