Monoidal annotations which travel up the diagram tree, i.e. which are aggregated from component diagrams to the whole:

• envelopes (see Diagrams.Core.Envelope). The envelopes are "deletable" meaning that at any point we can throw away the existing envelope and replace it with a new one; sometimes we want to consider a diagram as having a different envelope unrelated to its "natural" envelope.
• traces (see Diagrams.Core.Trace), also deletable.
• name/subdiagram associations (see Diagrams.Core.Names)
• query functions (see Diagrams.Core.Query)

Monoidal annotations which travel down the diagram tree, i.e. which accumulate along each path to a leaf (and which can act on the upwards-travelling annotations):

• transformations (split at the innermost freeze): see Diagrams.Core.Transform
• styles (see Diagrams.Core.Style)
• names (see Diagrams.Core.Names)

The fundamental diagram type is represented by trees of primitives with various monoidal annotations. The Q in QDiagram stands for "Queriable", as distinguished from Diagram, a synonym for QDiagram with the query type specialized to Any.

Create a diagram from a single primitive, along with an envelope, trace, subdiagram map, and query function.

The default sort of diagram is one where querying at a point simply tells you whether the diagram contains that point or not. Transforming a default diagram into one with a more interesting query can be done via the Functor instance of QDiagram b or the value function.

Extract a list of primitives from a diagram, together with their associated transformations and styles.

Get the envelope of a diagram.

Get the trace of a diagram.

Get the subdiagram map (i.e. an association from names to subdiagrams) of a diagram.

Get a list of names of subdiagrams and their locations.

Get the query function associated with a diagram.

Sample a diagram's query function at a given point.

Set the query value for True points in a diagram (i.e. points "inside" the diagram); False points will be set to mempty.

Reset the query values of a diagram to True/False: any values equal to mempty are set to False; any other values are set to True.

Set all the query values of a diagram to False.

A convenient synonym for mappend on diagrams, designed to be used infix (to help remember which diagram goes on top of which when combining them, namely, the first on top of the second).

Attach an atomic name to a diagram.

Attach an atomic name to a certain subdiagram, computed from the given diagram.

Attach an atomic name to a certain point (which may be computed from the given diagram), treated as a subdiagram with no content and a point envelope.

Given a name and a diagram transformation indexed by a subdiagram, perform the transformation using the most recent subdiagram associated with (some qualification of) the name, or perform the identity transformation if the name does not exist.

Given a name and a diagram transformation indexed by a list of subdiagrams, perform the transformation using the collection of all such subdiagrams associated with (some qualification of) the given name.

Given a list of names and a diagram transformation indexed by a list of subdiagrams, perform the transformation using the list of most recent subdiagrams associated with (some qualification of) each name. Do nothing (the identity transformation) if any of the names do not exist.

By default, diagram attributes are not affected by transformations. This means, for example, that lw 0.01 circle and scale 2 (lw 0.01 circle) will be drawn with lines of the same width, and scaleY 3 circle will be an ellipse drawn with a uniform line. Once a diagram is frozen, however, transformations do affect attributes, so, for example, scale 2 (freeze (lw 0.01 circle)) will be drawn with a line twice as thick as lw 0.01 circle, and scaleY 3 (freeze circle) will be drawn with a "stretched", variable-width line.

Another way of thinking about it is that pre-freeze, we are transforming the "abstract idea" of a diagram, and the transformed version is then drawn; when doing a freeze, we produce a concrete drawing of the diagram, and it is this visual representation itself which is acted upon by subsequent transformations.

Replace the envelope of a diagram.

Replace the trace of a diagram.

A Subdiagram represents a diagram embedded within the context of a larger diagram. Essentially, it consists of a diagram paired with any accumulated information from the larger context (transformations, attributes, etc.).

Turn a diagram into a subdiagram with no accumulated context.

Turn a subdiagram into a normal diagram, including the enclosing context. Concretely, a subdiagram is a pair of (1) a diagram and (2) a "context" consisting of an extra transformation and attributes. getSub simply applies the transformation and attributes to the diagram to get the corresponding "top-level" diagram.

Extract the "raw" content of a subdiagram, by throwing away the context.

Get the location of a subdiagram; that is, the location of its local origin with respect to the vector space of its parent diagram. In other words, the point where its local origin "ended up".

Create a "point subdiagram", that is, a pointDiagram (with no content and a point envelope) treated as a subdiagram with local origin at the given point. Note this is not the same as mkSubdiagram . pointDiagram, which would result in a subdiagram with local origin at the parent origin, rather than at the given point.

A SubMap is a map associating names to subdiagrams. There can be multiple associations for any given name.

Construct a SubMap from a list of associations between names and subdiagrams.

Add a name/diagram association to a submap.

Look for the given name in a name map, returning a list of subdiagrams associated with that name. If no names match the given name exactly, return all the subdiagrams associated with names of which the given name is a suffix.

A value of type Prim b v is an opaque (existentially quantified) primitive which backend b knows how to render in vector space v.

The null primitive, which every backend can render by doing nothing.

Abstract diagrams are rendered to particular formats by backends. Each backend/vector space combination must be an instance of the Backend class. A minimal complete definition consists of the three associated types and implementations for withStyle and doRender.

A class for backends which support rendering multiple diagrams, e.g. to a multi-page pdf or something similar.

A null backend which does no actual rendering. It is provided mainly for convenience in situations where you must give a diagram a concrete, monomorphic type, but don't actually care which one. See D for more explanation and examples.

It is courteous, when defining a new primitive P, to make an instance

 instance Renderable P NullBackend where
   render _ _ = mempty

This ensures that the trick with D annotations can be used for diagrams containing your primitive.

The D type is provided for convenience in situations where you must give a diagram a concrete, monomorphic type, but don't care which one. Such situations arise when you pass a diagram to a function which is polymorphic in its input but monomorphic in its output, such as width, height, phantom, or names. Such functions compute some property of the diagram, or use it to accomplish some other purpose, but do not result in the diagram being rendered. If the diagram does not have a monomorphic type, GHC complains that it cannot determine the diagram's type.

For example, here is the error we get if we try to compute the width of an image (this example requires diagrams-lib):

 ghci> width (image "foo.png" 200 200)

 <interactive>:8:8:
     No instance for (Renderable Diagrams.TwoD.Image.Image b0)
       arising from a use of `image'
     Possible fix:
       add an instance declaration for
       (Renderable Diagrams.TwoD.Image.Image b0)
     In the first argument of `width', namely
       `(image "foo.png" 200 200)'
     In the expression: width (image "foo.png" 200 200)
     In an equation for `it': it = width (image "foo.png" 200 200)

GHC complains that there is no instance for Renderable Image b0; what is really going on is that it does not have enough information to decide what backend to use (hence the uninstantiated b0). This is annoying because we know that the choice of backend cannot possibly affect the width of the image (it's 200! it's right there in the code!); but there is no way for GHC to know that.

The solution is to annotate the call to image with the type D R2, like so:

 ghci> width (image "foo.png" 200 200 :: D R2)
 200.00000000000006

(It turns out the width wasn't 200 after all...)

As another example, here is the error we get if we try to compute the width of a radius-1 circle:

 ghci> width (circle 1)

 <interactive>:4:1:
     Couldn't match type `V a0' with `R2'
     In the expression: width (circle 1)
     In an equation for `it': it = width (circle 1)

There's even more ambiguity here. Whereas image always returns a Diagram, the circle function can produce any PathLike type, and the width function can consume any Enveloped type, so GHC has no idea what type to pick to go in the middle. However, the solution is the same:

 ghci> width (circle 1 :: D R2)
 1.9999999999999998

The Renderable type class connects backends to primitives which they know how to render.