springy.js

/**
Copyright (c) 2010 Dennis Hotson

 Permission is hereby granted, free of charge, to any person
 obtaining a copy of this software and associated documentation
 files (the "Software"), to deal in the Software without
 restriction, including without limitation the rights to use,
 copy, modify, merge, publish, distribute, sublicense, and/or sell
 copies of the Software, and to permit persons to whom the
 Software is furnished to do so, subject to the following
 conditions:

 The above copyright notice and this permission notice shall be
 included in all copies or substantial portions of the Software.

 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
 OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
 NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
 HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
 WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
 OTHER DEALINGS IN THE SOFTWARE.
*/

var Graph = function() {
	this.nodeSet = {};
	this.nodes = [];
	this.edges = [];
	this.adjacency = {};

	this.nextNodeId = 0;
	this.nextEdgeId = 0;
	this.eventListeners = [];
};

var Node = function(id, data) {
	this.id = id;
	this.data = typeof(data) !== 'undefined' ? data : {};
};

var Edge = function(id, source, target, data) {
	this.id = id;
	this.source = source;
	this.target = target;
	this.data = typeof(data) !== 'undefined' ? data : {};
};

Graph.prototype.addNode = function(node) {
	if (typeof(this.nodeSet[node.id]) === 'undefined') {
		this.nodes.push(node);
	}

	this.nodeSet[node.id] = node;

	this.notify();
	return node;
};

Graph.prototype.addEdge = function(edge) {
	var exists = false;
	this.edges.forEach(function(e) {
		if (edge.id === e.id) { exists = true; }
	});

	if (!exists) {
		this.edges.push(edge);
	}

	if (typeof(this.adjacency[edge.source.id]) === 'undefined') {
		this.adjacency[edge.source.id] = {};
	}
	if (typeof(this.adjacency[edge.source.id][edge.target.id]) === 'undefined') {
		this.adjacency[edge.source.id][edge.target.id] = [];
	}

	exists = false;
	this.adjacency[edge.source.id][edge.target.id].forEach(function(e) {
			if (edge.id === e.id) { exists = true; }
	});

	if (!exists) {
		this.adjacency[edge.source.id][edge.target.id].push(edge);
	}

	this.notify();
	return edge;
};

Graph.prototype.newNode = function(data) {
	var node = new Node(this.nextNodeId++, data);
	this.addNode(node);
	return node;
};

Graph.prototype.newEdge = function(source, target, data) {
	var edge = new Edge(this.nextEdgeId++, source, target, data);
	this.addEdge(edge);
	return edge;
};

// find the edges from node1 to node2
Graph.prototype.getEdges = function(node1, node2) {
	if (typeof(this.adjacency[node1.id]) !== 'undefined'
		&& typeof(this.adjacency[node1.id][node2.id]) !== 'undefined') {
		return this.adjacency[node1.id][node2.id];
	}

	return [];
};

// remove a node and it's associated edges from the graph
Graph.prototype.removeNode = function(node) {
	if (typeof(this.nodeSet[node.id]) !== 'undefined') {
		delete this.nodeSet[node.id];
	}

	for (var i = this.nodes.length - 1; i >= 0; i--) {
		if (this.nodes[i].id === node.id) {
			this.nodes.splice(i, 1);
		}
	}

	this.detachNode(node);

};

// removes edges associated with a given node
Graph.prototype.detachNode = function(node) {
	var tmpEdges = this.edges.slice();
	tmpEdges.forEach(function(e) {
		if (e.source.id === node.id || e.target.id === node.id) {
			this.removeEdge(e);
		}
	}, this);

	this.notify();
};

// remove a node and it's associated edges from the graph
Graph.prototype.removeEdge = function(edge) {
	for (var i = this.edges.length - 1; i >= 0; i--) {
		if (this.edges[i].id === edge.id) {
			this.edges.splice(i, 1);
		}
	}

	for (var x in this.adjacency) {
		for (var y in this.adjacency[x]) {
			var edges = this.adjacency[x][y];

			for (var j=edges.length - 1; j>=0; j--) {
				if (this.adjacency[x][y][j].id === edge.id) {
					this.adjacency[x][y].splice(j, 1);
				}
			}
		}
	}

	this.notify();
};

/* Merge a list of nodes and edges into the current graph. eg.
var o = {
	nodes: [
		{id: 123, data: {type: 'user', userid: 123, displayname: 'aaa'}},
		{id: 234, data: {type: 'user', userid: 234, displayname: 'bbb'}}
	],
	edges: [
		{from: 0, to: 1, type: 'submitted_design', directed: true, data: {weight: }}
	]
}
*/
Graph.prototype.merge = function(data) {
	var nodes = [];
	data.nodes.forEach(function(n) {
		nodes.push(this.addNode(new Node(n.id, n.data)));
	}, this);

	data.edges.forEach(function(e) {
		var from = nodes[e.from];
		var to = nodes[e.to];

		var id = (e.directed)
			? (id = e.type + "-" + from.id + "-" + to.id)
			: (from.id < to.id) // normalise id for non-directed edges
				? e.type + "-" + from.id + "-" + to.id
				: e.type + "-" + to.id + "-" + from.id;

		var edge = this.addEdge(new Edge(id, from, to, e.data));
		edge.data.type = e.type;
	}, this);
};

Graph.prototype.filterNodes = function(fn) {
	var tmpNodes = this.nodes.slice();
	tmpNodes.forEach(function(n) {
		if (!fn(n)) {
			this.removeNode(n);
		}
	}, this);
};

Graph.prototype.filterEdges = function(fn) {
	var tmpEdges = this.edges.slice();
	tmpEdges.forEach(function(e) {
		if (!fn(e)) {
			this.removeEdge(e);
		}
	}, this);
};


Graph.prototype.addGraphListener = function(obj) {
	this.eventListeners.push(obj);
};

Graph.prototype.notify = function() {
	this.eventListeners.forEach(function(obj){
		obj.graphChanged();
	});
};

// -----------
var Layout = {};
Layout.ForceDirected = function(graph, stiffness, repulsion, damping) {
	this.graph = graph;
	this.stiffness = stiffness; // spring stiffness constant
	this.repulsion = repulsion; // repulsion constant
	this.damping = damping; // velocity damping factor

	this.nodePoints = {}; // keep track of points associated with nodes
	this.edgeSprings = {}; // keep track of springs associated with edges
};

Layout.ForceDirected.prototype.point = function(node) {
	if (typeof(this.nodePoints[node.id]) === 'undefined') {
		var mass = typeof(node.data.mass) !== 'undefined' ? node.data.mass : 1.0;
		this.nodePoints[node.id] = new Layout.ForceDirected.Point(Vector.random(), mass);
	}

	return this.nodePoints[node.id];
};

Layout.ForceDirected.prototype.spring = function(edge) {
	if (typeof(this.edgeSprings[edge.id]) === 'undefined') {
		var length = typeof(edge.data.length) !== 'undefined' ? edge.data.length : 1.0;

		var existingSpring = false;

		var from = this.graph.getEdges(edge.source, edge.target);
		from.forEach(function(e) {
			if (existingSpring === false && typeof(this.edgeSprings[e.id]) !== 'undefined') {
				existingSpring = this.edgeSprings[e.id];
			}
		}, this);

		if (existingSpring !== false) {
			return new Layout.ForceDirected.Spring(existingSpring.point1, existingSpring.point2, 0.0, 0.0);
		}

		var to = this.graph.getEdges(edge.target, edge.source);
		from.forEach(function(e){
			if (existingSpring === false && typeof(this.edgeSprings[e.id]) !== 'undefined') {
				existingSpring = this.edgeSprings[e.id];
			}
		}, this);

		if (existingSpring !== false) {
			return new Layout.ForceDirected.Spring(existingSpring.point2, existingSpring.point1, 0.0, 0.0);
		}

		this.edgeSprings[edge.id] = new Layout.ForceDirected.Spring(
			this.point(edge.source), this.point(edge.target), length, this.stiffness
		);
	}

	return this.edgeSprings[edge.id];
};

// callback should accept two arguments: Node, Point
Layout.ForceDirected.prototype.eachNode = function(callback) {
	var t = this;
	this.graph.nodes.forEach(function(n){
		callback.call(t, n, t.point(n));
	});
};

// callback should accept two arguments: Edge, Spring
Layout.ForceDirected.prototype.eachEdge = function(callback) {
	var t = this;
	this.graph.edges.forEach(function(e){
		callback.call(t, e, t.spring(e));
	});
};

// callback should accept one argument: Spring
Layout.ForceDirected.prototype.eachSpring = function(callback) {
	var t = this;
	this.graph.edges.forEach(function(e){
		callback.call(t, t.spring(e));
	});
};


// Physics stuff
Layout.ForceDirected.prototype.applyCoulombsLaw = function() {
	this.eachNode(function(n1, point1) {
		this.eachNode(function(n2, point2) {
			if (point1 !== point2)
			{
				var d = point1.p.subtract(point2.p);
				var distance = d.magnitude() + 0.1; // avoid massive forces at small distances (and divide by zero)
				var direction = d.normalise();

				// apply force to each end point
				point1.applyForce(direction.multiply(this.repulsion).divide(distance * distance * 0.5));
				point2.applyForce(direction.multiply(this.repulsion).divide(distance * distance * -0.5));
			}
		});
	});
};

Layout.ForceDirected.prototype.applyHookesLaw = function() {
	this.eachSpring(function(spring){
		var d = spring.point2.p.subtract(spring.point1.p); // the direction of the spring
		var displacement = spring.length - d.magnitude();
		var direction = d.normalise();

		// apply force to each end point
		spring.point1.applyForce(direction.multiply(spring.k * displacement * -0.5));
		spring.point2.applyForce(direction.multiply(spring.k * displacement * 0.5));
	});
};

Layout.ForceDirected.prototype.attractToCentre = function() {
	this.eachNode(function(node, point) {
		var direction = point.p.multiply(-1.0);
		point.applyForce(direction.multiply(this.repulsion / 50.0));
	});
};


Layout.ForceDirected.prototype.updateVelocity = function(timestep) {
	this.eachNode(function(node, point) {
		// Is this, along with updatePosition below, the only places that your
		// integration code exist?
		point.v = point.v.add(point.a.multiply(timestep)).multiply(this.damping);
		point.a = new Vector(0,0);
	});
};

Layout.ForceDirected.prototype.updatePosition = function(timestep) {
	this.eachNode(function(node, point) {
		// Same question as above; along with updateVelocity, is this all of
		// your integration code?
		point.p = point.p.add(point.v.multiply(timestep));
	});
};

// Calculate the total kinetic energy of the system
Layout.ForceDirected.prototype.totalEnergy = function(timestep) {
	var energy = 0.0;
	this.eachNode(function(node, point) {
		var speed = point.v.magnitude();
		energy += 0.5 * point.m * speed * speed;
	});

	return energy;
};

var __bind = function(fn, me){ return function(){ return fn.apply(me, arguments); }; }; // stolen from coffeescript, thanks jashkenas! ;-)

Layout.requestAnimationFrame = __bind(window.requestAnimationFrame ||
	window.webkitRequestAnimationFrame ||
	window.mozRequestAnimationFrame ||
	window.oRequestAnimationFrame ||
	window.msRequestAnimationFrame ||
	function(callback, element) {
		window.setTimeout(callback, 10);
	}, window);


// start simulation
Layout.ForceDirected.prototype.start = function(interval, render, done) {
	var t = this;

	if (this._started) return;
	this._started = true;

	Layout.requestAnimationFrame(function step() {
		t.applyCoulombsLaw();
		t.applyHookesLaw();
		t.attractToCentre();
		t.updateVelocity(0.03);
		t.updatePosition(0.03);

		if (typeof(render) !== 'undefined')
			render();

		// stop simulation when energy of the system goes below a threshold
		if (t.totalEnergy() < 0.01) {
			t._started = false;
			if (typeof(done) !== 'undefined') { done(); }
		} else {
			Layout.requestAnimationFrame(step);
		}
	});
};

// Find the nearest point to a particular position
Layout.ForceDirected.prototype.nearest = function(pos) {
	var min = {node: null, point: null, distance: null};
	var t = this;
	this.graph.nodes.forEach(function(n){
		var point = t.point(n);
		var distance = point.p.subtract(pos).magnitude();

		if (min.distance === null || distance < min.distance) {
			min = {node: n, point: point, distance: distance};
		}
	});

	return min;
};

// returns [bottomleft, topright]
Layout.ForceDirected.prototype.getBoundingBox = function() {
	var bottomleft = new Vector(-2,-2);
	var topright = new Vector(2,2);

	this.eachNode(function(n, point) {
		if (point.p.x < bottomleft.x) {
			bottomleft.x = point.p.x;
		}
		if (point.p.y < bottomleft.y) {
			bottomleft.y = point.p.y;
		}
		if (point.p.x > topright.x) {
			topright.x = point.p.x;
		}
		if (point.p.y > topright.y) {
			topright.y = point.p.y;
		}
	});

	var padding = topright.subtract(bottomleft).multiply(0.07); // ~5% padding

	return {bottomleft: bottomleft.subtract(padding), topright: topright.add(padding)};
};


// Vector
Vector = function(x, y) {
	this.x = x;
	this.y = y;
};

Vector.random = function() {
	return new Vector(10.0 * (Math.random() - 0.5), 10.0 * (Math.random() - 0.5));
};

Vector.prototype.add = function(v2) {
	return new Vector(this.x + v2.x, this.y + v2.y);
};

Vector.prototype.subtract = function(v2) {
	return new Vector(this.x - v2.x, this.y - v2.y);
};

Vector.prototype.multiply = function(n) {
	return new Vector(this.x * n, this.y * n);
};

Vector.prototype.divide = function(n) {
	return new Vector((this.x / n) || 0, (this.y / n) || 0); // Avoid divide by zero errors..
};

Vector.prototype.magnitude = function() {
	return Math.sqrt(this.x*this.x + this.y*this.y);
};

Vector.prototype.normal = function() {
	return new Vector(-this.y, this.x);
};

Vector.prototype.normalise = function() {
	return this.divide(this.magnitude());
};

// Point
Layout.ForceDirected.Point = function(position, mass) {
	this.p = position; // position
	this.m = mass; // mass
	this.v = new Vector(0, 0); // velocity
	this.a = new Vector(0, 0); // acceleration
};

Layout.ForceDirected.Point.prototype.applyForce = function(force) {
	this.a = this.a.add(force.divide(this.m));
};

// Spring
Layout.ForceDirected.Spring = function(point1, point2, length, k) {
	this.point1 = point1;
	this.point2 = point2;
	this.length = length; // spring length at rest
	this.k = k; // spring constant (See Hooke's law) .. how stiff the spring is
};

// Layout.ForceDirected.Spring.prototype.distanceToPoint = function(point)
// {
// 	// hardcore vector arithmetic.. ohh yeah!
// 	// .. see http://stackoverflow.com/questions/849211/shortest-distance-between-a-point-and-a-line-segment/865080#865080
// 	var n = this.point2.p.subtract(this.point1.p).normalise().normal();
// 	var ac = point.p.subtract(this.point1.p);
// 	return Math.abs(ac.x * n.x + ac.y * n.y);
// };

// Renderer handles the layout rendering loop
function Renderer(interval, layout, clear, drawEdge, drawNode) {
	this.interval = interval;
	this.layout = layout;
	this.clear = clear;
	this.drawEdge = drawEdge;
	this.drawNode = drawNode;

	this.layout.graph.addGraphListener(this);
}

Renderer.prototype.graphChanged = function(e) {
	this.start();
};

Renderer.prototype.start = function() {
	var t = this;
	this.layout.start(50, function render() {
		t.clear();

		t.layout.eachEdge(function(edge, spring) {
			t.drawEdge(edge, spring.point1.p, spring.point2.p);
		});

		t.layout.eachNode(function(node, point) {
			t.drawNode(node, point.p);
		});
	});
};