diagrams-lib-1.1.0.7: Embedded domain-specific language for declarative graphics

Copyright(c) 2014 diagrams-lib team (see LICENSE)
LicenseBSD-style (see LICENSE)
Maintainerdiagrams-discuss@googlegroups.com
Safe HaskellNone
LanguageHaskell2010

Diagrams.Prelude.ThreeD

Contents

Description

A module to re-export most of the functionality of the diagrams core and standard library, including 3D types and functions.

Synopsis

Core library

The core definitions of transformations, diagrams, backends, and so on.

Standard library

Attributes (color, line style, etc.) and styles.

Alignment of diagrams relative to their envelopes.

Combining multiple diagrams into one.

Giving concrete locations to translation-invariant things.

Linear and cubic bezier segments.

Trails.

Parametrization of segments and trails.

Adjusting the length of parameterized objects.

Computing tangent and normal vectors of segments and trails.

Trail-like things.

Paths.

Cubic splines.

Some additional transformation-related functions, like conjugation of transformations.

Giving names to subdiagrams and later retrieving subdiagrams by name.

Envelopes, aka functional bounding regions.

Traces, aka embedded raytracers, for finding points on the boundary of a diagram.

A query is a function that maps points in a vector space to values in some monoid; they can be used to annotate the points of a diagram with some values.

Utilities for working with points.

Convenience infix operators for working with coordinates.

things (shapes, transformations, combinators) specific to creating three-dimensional diagrams.

Tools for making animations.

Various utility definitions.

Convenience re-exports

For representing and operating on colors.

A large list of color names.

Semigroups and monoids show up all over the place, so things from Data.Semigroup and Data.Monoid often come in handy.

For computing with vectors.

For computing with points and vectors.

For working with Active (i.e. animated) things.

Essential Lens Combinators

(&) :: a -> (a -> b) -> b infixl 1

Passes the result of the left side to the function on the right side (forward pipe operator).

This is the flipped version of ($), which is more common in languages like F# as (|>) where it is needed for inference. Here it is supplied for notational convenience and given a precedence that allows it to be nested inside uses of ($).

>>> a & f
f a
>>> "hello" & length & succ
6

This combinator is commonly used when applying multiple Lens operations in sequence.

>>> ("hello","world") & _1.element 0 .~ 'j' & _1.element 4 .~ 'y'
("jelly","world")

This reads somewhat similar to:

>>> flip execState ("hello","world") $ do _1.element 0 .= 'j'; _1.element 4 .= 'y'
("jelly","world")

(.~) :: ASetter s t a b -> b -> s -> t infixr 4

Replace the target of a Lens or all of the targets of a Setter or Traversal with a constant value.

This is an infix version of set, provided for consistency with (.=).

f <$ a ≡ mapped .~ f $ a
>>> (a,b,c,d) & _4 .~ e
(a,b,c,e)
>>> (42,"world") & _1 .~ "hello"
("hello","world")
>>> (a,b) & both .~ c
(c,c)
(.~) :: Setter s t a b    -> b -> s -> t
(.~) :: Iso s t a b       -> b -> s -> t
(.~) :: Lens s t a b      -> b -> s -> t
(.~) :: Traversal s t a b -> b -> s -> t

(%~) :: Profunctor p => Setting p s t a b -> p a b -> s -> t infixr 4

Modifies the target of a Lens or all of the targets of a Setter or Traversal with a user supplied function.

This is an infix version of over.

fmap f ≡ mapped %~ f
fmapDefault f ≡ traverse %~ f
>>> (a,b,c) & _3 %~ f
(a,b,f c)
>>> (a,b) & both %~ f
(f a,f b)
>>> _2 %~ length $ (1,"hello")
(1,5)
>>> traverse %~ f $ [a,b,c]
[f a,f b,f c]
>>> traverse %~ even $ [1,2,3]
[False,True,False]
>>> traverse.traverse %~ length $ [["hello","world"],["!!!"]]
[[5,5],[3]]
(%~) :: Setter s t a b    -> (a -> b) -> s -> t
(%~) :: Iso s t a b       -> (a -> b) -> s -> t
(%~) :: Lens s t a b      -> (a -> b) -> s -> t
(%~) :: Traversal s t a b -> (a -> b) -> s -> t

class Functor f => Applicative f where

A functor with application, providing operations to

  • embed pure expressions (pure), and
  • sequence computations and combine their results (<*>).

A minimal complete definition must include implementations of these functions satisfying the following laws:

identity
pure id <*> v = v
composition
pure (.) <*> u <*> v <*> w = u <*> (v <*> w)
homomorphism
pure f <*> pure x = pure (f x)
interchange
u <*> pure y = pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

As a consequence of these laws, the Functor instance for f will satisfy

If f is also a Monad, it should satisfy

(which implies that pure and <*> satisfy the applicative functor laws).

Minimal complete definition

pure, (<*>)

Methods

pure :: a -> f a

Lift a value.

(<*>) :: f (a -> b) -> f a -> f b infixl 4

Sequential application.

(*>) :: f a -> f b -> f b infixl 4

Sequence actions, discarding the value of the first argument.

(<*) :: f a -> f b -> f a infixl 4

Sequence actions, discarding the value of the second argument.

Instances

Applicative [] 
Applicative IO 
Applicative Q 
Applicative Active 
Applicative Maybe 
Applicative Result 
Applicative Parser 
Applicative Id 
Applicative ZipList 
Applicative STM 
Applicative ReadPrec 
Applicative ReadP 
Applicative RGB 
Applicative Identity 
Applicative Id 
Applicative Tree 
Applicative Seq 
Applicative DList 
Applicative Interval 
Applicative Vector 
Applicative ReadM 
Applicative Parser 
Applicative ParserM 
Applicative Min 
Applicative Max 
Applicative First 
Applicative Last 
Applicative Option 
Applicative NonEmpty 
Applicative PprM 
Applicative Id 
Applicative Box 
Applicative Sum 
Applicative ((->) a) 
Applicative (Either e) 
Monoid a => Applicative ((,) a) 
HasTrie a => Applicative ((:->:) a) 
Applicative (ST s) 
Applicative (Parser i) 
Applicative (StateL s) 
Applicative (StateR s) 
Monoid m => Applicative (Const m) 
Monad m => Applicative (WrappedMonad m) 
Applicative (ST s) 
Arrow a => Applicative (ArrowMonad a) 
Applicative (Proxy *) 
Applicative m => Applicative (IdentityT m) 
Applicative (State s) 
Applicative (Query v) 
Applicative f => Applicative (Backwards f)

Apply f-actions in the reverse order.

Applicative m => Applicative (ListT m) 
(Functor m, Monad m) => Applicative (MaybeT m) 
Applicative (ReifiedGetter s) 
Applicative (ReifiedFold s) 
Applicative f => Applicative (Indexing f) 
Applicative f => Applicative (Indexing64 f) 
Applicative f => Applicative (WrappedApplicative f) 
Apply f => Applicative (MaybeApply f) 
Applicative f => Applicative (Reverse f)

Derived instance.

Applicative f => Applicative (Lift f)

A combination is Pure only if both parts are.

Monoid a => Applicative (Constant a) 
Arrow a => Applicative (WrappedArrow a b) 
Applicative w => Applicative (TracedT m w) 
Applicative (Cokleisli w a) 
(Functor m, Monad m) => Applicative (ErrorT e m) 
(Monad m, Monoid s) => Applicative (Focusing m s) 
Applicative (k (May s)) => Applicative (FocusingMay k s) 
(Monad m, Monoid r) => Applicative (Effect m r) 
Applicative (Indexed i a) 
Applicative (ContT r m) 
Applicative m => Applicative (ReaderT r m) 
(Functor m, Monad m) => Applicative (StateT s m) 
(Functor m, Monad m) => Applicative (StateT s m) 
(Monoid w, Applicative m) => Applicative (WriterT w m) 
(Monoid w, Applicative m) => Applicative (WriterT w m) 
(Applicative f, Applicative g) => Applicative (Compose f g) 
Applicative f => Applicative (UpStar f a) 
Applicative (DownStar f a) 
Applicative (Tagged k s) 
(Applicative f, Applicative g) => Applicative (Product f g) 
Typeable ((* -> *) -> Constraint) Applicative 
(Monad m, Monoid s, Monoid w) => Applicative (FocusingWith w m s) 
Applicative (k (s, w)) => Applicative (FocusingPlus w k s) 
Applicative (k (f s)) => Applicative (FocusingOn f k s) 
Applicative (k (Err e s)) => Applicative (FocusingErr e k s) 
(Monoid s, Monoid w, Monad m) => Applicative (EffectRWS w st m s) 
(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m) 
(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m) 

(*>) :: Applicative f => forall a b. f a -> f b -> f b

Sequence actions, discarding the value of the first argument.

(<*) :: Applicative f => forall a b. f a -> f b -> f a

Sequence actions, discarding the value of the second argument.

(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4

An infix synonym for fmap.

(<$) :: Functor f => forall a b. a -> f b -> f a

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

liftA :: Applicative f => (a -> b) -> f a -> f b

Lift a function to actions. This function may be used as a value for fmap in a Functor instance.

liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c

Lift a binary function to actions.

liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d

Lift a ternary function to actions.