venn = {
let venn = {};
venn.venn = function(sets, overlaps, parameters) {
parameters = parameters || {};
parameters.maxIterations = parameters.maxIterations || 500;
var lossFunction = parameters.lossFunction || venn.lossFunction;
var initialLayout = parameters.layoutFunction || venn.greedyLayout;
sets = initialLayout(sets, overlaps);
var initial = new Array(2*sets.length);
for (var i = 0; i < sets.length; ++i) {
initial[2 * i] = sets[i].x;
initial[2 * i + 1] = sets[i].y;
}
var totalFunctionCalls = 0;
var solution = venn.fmin(
function(values) {
totalFunctionCalls += 1;
var current = new Array(sets.length);
for (var i = 0; i < sets.length; ++i) {
current[i] = {x: values[2 * i],
y: values[2 * i + 1],
radius : sets[i].radius,
size : sets[i].size};
}
return lossFunction(current, overlaps);
},
initial,
parameters);
// transform solution vector back to x/y points
var positions = solution.solution;
for (i = 0; i < sets.length; ++i) {
sets[i].x = positions[2 * i];
sets[i].y = positions[2 * i + 1];
}
return sets;
};
/** 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) {
return Math.abs(r1 - r2);
}
return venn.bisect(function(distance) {
return circleIntersection.circleOverlap(r1, r2, distance) - overlap;
}, 0, r1 + r2);
};
/// gets a matrix of euclidean distances between all sets in venn diagram
venn.getDistanceMatrix = function(sets, overlaps) {
// initialize an empty distance matrix between all the points
var distances = [];
for (var i = 0; i < sets.length; ++i) {
distances.push([]);
for (var j = 0; j < sets.length; ++j) {
distances[i].push(0);
}
}
// compute distances between all the points
for (i = 0; i < overlaps.length; ++i) {
var current = overlaps[i];
if (current.sets.length !== 2) {
continue;
}
var left = current.sets[0],
right = 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;
}
return distances;
};
/** 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(sets, overlaps) {
// give each set a default position + radius
var setOverlaps = {};
for (var i = 0; i < sets.length; ++i) {
setOverlaps[i] = [];
sets[i].radius = Math.sqrt(sets[i].size / Math.PI);
sets[i].x = sets[i].y = 0;
}
// map each set to a list of all the other sets that overlap it
for (i = 0; i < overlaps.length; ++i) {
var current = overlaps[i];
if (current.sets.length !== 2) {
continue;
}
var left = current.sets[0], right = current.sets[1];
setOverlaps[left].push ({set:right, size:current.size});
setOverlaps[right].push({set:left, size:current.size});
}
// get list of most overlapped sets
var mostOverlapped = [];
for (var set in setOverlaps) {
if (setOverlaps.hasOwnProperty(set)) {
var size = 0;
for (i = 0; i < setOverlaps[set].length; ++i) {
size += setOverlaps[set][i].size;
}
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) {
sets[index].x = point.x;
sets[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
var distances = venn.getDistanceMatrix(sets, overlaps);
for (i = 1; i < mostOverlapped.length; ++i) {
var setIndex = mostOverlapped[i].set,
overlap = setOverlaps[setIndex].filter(isPositioned);
set = sets[setIndex];
overlap.sort(sortOrder);
if (overlap.length === 0) {
throw "Need overlap information for set " + JSON.stringify( set );
}
var points = [];
for (var j = 0; j < overlap.length; ++j) {
// get appropriate distance from most overlapped already added set
var p1 = sets[overlap[j].set],
d1 = distances[setIndex][overlap[j].set];
// 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 = sets[overlap[k].set],
d2 = distances[setIndex][overlap[k].set];
var extraPoints = circleIntersection.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) {
sets[setIndex].x = points[j].x;
sets[setIndex].y = points[j].y;
var loss = venn.lossFunction(sets, overlaps);
if (loss < bestLoss) {
bestLoss = loss;
bestPoint = points[j];
}
}
positionSet(bestPoint, setIndex);
}
return sets;
};
/// Uses multidimensional scaling to approximate a first layout here
venn.classicMDSLayout = function(sets, overlaps) {
// get the distance matrix
var distances = venn.getDistanceMatrix(sets, overlaps);
// get positions for each set
var positions = mds.classic(distances);
// translate back to (x,y,radius) coordinates
for (var i = 0; i < sets.length; ++i) {
sets[i].x = positions[i][0];
sets[i].y = positions[i][1];
sets[i].radius = Math.sqrt(sets[i].size / Math.PI);
}
return sets;
};
/** 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 == 2) {
var left = sets[area.sets[0]],
right = sets[area.sets[1]];
overlap = circleIntersection.circleOverlap(left.radius, right.radius,
circleIntersection.distance(left, right));
} else {
overlap = circleIntersection.intersectionArea(getCircles(area.sets));
}
output += (overlap - area.size) * (overlap - area.size);
}
return output;
};
/** Scales a solution from venn.venn or venn.greedyLayout such that it fits in
a rectangle of width/height - with padding around the borders. */
venn.scaleSolution = function(solution, width, height, padding) {
var minMax = function(d) {
var hi = Math.max.apply(null, solution.map(
function(c) { return c[d] + c.radius; } )),
lo = Math.min.apply(null, solution.map(
function(c) { return c[d] - c.radius;} ));
return {max:hi, min:lo};
};
width -= 2*padding;
height -= 2*padding;
var xRange = minMax('x'),
yRange = minMax('y'),
xScaling = width / (xRange.max - xRange.min),
yScaling = height / (yRange.max - yRange.min),
scaling = Math.min(yScaling, xScaling);
var tempSolution = [];
for (var i = 0; i < solution.length; ++i) {
var set = solution[i];
tempSolution[i] = {};
tempSolution[i]['radius'] = scaling * set.radius;
tempSolution[i]['x'] = padding + (set.x - xRange.min) * scaling;
tempSolution[i]['y'] = padding + (set.y - yRange.min) * scaling;
tempSolution[i]['size'] = set.size
}
var xMinPos = 10000;
var xMaxPos = 0;
var yMinPos = 100000;
var yMaxPos = 0;
tempSolution.forEach((item) => {
if(item.size >0){
var deltaMinX = item.x - item.radius;
var deltaMaxX = item.x + item.radius;
var deltaMinY = item.y - item.radius;
var deltaMaxY = item.y + item.radius;
if(deltaMinX < xMinPos) { xMinPos = deltaMinX }
if(deltaMaxX > xMaxPos) { xMaxPos = deltaMaxX}
if(deltaMinY < yMinPos) { yMinPos = deltaMinY}
if(deltaMaxY > yMaxPos) { yMaxPos = deltaMaxY}
}
})
let vennWidth = xMaxPos - xMinPos + padding * 4 * solution.length + padding * 2
let vennHeight = yMaxPos - yMinPos + padding * 4 * solution.length + padding * 2
if(height < vennHeight){
scaling = height / vennHeight * scaling;
}
for (var i = 0; i < solution.length; ++i) {
var set = solution[i];
set.radius = scaling * set.radius;
set.x = padding + (set.x - xRange.min) * scaling;
set.y = padding + (set.y - yRange.min) * scaling;
}
solution.scaling = scaling;
return solution;
};
function weightedSum(a, b) {
var ret = new Array(a[1].length || 0);
for (var j = 0; j < ret.length; ++j) {
ret[j] = a[0] * a[1][j] + b[0] * b[1][j];
}
return ret;
}
function centerVennDiagram( diagram, width, height, padding ) {
var diagramBoundaries;
var allowedWidth = width - ( 2 * ( padding || 20 ) );
var allowedHeight = height - ( 2 * ( padding || 20 ) );
var scale;
var transformX, transformY;
var transform = "";
if ( diagram ) {
diagramBoundaries = diagram[ 0 ][ 0 ].getBBox();
if ( diagramBoundaries && width && height ) {
// See if we need to scale to fit the width/height
if ( diagramBoundaries.width > allowedWidth ) {
scale = allowedWidth / diagramBoundaries.width;
}
if ( diagramBoundaries.height > allowedHeight ) {
if ( !scale || ( allowedHeight / diagramBoundaries.height ) < scale ) {
scale = allowedHeight / diagramBoundaries.height;
}
}
if ( scale ) {
transform = "scale(" + scale + ")";
}
else {
scale = 1;
}
var xMinPos = 10000;
var xMaxPos = 0;
var yMinPos = 100000;
var yMaxPos = 0;
data.sets.forEach((item) => {
var deltaMinX = item.x - item.radius;
var deltaMaxX = item.x + item.radius;
var deltaMinY = item.y - item.radius;
var deltaMaxY = item.y + item.radius;
if(deltaMinX < xMinPos) { xMinPos = deltaMinX }
if(deltaMaxX > xMaxPos) { xMaxPos = deltaMaxX}
if(deltaMinY < yMinPos) { yMinPos = deltaMinY}
if(deltaMaxY > yMaxPos) { yMaxPos = deltaMaxY}
})
let vennWidth = xMaxPos - xMinPos + padding * 2
let vennHeight = yMaxPos - yMinPos + padding * 2
transformX = hRect / 2 - vennWidth / 2 ;
transformY = wRect / 2 - vennHeight / 2 - 10;
diagram.attr( "transform", "translate(" + transformX + "," + transformY + ") " + transform );
}
}
}
/** 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;
};
/** 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-5,
rho = parameters.rho || 1,
chi = parameters.chi || 2,
psi = parameters.psi || -0.5,
sigma = parameters.sigma || 0.5,
callback = parameters.callback;
// 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; };
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
var centroid = new Array(N);
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];
var reflected = weightedSum([1+rho, centroid], [-rho, worst]);
reflected.fx = f(reflected);
var replacement = reflected;
// if the reflected point is the best seen, then possibly expand
if (reflected.fx <= simplex[0].fx) {
var expanded = weightedSum([1+chi, centroid], [-chi, worst]);
expanded.fx = f(expanded);
if (expanded.fx < reflected.fx) {
replacement = expanded;
}
}
// 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;
var contracted;
if (reflected.fx <= worst.fx) {
// do an inside contraction
contracted = weightedSum([1+psi, centroid], [-psi, worst]);
contracted.fx = f(contracted);
if (contracted.fx < worst.fx) {
replacement = contracted;
} else {
shouldReduce = true;
}
} else {
// do an outside contraction
contracted = weightedSum([1-psi * rho, centroid], [psi*rho, worst]);
contracted.fx = f(contracted);
if (contracted.fx <= reflected.fx) {
replacement = contracted;
} else {
shouldReduce = true;
}
}
if (shouldReduce) {
// do reduction. doesn't actually happen that often
for (i = 1; i < simplex.length; ++i) {
simplex[i] = weightedSum([1 - sigma, simplex[0]],
[sigma - 1, simplex[i]]);
simplex[i].fx = f(simplex[i]);
}
}
}
simplex[N] = replacement;
}
simplex.sort(sortOrder);
return {f : simplex[0].fx,
solution : simplex[0]};
};
/** returns a svg path of the intersection area of a bunch of circles */
venn.intersectionAreaPath = function(circles) {
var stats = {};
circleIntersection.intersectionArea(circles, stats);
var arcs = stats.arcs;
if (arcs.length == 0) {
return "M 0 0";
}
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.getIntersectionAll = function(circles) {
const filteredCircles = circles.filter(circle => circle.size > 0);
var stats = {};
circleIntersection.intersectionArea(filteredCircles, stats);
const intersectionAll = stats.arcs;
if (intersectionAll.length > 0) {
var ret = [
"\nM",
intersectionAll[intersectionAll.length - 1].p1.x,
intersectionAll[intersectionAll.length - 1].p1.y
];
for (var i = 0; i < intersectionAll.length; ++i) {
var arc = intersectionAll[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(" ");
} else {
return "M 0 0";
}
};
venn.intersectionAreaSplitPath = function(circles, isRightPath, isLeftPath) {
var stats = {};
circleIntersection.intersectionArea(circles, stats);
var arcs = stats.arcs;
if (arcs.length == 0) {
return "M 0 0";
}
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;
if( (i==1 && isRightPath) || (i==0 && isLeftPath)){
ret.push("\nA", r, r, 0, wide ? 1 : 0, 1, arc.p1.x, arc.p1.y);
}
else{
ret.push("\nA", 0, 0, 0, wide ? 1 : 0, 1, arc.p1.x, arc.p1.y);
}
}
return ret.join(" ");
}
venn.drawD3Diagram = function(element, dataset, width, height, parameters) {
parameters = parameters || {};
var colours = d3.scale.category10(),
circleFillColours = parameters.circleFillColours || colours,
circleStrokeColours = parameters.circleStrokeColours || circleFillColours,
circleStrokeWidth = parameters.circleStrokeWidth || function(i) { return 0; },
textFillColours = parameters.textFillColours || colours,
textStrokeColours = parameters.textStrokeColours || textFillColours,
nodeOpacity = parameters.opacity || 0.3,
padding = parameters.padding || 20;
dataset = venn.scaleSolution(dataset, width, height, padding);
dataset = dataset.filter(item => {
return item.size > 0;
})
var svg = element.append("svg").attr('id', 'svg-wrapper');
var diagram = svg.append( "g" ).attr('id', 'union-all');
var nodes = diagram.append("g").selectAll("g")
.data(dataset, function(d) {
return d.label;
});
var nodeEnter = nodes.enter()
.append("g").attr("style", "transition: opacity 2s")
.attr('class', 'node');
nodeEnter.append("circle").attr("id", function(d) { return `circle-${d.label}` })
.attr("r", function(d) { return d.radius })
.style("fill-opacity", nodeOpacity)
.attr("cx", function(d) { return d.x; })
.attr("cy", function(d) { return d.y; })
.style("stroke", function(d, i) { return circleStrokeColours(i); })
.style("stroke-width", function(d, i) { return circleStrokeWidth(i); })
.style("fill", function(d, i) { return circleFillColours(i); });
nodeEnter.append("text")
.attr("x", function(d, i) { return d.x + (d.radius + 20) * Math.sin(-Math.PI / 3 + i * 2 * Math.PI / 3); })
.attr("y", function(d, i) { return d.y - (d.radius + 20) * Math.cos(-Math.PI / 3 + i * 2 * Math.PI / 3); })
.attr("text-anchor", "middle")
.attr("dy", "0.35em")
.attr("font-size", fontSize)
.style("stroke", function(d, i) { return textStrokeColours(i); })
.style("fill", function(d, i) { return textFillColours(i); })
.text(function(d) { return d.label; });
var circles = nodes.selectAll("circle");
var text = nodes.selectAll("text");
centerVennDiagram( diagram, width, height, padding );
return {'svg' : svg,
'nodes' : nodes,
'circles' : circles,
'text' : text };
};
venn.updateD3Diagram = function(element, dataset, parameters) {
parameters = parameters || {};
var colours = d3.scale.category10(),
circleFillColours = parameters.circleFillColours || colours,
circleStrokeColours = parameters.circleStrokeColours || circleFillColours,
circleStrokeWidth = parameters.circleStrokeWidth || function(i) { return 0; },
textFillColours = parameters.textFillColours || colours,
textStrokeColours = parameters.textStrokeColours || textFillColours,
nodeOpacity = parameters.opacity || 0.3,
padding = parameters.padding || 20;
var svg = element.select("svg"),
width = parseInt(svg.attr('width'), 10),
height = parseInt(svg.attr('height'), 10),
circles, texts;
dataset = venn.scaleSolution(dataset, width, height, 0);
var nodes = svg.select('g').select('g').selectAll("g.node")
.data(dataset, function(d) { return d.label; });
nodes.exit().remove();
var nodeEnter = nodes.enter()
.append("g")
.attr('class', 'node');
nodeEnter.append("circle")
.style("fill-opacity", nodeOpacity)
.style("stroke", function(d, i) { return circleStrokeColours(i); })
.style("stroke-width", function(d, i) { return circleStrokeWidth(i); })
.style("fill", function(d, i) { return circleFillColours(i); });
nodeEnter.append("text")
.attr("text-anchor", "middle")
.attr("dy", "0.35em")
.attr("font-size", fontSize)
.style("stroke", function(d, i) { return textStrokeColours(i); })
.style("fill", function(d, i) { return textFillColours(i); })
nodes.select("circle")
.transition()
.duration(400)
.attr("cx", function(d) { return d.x; })
.attr("cy", function(d) { return d.y; })
.attr("r", function(d) { return d.radius; });
nodes.select("text")
.transition()
.duration(400)
.text(function(d) { return d.label; })
.attr("font-size", fontSize)
.attr("x", function(d) { return d.x; })
.attr("y", function(d) { return d.y; });
};
return venn;
}