dev-chiefworks
849 lines
31 KiB
JavaScript
849 lines
31 KiB
JavaScript
(function(venn) {
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"use strict";
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/** given a list of set objects, and their corresponding overlaps.
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updates the (x, y, radius) attribute on each set such that their positions
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roughly correspond to the desired overlaps */
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venn.venn = function(sets, overlaps, parameters) {
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parameters = parameters || {};
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parameters.maxIterations = parameters.maxIterations || 500;
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var lossFunction = parameters.lossFunction || venn.lossFunction;
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var initialLayout = parameters.layoutFunction || venn.greedyLayout;
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// initial layout is done greedily
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sets = initialLayout(sets, overlaps);
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// transform x/y coordinates to a vector to optimize
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var initial = new Array(2*sets.length);
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for (var i = 0; i < sets.length; ++i) {
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initial[2 * i] = sets[i].x;
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initial[2 * i + 1] = sets[i].y;
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}
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// optimize initial layout from our loss function
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var totalFunctionCalls = 0;
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var solution = venn.fmin(
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function(values) {
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totalFunctionCalls += 1;
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var current = new Array(sets.length);
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for (var i = 0; i < sets.length; ++i) {
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current[i] = {x: values[2 * i],
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y: values[2 * i + 1],
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radius : sets[i].radius,
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size : sets[i].size};
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}
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return lossFunction(current, overlaps);
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},
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initial,
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parameters);
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// transform solution vector back to x/y points
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var positions = solution.solution;
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for (i = 0; i < sets.length; ++i) {
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sets[i].x = positions[2 * i];
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sets[i].y = positions[2 * i + 1];
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}
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return sets;
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};
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/** Returns the distance necessary for two circles of radius r1 + r2 to
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have the overlap area 'overlap' */
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venn.distanceFromIntersectArea = function(r1, r2, overlap) {
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// handle complete overlapped circles
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if (Math.min(r1, r2) * Math.min(r1,r2) * Math.PI <= overlap) {
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return Math.abs(r1 - r2);
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}
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return venn.bisect(function(distance) {
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return venn.circleOverlap(r1, r2, distance) - overlap;
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}, 0, r1 + r2);
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};
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/// gets a matrix of euclidean distances between all sets in venn diagram
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venn.getDistanceMatrix = function(sets, overlaps) {
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// initialize an empty distance matrix between all the points
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var distances = [];
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for (var i = 0; i < sets.length; ++i) {
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distances.push([]);
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for (var j = 0; j < sets.length; ++j) {
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distances[i].push(0);
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}
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}
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// compute distances between all the points
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for (i = 0; i < overlaps.length; ++i) {
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var current = overlaps[i];
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if (current.sets.length !== 2) {
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continue;
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}
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var left = current.sets[0],
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right = current.sets[1],
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r1 = Math.sqrt(sets[left].size / Math.PI),
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r2 = Math.sqrt(sets[right].size / Math.PI),
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distance = venn.distanceFromIntersectArea(r1, r2, current.size);
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distances[left][right] = distances[right][left] = distance;
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}
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return distances;
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};
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/** Lays out a Venn diagram greedily, going from most overlapped sets to
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least overlapped, attempting to position each new set such that the
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overlapping areas to already positioned sets are basically right */
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venn.greedyLayout = function(sets, overlaps) {
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// give each set a default position + radius
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var setOverlaps = {};
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for (var i = 0; i < sets.length; ++i) {
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setOverlaps[i] = [];
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sets[i].radius = Math.sqrt(sets[i].size / Math.PI);
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sets[i].x = sets[i].y = 0;
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}
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// map each set to a list of all the other sets that overlap it
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for (i = 0; i < overlaps.length; ++i) {
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var current = overlaps[i];
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if (current.sets.length !== 2) {
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continue;
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}
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var weight = (current.weight == null) ? 1.0 : current.weight;
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var left = current.sets[0], right = current.sets[1];
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setOverlaps[left].push ({set:right, size:current.size, weight:weight});
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setOverlaps[right].push({set:left, size:current.size, weight:weight});
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}
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// get list of most overlapped sets
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var mostOverlapped = [];
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for (var set in setOverlaps) {
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if (setOverlaps.hasOwnProperty(set)) {
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var size = 0;
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for (i = 0; i < setOverlaps[set].length; ++i) {
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size += setOverlaps[set][i].size * setOverlaps[set][i].weight;
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}
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mostOverlapped.push({set: set, size:size});
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}
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}
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// sort by size desc
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function sortOrder(a,b) {
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return b.size - a.size;
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}
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mostOverlapped.sort(sortOrder);
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// keep track of what sets have been laid out
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var positioned = {};
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function isPositioned(element) {
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return element.set in positioned;
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}
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// adds a point to the output
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function positionSet(point, index) {
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sets[index].x = point.x;
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sets[index].y = point.y;
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positioned[index] = true;
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}
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// add most overlapped set at (0,0)
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positionSet({x: 0, y: 0}, mostOverlapped[0].set);
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// get distances between all points
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var distances = venn.getDistanceMatrix(sets, overlaps);
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for (i = 1; i < mostOverlapped.length; ++i) {
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var setIndex = mostOverlapped[i].set,
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overlap = setOverlaps[setIndex].filter(isPositioned);
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set = sets[setIndex];
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overlap.sort(sortOrder);
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if (overlap.length === 0) {
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throw "Need overlap information for set " + JSON.stringify( set );
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}
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var points = [];
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for (var j = 0; j < overlap.length; ++j) {
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// get appropriate distance from most overlapped already added set
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var p1 = sets[overlap[j].set],
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d1 = distances[setIndex][overlap[j].set];
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// sample positions at 90 degrees for maximum aesthetics
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points.push({x : p1.x + d1, y : p1.y});
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points.push({x : p1.x - d1, y : p1.y});
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points.push({y : p1.y + d1, x : p1.x});
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points.push({y : p1.y - d1, x : p1.x});
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// if we have at least 2 overlaps, then figure out where the
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// set should be positioned analytically and try those too
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for (var k = j + 1; k < overlap.length; ++k) {
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var p2 = sets[overlap[k].set],
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d2 = distances[setIndex][overlap[k].set];
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var extraPoints = venn.circleCircleIntersection(
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{ x: p1.x, y: p1.y, radius: d1},
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{ x: p2.x, y: p2.y, radius: d2});
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for (var l = 0; l < extraPoints.length; ++l) {
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points.push(extraPoints[l]);
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}
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}
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}
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// we have some candidate positions for the set, examine loss
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// at each position to figure out where to put it at
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var bestLoss = 1e50, bestPoint = points[0];
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for (j = 0; j < points.length; ++j) {
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sets[setIndex].x = points[j].x;
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sets[setIndex].y = points[j].y;
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var loss = venn.lossFunction(sets, overlaps);
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if (loss < bestLoss) {
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bestLoss = loss;
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bestPoint = points[j];
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}
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}
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positionSet(bestPoint, setIndex);
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}
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return sets;
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};
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/// Uses multidimensional scaling to approximate a first layout here
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venn.classicMDSLayout = function(sets, overlaps) {
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// get the distance matrix
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var distances = venn.getDistanceMatrix(sets, overlaps);
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// get positions for each set
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var positions = mds.classic(distances);
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// translate back to (x,y,radius) coordinates
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for (var i = 0; i < sets.length; ++i) {
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sets[i].x = positions[i][0];
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sets[i].y = positions[i][1];
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sets[i].radius = Math.sqrt(sets[i].size / Math.PI);
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}
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return sets;
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};
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/** Given a bunch of sets, and the desired overlaps between these sets - computes
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the distance from the actual overlaps to the desired overlaps. Note that
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this method ignores overlaps of more than 2 circles */
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venn.lossFunction = function(sets, overlaps) {
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var output = 0;
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function getCircles(indices) {
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return indices.map(function(i) { return sets[i]; });
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}
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for (var i = 0; i < overlaps.length; ++i) {
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var area = overlaps[i], overlap;
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if (area.sets.length == 2) {
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var left = sets[area.sets[0]],
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right = sets[area.sets[1]];
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overlap = venn.circleOverlap(left.radius, right.radius,
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venn.distance(left, right));
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} else {
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overlap = venn.intersectionArea(getCircles(area.sets));
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}
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var weight = (area.weight == null) ? 1.0 : area.weight;
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output += weight * (overlap - area.size) * (overlap - area.size);
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}
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return output;
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};
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/** Scales a solution from venn.venn or venn.greedyLayout such that it fits in
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a rectangle of width/height - with padding around the borders. also
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centers the diagram in the available space at the same time */
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venn.scaleSolution = function(solution, width, height, padding) {
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var minMax = function(d) {
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var hi = Math.max.apply(null, solution.map(
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function(c) { return c[d] + c.radius; } )),
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lo = Math.min.apply(null, solution.map(
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function(c) { return c[d] - c.radius;} ));
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return {max:hi, min:lo};
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};
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width -= 2*padding;
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height -= 2*padding;
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var xRange = minMax('x'),
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yRange = minMax('y'),
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xScaling = width / (xRange.max - xRange.min),
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yScaling = height / (yRange.max - yRange.min),
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scaling = Math.min(yScaling, xScaling),
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// while we're at it, center the diagram too
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xOffset = (width - (xRange.max - xRange.min) * scaling) / 2,
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yOffset = (height - (yRange.max - yRange.min) * scaling) / 2;
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for (var i = 0; i < solution.length; ++i) {
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var set = solution[i];
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set.radius = scaling * set.radius;
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set.x = padding + xOffset + (set.x - xRange.min) * scaling;
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set.y = padding + yOffset + (set.y - yRange.min) * scaling;
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}
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return solution;
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};
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// sometimes text doesn't fit inside the circle, if thats the case lets wrap
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// the text here such that it fits
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// todo: looks like this might be merged into d3 (
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// https://github.com/mbostock/d3/issues/1642),
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// also worth checking out is
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// http://engineering.findthebest.com/wrapping-axis-labels-in-d3-js/
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// this seems to be one of those things that should be easy but isn't
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function wrapText() {
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var text = d3.select(this),
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data = text.datum(),
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width = data.radius,
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words = data.label.split(/\s+/).reverse(),
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maxLines = 3,
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minChars = (data.label.length + words.length) / maxLines,
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word = words.pop(),
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line = [word],
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joined,
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lineNumber = 0,
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lineHeight = 1.1, // ems
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tspan = text.text(null).append("tspan").text(word);
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while (word = words.pop()) {
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line.push(word);
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joined = line.join(" ");
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tspan.text(joined);
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if (joined.length > minChars && tspan.node().getComputedTextLength() > width) {
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line.pop();
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tspan.text(line.join(" "));
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line = [word];
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tspan = text.append("tspan").text(word);
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lineNumber++;
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}
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}
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var initial = 0.35 - lineNumber * lineHeight / 2,
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x = Math.floor(data.textCenter.x),
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y = Math.floor(data.textCenter.y);
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text.selectAll("tspan")
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.attr("x", x)
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.attr("y", y)
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.attr("dy", function(d, i) {
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return (initial + i * lineHeight) + "em";
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});
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}
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function weightedSum(a, b) {
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var ret = new Array(a[1].length || 0);
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for (var j = 0; j < ret.length; ++j) {
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ret[j] = a[0] * a[1][j] + b[0] * b[1][j];
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}
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return ret;
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}
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/** finds the zeros of a function, given two starting points (which must
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* have opposite signs */
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venn.bisect = function(f, a, b, parameters) {
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parameters = parameters || {};
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var maxIterations = parameters.maxIterations || 100,
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tolerance = parameters.tolerance || 1e-10,
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fA = f(a),
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fB = f(b),
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delta = b - a;
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if (fA * fB > 0) {
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throw "Initial bisect points must have opposite signs";
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}
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if (fA === 0) return a;
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if (fB === 0) return b;
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for (var i = 0; i < maxIterations; ++i) {
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delta /= 2;
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var mid = a + delta,
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fMid = f(mid);
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if (fMid * fA >= 0) {
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a = mid;
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}
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if ((Math.abs(delta) < tolerance) || (fMid === 0)) {
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return mid;
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}
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}
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return a + delta;
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};
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/** minimizes a function using the downhill simplex method */
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venn.fmin = function(f, x0, parameters) {
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parameters = parameters || {};
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var maxIterations = parameters.maxIterations || x0.length * 200,
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nonZeroDelta = parameters.nonZeroDelta || 1.1,
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zeroDelta = parameters.zeroDelta || 0.001,
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minErrorDelta = parameters.minErrorDelta || 1e-5,
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rho = parameters.rho || 1,
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chi = parameters.chi || 2,
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psi = parameters.psi || -0.5,
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sigma = parameters.sigma || 0.5,
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callback = parameters.callback;
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// initialize simplex.
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var N = x0.length,
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simplex = new Array(N + 1);
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simplex[0] = x0;
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simplex[0].fx = f(x0);
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for (var i = 0; i < N; ++i) {
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var point = x0.slice();
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point[i] = point[i] ? point[i] * nonZeroDelta : zeroDelta;
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simplex[i+1] = point;
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simplex[i+1].fx = f(point);
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}
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var sortOrder = function(a, b) { return a.fx - b.fx; };
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for (var iteration = 0; iteration < maxIterations; ++iteration) {
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simplex.sort(sortOrder);
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if (callback) {
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callback(simplex);
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}
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if (Math.abs(simplex[0].fx - simplex[N].fx) < minErrorDelta) {
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break;
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}
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// compute the centroid of all but the worst point in the simplex
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var centroid = new Array(N);
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for (i = 0; i < N; ++i) {
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centroid[i] = 0;
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for (var j = 0; j < N; ++j) {
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centroid[i] += simplex[j][i];
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}
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centroid[i] /= N;
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}
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// reflect the worst point past the centroid and compute loss at reflected
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// point
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var worst = simplex[N];
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var reflected = weightedSum([1+rho, centroid], [-rho, worst]);
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reflected.fx = f(reflected);
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var replacement = reflected;
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// if the reflected point is the best seen, then possibly expand
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if (reflected.fx <= simplex[0].fx) {
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var expanded = weightedSum([1+chi, centroid], [-chi, worst]);
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expanded.fx = f(expanded);
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if (expanded.fx < reflected.fx) {
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replacement = expanded;
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}
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}
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// if the reflected point is worse than the second worst, we need to
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// contract
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else if (reflected.fx >= simplex[N-1].fx) {
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var shouldReduce = false;
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var contracted;
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if (reflected.fx <= worst.fx) {
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// do an inside contraction
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contracted = weightedSum([1+psi, centroid], [-psi, worst]);
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contracted.fx = f(contracted);
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if (contracted.fx < worst.fx) {
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replacement = contracted;
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} else {
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shouldReduce = true;
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}
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} else {
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// do an outside contraction
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contracted = weightedSum([1-psi * rho, centroid], [psi*rho, worst]);
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contracted.fx = f(contracted);
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if (contracted.fx <= reflected.fx) {
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replacement = contracted;
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} else {
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shouldReduce = true;
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}
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}
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if (shouldReduce) {
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// do reduction. doesn't actually happen that often
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for (i = 1; i < simplex.length; ++i) {
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simplex[i] = weightedSum([1 - sigma, simplex[0]],
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[sigma - 1, simplex[i]]);
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simplex[i].fx = f(simplex[i]);
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}
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}
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}
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simplex[N] = replacement;
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}
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simplex.sort(sortOrder);
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return {f : simplex[0].fx,
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solution : simplex[0]};
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};
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/** returns a svg path of the intersection area of a bunch of circles */
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venn.intersectionAreaPath = function(circles) {
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var stats = {};
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venn.intersectionArea(circles, stats);
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var arcs = stats.arcs;
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if (arcs.length === 0) {
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return "M 0 0";
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}
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var ret = ["\nM", arcs[0].p2.x, arcs[0].p2.y];
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for (var i = 0; i < arcs.length; ++i) {
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var arc = arcs[i], r = arc.circle.radius, wide = arc.width > r;
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ret.push("\nA", r, r, 0, wide ? 1 : 0, 1, arc.p1.x, arc.p1.y);
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}
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return ret.join(" ");
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};
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// computes the center for text by sampling perimiter of circle, and taking
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// the average of points on perimeter that are only in that circle
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function computeTextCenters(sets, width, height, diagram) {
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// basically just finding the center point of each region by sampling
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// points in a grid and taking the average sampled point for each region
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// There is probably an analytic way of computing this exactly, but
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// this works well enough for our purposes
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var sums = [];
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for (var i = 0; i < sets.length; ++i) {
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sums.push({'x' : 0, 'y' : 0, 'count' : 0});
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}
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var samples = 32;
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for (var i = 0; i < samples; ++i) {
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var x = i * width / samples;
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for (var j = 0; j < samples; ++j) {
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var y = j * height / samples;
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var point = {'x' : x, 'y' : y};
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var contained = []
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for (var k = 0; k < sets.length; ++k) {
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if (venn.distance(point, sets[k]) <= sets[k].radius) {
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contained.push(k);
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}
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}
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if (contained.length == 1) {
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var sum = sums[contained[0]];
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sum.x += point.x;
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sum.y += point.y;
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sum.count += 1;
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}
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}
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}
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for (var i = 0; i < sets.length; ++i) {
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var sum = sums[i];
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if (sum.count) {
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sets[i].textCenter = { 'x' : sum.x / sum.count,
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'y' : sum.y / sum.count};
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} else {
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// no sampled points, possibly completely overlapped (or tiny)
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// use circle centre
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sets[i].textCenter = { 'x' : sets[i].x,
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'y' : sets[i].y};
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}
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}
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}
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venn.drawD3Diagram = function(element, dataset, width, height, parameters) {
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parameters = parameters || {};
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var colours = d3.scale.category10(),
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padding = ('padding' in parameters) ? parameters.padding : 6;
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dataset = venn.scaleSolution(dataset, width, height, padding);
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computeTextCenters(dataset, width, height);
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var svg = element.append("svg")
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.attr("width", width)
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.attr("height", height);
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var diagram = svg.append( "g" );
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var nodes = diagram.append("g").selectAll("circle")
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.data(dataset)
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.enter()
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.append("g");
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var circles = nodes.append("circle")
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.attr("r", function(d) { return d.radius; })
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.style("fill-opacity", 0.3)
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.attr("cx", function(d) { return d.x; })
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.attr("cy", function(d) { return d.y; })
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.style("fill", function(d, i) { return colours(i); });
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var text = nodes.append("text")
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.attr("dy", ".35em")
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.attr("x", function(d) { return Math.floor(d.textCenter.x); })
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.attr("y", function(d) { return Math.floor(d.textCenter.y); })
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.attr("text-anchor", "middle")
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.style("fill", function(d, i) { return colours(i); })
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.call(function (text) { text.each(wrapText); });
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return {'svg' : svg,
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'nodes' : nodes,
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'circles' : circles,
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'text' : text };
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};
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venn.updateD3Diagram = function(diagram, dataset, parameters) {
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parameters = parameters || {};
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var padding = ('padding' in parameters) ? parameters.padding : 6,
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duration = ('duration' in parameters) ? parameters.duration : 400;
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var svg = diagram.svg,
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width = parseInt(svg.attr('width'), 10),
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height = parseInt(svg.attr('height'), 10);
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dataset = venn.scaleSolution(dataset, width, height, padding);
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computeTextCenters(dataset, width, height);
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var transition = diagram.nodes
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.data(dataset)
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.transition()
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.duration(duration);
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transition.select("circle")
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.attr("cx", function(d) { return d.x; })
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.attr("cy", function(d) { return d.y; })
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.attr("r", function(d) { return d.radius; });
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// transtitioning the text is a little tricky in the case
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// of wrapping. so lets basically transition unwrapped text
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// and at the end of the transition we'll wrap it again
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transition.select("text")
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.text(function (d) { return d.label; } )
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.each("end", wrapText)
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.attr("x", function(d) { return Math.floor(d.textCenter.x); })
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.attr("y", function(d) { return Math.floor(d.textCenter.y); });
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};
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var SMALL = 1e-10;
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/** Returns the intersection area of a bunch of circles (where each circle
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is an object having an x,y and radius property) */
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venn.intersectionArea = function(circles, stats) {
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// get all the intersection points of the circles
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var intersectionPoints = getIntersectionPoints(circles);
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// filter out points that aren't included in all the circles
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var innerPoints = intersectionPoints.filter(function (p) {
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return venn.containedInCircles(p, circles);
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});
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var arcArea = 0, polygonArea = 0, arcs = [], i;
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// if we have intersection points that are within all the circles,
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// then figure out the area contained by them
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if (innerPoints.length > 1) {
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// sort the points by angle from the center of the polygon, which lets
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// us just iterate over points to get the edges
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var center = venn.getCenter(innerPoints);
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for (i = 0; i < innerPoints.length; ++i ) {
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var p = innerPoints[i];
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p.angle = Math.atan2(p.x - center.x, p.y - center.y);
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}
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innerPoints.sort(function(a,b) { return b.angle - a.angle;});
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// iterate over all points, get arc between the points
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// and update the areas
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var p2 = innerPoints[innerPoints.length - 1];
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for (i = 0; i < innerPoints.length; ++i) {
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var p1 = innerPoints[i];
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// polygon area updates easily ...
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polygonArea += (p2.x + p1.x) * (p1.y - p2.y);
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// updating the arc area is a little more involved
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var midPoint = {x : (p1.x + p2.x) / 2,
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y : (p1.y + p2.y) / 2},
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arc = null;
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for (var j = 0; j < p1.parentIndex.length; ++j) {
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if (p2.parentIndex.indexOf(p1.parentIndex[j]) > -1) {
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// figure out the angle halfway between the two points
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// on the current circle
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var circle = circles[p1.parentIndex[j]],
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a1 = Math.atan2(p1.x - circle.x, p1.y - circle.y),
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a2 = Math.atan2(p2.x - circle.x, p2.y - circle.y);
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var angleDiff = (a2 - a1);
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if (angleDiff < 0) {
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angleDiff += 2*Math.PI;
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}
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// and use that angle to figure out the width of the
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// arc
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var a = a2 - angleDiff/2,
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width = venn.distance(midPoint, {
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x : circle.x + circle.radius * Math.sin(a),
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y : circle.y + circle.radius * Math.cos(a)
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});
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// pick the circle whose arc has the smallest width
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if ((arc === null) || (arc.width > width)) {
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arc = { circle : circle,
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width : width,
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p1 : p1,
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p2 : p2};
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}
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}
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}
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arcs.push(arc);
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arcArea += venn.circleArea(arc.circle.radius, arc.width);
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p2 = p1;
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}
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} else {
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// no intersection points, is either disjoint - or is completely
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// overlapped. figure out which by examining the smallest circle
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var smallest = circles[0];
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for (i = 1; i < circles.length; ++i) {
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if (circles[i].radius < smallest.radius) {
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smallest = circles[i];
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}
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}
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// make sure the smallest circle is completely contained in all
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// the other circles
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var disjoint = false;
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for (i = 0; i < circles.length; ++i) {
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if (venn.distance(circles[i], smallest) > Math.abs(smallest.radius - circles[i].radius)) {
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disjoint = true;
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break;
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}
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}
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if (disjoint) {
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arcArea = polygonArea = 0;
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} else {
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arcArea = smallest.radius * smallest.radius * Math.PI;
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arcs.push({circle : smallest,
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p1: { x: smallest.x, y : smallest.y + smallest.radius},
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p2: { x: smallest.x - SMALL, y : smallest.y + smallest.radius},
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width : smallest.radius * 2 });
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}
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}
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polygonArea /= 2;
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if (stats) {
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stats.area = arcArea + polygonArea;
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stats.arcArea = arcArea;
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stats.polygonArea = polygonArea;
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stats.arcs = arcs;
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stats.innerPoints = innerPoints;
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stats.intersectionPoints = intersectionPoints;
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}
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return arcArea + polygonArea;
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};
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/** returns whether a point is contained by all of a list of circles */
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venn.containedInCircles = function(point, circles) {
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for (var i = 0; i < circles.length; ++i) {
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if (venn.distance(point, circles[i]) > circles[i].radius + SMALL) {
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return false;
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}
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}
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return true;
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};
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/** Gets all intersection points between a bunch of circles */
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function getIntersectionPoints(circles) {
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var ret = [];
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for (var i = 0; i < circles.length; ++i) {
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for (var j = i + 1; j < circles.length; ++j) {
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var intersect = venn.circleCircleIntersection(circles[i],
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circles[j]);
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for (var k = 0; k < intersect.length; ++k) {
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var p = intersect[k];
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p.parentIndex = [i,j];
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ret.push(p);
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}
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}
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}
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return ret;
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}
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venn.circleIntegral = function(r, x) {
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var y = Math.sqrt(r * r - x * x);
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return x * y + r * r * Math.atan2(x, y);
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};
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/** Returns the area of a circle of radius r - up to width */
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venn.circleArea = function(r, width) {
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return venn.circleIntegral(r, width - r) - venn.circleIntegral(r, -r);
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};
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|
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/** euclidean distance between two points */
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venn.distance = function(p1, p2) {
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return Math.sqrt((p1.x - p2.x) * (p1.x - p2.x) +
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(p1.y - p2.y) * (p1.y - p2.y));
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};
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|
|
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/** Returns the overlap area of two circles of radius r1 and r2 - that
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have their centers separated by distance d. Simpler faster
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|
circle intersection for only two circles */
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venn.circleOverlap = function(r1, r2, d) {
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// no overlap
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if (d >= r1 + r2) {
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return 0;
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}
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// completely overlapped
|
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if (d <= Math.abs(r1 - r2)) {
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return Math.PI * Math.min(r1, r2) * Math.min(r1, r2);
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}
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var w1 = r1 - (d * d - r2 * r2 + r1 * r1) / (2 * d),
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w2 = r2 - (d * d - r1 * r1 + r2 * r2) / (2 * d);
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return venn.circleArea(r1, w1) + venn.circleArea(r2, w2);
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};
|
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|
|
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/** Given two circles (containing a x/y/radius attributes),
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returns the intersecting points if possible.
|
|
note: doesn't handle cases where there are infinitely many
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intersection points (circles are equivalent):, or only one intersection point*/
|
|
venn.circleCircleIntersection = function(p1, p2) {
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var d = venn.distance(p1, p2),
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r1 = p1.radius,
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r2 = p2.radius;
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// if to far away, or self contained - can't be done
|
|
if ((d >= (r1 + r2)) || (d <= Math.abs(r1 - r2))) {
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return [];
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}
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|
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var a = (r1 * r1 - r2 * r2 + d * d) / (2 * d),
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h = Math.sqrt(r1 * r1 - a * a),
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x0 = p1.x + a * (p2.x - p1.x) / d,
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y0 = p1.y + a * (p2.y - p1.y) / d,
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rx = -(p2.y - p1.y) * (h / d),
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ry = -(p2.x - p1.x) * (h / d);
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return [{ x: x0 + rx, y : y0 - ry },
|
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{ x: x0 - rx, y : y0 + ry }];
|
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};
|
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|
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/** Returns the center of a bunch of points */
|
|
venn.getCenter = function(points) {
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|
var center = { x: 0, y: 0};
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|
for (var i =0; i < points.length; ++i ) {
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center.x += points[i].x;
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center.y += points[i].y;
|
|
}
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center.x /= points.length;
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|
center.y /= points.length;
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return center;
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|
};
|
|
}(window.venn = window.venn || {}));
|