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

3D Euclidean space

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

Construct a 3D vector from a triple of components.

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

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

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

Curried version of r3.

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

Construct a 3D point from a triple of coordinates.

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

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

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

Curried version of r3.

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 #

project u v computes the projection of v onto u.

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

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

data V3 a :: * -> * #

A 3-dimensional vector

Constructors

V3 ~a ~a ~a

Instances

Monad V3
Methods (>>=) :: V3 a -> (a -> V3 b) -> V3 b # (>>) :: V3 a -> V3 b -> V3 b # return :: a -> V3 a # fail :: String -> V3 a #
Functor V3
Methods fmap :: (a -> b) -> V3 a -> V3 b # (<$) :: a -> V3 b -> V3 a #
MonadFix V3
Methods mfix :: (a -> V3 a) -> V3 a #
Applicative V3
Methods pure :: a -> V3 a # (<>) :: V3 (a -> b) -> V3 a -> V3 b # (>) :: V3 a -> V3 b -> V3 b # (<*) :: V3 a -> V3 b -> V3 a #
Foldable V3
Methods fold :: Monoid m => V3 m -> 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
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) #
Generic1 V3
Associated Types type Rep1 (V3 :: * -> ) :: -> * # Methods from1 :: V3 a -> Rep1 V3 a # to1 :: Rep1 V3 a -> V3 a #
Apply V3
Methods (<.>) :: V3 (a -> b) -> V3 a -> V3 b # (.>) :: V3 a -> V3 b -> V3 b # (<.) :: V3 a -> V3 b -> V3 a #
Distributive 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
Associated Types type Rep (V3 :: * -> ) :: # Methods tabulate :: (Rep V3 -> a) -> V3 a # index :: V3 a -> Rep V3 -> a #
Eq1 V3
Methods liftEq :: (a -> b -> Bool) -> V3 a -> V3 b -> Bool #
Ord1 V3
Methods liftCompare :: (a -> b -> Ordering) -> V3 a -> V3 b -> Ordering #
Read1 V3
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V3 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V3 a] #
Show1 V3
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V3 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V3 a] -> ShowS #
MonadZip 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
Methods serializeWith :: MonadPut m => (a -> m ()) -> V3 a -> m () # deserializeWith :: MonadGet m => m a -> m (V3 a) #
Additive 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 #
Traversable1 V3
Methods traverse1 :: Apply f => (a -> f b) -> V3 a -> f (V3 b) # sequence1 :: Apply f => V3 (f b) -> f (V3 b) #
Affine V3
Associated Types type Diff (V3 :: * -> ) :: -> * # 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 #
R3 V3
Methods _z :: Functor f => (a -> f a) -> V3 a -> f (V3 a) # _xyz :: Functor f => (V3 a -> f (V3 a)) -> V3 a -> f (V3 a) #
R2 V3
Methods _y :: Functor f => (a -> f a) -> V3 a -> f (V3 a) # _xy :: Functor f => (V2 a -> f (V2 a)) -> V3 a -> f (V3 a) #
R1 V3
Methods _x :: Functor f => (a -> f a) -> V3 a -> f (V3 a) #
Finite V3
Associated Types type Size (V3 :: * -> *) :: Nat # Methods toV :: V3 a -> V Nat (Size V3) a # fromV :: V Nat (Size V3) a -> V3 a #
Metric 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
Methods (>>-) :: V3 a -> (a -> V3 b) -> V3 b # join :: V3 (V3 a) -> V3 a #
Foldable1 V3
Methods fold1 :: Semigroup m => V3 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V3 a -> m # toNonEmpty :: V3 a -> NonEmpty a #
Unbox a => Vector Vector (V3 a)
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 #
Unbox a => MVector MVector (V3 a)
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)
Methods minBound :: V3 a # maxBound :: V3 a #
Eq a => Eq (V3 a)
Methods (==) :: V3 a -> V3 a -> Bool # (/=) :: V3 a -> V3 a -> Bool #
Floating a => Floating (V3 a)
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)
Methods (/) :: V3 a -> V3 a -> V3 a # recip :: V3 a -> V3 a # fromRational :: Rational -> V3 a #
Data a => Data (V3 a)
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 :: (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)
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)
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)
Methods readsPrec :: Int -> ReadS (V3 a) # readList :: ReadS [V3 a] # readPrec :: ReadPrec (V3 a) # readListPrec :: ReadPrec [V3 a] #
Show a => Show (V3 a)
Methods showsPrec :: Int -> V3 a -> ShowS # show :: V3 a -> String # showList :: [V3 a] -> ShowS #
Ix a => Ix (V3 a)
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)
Associated Types type Rep (V3 a) :: * -> * # Methods from :: V3 a -> Rep (V3 a) x # to :: Rep (V3 a) x -> V3 a #
Storable a => Storable (V3 a)
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)
Methods put :: V3 a -> Put # get :: Get (V3 a) # putList :: [V3 a] -> Put #
Serial a => Serial (V3 a)
Methods serialize :: MonadPut m => V3 a -> m () # deserialize :: MonadGet m => m (V3 a) #
Serialize a => Serialize (V3 a)
Methods put :: Putter (V3 a) # get :: Get (V3 a) #
NFData a => NFData (V3 a)
Methods rnf :: V3 a -> () #
Hashable a => Hashable (V3 a)
Methods hashWithSalt :: Int -> V3 a -> Int # hash :: V3 a -> Int #
Unbox a => Unbox (V3 a)

Ixed (V3 a)
Methods ix :: Index (V3 a) -> Traversal' (V3 a) (IxValue (V3 a)) #
Epsilon a => Epsilon (V3 a)
Methods nearZero :: V3 a -> Bool #
Coordinates (V3 n) #
Associated Types type FinalCoord (V3 n) :: * # type PrevDim (V3 n) :: * # type Decomposition (V3 n) :: * # Methods (^&) :: PrevDim (V3 n) -> FinalCoord (V3 n) -> V3 n # pr :: PrevDim (V3 n) -> FinalCoord (V3 n) -> V3 n # coords :: V3 n -> Decomposition (V3 n) #
FunctorWithIndex (E V3) V3
Methods imap :: (E V3 -> a -> b) -> V3 a -> V3 b # imapped :: (Indexable (E V3) p, Settable f) => p a (f b) -> V3 a -> f (V3 b) #
FoldableWithIndex (E V3) V3
Methods ifoldMap :: Monoid m => (E V3 -> a -> m) -> V3 a -> m # ifolded :: (Indexable (E V3) p, Contravariant f, Applicative f) => p a (f a) -> V3 a -> f (V3 a) # 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
Methods itraverse :: Applicative f => (E V3 -> a -> f b) -> V3 a -> f (V3 b) # itraversed :: (Indexable (E V3) p, Applicative f) => p a (f b) -> V3 a -> f (V3 b) #
Each (V3 a) (V3 b) a b
Methods each :: Traversal (V3 a) (V3 b) a b #
TypeableFloat n => Traced (BoundingBox V3 n) #
Methods getTrace :: BoundingBox V3 n -> Trace (V (BoundingBox V3 n)) (N (BoundingBox V3 n)) #
type Rep1 V3
type Rep1 V3 = D1 (MetaData "V3" "Linear.V3" "linear-1.20.7-LM9jZhdWZ2yIxbtdhUjC67" False) (C1 (MetaCons "V3" PrefixI False) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1))))
type Rep V3
type Rep V3 = E V3
type Diff V3
type Diff V3 = V3
type Size V3
type Size V3 = 3
data MVector s (V3 a)
data MVector s (V3 a) = MV_V3 ~Int ~(MVector s a)
type Rep (V3 a)
type Rep (V3 a) = D1 (MetaData "V3" "Linear.V3" "linear-1.20.7-LM9jZhdWZ2yIxbtdhUjC67" False) (C1 (MetaCons "V3" PrefixI False) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)))))
type V (V3 n) #
type V (V3 n) = V3
type N (V3 n) #
type N (V3 n) = n
data Vector (V3 a)
data Vector (V3 a) = V_V3 ~Int ~(Vector a)
type Index (V3 a)
type Index (V3 a) = E V3
type IxValue (V3 a)
type IxValue (V3 a) = a
type FinalCoord (V3 n) #
type FinalCoord (V3 n) = n
type PrevDim (V3 n) #
type PrevDim (V3 n) = V2 n
type Decomposition (V3 n) #
type Decomposition (V3 n) = (:&) ((:&) n n) n

type P3 = Point V3 #

type T3 = Transformation V3 #

class R1 t where #

A space that has at least 1 basis vector _x.

Methods

_x :: Functor f => (a -> f a) -> t a -> f (t a) #

>>> V1 2 ^._x
2

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

Instances

R1 Identity
Methods _x :: Functor f => (a -> f a) -> Identity a -> f (Identity a) #
R1 V4
Methods _x :: Functor f => (a -> f a) -> V4 a -> f (V4 a) #
R1 V3
Methods _x :: Functor f => (a -> f a) -> V3 a -> f (V3 a) #
R1 V2
Methods _x :: Functor f => (a -> f a) -> V2 a -> f (V2 a) #
R1 V1
Methods _x :: Functor f => (a -> f a) -> V1 a -> f (V1 a) #
R1 f => R1 (Point f)
Methods _x :: Functor f => (a -> f a) -> Point f a -> f (Point f a) #

class R1 t => R2 t where #

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

Methods

_y :: Functor f => (a -> f a) -> t a -> f (t a) #

>>> V2 1 2 ^._y
2

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

_xy :: Functor f => (V2 a -> f (V2 a)) -> t a -> f (t a) #

Instances

R2 V4
Methods _y :: Functor f => (a -> f a) -> V4 a -> f (V4 a) # _xy :: Functor f => (V2 a -> f (V2 a)) -> V4 a -> f (V4 a) #
R2 V3
Methods _y :: Functor f => (a -> f a) -> V3 a -> f (V3 a) # _xy :: Functor f => (V2 a -> f (V2 a)) -> V3 a -> f (V3 a) #
R2 V2
Methods _y :: Functor f => (a -> f a) -> V2 a -> f (V2 a) # _xy :: Functor f => (V2 a -> f (V2 a)) -> V2 a -> f (V2 a) #
R2 f => R2 (Point f)
Methods _y :: Functor f => (a -> f a) -> Point f a -> f (Point f a) # _xy :: Functor f => (V2 a -> f (V2 a)) -> Point f a -> f (Point f a) #

class R2 t => R3 t where #

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

Methods

_z :: Functor f => (a -> f a) -> t a -> f (t a) #

>>> V3 1 2 3 ^. _z
3

_xyz :: Functor f => (V3 a -> f (V3 a)) -> t a -> f (t a) #

Instances

R3 V4
Methods _z :: Functor f => (a -> f a) -> V4 a -> f (V4 a) # _xyz :: Functor f => (V3 a -> f (V3 a)) -> V4 a -> f (V4 a) #
R3 V3
Methods _z :: Functor f => (a -> f a) -> V3 a -> f (V3 a) # _xyz :: Functor f => (V3 a -> f (V3 a)) -> V3 a -> f (V3 a) #
R3 f => R3 (Point f)
Methods _z :: Functor f => (a -> f a) -> Point f a -> f (Point f a) # _xyz :: Functor f => (V3 a -> f (V3 a)) -> Point f a -> f (Point f a) #

Orphan instances

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