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D3 Venn Diagram Example
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index.html
<!doctype html>
<head>
<title>Audience Comparison</title>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1">
<script src="https://cdnjs.cloudflare.com/ajax/libs/d3/3.5.6/d3.min.js" charset="utf-8"></script>
<link href='https://fonts.googleapis.com/css?family=Quicksand:400,700' rel='stylesheet' type='text/css'>
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/css/bootstrap.min.css">
<script src="venn.js"></script>
<style>
body {
font-family: 'Quicksand', sans-serif;
font-weight: 700;
font-size : 14px;
margin: 2% 2% 2% 2%;
}
.venntooltip {
font-size : 14px;
position: absolute;
text-align: center;
width: 128px;
height: 85px;
background: #333;
color: #fff;
padding: 2px;
border: 0px;
border-radius: 8px;
opacity: 0;
}
</style>
</head>
<body>
<div id="container">
<h1>Audience Comparison</h1>
<p>Venn Diagram created with Ben Federickson's "<a href="http://www.benfrederickson.com/better-venn-diagrams/">A Better Algorithm for Area Proportional Venn and Euler Diagrams</a>"</p>
<div id="venn_one" style=float:left>
<h3>Audience One</h3>
</div>
<div id="venn_two" style=float:left>
<h3>Audience Two</h3>
</div>
<script>
var sets = [
{sets:["Audio"], figure: 8.91, label: "Audio", size: 8.91},
{sets:["Direct Buy"], figure: 34.53, label: "Direct Buy", size: 34.53},
{sets:["Branded Takeover"], figure: 40.9, label: "Branded Takeover", size: 40.9},
{sets: ["Audio", "Direct Buy"], figure: 5.05, label: "Audio and Direct Buy", size: 5.05},
{sets: ["Audio", "Branded Takeover"], figure: 3.65, label: "Audio and Branded Takeover", size: 3.65},
{sets: ["Direct Buy", "Branded Takeover"], figure: 4.08, label: "Direct Buy and Branded Takeover", size: 4.08},
{sets: ["Audio", "Direct Buy", "Branded Takeover"], figure: 2.8, label: "Audio, Direct Buy, and Branded Takeover", size: 2.8}
];
var chart = venn.VennDiagram()
.width(500)
.height(400)
var div = d3.select("#venn_one").datum(sets).call(chart);
div.selectAll("text").style("fill", "white");
div.selectAll(".venn-circle path")
.style("fill-opacity", .8)
.style("stroke-width", 1)
.style("stroke-opacity", 1)
.style("stroke", "fff");
var tooltip = d3.select("#venn_one").append("div")
.attr("class", "venntooltip");
div.selectAll("g")
.on("mouseover", function(d, i) {
// sort all the areas relative to the current item
venn.sortAreas(div, d);
// Display a tooltip with the current size
tooltip.transition().duration(40).style("opacity", 1);
tooltip.text(d.size + "% of Audience One saw " + d.label);
// highlight the current path
// highlight the current path
var selection = d3.select(this).transition("tooltip").duration(400);
selection.select("path")
.style("stroke-width", 3)
.style("fill-opacity", d.sets.length == 1 ? .8 : 0)
.style("stroke-opacity", 1);
})
.on("mousemove", function() {
tooltip.style("left", (d3.event.pageX) + "px")
.style("top", (d3.event.pageY - 28) + "px");
})
.on("mouseout", function(d, i) {
tooltip.transition().duration(2000).style("opacity", 0);
var selection = d3.select(this).transition("tooltip").duration(400);
selection.select("path")
.style("stroke-width", 3)
.style("fill-opacity", d.sets.length == 1 ? .8 : 0)
.style("stroke-opacity", 1);
});
var sets = [
{sets:["Audio"], figure: 27.92, label: "Audio", size: 27.92},
{sets:["Direct Buy"], figure: 55.28, label: "Direct Buy", size: 55.28},
{sets:["Branded Takeover"], figure: 7.62, label: "Branded Takeover", size: 7.62},
{sets: ["Audio", "Direct Buy"], figure: 3.03, label: "Audio and Direct Buy", size: 3.03},
{sets: ["Audio", "Branded Takeover"], figure: 1.66, label: "Audio and Branded Takeover", size: 1.66},
{sets: ["Direct Buy", "Branded Takeover"], figure: 2.40, label: "Direct Buy and Branded Takeover", size: 2.40},
{sets: ["Audio", "Direct Buy", "Branded Takeover"], figure: 1.08, label: "Audio, Direct Buy, and Branded Takeover", size: 1.08}
];
var chart = venn.VennDiagram()
.width(500)
.height(400)
var div2 = d3.select("#venn_two").datum(sets).call(chart);
div2.selectAll("text").style("fill", "white");
div2.selectAll(".venn-circle path")
.style("fill-opacity", .8)
.style("stroke-width", 1)
.style("stroke-opacity", 1)
.style("stroke", "fff");
var tooltip = d3.select("body").append("div")
.attr("class", "venntooltip");
div2.selectAll("g")
.on("mouseover", function(d, i) {
// sort all the areas relative to the current item
venn.sortAreas(div2, d);
// Display a tooltip with the current size
tooltip.transition().duration(40).style("opacity", 1);
tooltip.text(d.size + "% of Audience Two saw " + d.label);
// highlight the current path
var selection = d3.select(this).transition("tooltip").duration(400);
selection.select("path")
.style("stroke-width", 3)
.style("fill-opacity", d.sets.length == 1 ? .8 : 0)
.style("stroke-opacity", 1);
})
.on("mousemove", function() {
tooltip.style("left", (d3.event.pageX) + "px")
.style("top", (d3.event.pageY - 28) + "px");
})
.on("mouseout", function(d, i) {
tooltip.transition().duration(2500).style("opacity", 0);
var selection = d3.select(this).transition("tooltip").duration(400);
selection.select("path")
.style("stroke-width", 3)
.style("fill-opacity", d.sets.length == 1 ? .8 : 0)
.style("stroke-opacity", 1);
});
//https://github.com/benfred/venn.js/issues/22
</script>
</div>
</body>
</html>
Raw
venn.js
var venn = venn || {'version' : '0.2.5'};
(function(venn) {
"use strict";
venn.VennDiagram = function() {
var width = 800,
height = 650,
padding = 15,
duration = 1000,
orientation = Math.PI / 2,
normalize = true,
wrap = true,
styled = true,
fontSize = null,
colours = d3.scale.ordinal()
.range(["#0a2756","#e60024","#45CFD7","#a173d1", "#0FF66A3","#00FFFF","#6ab975","#5687d1", "#F5E94B", "bbbbbb", "#00B8E6"]),
layoutFunction = venn.venn;
function chart(selection) {
var data = selection.datum();
var solution = layoutFunction(data);
if (normalize) {
solution = venn.normalizeSolution(solution, orientation);
}
var circles = venn.scaleSolution(solution, width, height, padding);
var textCentres = computeTextCentres(circles, data);
// draw out a svg
var svg = selection.selectAll("svg").data([circles]);
svg.enter().append("svg");
svg.attr("width", width)
.attr("height", height);
// to properly transition intersection areas, we need the
// previous circles locations. load from elements
var previous = {}, hasPrevious = false;
svg.selectAll("g").each(function (d) {
var path = d3.select(this).select("path").attr("d");
if ((d.sets.length == 1) && path) {
hasPrevious = true;
previous[d.sets[0]] = venn.circleFromPath(path);
}
});
// interpolate intersection area paths between previous and
// current paths
var pathTween = function(d) {
return function(t) {
var c = d.sets.map(function(set) {
var start = previous[set], end = circles[set];
if (!start) {
start = {x : width/2, y : height/2, radius : 1};
}
if (!end) {
end = {x : width/2, y : height/2, radius : 1};
}
return {'x' : start.x * (1 - t) + end.x * t,
'y' : start.y * (1 - t) + end.y * t,
'radius' : start.radius * (1 - t) + end.radius * t};
});
return venn.intersectionAreaPath(c);
};
};
// update data, joining on the set ids
var nodes = svg.selectAll("g")
.data(data, function(d) { return d.sets; });
// create new nodes
var enter = nodes.enter()
.append('g')
.attr("class", function(d) {
return "venn-area venn-" +
(d.sets.length == 1 ? "circle" : "intersection");
})
.attr("data-venn-sets", function(d) {
return d.sets.join("_");
});
var enterPath = enter.append("path"),
enterText = enter.append("text")
.attr("class", "label")
.text(function (d) { return label(d); } )
.attr("text-anchor", "middle")
.attr("dy", ".35em")
.attr("x", width/2)
.attr("y", height/2);
// apply minimal style if wanted
if (styled) {
enterPath.style("fill-opacity", "0")
.filter(function (d) { return d.sets.length == 1; } )
.style("fill", function(d) { return colours(label(d)); })
.style("fill-opacity", ".25");
enterText
.style("fill", function(d) { return d.sets.length == 1 ? colours(label(d)) : "#444"; });
}
// update existing
var update = nodes.transition("venn").duration(hasPrevious ? duration : 0);
update.select("path")
.attrTween("d", pathTween);
var updateText = update.select("text")
.text(function (d) { return label(d); } )
.attr("x", function(d) {
return Math.floor(textCentres[d.sets].x);
})
.attr("y", function(d) {
return Math.floor(textCentres[d.sets].y);
});
if (wrap) {
updateText.each("end", venn.wrapText(circles, label));
}
// remove old
var exit = nodes.exit().transition('venn').duration(duration).remove();
exit.select("path")
.attrTween("d", pathTween);
var exitText = exit.select("text")
.text(function (d) { return label(d); } )
.attr("x", width/2)
.attr("y", height/2);
// if we've been passed a fontSize explicitly, use it to
// transition
if (fontSize !== null) {
enterText.style("font-size", "0px");
updateText.style("font-size", fontSize);
exitText.style("font-size", "0px");
}
return {'circles': circles,
'textCentres': textCentres,
'nodes': nodes,
'enter': enter,
'update': update,
'exit': exit};
}
function label(d) {
if (d.sets.length == 1) {
return '' + d.sets[0];
}
}
chart.wrap = function(_) {
if (!arguments.length) return wrap;
wrap = _;
return chart;
};
chart.width = function(_) {
if (!arguments.length) return width;
width = _;
return chart;
};
chart.height = function(_) {
if (!arguments.length) return height;
height = _;
return chart;
};
chart.padding = function(_) {
if (!arguments.length) return padding;
padding = _;
return chart;
};
chart.colours = function(_) {
if (!arguments.length) return colours;
colours = _;
return chart;
};
chart.fontSize = function(_) {
if (!arguments.length) return fontSize;
fontSize = _;
return chart;
};
chart.duration = function(_) {
if (!arguments.length) return duration;
duration = _;
return chart;
};
chart.layoutFunction = function(_) {
if (!arguments.length) return layoutFunction;
layoutFunction = _;
return chart;
};
chart.normalize = function(_) {
if (!arguments.length) return normalize;
normalize = _;
return chart;
};
chart.styled = function(_) {
if (!arguments.length) return styled;
styled = _;
return chart;
};
chart.orientation = function(_) {
if (!arguments.length) return orientation;
orientation = _;
return chart;
};
return chart;
};
// sometimes text doesn't fit inside the circle, if thats the case lets wrap
// the text here such that it fits
// todo: looks like this might be merged into d3 (
// https://github.com/mbostock/d3/issues/1642),
// also worth checking out is
// http://engineering.findthebest.com/wrapping-axis-labels-in-d3-js/
// this seems to be one of those things that should be easy but isn't
venn.wrapText = function(circles, labeller) {
return function() {
var text = d3.select(this),
data = text.datum(),
width = circles[data.sets[0]].radius || 50,
label = labeller(data) || '';
var words = label.split(/\s+/).reverse(),
maxLines = 3,
minChars = (label.length + words.length) / maxLines,
word = words.pop(),
line = [word],
joined,
lineNumber = 0,
lineHeight = 1.1, // ems
tspan = text.text(null).append("tspan").text(word);
while (true) {
word = words.pop();
if (!word) break;
line.push(word);
joined = line.join(" ");
tspan.text(joined);
if (joined.length > minChars && tspan.node().getComputedTextLength() > width) {
line.pop();
tspan.text(line.join(" "));
line = [word];
tspan = text.append("tspan").text(word);
lineNumber++;
}
}
var initial = 0.35 - lineNumber * lineHeight / 2,
x = text.attr("x"),
y = text.attr("y");
text.selectAll("tspan")
.attr("x", x)
.attr("y", y)
.attr("dy", function(d, i) {
return (initial + i * lineHeight) + "em";
});
};
};
function circleMargin(current, interior, exterior) {
var margin = interior[0].radius - venn.distance(interior[0], current), i, m;
for (i = 1; i < interior.length; ++i) {
m = interior[i].radius - venn.distance(interior[i], current);
if (m <= margin) {
margin = m;
}
}
for (i = 0; i < exterior.length; ++i) {
m = venn.distance(exterior[i], current) - exterior[i].radius;
if (m <= margin) {
margin = m;
}
}
return margin;
}
// compute the center of some circles by maximizing the margin of
// the center point relative to the circles (interior) after subtracting
// nearby circles (exterior)
function computeTextCentre(interior, exterior) {
// get an initial estimate by sampling around the interior circles
// and taking the point with the biggest margin
var points = [], i;
for (i = 0; i < interior.length; ++i) {
var c = interior[i];
points.push({x: c.x, y: c.y});
points.push({x: c.x + c.radius/2, y: c.y});
points.push({x: c.x - c.radius/2, y: c.y});
points.push({x: c.x, y: c.y + c.radius/2});
points.push({x: c.x, y: c.y - c.radius/2});
}
var initial = points[0], margin = circleMargin(points[0], interior, exterior);
for (i = 1; i < points.length; ++i) {
var m = circleMargin(points[i], interior, exterior);
if (m >= margin) {
initial = points[i];
margin = m;
}
}
// maximize the margin numerically
var solution = venn.fmin(
function(p) { return -1 * circleMargin({x: p[0], y: p[1]}, interior, exterior); },
[initial.x, initial.y],
{maxIterations:500, minErrorDelta:1e-10}).solution;
var ret = {x: solution[0], y: solution[1]};
// check solution, fallback as needed (happens if fully overlapped
// etc)
var valid = true;
for (i = 0; i < interior.length; ++i) {
if (venn.distance(ret, interior[i]) > interior[i].radius) {
valid = false;
break;
}
}
for (i = 0; i < exterior.length; ++i) {
if (venn.distance(ret, exterior[i]) < exterior[i].radius) {
valid = false;
break;
}
}
if (!valid) {
if (interior.length == 1) {
ret = {x: interior[0].x, y: interior[0].y};
} else {
var areaStats = {};
venn.intersectionArea(interior, areaStats);
if (areaStats.arcs.length === 0) {
ret = {'x': 0, 'y': -1000, disjoint:true};
} else if (areaStats.arcs.length == 1) {
ret = {'x': areaStats.arcs[0].circle.x,
'y': areaStats.arcs[0].circle.y};
} else if (exterior.length) {
// try again without other circles
ret = computeTextCentre(interior, []);
} else {
// take average of all the points in the intersection
// polygon. this should basically never happen
// and has some issues:
// https://github.com/benfred/venn.js/issues/48#issuecomment-146069777
ret = venn.getCenter(areaStats.arcs.map(function (a) { return a.p1; }));
}
}
}
return ret;
}
venn.computeTextCentre = computeTextCentre;
// given a dictionary of {setid : circle}, returns
// a dictionary of setid to list of circles that completely overlap it
function getOverlappingCircles(circles) {
var ret = {}, circleids = [];
for (var circleid in circles) {
circleids.push(circleid);
ret[circleid] = [];
}
for (var i = 0; i < circleids.length; i++) {
var a = circles[circleids[i]];
for (var j = i + 1; j < circleids.length; ++j) {
var b = circles[circleids[j]],
d = venn.distance(a, b);
if (d + b.radius <= a.radius + 1e-10) {
ret[circleids[j]].push(circleids[i]);
} else if (d + a.radius <= b.radius + 1e-10) {
ret[circleids[i]].push(circleids[j]);
}
}
}
return ret;
}
function computeTextCentres(circles, areas) {
var ret = {}, overlapped = getOverlappingCircles(circles);
for (var i = 0; i < areas.length; ++i) {
var area = areas[i].sets, areaids = {}, exclude = {};
for (var j = 0; j < area.length; ++j) {
areaids[area[j]] = true;
var overlaps = overlapped[area[j]];
// keep track of any circles that overlap this area,
// and don't consider for purposes of computing the text
// centre
for (var k = 0; k < overlaps.length; ++k) {
exclude[overlaps[k]] = true;
}
}
var interior = [], exterior = [];
for (var setid in circles) {
if (setid in areaids) {
interior.push(circles[setid]);
} else if (!(setid in exclude)) {
exterior.push(circles[setid]);
}
}
var centre = computeTextCentre(interior, exterior);
ret[area] = centre;
if (centre.disjoint && (areas[i].size > 0)) {
console.log("WARNING: area " + area + " not represented on screen");
}
}
return ret;
}
venn.computeTextCentres = computeTextCentres;
// sorts all areas in the venn diagram, so that
// a particular area is on top (relativeTo) - and
// all other areas are so that the smallest areas are on top
venn.sortAreas = function(div, relativeTo) {
// figure out sets that are completly overlapped by relativeTo
var overlaps = getOverlappingCircles(div.selectAll("svg").datum());
var exclude = {};
for (var i = 0; i < relativeTo.sets.length; ++i) {
var check = relativeTo.sets[i];
for (var setid in overlaps) {
var overlap = overlaps[setid];
for (var j = 0; j < overlap.length; ++j) {
if (overlap[j] == check) {
exclude[setid] = true;
break;
}
}
}
}
// checks that all sets are in exclude;
function shouldExclude(sets) {
for (var i = 0; i < sets.length; ++i) {
if (!(sets[i] in exclude)) {
return false;
}
}
return true;
}
// need to sort div's so that Z order is correct
div.selectAll("g").sort(function (a, b) {
// highest order set intersections first
if (a.sets.length != b.sets.length) {
return a.sets.length - b.sets.length;
}
if (a == relativeTo) {
return shouldExclude(b.sets) ? -1 : 1;
}
if (b == relativeTo) {
return shouldExclude(a.sets) ? 1 : -1;
}
// finally by size
return b.size - a.size;
});
};
venn.circlePath = function(x, y, r) {
var ret = [];
ret.push("\nM", x, y);
ret.push("\nm", -r, 0);
ret.push("\na", r, r, 0, 1, 0, r *2, 0);
ret.push("\na", r, r, 0, 1, 0,-r *2, 0);
return ret.join(" ");
};
// inverse of the circlePath function, returns a circle object from an svg path
venn.circleFromPath = function(path) {
var tokens = path.split(' ');
return {'x' : parseFloat(tokens[1]),
'y' : parseFloat(tokens[2]),
'radius' : -parseFloat(tokens[4])
};
};
/** returns a svg path of the intersection area of a bunch of circles */
venn.intersectionAreaPath = function(circles) {
var stats = {};
venn.intersectionArea(circles, stats);
var arcs = stats.arcs;
if (arcs.length === 0) {
return "M 0 0";
} else if (arcs.length == 1) {
var circle = arcs[0].circle;
return venn.circlePath(circle.x, circle.y, circle.radius);
} else {
// draw path around arcs
var ret = ["\nM", arcs[0].p2.x, arcs[0].p2.y];
for (var i = 0; i < arcs.length; ++i) {
var arc = arcs[i], r = arc.circle.radius, wide = arc.width > r;
ret.push("\nA", r, r, 0, wide ? 1 : 0, 1,
arc.p1.x, arc.p1.y);
}
return ret.join(" ");
}
};
})(venn);
(function(venn) {
"use strict";
/** given a list of set objects, and their corresponding overlaps.
updates the (x, y, radius) attribute on each set such that their positions
roughly correspond to the desired overlaps */
venn.venn = function(areas, parameters) {
parameters = parameters || {};
parameters.maxIterations = parameters.maxIterations || 500;
var lossFunction = parameters.lossFunction || venn.lossFunction;
var initialLayout = parameters.initialLayout || venn.bestInitialLayout;
var fmin = parameters.fmin || venn.fmin;
// add in missing pairwise areas as having 0 size
areas = addMissingAreas(areas);
// initial layout is done greedily
var circles = initialLayout(areas);
// transform x/y coordinates to a vector to optimize
var initial = [], setids = [], setid;
for (setid in circles) {
if (circles.hasOwnProperty(setid)) {
initial.push(circles[setid].x);
initial.push(circles[setid].y);
setids.push(setid);
}
}
// optimize initial layout from our loss function
var totalFunctionCalls = 0;
var solution = fmin(
function(values) {
totalFunctionCalls += 1;
var current = {};
for (var i = 0; i < setids.length; ++i) {
var setid = setids[i];
current[setid] = {x: values[2 * i],
y: values[2 * i + 1],
radius : circles[setid].radius,
// size : circles[setid].size
};
}
return lossFunction(current, areas);
},
initial,
parameters);
// transform solution vector back to x/y points
var positions = solution.solution;
for (var i = 0; i < setids.length; ++i) {
setid = setids[i];
circles[setid].x = positions[2 * i];
circles[setid].y = positions[2 * i + 1];
}
return circles;
};
var SMALL = 1e-10;
/** Returns the distance necessary for two circles of radius r1 + r2 to
have the overlap area 'overlap' */
venn.distanceFromIntersectArea = function(r1, r2, overlap) {
// handle complete overlapped circles
if (Math.min(r1, r2) * Math.min(r1,r2) * Math.PI <= overlap + SMALL) {
return Math.abs(r1 - r2);
}
return venn.bisect(function(distance) {
return venn.circleOverlap(r1, r2, distance) - overlap;
}, 0, r1 + r2);
};
/** Missing pair-wise intersection area data can cause problems:
treating as an unknown means that sets will be laid out overlapping,
which isn't what people expect. To reflect that we want disjoint sets
here, set the overlap to 0 for all missing pairwise set intersections */
function addMissingAreas(areas) {
areas = areas.slice();
// two circle intersections that aren't defined
var ids = [], pairs = {}, i, j, a, b;
for (i = 0; i < areas.length; ++i) {
var area = areas[i];
if (area.sets.length == 1) {
ids.push(area.sets[0]);
} else if (area.sets.length == 2) {
a = area.sets[0];
b = area.sets[1];
pairs[[a, b]] = true;
pairs[[b, a]] = true;
}
}
ids.sort(function(a, b) { return a > b; });
for (i = 0; i < ids.length; ++i) {
a = ids[i];
for (j = i + 1; j < ids.length; ++j) {
b = ids[j];
if (!([a, b] in pairs)) {
areas.push({'sets': [a, b],
'size': 0});
}
}
}
return areas;
}
/// Returns two matrices, one of the euclidean distances between the sets
/// and the other indicating if there are subset or disjoint set relationships
venn.getDistanceMatrices = function(areas, sets, setids) {
// initialize an empty distance matrix between all the points
var distances = venn.zerosM(sets.length, sets.length),
constraints = venn.zerosM(sets.length, sets.length);
// compute required distances between all the sets such that
// the areas match
areas.filter(function(x) { return x.sets.length == 2; })
.map(function(current) {
var left = setids[current.sets[0]],
right = setids[current.sets[1]],
r1 = Math.sqrt(sets[left].size / Math.PI),
r2 = Math.sqrt(sets[right].size / Math.PI),
distance = venn.distanceFromIntersectArea(r1, r2, current.size);
distances[left][right] = distances[right][left] = distance;
// also update constraints to indicate if its a subset or disjoint
// relationship
var c = 0;
if (current.size + 1e-10 >= Math.min(sets[left].size,
sets[right].size)) {
c = 1;
} else if (current.size <= 1e-10) {
c = -1;
}
constraints[left][right] = constraints[right][left] = c;
});
return {distances: distances, constraints: constraints};
};
/// computes the gradient and loss simulatenously for our constrained MDS optimizer
function constrainedMDSGradient(x, fxprime, distances, constraints) {
var loss = 0, i;
for (i = 0; i < fxprime.length; ++i) {
fxprime[i] = 0;
}
for (i = 0; i < distances.length; ++i) {
var xi = x[2 * i], yi = x[2 * i + 1];
for (var j = i + 1; j < distances.length; ++j) {
var xj = x[2 * j], yj = x[2 * j + 1],
dij = distances[i][j],
constraint = constraints[i][j];
var squaredDistance = (xj - xi) * (xj - xi) + (yj - yi) * (yj - yi),
distance = Math.sqrt(squaredDistance),
delta = squaredDistance - dij * dij;
if (((constraint > 0) && (distance <= dij)) ||
((constraint < 0) && (distance >= dij))) {
continue;
}
loss += 2 * delta * delta;
fxprime[2*i] += 4 * delta * (xi - xj);
fxprime[2*i + 1] += 4 * delta * (yi - yj);
fxprime[2*j] += 4 * delta * (xj - xi);
fxprime[2*j + 1] += 4 * delta * (yj - yi);
}
}
return loss;
}
/// takes the best working variant of either constrained MDS or greedy
venn.bestInitialLayout = function(areas, params) {
var initial = venn.greedyLayout(areas, params);
// greedylayout is sufficient for all 2/3 circle cases. try out
// constrained MDS for higher order problems, take its output
// if it outperforms. (greedy is aesthetically better on 2/3 circles
// since it axis aligns)
if (areas.length >= 8) {
var constrained = venn.constrainedMDSLayout(areas, params),
constrainedLoss = venn.lossFunction(constrained, areas),
greedyLoss = venn.lossFunction(initial, areas);
if (constrainedLoss + 1e-8 < greedyLoss) {
initial = constrained;
}
}
return initial;
};
/// use the constrained MDS variant to generate an initial layout
venn.constrainedMDSLayout = function(areas, params) {
params = params || {};
var restarts = params.restarts || 10;
// bidirectionally map sets to a rowid (so we can create a matrix)
var sets = [], setids = {}, i;
for (i = 0; i < areas.length; ++i ) {
var area = areas[i];
if (area.sets.length == 1) {
setids[area.sets[0]] = sets.length;
sets.push(area);
}
}
var matrices = venn.getDistanceMatrices(areas, sets, setids),
distances = matrices.distances,
constraints = matrices.constraints;
// keep distances bounded, things get messed up otherwise.
// TODO: proper preconditioner?
var norm = venn.norm2(distances.map(venn.norm2))/(distances.length);
distances = distances.map(function (row) {
return row.map(function (value) { return value / norm; });});
var obj = function(x, fxprime) {
return constrainedMDSGradient(x, fxprime, distances, constraints);
};
var best, current;
for (i = 0; i < restarts; ++i) {
var initial = venn.zeros(distances.length*2).map(Math.random);
current = venn.minimizeConjugateGradient(obj, initial, params);
if (!best || (current.fx < best.fx)) {
best = current;
}
}
var positions = best.x;
// translate rows back to (x,y,radius) coordinates
var circles = {};
for (i = 0; i < sets.length; ++i) {
var set = sets[i];
circles[set.sets[0]] = {
x: positions[2*i] * norm,
y: positions[2*i + 1] * norm,
radius: Math.sqrt(set.size / Math.PI)
};
}
if (params.history) {
for (i = 0; i < params.history.length; ++i) {
venn.multiplyBy(params.history[i].x, norm);
}
}
return circles;
};
/** Lays out a Venn diagram greedily, going from most overlapped sets to
least overlapped, attempting to position each new set such that the
overlapping areas to already positioned sets are basically right */
venn.greedyLayout = function(areas) {
// define a circle for each set
var circles = {}, setOverlaps = {}, set;
for (var i = 0; i < areas.length; ++i) {
var area = areas[i];
if (area.sets.length == 1) {
set = area.sets[0];
circles[set] = {x: 1e10, y: 1e10,
rowid: circles.length,
size: area.size,
radius: Math.sqrt(area.size / Math.PI)};
setOverlaps[set] = [];
}
}
areas = areas.filter(function(a) { return a.sets.length == 2; });
// map each set to a list of all the other sets that overlap it
for (i = 0; i < areas.length; ++i) {
var current = areas[i];
var weight = current.hasOwnProperty('weight') ? current.weight : 1.0;
var left = current.sets[0], right = current.sets[1];
// completely overlapped circles shouldn't be positioned early here
if (current.size + SMALL >= Math.min(circles[left].size,
circles[right].size)) {
weight = 0;
}
setOverlaps[left].push ({set:right, size:current.size, weight:weight});
setOverlaps[right].push({set:left, size:current.size, weight:weight});
}
// get list of most overlapped sets
var mostOverlapped = [];
for (set in setOverlaps) {
if (setOverlaps.hasOwnProperty(set)) {
var size = 0;
for (i = 0; i < setOverlaps[set].length; ++i) {
size += setOverlaps[set][i].size * setOverlaps[set][i].weight;
}
mostOverlapped.push({set: set, size:size});
}
}
// sort by size desc
function sortOrder(a,b) {
return b.size - a.size;
}
mostOverlapped.sort(sortOrder);
// keep track of what sets have been laid out
var positioned = {};
function isPositioned(element) {
return element.set in positioned;
}
// adds a point to the output
function positionSet(point, index) {
circles[index].x = point.x;
circles[index].y = point.y;
positioned[index] = true;
}
// add most overlapped set at (0,0)
positionSet({x: 0, y: 0}, mostOverlapped[0].set);
// get distances between all points. TODO, necessary?
// answer: probably not
// var distances = venn.getDistanceMatrices(circles, areas).distances;
for (i = 1; i < mostOverlapped.length; ++i) {
var setIndex = mostOverlapped[i].set,
overlap = setOverlaps[setIndex].filter(isPositioned);
set = circles[setIndex];
overlap.sort(sortOrder);
if (overlap.length === 0) {
// this shouldn't happen anymore with addMissingAreas
throw "ERROR: missing pairwise overlap information";
}
var points = [];
for (var j = 0; j < overlap.length; ++j) {
// get appropriate distance from most overlapped already added set
var p1 = circles[overlap[j].set],
d1 = venn.distanceFromIntersectArea(set.radius, p1.radius,
overlap[j].size);
// sample positions at 90 degrees for maximum aesthetics
points.push({x : p1.x + d1, y : p1.y});
points.push({x : p1.x - d1, y : p1.y});
points.push({y : p1.y + d1, x : p1.x});
points.push({y : p1.y - d1, x : p1.x});
// if we have at least 2 overlaps, then figure out where the
// set should be positioned analytically and try those too
for (var k = j + 1; k < overlap.length; ++k) {
var p2 = circles[overlap[k].set],
d2 = venn.distanceFromIntersectArea(set.radius, p2.radius,
overlap[k].size);
var extraPoints = venn.circleCircleIntersection(
{ x: p1.x, y: p1.y, radius: d1},
{ x: p2.x, y: p2.y, radius: d2});
for (var l = 0; l < extraPoints.length; ++l) {
points.push(extraPoints[l]);
}
}
}
// we have some candidate positions for the set, examine loss
// at each position to figure out where to put it at
var bestLoss = 1e50, bestPoint = points[0];
for (j = 0; j < points.length; ++j) {
circles[setIndex].x = points[j].x;
circles[setIndex].y = points[j].y;
var loss = venn.lossFunction(circles, areas);
if (loss < bestLoss) {
bestLoss = loss;
bestPoint = points[j];
}
}
positionSet(bestPoint, setIndex);
}
return circles;
};
/// Uses multidimensional scaling to approximate a first layout here
venn.classicMDSLayout = function(areas) {
// bidirectionally map sets to a rowid (so we can create a matrix)
var sets = [], setids = {};
for (var i = 0; i < areas.length; ++i ) {
var area = areas[i];
if (area.sets.length == 1) {
setids[area.sets[0]] = sets.length;
sets.push(area);
}
}
// get the distance matrix, and use to position sets
var distances = venn.getDistanceMatrices(areas, sets, setids).distances;
var positions = mds.classic(distances);
// translate rows back to (x,y,radius) coordinates
var circles = {};
for (i = 0; i < sets.length; ++i) {
var set = sets[i];
circles[set.sets[0]] = {
x: positions[i][0],
y: positions[i][1],
radius: Math.sqrt(set.size / Math.PI)
};
}
return circles;
};
/** Given a bunch of sets, and the desired overlaps between these sets - computes
the distance from the actual overlaps to the desired overlaps. Note that
this method ignores overlaps of more than 2 circles */
venn.lossFunction = function(sets, overlaps) {
var output = 0;
function getCircles(indices) {
return indices.map(function(i) { return sets[i]; });
}
for (var i = 0; i < overlaps.length; ++i) {
var area = overlaps[i], overlap;
if (area.sets.length == 1) {
continue;
} else if (area.sets.length == 2) {
var left = sets[area.sets[0]],
right = sets[area.sets[1]];
overlap = venn.circleOverlap(left.radius, right.radius,
venn.distance(left, right));
} else {
overlap = venn.intersectionArea(getCircles(area.sets));
}
var weight = area.hasOwnProperty('weight') ? area.weight : 1.0;
output += weight * (overlap - area.size) * (overlap - area.size);
}
return output;
};
// orientates a bunch of circles to point in orientation
function orientateCircles(circles, orientation) {
// sort circles by size
circles.sort(function (a, b) { return b.radius - a.radius; });
var i;
// shift circles so largest circle is at (0, 0)
if (circles.length > 0) {
var largestX = circles[0].x,
largestY = circles[0].y;
for (i = 0; i < circles.length; ++i) {
circles[i].x -= largestX;
circles[i].y -= largestY;
}
}
// rotate circles so that second largest is at an angle of 'orientation'
// from largest
if (circles.length > 1) {
var rotation = Math.atan2(circles[1].x, circles[1].y) - orientation,
c = Math.cos(rotation),
s = Math.sin(rotation), x, y;
for (i = 0; i < circles.length; ++i) {
x = circles[i].x;
y = circles[i].y;
circles[i].x = c * x - s * y;
circles[i].y = s * x + c * y;
}
}
// mirror solution if third solution is above plane specified by
// first two circles
if (circles.length > 2) {
var angle = Math.atan2(circles[2].x, circles[2].y) - orientation;
while (angle < 0) { angle += 2* Math.PI; }
while (angle > 2*Math.PI) { angle -= 2* Math.PI; }
if (angle > Math.PI) {
var slope = circles[1].y / (1e-10 + circles[1].x);
for (i = 0; i < circles.length; ++i) {
var d = (circles[i].x + slope * circles[i].y) / (1 + slope*slope);
circles[i].x = 2 * d - circles[i].x;
circles[i].y = 2 * d * slope - circles[i].y;
}
}
}
}
venn.disjointCluster = function(circles) {
// union-find clustering to get disjoint sets
circles.map(function(circle) { circle.parent = circle; });
// path compression step in union find
function find(circle) {
if (circle.parent !== circle) {
circle.parent = find(circle.parent);
}
return circle.parent;
}
function union(x, y) {
var xRoot = find(x), yRoot = find(y);
xRoot.parent = yRoot;
}
// get the union of all overlapping sets
for (var i = 0; i < circles.length; ++i) {
for (var j = i + 1; j < circles.length; ++j) {
var maxDistance = circles[i].radius + circles[j].radius;
if (venn.distance(circles[i], circles[j]) + 1e-10 < maxDistance) {
union(circles[j], circles[i]);
}
}
}
// find all the disjoint clusters and group them together
var disjointClusters = {}, setid;
for (i = 0; i < circles.length; ++i) {
setid = find(circles[i]).parent.setid;
if (!(setid in disjointClusters)) {
disjointClusters[setid] = [];
}
disjointClusters[setid].push(circles[i]);
}
// cleanup bookkeeping
circles.map(function(circle) { delete circle.parent; });
// return in more usable form
var ret = [];
for (setid in disjointClusters) {
if (disjointClusters.hasOwnProperty(setid)) {
ret.push(disjointClusters[setid]);
}
}
return ret;
};
function getBoundingBox(circles) {
var minMax = function(d) {
var hi = Math.max.apply(null, circles.map(
function(c) { return c[d] + c.radius; } )),
lo = Math.min.apply(null, circles.map(
function(c) { return c[d] - c.radius;} ));
return {max:hi, min:lo};
};
return {xRange: minMax('x'), yRange: minMax('y')};
}
venn.normalizeSolution = function(solution, orientation) {
orientation = orientation || Math.PI/2;
// work with a list instead of a dictionary, and take a copy so we
// don't mutate input
var circles = [], i, setid;
for (setid in solution) {
if (solution.hasOwnProperty(setid)) {
var previous = solution[setid];
circles.push({x: previous.x,
y: previous.y,
radius: previous.radius,
setid: setid});
}
}
// get all the disjoint clusters
var clusters = venn.disjointCluster(circles);
// orientate all disjoint sets, get sizes
for (i = 0; i < clusters.length; ++i) {
orientateCircles(clusters[i], orientation);
var bounds = getBoundingBox(clusters[i]);
clusters[i].size = (bounds.xRange.max - bounds.xRange.min) * (bounds.yRange.max - bounds.yRange.min);
clusters[i].bounds = bounds;
}
clusters.sort(function(a, b) { return b.size - a.size; });
// orientate the largest at 0,0, and get the bounds
circles = clusters[0];
var returnBounds = circles.bounds;
var spacing = (returnBounds.xRange.max - returnBounds.xRange.min)/50;
function addCluster(cluster, right, bottom) {
if (!cluster) return;
var bounds = cluster.bounds, xOffset, yOffset, centreing;
if (right) {
xOffset = returnBounds.xRange.max - bounds.xRange.min + spacing;
} else {
xOffset = returnBounds.xRange.max - bounds.xRange.max - spacing;
centreing = (bounds.xRange.max - bounds.xRange.min) / 2 -
(returnBounds.xRange.max - returnBounds.xRange.min) / 2;
if (centreing < 0) xOffset += centreing;
}
if (bottom) {
yOffset = returnBounds.yRange.max - bounds.yRange.min + spacing;
} else {
yOffset = returnBounds.yRange.max - bounds.yRange.max - spacing;
centreing = (bounds.yRange.max - bounds.yRange.min) / 2 -
(returnBounds.yRange.max - returnBounds.yRange.min) / 2;
if (centreing < 0) yOffset += centreing;
}
for (var j = 0; j < cluster.length; ++j) {
cluster[j].x += xOffset;
cluster[j].y += yOffset;
circles.push(cluster[j]);
}
}
var index = 1;
while (index < clusters.length) {
addCluster(clusters[index], true, false);
addCluster(clusters[index+1], false, true);
addCluster(clusters[index+2], true, true);
index += 3;
// have one cluster (in top left). lay out next three relative
// to it in a grid
returnBounds = getBoundingBox(circles);
}
// convert back to solution form
var ret = {};
for (i = 0; i < circles.length; ++i) {
ret[circles[i].setid] = circles[i];
}
return ret;
};
/** Scales a solution from venn.venn or venn.greedyLayout such that it fits in
a rectangle of width/height - with padding around the borders. also
centers the diagram in the available space at the same time */
venn.scaleSolution = function(solution, width, height, padding) {
var circles = [], setids = [];
for (var setid in solution) {
if (solution.hasOwnProperty(setid)) {
setids.push(setid);
circles.push(solution[setid]);
}
}
width -= 2*padding;
height -= 2*padding;
var bounds = getBoundingBox(circles),
xRange = bounds.xRange,
yRange = bounds.yRange,
xScaling = width / (xRange.max - xRange.min),
yScaling = height / (yRange.max - yRange.min),
scaling = Math.min(yScaling, xScaling),
// while we're at it, center the diagram too
xOffset = (width - (xRange.max - xRange.min) * scaling) / 2,
yOffset = (height - (yRange.max - yRange.min) * scaling) / 2;
var scaled = {};
for (var i = 0; i < circles.length; ++i) {
var circle = circles[i];
scaled[setids[i]] = {
radius: scaling * circle.radius,
x: padding + xOffset + (circle.x - xRange.min) * scaling,
y: padding + yOffset + (circle.y - yRange.min) * scaling,
};
}
return scaled;
};
})(venn);
(function(venn) {
"use strict";
/** finds the zeros of a function, given two starting points (which must
* have opposite signs */
venn.bisect = function(f, a, b, parameters) {
parameters = parameters || {};
var maxIterations = parameters.maxIterations || 100,
tolerance = parameters.tolerance || 1e-10,
fA = f(a),
fB = f(b),
delta = b - a;
if (fA * fB > 0) {
throw "Initial bisect points must have opposite signs";
}
if (fA === 0) return a;
if (fB === 0) return b;
for (var i = 0; i < maxIterations; ++i) {
delta /= 2;
var mid = a + delta,
fMid = f(mid);
if (fMid * fA >= 0) {
a = mid;
}
if ((Math.abs(delta) < tolerance) || (fMid === 0)) {
return mid;
}
}
return a + delta;
};
// need some basic operations on vectors, rather than adding a dependency,
// just define here
function zeros(x) { var r = new Array(x); for (var i = 0; i < x; ++i) { r[i] = 0; } return r; }
function zerosM(x,y) { return zeros(x).map(function() { return zeros(y); }); }
venn.zerosM = zerosM;
venn.zeros = zeros;
function dot(a, b) {
var ret = 0;
for (var i = 0; i < a.length; ++i) {
ret += a[i] * b[i];
}
return ret;
}
function norm2(a) {
return Math.sqrt(dot(a, a));
}
venn.norm2 = norm2;
function multiplyBy(a, c) {
for (var i = 0; i < a.length; ++i) {
a[i] *= c;
}
}
venn.multiplyBy = multiplyBy;
function weightedSum(ret, w1, v1, w2, v2) {
for (var j = 0; j < ret.length; ++j) {
ret[j] = w1 * v1[j] + w2 * v2[j];
}
}
/** minimizes a function using the downhill simplex method */
venn.fmin = function(f, x0, parameters) {
parameters = parameters || {};
var maxIterations = parameters.maxIterations || x0.length * 200,
nonZeroDelta = parameters.nonZeroDelta || 1.1,
zeroDelta = parameters.zeroDelta || 0.001,
minErrorDelta = parameters.minErrorDelta || 1e-6,
rho = parameters.rho || 1,
chi = parameters.chi || 2,
psi = parameters.psi || -0.5,
sigma = parameters.sigma || 0.5,
callback = parameters.callback,
temp;
// initialize simplex.
var N = x0.length,
simplex = new Array(N + 1);
simplex[0] = x0;
simplex[0].fx = f(x0);
for (var i = 0; i < N; ++i) {
var point = x0.slice();
point[i] = point[i] ? point[i] * nonZeroDelta : zeroDelta;
simplex[i+1] = point;
simplex[i+1].fx = f(point);
}
var sortOrder = function(a, b) { return a.fx - b.fx; };
var centroid = x0.slice(),
reflected = x0.slice(),
contracted = x0.slice(),
expanded = x0.slice();
for (var iteration = 0; iteration < maxIterations; ++iteration) {
simplex.sort(sortOrder);
if (callback) {
callback(simplex);
}
if (Math.abs(simplex[0].fx - simplex[N].fx) < minErrorDelta) {
break;
}
// compute the centroid of all but the worst point in the simplex
for (i = 0; i < N; ++i) {
centroid[i] = 0;
for (var j = 0; j < N; ++j) {
centroid[i] += simplex[j][i];
}
centroid[i] /= N;
}
// reflect the worst point past the centroid and compute loss at reflected
// point
var worst = simplex[N];
weightedSum(reflected, 1+rho, centroid, -rho, worst);
reflected.fx = f(reflected);
// if the reflected point is the best seen, then possibly expand
if (reflected.fx <= simplex[0].fx) {
weightedSum(expanded, 1+chi, centroid, -chi, worst);
expanded.fx = f(expanded);
if (expanded.fx < reflected.fx) {
temp = simplex[N];
simplex[N] = expanded;
expanded = temp;
} else {
temp = simplex[N];
simplex[N] = reflected;
reflected = temp;
}
}
// if the reflected point is worse than the second worst, we need to
// contract
else if (reflected.fx >= simplex[N-1].fx) {
var shouldReduce = false;
if (reflected.fx <= worst.fx) {
// do an inside contraction
weightedSum(contracted, 1+psi, centroid, -psi, worst);
contracted.fx = f(contracted);
if (contracted.fx < worst.fx) {
temp = simplex[N];
simplex[N] = contracted;
contracted = temp;
} else {
shouldReduce = true;
}
} else {
// do an outside contraction
weightedSum(contracted, 1-psi * rho, centroid, psi*rho, worst);
contracted.fx = f(contracted);
if (contracted.fx <= reflected.fx) {
temp = simplex[N];
simplex[N] = contracted;
contracted = temp;
} else {
shouldReduce = true;
}
}
if (shouldReduce) {
// do reduction. doesn't actually happen that often
for (i = 1; i < simplex.length; ++i) {
weightedSum(simplex[i], 1 - sigma, simplex[0], sigma - 1, simplex[i]);
simplex[i].fx = f(simplex[i]);
}
}
} else {
temp = simplex[N];
simplex[N] = reflected;
reflected = temp;
}
}
simplex.sort(sortOrder);
return {f : simplex[0].fx,
solution : simplex[0]};
};
venn.minimizeConjugateGradient = function(f, initial, params) {
// allocate all memory up front here, keep out of the loop for perfomance
// reasons
var current = {x: initial.slice(), fx: 0, fxprime: initial.slice()},
next = {x: initial.slice(), fx: 0, fxprime: initial.slice()},
yk = initial.slice(),
pk, temp,
a = 1,
maxIterations;
params = params || {};
maxIterations = params.maxIterations || initial.length * 5;
current.fx = f(current.x, current.fxprime);
pk = current.fxprime.slice();
multiplyBy(pk, -1);
for (var i = 0; i < maxIterations; ++i) {
if (params.history) {
params.history.push({x: current.x.slice(),
fx: current.fx,
fxprime: current.fxprime.slice()});
}
a = venn.wolfeLineSearch(f, pk, current, next, a);
if (!a) {
// faiiled to find point that satifies wolfe conditions.
// reset direction for next iteration
for (var j = 0; j < pk.length; ++j) {
pk[j] = -1 * current.fxprime[j];
}
} else {
// update direction using Polak–Ribiere CG method
weightedSum(yk, 1, next.fxprime, -1, current.fxprime);
var delta_k = dot(current.fxprime, current.fxprime),
beta_k = Math.max(0, dot(yk, next.fxprime) / delta_k);
weightedSum(pk, beta_k, pk, -1, next.fxprime);
temp = current;
current = next;
next = temp;
}
if (norm2(current.fxprime) <= 1e-5) {
break;
}
}
if (params.history) {
params.history.push({x: current.x.slice(),
fx: current.fx,
fxprime: current.fxprime.slice()});
}
return current;
};
var c1 = 1e-6, c2 = 0.1;
/// searches along line 'pk' for a point that satifies the wolfe conditions
/// See 'Numerical Optimization' by Nocedal and Wright p59-60
venn.wolfeLineSearch = function(f, pk, current, next, a) {
var phi0 = current.fx, phiPrime0 = dot(current.fxprime, pk),
phi = phi0, phi_old = phi0,
phiPrime = phiPrime0,
a0 = 0;
a = a || 1;
function zoom(a_lo, a_high, phi_lo) {
for (var iteration = 0; iteration < 16; ++iteration) {
a = (a_lo + a_high)/2;
weightedSum(next.x, 1.0, current.x, a, pk);
phi = next.fx = f(next.x, next.fxprime);
phiPrime = dot(next.fxprime, pk);
if ((phi > (phi0 + c1 * a * phiPrime0)) ||
(phi >= phi_lo)) {
a_high = a;
} else {
if (Math.abs(phiPrime) <= -c2 * phiPrime0) {
return a;
}
if (phiPrime * (a_high - a_lo) >=0) {
a_high = a_lo;
}
a_lo = a;
phi_lo = phi;
}
}
return 0;
}
for (var iteration = 0; iteration < 10; ++iteration) {
weightedSum(next.x, 1.0, current.x, a, pk);
phi = next.fx = f(next.x, next.fxprime);
phiPrime = dot(next.fxprime, pk);
if ((phi > (phi0 + c1 * a * phiPrime0)) ||
(iteration && (phi >= phi_old))) {
return zoom(a0, a, phi_old);
}
if (Math.abs(phiPrime) <= -c2 * phiPrime0) {
return a;
}
if (phiPrime >= 0 ) {
return zoom(a, a0, phi);
}
phi_old = phi;
a0 = a;
a *= 2;
}
return 0;
};
})(venn);
(function(venn) {
"use strict";
var SMALL = 1e-10;
/** Returns the intersection area of a bunch of circles (where each circle
is an object having an x,y and radius property) */
venn.intersectionArea = function(circles, stats) {
// get all the intersection points of the circles
var intersectionPoints = getIntersectionPoints(circles);
// filter out points that aren't included in all the circles
var innerPoints = intersectionPoints.filter(function (p) {
return venn.containedInCircles(p, circles);
});
var arcArea = 0, polygonArea = 0, arcs = [], i;
// if we have intersection points that are within all the circles,
// then figure out the area contained by them
if (innerPoints.length > 1) {
// sort the points by angle from the center of the polygon, which lets
// us just iterate over points to get the edges
var center = venn.getCenter(innerPoints);
for (i = 0; i < innerPoints.length; ++i ) {
var p = innerPoints[i];
p.angle = Math.atan2(p.x - center.x, p.y - center.y);
}
innerPoints.sort(function(a,b) { return b.angle - a.angle;});
// iterate over all points, get arc between the points
// and update the areas
var p2 = innerPoints[innerPoints.length - 1];
for (i = 0; i < innerPoints.length; ++i) {
var p1 = innerPoints[i];
// polygon area updates easily ...
polygonArea += (p2.x + p1.x) * (p1.y - p2.y);
// updating the arc area is a little more involved
var midPoint = {x : (p1.x + p2.x) / 2,
y : (p1.y + p2.y) / 2},
arc = null;
for (var j = 0; j < p1.parentIndex.length; ++j) {
if (p2.parentIndex.indexOf(p1.parentIndex[j]) > -1) {
// figure out the angle halfway between the two points
// on the current circle
var circle = circles[p1.parentIndex[j]],
a1 = Math.atan2(p1.x - circle.x, p1.y - circle.y),
a2 = Math.atan2(p2.x - circle.x, p2.y - circle.y);
var angleDiff = (a2 - a1);
if (angleDiff < 0) {
angleDiff += 2*Math.PI;
}
// and use that angle to figure out the width of the
// arc
var a = a2 - angleDiff/2,
width = venn.distance(midPoint, {
x : circle.x + circle.radius * Math.sin(a),
y : circle.y + circle.radius * Math.cos(a)
});
// pick the circle whose arc has the smallest width
if ((arc === null) || (arc.width > width)) {
arc = { circle : circle,
width : width,
p1 : p1,
p2 : p2};
}
}
}
arcs.push(arc);
arcArea += venn.circleArea(arc.circle.radius, arc.width);
p2 = p1;
}
} else {
// no intersection points, is either disjoint - or is completely
// overlapped. figure out which by examining the smallest circle
var smallest = circles[0];
for (i = 1; i < circles.length; ++i) {
if (circles[i].radius < smallest.radius) {
smallest = circles[i];
}
}
// make sure the smallest circle is completely contained in all
// the other circles
var disjoint = false;
for (i = 0; i < circles.length; ++i) {
if (venn.distance(circles[i], smallest) > Math.abs(smallest.radius - circles[i].radius)) {
disjoint = true;
break;
}
}
if (disjoint) {
arcArea = polygonArea = 0;
} else {
arcArea = smallest.radius * smallest.radius * Math.PI;
arcs.push({circle : smallest,
p1: { x: smallest.x, y : smallest.y + smallest.radius},
p2: { x: smallest.x - SMALL, y : smallest.y + smallest.radius},
width : smallest.radius * 2 });
}
}
polygonArea /= 2;
if (stats) {
stats.area = arcArea + polygonArea;
stats.arcArea = arcArea;
stats.polygonArea = polygonArea;
stats.arcs = arcs;
stats.innerPoints = innerPoints;
stats.intersectionPoints = intersectionPoints;
}
return arcArea + polygonArea;
};
/** returns whether a point is contained by all of a list of circles */
venn.containedInCircles = function(point, circles) {
for (var i = 0; i < circles.length; ++i) {
if (venn.distance(point, circles[i]) > circles[i].radius + SMALL) {
return false;
}
}
return true;
};
/** Gets all intersection points between a bunch of circles */
function getIntersectionPoints(circles) {
var ret = [];
for (var i = 0; i < circles.length; ++i) {
for (var j = i + 1; j < circles.length; ++j) {
var intersect = venn.circleCircleIntersection(circles[i],
circles[j]);
for (var k = 0; k < intersect.length; ++k) {
var p = intersect[k];
p.parentIndex = [i,j];
ret.push(p);
}
}
}
return ret;
}
venn.circleIntegral = function(r, x) {
var y = Math.sqrt(r * r - x * x);
return x * y + r * r * Math.atan2(x, y);
};
/** Returns the area of a circle of radius r - up to width */
venn.circleArea = function(r, width) {
return venn.circleIntegral(r, width - r) - venn.circleIntegral(r, -r);
};
/** euclidean distance between two points */
venn.distance = function(p1, p2) {
return Math.sqrt((p1.x - p2.x) * (p1.x - p2.x) +
(p1.y - p2.y) * (p1.y - p2.y));
};
/** Returns the overlap area of two circles of radius r1 and r2 - that
have their centers separated by distance d. Simpler faster
circle intersection for only two circles */
venn.circleOverlap = function(r1, r2, d) {
// no overlap
if (d >= r1 + r2) {
return 0;
}
// completely overlapped
if (d <= Math.abs(r1 - r2)) {
return Math.PI * Math.min(r1, r2) * Math.min(r1, r2);
}
var w1 = r1 - (d * d - r2 * r2 + r1 * r1) / (2 * d),
w2 = r2 - (d * d - r1 * r1 + r2 * r2) / (2 * d);
return venn.circleArea(r1, w1) + venn.circleArea(r2, w2);
};
/** Given two circles (containing a x/y/radius attributes),
returns the intersecting points if possible.
note: doesn't handle cases where there are infinitely many
intersection points (circles are equivalent):, or only one intersection point*/
venn.circleCircleIntersection = function(p1, p2) {
var d = venn.distance(p1, p2),
r1 = p1.radius,
r2 = p2.radius;
// if to far away, or self contained - can't be done
if ((d >= (r1 + r2)) || (d <= Math.abs(r1 - r2))) {
return [];
}
var a = (r1 * r1 - r2 * r2 + d * d) / (2 * d),
h = Math.sqrt(r1 * r1 - a * a),
x0 = p1.x + a * (p2.x - p1.x) / d,
y0 = p1.y + a * (p2.y - p1.y) / d,
rx = -(p2.y - p1.y) * (h / d),
ry = -(p2.x - p1.x) * (h / d);
return [{ x: x0 + rx, y : y0 - ry },
{ x: x0 - rx, y : y0 + ry }];
};
/** Returns the center of a bunch of points */
venn.getCenter = function(points) {
var center = { x: 0, y: 0};
for (var i =0; i < points.length; ++i ) {
center.x += points[i].x;
center.y += points[i].y;
}
center.x /= points.length;
center.y /= points.length;
return center;
};
})(venn);
(function(lib) {
if (typeof module === "undefined" || typeof module.exports === "undefined") {
window.venn = lib;
} else {
module.exports = lib;
}
})(venn);
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