Lost Among Notes

D3’s Messy Abstraction Path

D3 is a wonderful idea. A graphing library in Javascript that uses functional programming idioms, outputs SVG and is chock full of contributions from the community. No wonder it’s so popular.

And yet, D3 code has a tendency to grow unwieldy very quickly. As happens in SQL, the means of abstraction in the language (in our case in the library) are obscure, and details in “normal” code tend to pile up.

(Note that in SQL, the WITH statement allows abstraction and composition nicely, but a lot of people, or at least a lot of SQL codebases, do not leverage it.)

D3’s normal abstraction path: low abstraction

We begin with a simple toy problem, and then add a little complexity to see how D3 copes.

Say we’re plotting the result of a race. We have a list of runners, and for each of them we have a list of splits.

Take our first runner:

{
    "name": "Alice",
    "nationality": "UK",
    "splits": [5.05, 11.32, 17.49, 29.22]
}

Let’s display a line with the runner’s name, and circles representing the splits.

The way you do things in D3 is to build up your SVG graph by accretion. Start by putting a <div> in your HTML where you want the plot to render, and give it an ID so that we can locate it, for example, “single”. Then

var plot = d3.select("#single")
    .append("svg")
    .attr("width", 300)
    .attr("height", 20);

This generates an empty <svg> element with the desired dimensions. We want to show the runner’s name, so we add a <text> element. Bear in mind that our runner, Alice, lives in an array with other runners. She is runner[0].

plot.append("text")
    .text(runners[0].name)
    .attr("dy", 20);

To the right of the runner’s name, we want to mark splits by dots, placed at a distance proportional to the times.
Here we start to use D3’s core features: the binding operations, and selections. We’re going to select all the existing circles in the plot. There are none at this point; we’re doing this to get a selection, which is the main data type that D3 deals with. We now bind, to this empty selection, the array with the splits, and for each split, we shall add a red <circle>.

plot.selectAll("circle")
    .data(runners[0].splits)
    .enter()
    .append("circle")
        .attr("r", 5)
        .attr("cx", function(t) {return 100 + 5*t;})
        .attr("cy", 10)
        .style("stroke", "red")
        .style("fill", "red");

In the above, .data() binds the data to the selection, and .enter() returns the elements of the data array that were not already bound — i.e. all in our case, since the selection was empty. You can learn about D3’s selections, and enter(), exit(), update() in this D3 guide.

Note the line .attr("cx", function(t) {return 100 + 5*t;}), which takes a function as argument. This idiom is used widely in D3. It’s nothing more than the usual map from functional land; a function being mapped over the splits array that we bound previously with the .data() call.

Now, let’s plot all the runners.

Not much needs to be done on top of what we were doing before for a single runner. Firstly, we need to have fresh line to display each runner. Thanks to SVG’s <g> grouping element, and to SVG transforms, we can have a fresh canvas, with its own coordinate system, for each runner. In the code below, plotAll is an empty <svg> element we have defined on an identified <div>, as we did before with plot in the single runner case.

var runLines = plotAll.selectAll("g")
    .data(runners)
    .enter()
    .append("g")
        .attr("transform",
            function(ignore, k) {
                return "translate(0," + (k*30) + ")";
            });

The only novelty here is the signature function(ignore, k) {}. This is fairly standard in Javascript, and within D3. The second argument is the index of the datum within the data array. We name the first argument ignore as a convention to signal that in this case, the value of the argument is not used within the function body.

It is easy to repurpose the code that rendered the text and the splits. We just need to pull the data we’re interested in from each runner.
We can see here the rendering of the runner names. The rendering of the splits would work in the same way.

runLines.append("text")
    .text(function(d) {return d.name;})
    .attr("dy", 20);

Already you may have started to appreciate D3’s failing abstraction. In a typical functional programming approach, we would figure out how to plot individual runners, then iterate or map over an array to produce the full plot for all runners.

In D3, the default way of operating does not abstract the individual. To make it more visual: you can make 5 sandwiches by repeating the process of making a single sandwich 5 times, or you can put 5 slices of bread on 5 plates, then 5 pieces of cheese on the 5 slices, then 5 portions of ham on the 5 pieces of cheese, then 5 slices of bred on top of the portions of ham. This second way of operation is the default D3 way.

Problems due to low abstraction

This is working so far, but let’s see where the low abstraction can give rise to problems.
In our runner array, we keep track of each runner’s nationality, as we saw above with Alice, who is British. Let’s imagine we’d like to color the dots for the splits according to the runner’s nationality.

UK ==> blue
US ==> red
Spain ==> green

In the fragment we use to plot the circles, it’s not apparent how we could get the nationality, given that we’re iterating over the splits.

runLines.selectAll("circle")
    .data(function(d) {return d.splits;})
    .enter()
    .append("circle")
        .attr("r", 5)
        .attr("cx", function(t) {return 100 + 5*t;})
        .attr("cy", 10)
        .style("stroke", "red")
        .style("fill", "red");

One thing we could do is assign a CSS class on each of the runLines we defined before. We would add a line to the bottom of the definition of runLines.

var runLines = plotAll.selectAll("g")
    .data(runners)
    .enter()
    .append("g")
        .attr("transform",
            function(ignore, k) {
                return "translate(0," + (k*30) + ")";
            })
        .classed(function(d) {return d.nationality;}, true);

But this feels lazy. We now need supporting CSS directives, and we need to make sure the text is still rendered black, even if the splits are in color.

We could think of handing, to each circle in our splits code, not just the time, but the nationality. That is, we could define a procedure to convert the data.

function getNatlSplits(runner) ==> [..., {nationality, time_i}, ...]

Then do

runLines.selectAll("circle")
    .data(function(d) {return getNatlSplits(d);})
    .enter()
    ...

But this is even clunkier. We need an auxiliary function, and we’re repeating the same nationality for all those elements. And does the {nationality, time} pair have any meaning outside of making our code work?

The problem here is that, in iterating over the splits, we have lost access to the parent data that contained nationality.
We would solve this problem quite easily if we could keep the parent data in scope.

Abstraction the D3 way: too magical

The problem with coloring the circles, simple as it is, is an illustration of D3’s trouble with abstraction.

Now imagine that we had a procedure plotRunner(runner) that produced the line with the runner name and the splits. To color the circles based on nationality would be trivial. The function parameter would allow us access to both splits and nationality in the function body.

If we simply iterated over runners and called plotRunner for each, the code would need very little change. But plotRunner cannot function in a vacuum. It needs to do either of:

  • Output an SVG snippet, to be aggregated by a higher level function that generates the full SVG.
  • Receive an entry point into the overall SVG into which it will add its content.

The D3 way is the second. And D3 already has a handy type for entry points into SVG: selections.

Let’s write our plotRunner function, and for the moment let’s not worry about how we get the selection into it. Let’s just assume it’s there, and call it seln.

var plotRunner = function(runner) {
    // NOTE: incomplete. Future version to explain
    // how we get the selection "seln"

    seln.append("text")
        .text(runner.name)
        .attr("dy", 20);

    seln.selectAll("circle")
        .data(runner.splits)
        .enter()
        .append("circle")
            .attr("r", 5)
            .attr("cx", function(t) {return 100 + 5*t;})
            .attr("cy", 10)
            .style("stroke", "red")
            .style("fill", "red");
}

This is pretty much what we did previously, but there is one crucial difference: thanks to the function argument runner, we now have access to the parent data within the function body.

Let’s go back to our color-by-nationality problem. We just need to codify the color assignments, and modify plotRunner to leverage them:

var nationalColor = {
    "US": "red",
    "UK": "blue",
    "Spain": "green"};

var plotRunner = function(runner) {
    ...
    ...
    seln.selectAll("circle")
        ...
        ...
            .style("stroke", nationalColor[runner.nationality])
            .style("fill", nationalColor[runner.nationality]);
}

Easy as pie.

We need to hook this up. plotRunner, as its name implies, plots a single runner. As we saw in previous examples, selections in D3 are arrays. How do we iterate through them?

D3 has an operator .each() to iterate over selections. It takes a function argument that can itself have either one argument (the datum bound to the sub-selection), or two arguments (the datum, and the ordinal of the sub-selection within the selection).
There is one more piece of magic to .each(). Within the function passed to it, this will be the context of the current DOM element. We can get the current selection with d3.select(this).

So, the plotRunner function will be called from an .each() loop, and we can now fill in the part we had left undefined.

var plotRunner = function(runner) {

    var seln = d3.select(this);

    seln.append("text")
        ...
        ...

Now we need to build the selection we will iterate over. We have seen this before. We bind the runners array to an empty selection, append <g> elements for each runner, and translate vertically.

var runnerLines = runnersFinal.selectAll("g")
    .data(runners)
    .enter()
    .append("g")
        .attr("transform",
            function(ignore, k) {
                return "translate(0," + (k*30) + ")";
            }
        );

And, finally, we tie it all together.

runnerLines.each(plotRunner);

There we go.

Now, all this is very magical, in a bad way. Capturing selections inside of .each() by using this is flimsy. And so, we rendered the plot by calling

runnerLines.each(plotRunner);

but the following will not work:

runnerLines.each(function(d) {plotRunner(d);});

How can this be? this depends on context, and in the second version, plotRunner gets it from the enclosing function (d) { rather than from .each(). There goes your referential transparency.

D3 offers a lot of power, but its abstraction mechanism is somewhat finicky. I recommend that you use it, though. For all but simple plots, the functional decomposition can clarify your code and make it more flexible.

I wish there were less magic involved. React, for instance, achieves a very coherent abstraction and is also written in Javascript. I don’t know enough JS yet, but I’m getting interested in D3’s internals.



Final code listing:

var nationalColor = {
    "US": "red",
    "UK": "blue",
    "Spain": "green"};

var plotRunner = function(runner) {
    var seln = d3.select(this);

    seln.append("text")
        .text(runner.name)
        .attr("dy", 20);

    seln.selectAll("circle")
        .data(runner.splits)
        .enter()
        .append("circle")
            .attr("r", 5)
            .attr("cx", function(t) {return 100 + 5*t;})
            .attr("cy", 10)
            .style("stroke", nationalColor[runner.nationality])
            .style("fill", nationalColor[runner.nationality]);
}

var runnersFinal = d3.select("#allAbstracted")
    .append("svg")
    .attr("width", 300)
    .attr("height", 90);

var runnerLines = runnersFinal.selectAll("g")
    .data(runners)
    .enter()
    .append("g")
        .attr("transform",
            function(ignore, k) {
                return "translate(0," + (k*30) + ")";
            }
        );

runnerLines.each(plotRunner);
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