venn = { let venn = {}; /** 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(sets, overlaps, parameters) { parameters = parameters || {}; parameters.maxIterations = parameters.maxIterations || 500; var lossFunction = parameters.lossFunction || venn.lossFunction; var initialLayout = parameters.layoutFunction || venn.greedyLayout; // initial layout is done greedily sets = initialLayout(sets, overlaps); // transform x/y coordinates to a vector to optimize 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; } // optimize initial layout from our loss function 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); 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 || 0 ) ); var allowedHeight = height - ( 2 * ( padding || 0 ) ); 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; } let vennWidth = (data.sets[1].x - data.sets[0].x) + data.sets[0].radius + data.sets[1].radius transformX = hRect / 2 - vennWidth / 2; transformY = wRect / 2 - data.sets[1].y; 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.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 || 0; dataset = venn.scaleSolution(dataset, width, height, padding); var svg = element.append("svg"); var diagram = svg.append( "g" ); var nodes = diagram.append("g").selectAll("g") .data(dataset, function(d) { return d.label; }); var nodeEnter = nodes.enter() .append("g") .attr('class', 'node'); nodeEnter.append("circle") .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") .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 || 0; 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") .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("x", function(d) { return d.x; }) .attr("y", function(d) { return d.y; }); }; return venn; }