d3-force

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Installing

If you use NPM, npm install d3-force. Otherwise, download the latest release. You can also load directly from d3js.org, either as a standalone library or as part of D3 4.0 alpha. AMD, CommonJS, and vanilla environments are supported. In vanilla, a d3_force global is exported:

<script src="https://d3js.org/d3-collection.v0.1.min.js"></script>
<script src="https://d3js.org/d3-dispatch.v0.4.min.js"></script>
<script src="https://d3js.org/d3-quadtree.v0.7.min.js"></script>
<script src="https://d3js.org/d3-timer.v0.4.min.js"></script>
<script src="https://d3js.org/d3-force.v0.3.min.js"></script>
<script>

var simulation = d3_force.forceSimulation(nodes);

</script>

Try d3-force in your browser.

API Reference

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Simulation

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# d3.forceSimulation([nodes])

Creates a new velocity Verlet simulator with the specified array of nodes and no forces. If nodes is not specified, it defaults to the empty array. The simulator starts automatically; if you wish to run the simulation manually, call simulation.stop, and then call simulation.tick as desired.

# simulation.restart()

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# simulation.stop()

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# simulation.tick()

Invokes each registered force, passing the current alpha; then updates the positions and velocities of each node according to the following formula: velocity *= 1 - drag, position += velocity. Returns true if the current alpha is less than alphaMin, indicating that the simulation would normally stop after this tick, and false otherwise.

The current alpha is defined as exp(iteration × alphaDecay) where iteration is the number of times this method has been called since the simulation started. Thus, the exact number of iterations needed to terminate the simulation naturally is ⌈log(alphaMin) / -alphaDecay⌉. For example, to run the simulation manually, as when computing a static layout in a background web worker or on the server:

for (var i = 0, n = Math.ceil(Math.log(simulation.alphaMin()) / -simulation.alphaDecay()); i < n; ++i) {
  simulation.tick();
}

This method does not dispatch events; events are only dispatched by the internal timer when the simulation is started automatically upon creation or by calling simulation.restart.

# simulation.nodes([nodes])

If nodes is specified, sets the simulation’s nodes to the specified array, initializing their positions and velocities if necessary, and then re-initializes any bound forces; returns the simulation. If nodes is not specified, returns the simulation’s array of nodes as specified to the constructor. Each node must be an object; the following properties are initialized by the simulation:

• index - the node’s zero-based index into nodes
• x - the node’s current x-position
• y - the node’s current y-position
• vx - the node’s current x-velocity
• vy - the node’s current y-velocity

The position ⟨x,y⟩ and velocity ⟨vx,vy⟩ may be subsequently modified by forces and by the simulation. If either vx or vy is NaN, the velocity is initialized to ⟨0,0⟩. If either x or y is NaN, the position is initialized to with radius 10 * √index and angle π * (3 - √5), resulting in a phyllotaxis arrangement, so chosen because nodes are distributed deterministically with uniform density around the origin.

If the specified array of nodes is modified, such as when nodes are added to or removed from the simulation, this method must be called again with the new (or changed) array to notify the simulation and bound forces of the change; the simulation does not make a defensive copy of the specified array.

# simulation.alphaMin([alpha])

If alpha is specified, sets the minimum alpha to the specified number and returns this simulation. If alpha is not specified, returns the current minimum alpha value, which defaults to 0.001. The minimum alpha value determines when the simulation will stop automatically: when the current alpha is less than the minimum alpha. Assuming the default alpha decay rate of 0.02, this corresponds to 346 iterations.

# simulation.alphaDecay([decay])

If decay is specified, sets the exponential decay rate constant λ to the specified number and returns this simulation. If decay is not specified, returns the current alpha decay rate, which defaults to 0.02. The alpha decay rate determines how quickly the simulation stabilizes. Higher values cause the simulation to stabilize more quickly, but risk getting stuck in a local minimum; lower values cause the simulation to take longer to run, but typically converge on a better layout. To have the simulation run forever, set the decay rate to zero.

# simulation.drag([drag])

If drag is specified, sets the drag factor to the specified number in the range [0,1] and returns this simulation. If drag is not specified, returns the current drag factor, which defaults to 0.4. The drag factor affects how quickly nodes’ velocities decay; at each tick, the velocities are updated according to the following formula: velocity *= 1 - drag. As with lowering the alpha decay rate, less drag may converge on a better solution, but it also risks numerical instabilities and oscillations.

# simulation.force(name[, force])

If force is specified, assigns the force for the specified name and returns this simulation. If force is not specified, returns the force with the specified name, or undefined if there is no such force. (By default, new simulations have no forces.) For example, to create a new simulation to layout a graph, you might say:

var simulation = d3.forceSimulation(nodes)
    .force("charge", d3.forceManyBody())
    .force("link", d3.forceLink(links))
    .force("center", d3.forceCenter());

# simulation.on(typenames, [listener])

If listener is specified, sets the event listener for the specified typenames and returns this simulation. If an event listener was already registered for the same type and name, the existing listener is removed before the new listener is added. If listener is null, removes the current event listeners for the specified typenames, if any. If listener is not specified, returns the first currently-assigned listener matching the specified typenames, if any. When a specified event is dispatched, each listener will be invoked with the this context as the simulation.

The typenames is a string containing one or more typename separated by whitespace. Each typename is a type, optionally followed by a period (.) and a name, such as tick.foo and tick.bar; the name allows multiple listeners to be registered for the same type. The type must be one of the following:

• tick - after each tick of the simulation.
• end - after the simulation ends, when alpha < alphaMin.

See dispatch.on for details.

Forces

A force is simply a function that modifies nodes’ positions or velocities; in this context, a force can apply a classical physical force such as electrical charge or gravity, or it can resolve a geometric constraint, such as keeping nodes within a bounding box or keeping linked nodes a fixed distance apart. For example, a simple positioning force that moves nodes towards the origin ⟨0,0⟩ might be implemented as:

function force(alpha) {
  for (var i = 0, n = nodes.length, node, k = alpha * 0.1; i < n; ++i) {
    node = nodes[i];
    node.vx -= node.x * k;
    node.vy -= node.y * k;
  }
}

Forces typically read the node’s current position ⟨x,y⟩ and then add to (or subtract from) the node’s velocity ⟨vx,vy⟩. However, forces may also “peek ahead” to the anticipated next position of the node, ⟨x + vx,y + vy⟩; this is necessary for resolving geometric constraints through iterative relaxation. Forces may also modify the position directly, which is sometimes useful to avoid adding energy to the simulation, such as when recentering the simulation in the viewport.

Simulations typically compose multiple forces as desired. This module provides several for your enjoyment:

• Centering
• Circle Collision
• Circle Containment
• Links
• Many-Body
• Positioning

Forces may optionally implement force.initialize to receive the simulation’s array of nodes.

# force(alpha)

Applies this force, optionally observing the specified alpha. Typically, the force is applied to the array of nodes previously passed to force.initialize, however, some forces may apply to a subset of nodes, or behave differently. For example, d3.forceLink applies to the source and target of each link.

# force.initialize(nodes)

Assigns the array of nodes to this force. This method is called when a force is bound to a simulation via simulation.force and when the simulation’s nodes change via simulation.nodes. A force may perform necessary work during initialization, such as evaluating per-node parameters, to avoid repeatedly performing work during each application of the force.

Centering

The centering force moves nodes so that their center of mass (assuming all nodes are equal-weight) is at the given position ⟨x,y⟩. (These parameters are only recomputed when the force is initialized, not on every application.)

# d3.forceCenter([x, y])

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# center.x([x])

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# center.y([y])

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Circle Collision

The circle collision force prevents circular nodes with a given radius from overlapping. More formally, two nodes a and b are separated so that the distance between a and b is at least radius(a) + radius(b). To reduce jitter, this is by default a “soft” constraint with a configurable strength. (These parameters are only recomputed when the force is initialized, not on every application.)

# d3.forceCollide([radius])

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# collide.radius([radius])

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# collide.strength([strength])

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# collide.iterations([iterations])

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Circle Containment

The circle containment force constrains nodes to fit within a circle of a given radius and center ⟨x,y⟩. The radius and center can be specified on a per-node basis. (These parameters are only recomputed when the force is initialized, not on every application.)

# d3.forceContain([radius[, x, y]])

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# contain.radius([radius])

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# contain.x([x])

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# contain.y([y])

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Links

The link force pushes linked nodes closer together or farther apart according to the desired link distance, which may be specified on a per-node basis. (These parameters are only recomputed when the force is initialized, not on every application.)

# d3.forceLink([links])

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# link.links([links])

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• index - the zero-based index into links
• source - the link’s source node; see simulation.nodes
• target - the link’s target node; see simulation.nodes

The source and target properties may be initialized using link.id.

# link.id([id])

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# link.distance([distance])

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# link.strength([strength])

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# link.iterations([iterations])

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Many-Body

The many-body (or n-body) force applies mutally amongst all nodes. It can be used to simulate gravity (attraction) if the strength is positive, or eletrical charge (repulsion) if the strength is negative. This implementation uses quadtrees and the Barnes–Hut approximation to greatly improve performance; the accuracy can be customized using the theta parameter. The strength can be specified on a per-node basis. (This parameter is only recomputed when the force is initialized, not on every application.)

# d3.forceManyBody()

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# manyBody.strength([strength])

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# manyBody.theta([theta])

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# manyBody.distanceMin([distance])

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# manyBody.distanceMax([distance])

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Positioning

The positioning force pushes nodes towards a desired position ⟨x,y⟩. The position and strength can be specified on a per-node basis. (These parameters are only recomputed when the force is initialized, not on every application.)

# d3.forcePosition([x, y])

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# position.strength([strength])

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# position.x([x])

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# position.y([y])

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