d3-flextree

D3 flextree plugin

This plugin provides a more general version of the D3 tree layout module. Unlike tree, this plugin allows for nodes of variable sizes; like tree, the algorithm is fast, running in O(n) time.

See the demo.

flextree() is a factory function that returns a layout instance. A layout is a function that computes the positions of nodes in a tree diagram. Properties attached to the layout control various parameters of the algorithm.

Try d3-flextree in your browser.

Installing

If you use npm, npm install d3-flextree. Otherwise, download the latest release. AMD, CommonJS, and browser environments are supported.

Alternatively, you can use it straight from the jsdelivr CDN at https://cdn.jsdelivr.net/npm/d3-flextree@2.0.0/build/d3-flextree.min.js. or d3-flextree.js

Overview

Computing the layout of a tree data structure involves two steps: first, create a hierarchy from the data, and second, invoke the layout function.

In a Node environment:

const flextree = require('d3-flextree').flextree;
const layout = flextree();
const tree = layout.hierarchy({
  size: [1, 1],
  children: [
    { size: [2, 4] },
    { size: [3, 1],
      children: [
        { size: [4, 1] },
      ],
    },
  ],
});
layout(tree);
tree.each(node => console.log(`(${node.x}, ${node.y})`));

In a browser, flextree is attached to a d3 global (which is created if necessary):

<script src="d3-flextree.js"></script>
<script>
  const flextree = d3.flextree;
  ...
</script>

When creating the hierarchy, the library uses the children accessor function to determine the children of a data node. When the layout is computed, two other accessor functions are used: nodeSize (to get the node sizes) and spacing (to determine how far apart adjacent nodes in the diagram should be placed).

The example above uses the default accessors:

children: data => data.children,
nodeSize: node => node.data.size,
spacing: 0,

If the data is structured differently, the children and nodeSize accessors can be customized. For example, here is the same tree encoded in a nested array structure, along with the code to compute the layout using a spacing function that increases the gap between more distantly related nodes:

const data = [
  1, 1,
  [ 2, 4 ],
  [ 3, 1,
    [ 4, 1 ],
  ],
];
const layout = flextree({
  children: data => {
    const kd = data.slice(2);
    return kd.length ? kd : null;
  },
  nodeSize: node => node.data.slice(0, 2),
  spacing: (nodeA, nodeB) => nodeA.path(nodeB).length,
});
const tree = layout.hierarchy(data);
layout(tree);
console.log(layout.dump(tree));  //=> prints the results

The accessors can also be set using D3-style chained methods:

const layout = flextree()
  .children(data => {
    const kd = d.slice(2);
    return kd.length ? kd : null;
  })
  .nodeSize(node => node.data.slice(0, 2))
  .spacing((nodeA, nodeB) => nodeA.path(nodeB).length);

One thing to keep in mind is that the argument passed to the children accessor is a node in the data structure, whereas the arguments to nodeSize and spacing are nodes of the hierarchy.

The layout.hierarchy method is a convenience form of the d3.hierarchy function, and creates a set of objects that are instances of a class that derives from d3.hierarchy. It's not required to use the d3-flextree version. The following code is equivalent to the example above, with three custom accessors. Note that the children accessor needs to be passed as the second argument to the d3.hierarchy function:

const layout = flextree({
  nodeSize: node => node.data.slice(0, 2),
  spacing: (nodeA, nodeB) => nodeA.path(nodeB).length,
});
const tree = hierarchy(data, data => {
  const kd = d.slice(2);
  return kd.length ? kd : null;
});
layout(tree);

API Reference

# flextree(accessors)

Creates a new layout with the specified accessors. Any subset of children, nodeSize, and spacing can be specified in the argument object. If one is not specified, then the default is used:

children: data => data.children,
nodeSize: node => node.data.size,
spacing: 0,

The accessors can also be changed using chained methods, for example:

const layout = flextree()
  .spacing((nodeA, nodeB) => nodeA.path(nodeB).length);

# layout.hierarchy(data)

Creates a new hierarchy from the data, using the children accessors in effect when called. This is an enhanced version of the d3.hierarchy function, and produces a tree of instances of a class derived from d3.hierarchy.

Each node of the hierarchy inherits all of the methods defined in d3.hierarchy, including:

• node.ancestors()
• node.descendants()
• node.leaves()
• node.path(target)
• node.links()
• node.sum(value)
• node.count()
• node.sort(compare)
• node.each(function)
• node.eachAfter(function)
• node.eachBefore(function)
• node.copy() - this method is re-implemented in flextree, such that it preserves the class.

In addition, each of the objects in the returned hierarchy has several property getters. Many of these will be meaningless until layout is called on this tree. They include:

• x - the computed x-coordinate of the node position.
• y - the computed y-coordinate of the node position.
• data - reference to the original data object
• nodes - all of the nodes in this subtree (same as descendants())
• parent - the parent node, or null for the root.
• children - the array of child nodes, or null for leaf nodes.
• numChildren
• hasChildren
• noChildren
• depth - the depth of the node, starting at 0 for the root.
• height - the distance from this node to its deepest descendent, or 0 for leaf nodes.
• length - number of nodes in this subtree
• size - size of this node (the values fetched by the nodeSize accessor) as a two-element array.
• xSize
• ySize
• top
• bottom
• left
• right
• extents - the minimum top and left, and the maximum bottom and right values for all of the nodes in this subtree

# layout(tree)

Computes the layout of a hierarchy. x and y properties are set on each node, and many other properties useful in rendering are available -- see the list above.

Although the layout is defined in terms of x and y, these represent an arbitrary coordinate system. For example, you can treat x as a radius and y as an angle to produce a radial rather than Cartesian layout.

# layout.children([children])

If children is specified, sets the specified children accessor function. If children is not specified, returns the current children accessor function, which by default assumes that the input data is an object with a children property, whose value is either an array or null if there are no children:

data => data.children

Note that unlike the other accessors, this takes a data node as an argument. This is used only in the creation of a hierarchy, prior to computing the layout, by the layout.hierarchy method.

# layout.nodeSize([nodeSize])

If nodeSize is specified as a two-element array [xSize, ySize], then this sets that as the fixed size for every node in the tree. If nodeSize is a function, then that function is passed the hierarchy node as an argument, and should return a two-element array. If nodeSize is not specified, this returns the current setting.

The default nodeSize assumes that a node's size is available as a property on the data item:

node => node.data.size

# layout.spacing([spacing])

If a spacing argument is given as a constant number, then the layout will insert the given fixed spacing between every adjacent node. If it is given as a function, then that function will be passed two nodes, and should return the minimum allowable spacing between those nodes. If spacing is not specified, this returns the current spacing, which defaults to 0.

To increase the spacing for nodes as the distance of their relationship increases, you could use, for example:

layout.spacing((nodeA, nodeB) => nodeA.path(nodeB).length);

The Algorithm

The existing D3 tree layout is based on an algorithm developed originally by Reingold and Tilford in their paper from 1981, Tidier Drawings of Trees. The algorithm was improved over time by others, including Walker, in a paper in 1989, A Node-Positioning Algorithm for General Trees, and the latest improvement by Bucheim, Junger, and Leipert in 2002, described in their paper, Improving Walker's Algorithm to Run in Linear Time.

A limitation of that algorithm is that it applies to trees in which all of the nodes are the same size. This is adequate for many applications, but a more general solution, allowing variable node sizes, is often preferable.

In a paper from 2013, A.J. van der Ploeg enhanced the algorithm to allow for variable-sized nodes, while keeping its linear runtime nature. He described the algorithm in his paper, Drawing Non-layered Tidy Trees in Linear Time. The author also provided a working Java application on GitHub at cwi-swat/non-layered-tidy-trees.

This module is a port from that Java code into JavaScript.