(Initial notes on arrows (still need to finish))
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Latest revision as of 13:19, 29 March 2014
diagrams-lib ought to have a module with some convenient functions for creating arrows pointing from one part of a diagram to another. This page is for gathering ideas and plans for such a module.
 1 Arrowheads
There should probably be a collection of "standard" arrowheads for the user to choose from. In addition it ought to be possible for the user to specify any diagram they like for use as an arrowhead.
 1.1 Scale-invariance
The idea is for arrowheads to be scale-invariant, just like line width. We now have a
ScaleInv wrapper for accomplishing this, which works correctly with freezing etc.
 2 Drawing arrows
At the most basic level one could imagine an API like
arrow :: Arrowhead -> P2 -> P2 -> Diagram
and we probably should indeed have such a function, but we'll need to also generalize along several axes.
First, the most frequent use case will be drawing an arrow on top of an existing diagram in order to connect two points. So we want something like
arrow :: IsName n => Arrowhead -> n -> n -> (Diagram -> Diagram)
which draws an arrow between the named points on the given diagram. There are several ways this can be generalized:
- Instead of drawing an arrow between the named points one could draw the arrow between the named subdiagrams (using their traces to find the edges).
- There should also be a way to leave gaps, i.e. don't draw the arrow precisely from point to point or edge to edge, but leave a gap of a certain absolute size or a certain percentage of the arrow length on either end of the arrow.
Re: leaving gaps, this will require some generic code to shrink paths. There is already some code to shrink/extend individual segments (and compute the length of segments) in Diagrams.Segment. This would need to be extended to shrinking/extending trails and paths appropriately.
One might also want to have control over the middle of the arrow -- i.e. whether it curves, and if so how much and in which direction, etc.
 3 A History of Arrow.hs
 3.1 ScaleInv
The original semantics we choose for arrows was for only the shaft length to change under scaling transformations. This was done not only because we wanted the head size (from here on what ever I say about head applies to tail as well) to remain constant, but becuase non-uniorm scalings would cause the head to point in the wrong direction. See http://projects.haskell.org/diagrams/doc/manual.html#scale-invariance. It turned out that our solution (wrapping the head in the `ScaleInv` wrapper) was not enough. Once an arrow was stroked, it would not behave correctly under scales. We solved the problems of keeping the head size constant and making the arrow point in the correct direction, but now a scaling could cause the head and shaft to separate. As explained in https://github.com/diagrams/diagrams-lib/issues/112. Hence the birth of delayed subtrees.
 3.2 DelayedLeaf
At the risk of stating the obvious,
DualTrees) are created from the bottom (leaves) up, but
RTrees from the top (root) down. Suppose we are creating an arrow using
diagrams functions and combinators. When we are finished we have essentially added
a subtree to a diagram. That subtree cannot use any of the informtion about
transforms and styles above it in the tree (they have not yet been created) so
the arrow is unable to use its final size and location (i.e. accumulated
transform) in its subtree. Brent's elegant solution was twofold:
- To hold off on creating the arrow by creating a new type of leaf, the
DelayedLeafin addition to
Prim b vthat we already had. The
DelayedLeafcontains a funtion
DownAnnots v -> QDiagram b v m, in other words a set of instructions about how to create the arrow once its
- A modification of the
arrow'function so that it returns a
DelayedLeaf. The function wrapped in the
delayedArrowtakes as parameter the
DownAnnotsand hence the styles and transforms.
The upshot is that an arrow gets to know the accumulated
DownAnnots above it
to use it's conversion to a diagram.
Since creation of a
DTree is top down, by the time
we reach a
DelayedLeaf in the `DualTree` we already have all of the accumlated
transforms and styles that will be applied to the arrow. So the
can be expanded by running the function
DownAnnots v -> QDiagram b v m on
DownAnnots and recursively calling
fromDTree to insert the
arrow into the
DTree. It is import ant to note, though at this point the arrow
is essentially finished, all transforms and style have been applied. By the way, I'm pretty sure that at this point we could have removed the
scaleInv wrapper from the head.
(As a side benefit, we are able to use all of the
styles that are applied above the arrow in the tree to do things like change
the color of the entire arrow with functions like
There were still some enhancements we wanted to make, https://github.com/diagrams/diagrams-lib/issues/162, but for the most part all was well in Arrow land until ...
 3.3 Measure
With the death of
freeze and the switch to
Measure in the units branch, it
headSize should have a value of
Measure Double. This means that
headSize can have one of four possible units:
Localwhich are transformable and in particular scalable. Note that this is in contrast with our original notion of arrows having scale invariant heads. Although it is somewhat similar in behavior to a
freezefollowed by a uniform scaling.
Outputthis is what we have in 1.1.
Globalwhich scales based on the final size of the diagram.
Normalizedwhich scales in relation to a logical size.
See http://www.haskell.org/haskellwiki/Diagrams/Dev/Freezing for more detail or even better the implementation of `convert` in the units branch, https://github.com/diagrams/diagrams-core/blob/units/src/Diagrams/Core/Compile.hs#L167.
The backends should only see
Output units therefore before passing an
to a backend, all
Measures must be converted to
Output. This is done by
RTree and returning a new
RTree where all of the
have been properly converted. The important thing to notice is that this occurs
DelayedLeaf has been expanded and hence the arrow cannot make
any use to the units change to render.
 3.4 What to do
I really don't know but some things to think about are:
- I don't think it is possible to adjust the arrow
RTreelevel, since arrows make no further use of units after the
delayedArrowfunction is executed during the conversion to
DTree. Unless we can come up with another way of creating arrows.
- Does every attribute with a value of
Measurehave to implement all 4 value types? In particular is it OK for arrows to only implement
Local. If this is what we decide then we are done.
- Move the conversion to
Outputunits back up to the
QDiagram -> DTreelevel. We tried this and decided it was a bad idea.
- Find another way (as opposed to delayed leaves) to handle arrows.