608 lines
22 KiB
JavaScript
608 lines
22 KiB
JavaScript
/* *
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*
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* Experimental Highcharts module which enables visualization of a Venn
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* diagram.
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*
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* (c) 2016-2021 Highsoft AS
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* Authors: Jon Arild Nygard
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*
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* Layout algorithm by Ben Frederickson:
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* https://www.benfrederickson.com/better-venn-diagrams/
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*
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* License: www.highcharts.com/license
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*
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* !!!!!!! SOURCE GETS TRANSPILED BY TYPESCRIPT. EDIT TS FILE ONLY. !!!!!!!
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*
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* */
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'use strict';
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import CU from '../../Core/Geometry/CircleUtilities.js';
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var getAreaOfCircle = CU.getAreaOfCircle, getCircleCircleIntersection = CU.getCircleCircleIntersection, getOverlapBetweenCirclesByDistance = CU.getOverlapBetweenCircles, isPointInsideAllCircles = CU.isPointInsideAllCircles, isPointInsideCircle = CU.isPointInsideCircle, isPointOutsideAllCircles = CU.isPointOutsideAllCircles;
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import GU from '../../Core/Geometry/GeometryUtilities.js';
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var getDistanceBetweenPoints = GU.getDistanceBetweenPoints;
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import U from '../../Core/Utilities.js';
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var extend = U.extend, isArray = U.isArray, isNumber = U.isNumber, isObject = U.isObject, isString = U.isString;
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/* *
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*
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* Functions
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*
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* */
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/* eslint-disable valid-jsdoc */
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/**
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* Takes an array of relations and adds the properties `totalOverlap` and
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* `overlapping` to each set. The property `totalOverlap` is the sum of
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* value for each relation where this set is included. The property
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* `overlapping` is a map of how much this set is overlapping another set.
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* NOTE: This algorithm ignores relations consisting of more than 2 sets.
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* @private
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* @param {Array<Highcharts.VennRelationObject>} relations
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* The list of relations that should be sorted.
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* @return {Array<Highcharts.VennRelationObject>}
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* Returns the modified input relations with added properties `totalOverlap`
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* and `overlapping`.
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*/
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function addOverlapToSets(relations) {
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// Calculate the amount of overlap per set.
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var mapOfIdToProps = relations
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// Filter out relations consisting of 2 sets.
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.filter(function (relation) { return (relation.sets.length === 2); })
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// Sum up the amount of overlap for each set.
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.reduce(function (map, relation) {
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relation.sets.forEach(function (set, i, arr) {
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if (!isObject(map[set])) {
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map[set] = {
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overlapping: {},
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totalOverlap: 0
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};
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}
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map[set].totalOverlap += relation.value;
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map[set].overlapping[arr[1 - i]] = relation.value;
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});
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return map;
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}, {});
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relations
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// Filter out single sets
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.filter(isSet)
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// Extend the set with the calculated properties.
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.forEach(function (set) {
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var properties = mapOfIdToProps[set.sets[0]];
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extend(set, properties);
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});
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// Returns the modified relations.
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return relations;
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}
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/**
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* Finds the root of a given function. The root is the input value needed
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* for a function to return 0.
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*
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* See https://en.wikipedia.org/wiki/Bisection_method#Algorithm
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*
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* TODO: Add unit tests.
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*
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* @param {Function} f
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* The function to find the root of.
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* @param {number} a
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* The lowest number in the search range.
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* @param {number} b
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* The highest number in the search range.
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* @param {number} [tolerance=1e-10]
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* The allowed difference between the returned value and root.
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* @param {number} [maxIterations=100]
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* The maximum iterations allowed.
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* @return {number}
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* Root number.
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*/
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function bisect(f, a, b, tolerance, maxIterations) {
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var fA = f(a), fB = f(b), nMax = maxIterations || 100, tol = tolerance || 1e-10, delta = b - a, n = 1, x, fX;
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if (a >= b) {
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throw new Error('a must be smaller than b.');
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}
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else if (fA * fB > 0) {
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throw new Error('f(a) and f(b) must have opposite signs.');
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}
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if (fA === 0) {
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x = a;
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}
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else if (fB === 0) {
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x = b;
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}
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else {
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while (n++ <= nMax && fX !== 0 && delta > tol) {
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delta = (b - a) / 2;
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x = a + delta;
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fX = f(x);
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// Update low and high for next search interval.
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if (fA * fX > 0) {
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a = x;
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}
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else {
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b = x;
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}
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}
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}
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return x;
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}
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/**
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* @private
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*/
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function getCentroid(simplex) {
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var arr = simplex.slice(0, -1), length = arr.length, result = [], sum = function (data, point) {
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data.sum += point[data.i];
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return data;
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};
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for (var i = 0; i < length; i++) {
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result[i] = arr.reduce(sum, { sum: 0, i: i }).sum / length;
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}
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return result;
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}
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/**
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* Uses the bisection method to make a best guess of the ideal distance
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* between two circles too get the desired overlap.
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* Currently there is no known formula to calculate the distance from the
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* area of overlap, which makes the bisection method preferred.
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* @private
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* @param {number} r1
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* Radius of the first circle.
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* @param {number} r2
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* Radiues of the second circle.
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* @param {number} overlap
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* The wanted overlap between the two circles.
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* @return {number}
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* Returns the distance needed to get the wanted overlap between the two
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* circles.
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*/
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function getDistanceBetweenCirclesByOverlap(r1, r2, overlap) {
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var maxDistance = r1 + r2, distance;
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if (overlap <= 0) {
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// If overlap is below or equal to zero, then there is no overlap.
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distance = maxDistance;
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}
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else if (getAreaOfCircle(r1 < r2 ? r1 : r2) <= overlap) {
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// When area of overlap is larger than the area of the smallest
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// circle, then it is completely overlapping.
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distance = 0;
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}
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else {
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distance = bisect(function (x) {
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var actualOverlap = getOverlapBetweenCirclesByDistance(r1, r2, x);
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// Return the differance between wanted and actual overlap.
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return overlap - actualOverlap;
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}, 0, maxDistance);
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}
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return distance;
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}
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/**
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* Finds the available width for a label, by taking the label position and
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* finding the largest distance, which is inside all internal circles, and
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* outside all external circles.
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*
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* @private
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* @param {Highcharts.PositionObject} pos
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* The x and y coordinate of the label.
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* @param {Array<Highcharts.CircleObject>} internal
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* Internal circles.
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* @param {Array<Highcharts.CircleObject>} external
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* External circles.
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* @return {number}
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* Returns available width for the label.
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*/
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function getLabelWidth(pos, internal, external) {
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var radius = internal.reduce(function (min, circle) { return Math.min(circle.r, min); }, Infinity),
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// Filter out external circles that are completely overlapping.
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filteredExternals = external.filter(function (circle) {
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return !isPointInsideCircle(pos, circle);
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});
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var findDistance = function (maxDistance, direction) {
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return bisect(function (x) {
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var testPos = {
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x: pos.x + (direction * x),
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y: pos.y
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}, isValid = (isPointInsideAllCircles(testPos, internal) &&
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isPointOutsideAllCircles(testPos, filteredExternals));
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// If the position is valid, then we want to move towards the
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// max distance. If not, then we want to away from the max
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// distance.
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return -(maxDistance - x) + (isValid ? 0 : Number.MAX_VALUE);
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}, 0, maxDistance);
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};
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// Find the smallest distance of left and right.
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return Math.min(findDistance(radius, -1), findDistance(radius, 1)) * 2;
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}
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/**
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* Calculates a margin for a point based on the iternal and external
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* circles. The margin describes if the point is well placed within the
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* internal circles, and away from the external.
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* @private
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* @todo add unit tests.
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* @param {Highcharts.PositionObject} point
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* The point to evaluate.
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* @param {Array<Highcharts.CircleObject>} internal
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* The internal circles.
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* @param {Array<Highcharts.CircleObject>} external
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* The external circles.
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* @return {number}
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* Returns the margin.
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*/
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function getMarginFromCircles(point, internal, external) {
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var margin = internal.reduce(function (margin, circle) {
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var m = circle.r - getDistanceBetweenPoints(point, circle);
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return (m <= margin) ? m : margin;
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}, Number.MAX_VALUE);
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margin = external.reduce(function (margin, circle) {
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var m = getDistanceBetweenPoints(point, circle) - circle.r;
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return (m <= margin) ? m : margin;
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}, margin);
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return margin;
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}
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/**
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* Calculates the area of overlap between a list of circles.
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* @private
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* @todo add support for calculating overlap between more than 2 circles.
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* @param {Array<Highcharts.CircleObject>} circles
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* List of circles with their given positions.
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* @return {number}
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* Returns the area of overlap between all the circles.
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*/
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function getOverlapBetweenCircles(circles) {
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var overlap = 0;
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// When there is only two circles we can find the overlap by using their
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// radiuses and the distance between them.
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if (circles.length === 2) {
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var circle1 = circles[0];
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var circle2 = circles[1];
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overlap = getOverlapBetweenCirclesByDistance(circle1.r, circle2.r, getDistanceBetweenPoints(circle1, circle2));
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}
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return overlap;
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}
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// eslint-disable-next-line require-jsdoc
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function isSet(x) {
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return isArray(x.sets) && x.sets.length === 1;
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}
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// eslint-disable-next-line require-jsdoc
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function isValidRelation(x) {
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var map = {};
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return (isObject(x) &&
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(isNumber(x.value) && x.value > -1) &&
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(isArray(x.sets) && x.sets.length > 0) &&
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!x.sets.some(function (set) {
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var invalid = false;
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if (!map[set] && isString(set)) {
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map[set] = true;
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}
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else {
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invalid = true;
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}
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return invalid;
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}));
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}
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// eslint-disable-next-line require-jsdoc
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function isValidSet(x) {
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return (isValidRelation(x) && isSet(x) && x.value > 0);
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}
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/**
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* Uses a greedy approach to position all the sets. Works well with a small
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* number of sets, and are in these cases a good choice aesthetically.
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* @private
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* @param {Array<object>} relations List of the overlap between two or more
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* sets, or the size of a single set.
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* @return {Array<object>} List of circles and their calculated positions.
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*/
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function layoutGreedyVenn(relations) {
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var positionedSets = [], mapOfIdToCircles = {};
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// Define a circle for each set.
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relations
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.filter(function (relation) {
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return relation.sets.length === 1;
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}).forEach(function (relation) {
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mapOfIdToCircles[relation.sets[0]] = relation.circle = {
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x: Number.MAX_VALUE,
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y: Number.MAX_VALUE,
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r: Math.sqrt(relation.value / Math.PI)
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};
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});
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/**
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* Takes a set and updates the position, and add the set to the list of
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* positioned sets.
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* @private
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* @param {Object} set
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* The set to add to its final position.
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* @param {Object} coordinates
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* The coordinates to position the set at.
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*/
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var positionSet = function positionSet(set, coordinates) {
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var circle = set.circle;
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circle.x = coordinates.x;
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circle.y = coordinates.y;
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positionedSets.push(set);
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};
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// Find overlap between sets. Ignore relations with more then 2 sets.
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addOverlapToSets(relations);
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// Sort sets by the sum of their size from large to small.
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var sortedByOverlap = relations
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.filter(isSet)
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.sort(sortByTotalOverlap);
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// Position the most overlapped set at 0,0.
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positionSet(sortedByOverlap.shift(), { x: 0, y: 0 });
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var relationsWithTwoSets = relations.filter(function (x) {
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return x.sets.length === 2;
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});
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// Iterate and position the remaining sets.
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sortedByOverlap.forEach(function (set) {
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var circle = set.circle, radius = circle.r, overlapping = set.overlapping;
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var bestPosition = positionedSets.reduce(function (best, positionedSet, i) {
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var positionedCircle = positionedSet.circle, overlap = overlapping[positionedSet.sets[0]];
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// Calculate the distance between the sets to get the
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// correct overlap
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var distance = getDistanceBetweenCirclesByOverlap(radius, positionedCircle.r, overlap);
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// Create a list of possible coordinates calculated from
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// distance.
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var possibleCoordinates = [
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{ x: positionedCircle.x + distance, y: positionedCircle.y },
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{ x: positionedCircle.x - distance, y: positionedCircle.y },
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{ x: positionedCircle.x, y: positionedCircle.y + distance },
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{ x: positionedCircle.x, y: positionedCircle.y - distance }
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];
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// If there are more circles overlapping, then add the
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// intersection points as possible positions.
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positionedSets.slice(i + 1).forEach(function (positionedSet2) {
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var positionedCircle2 = positionedSet2.circle, overlap2 = overlapping[positionedSet2.sets[0]], distance2 = getDistanceBetweenCirclesByOverlap(radius, positionedCircle2.r, overlap2);
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// Add intersections to list of coordinates.
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possibleCoordinates = possibleCoordinates.concat(getCircleCircleIntersection({
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x: positionedCircle.x,
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y: positionedCircle.y,
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r: distance
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}, {
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x: positionedCircle2.x,
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y: positionedCircle2.y,
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r: distance2
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}));
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});
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// Iterate all suggested coordinates and find the best one.
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possibleCoordinates.forEach(function (coordinates) {
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circle.x = coordinates.x;
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circle.y = coordinates.y;
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// Calculate loss for the suggested coordinates.
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var currentLoss = loss(mapOfIdToCircles, relationsWithTwoSets);
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// If the loss is better, then use these new coordinates
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if (currentLoss < best.loss) {
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best.loss = currentLoss;
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best.coordinates = coordinates;
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}
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});
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// Return resulting coordinates.
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return best;
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}, {
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loss: Number.MAX_VALUE,
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coordinates: void 0
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});
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// Add the set to its final position.
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positionSet(set, bestPosition.coordinates);
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});
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// Return the positions of each set.
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return mapOfIdToCircles;
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}
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/**
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* Calculates the difference between the desired overlap and the actual
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* overlap between two circles.
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* @private
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* @param {Dictionary<Highcharts.CircleObject>} mapOfIdToCircle
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* Map from id to circle.
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* @param {Array<Highcharts.VennRelationObject>} relations
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* List of relations to calculate the loss of.
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* @return {number}
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* Returns the loss between positions of the circles for the given
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* relations.
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*/
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function loss(mapOfIdToCircle, relations) {
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var precision = 10e10;
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// Iterate all the relations and calculate their individual loss.
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return relations.reduce(function (totalLoss, relation) {
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var loss = 0;
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if (relation.sets.length > 1) {
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var wantedOverlap = relation.value;
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// Calculate the actual overlap between the sets.
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var actualOverlap = getOverlapBetweenCircles(
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// Get the circles for the given sets.
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relation.sets.map(function (set) {
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return mapOfIdToCircle[set];
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}));
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var diff = wantedOverlap - actualOverlap;
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loss = Math.round((diff * diff) * precision) / precision;
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}
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// Add calculated loss to the sum.
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return totalLoss + loss;
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}, 0);
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}
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/**
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* Finds an optimal position for a given point.
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* @todo add unit tests.
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* @todo add constraints to optimize the algorithm.
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* @private
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* @param {Highcharts.NelderMeadTestFunction} fn
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* The function to test a point.
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* @param {Highcharts.NelderMeadPointArray} initial
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* The initial point to optimize.
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* @return {Highcharts.NelderMeadPointArray}
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* Returns the opimized position of a point.
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*/
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function nelderMead(fn, initial) {
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var maxIterations = 100, sortByFx = function (a, b) {
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return a.fx - b.fx;
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}, pRef = 1, // Reflection parameter
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pExp = 2, // Expansion parameter
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pCon = -0.5, // Contraction parameter
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pOCon = pCon * pRef, // Outwards contraction parameter
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pShrink = 0.5; // Shrink parameter
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/**
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* @private
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*/
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var weightedSum = function (weight1, v1, weight2, v2) { return v1.map(function (x, i) { return weight1 * x + weight2 * v2[i]; }); };
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/**
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* @private
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*/
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var getSimplex = function (initial) {
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var n = initial.length, simplex = new Array(n + 1);
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// Initial point to the simplex.
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simplex[0] = initial;
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simplex[0].fx = fn(initial);
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// Create a set of extra points based on the initial.
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for (var i = 0; i < n; ++i) {
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var point = initial.slice();
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point[i] = point[i] ? point[i] * 1.05 : 0.001;
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point.fx = fn(point);
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simplex[i + 1] = point;
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}
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return simplex;
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};
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var updateSimplex = function (simplex, point) {
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point.fx = fn(point);
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simplex[simplex.length - 1] = point;
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return simplex;
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};
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var shrinkSimplex = function (simplex) {
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var best = simplex[0];
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return simplex.map(function (point) {
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var p = weightedSum(1 - pShrink, best, pShrink, point);
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p.fx = fn(p);
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return p;
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});
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};
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var getPoint = function (centroid, worst, a, b) {
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var point = weightedSum(a, centroid, b, worst);
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point.fx = fn(point);
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return point;
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};
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// Create a simplex
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var simplex = getSimplex(initial);
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// Iterate from 0 to max iterations
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for (var i = 0; i < maxIterations; i++) {
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// Sort the simplex
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simplex.sort(sortByFx);
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// Create a centroid from the simplex
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var worst = simplex[simplex.length - 1];
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var centroid = getCentroid(simplex);
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|
// Calculate the reflected point.
|
|
var reflected = getPoint(centroid, worst, 1 + pRef, -pRef);
|
|
if (reflected.fx < simplex[0].fx) {
|
|
// If reflected point is the best, then possibly expand.
|
|
var expanded = getPoint(centroid, worst, 1 + pExp, -pExp);
|
|
simplex = updateSimplex(simplex, (expanded.fx < reflected.fx) ? expanded : reflected);
|
|
}
|
|
else if (reflected.fx >= simplex[simplex.length - 2].fx) {
|
|
// If the reflected point is worse than the second worse, then
|
|
// contract.
|
|
var contracted = void 0;
|
|
if (reflected.fx > worst.fx) {
|
|
// If the reflected is worse than the worst point, do a
|
|
// contraction
|
|
contracted = getPoint(centroid, worst, 1 + pCon, -pCon);
|
|
if (contracted.fx < worst.fx) {
|
|
simplex = updateSimplex(simplex, contracted);
|
|
}
|
|
else {
|
|
simplex = shrinkSimplex(simplex);
|
|
}
|
|
}
|
|
else {
|
|
// Otherwise do an outwards contraction
|
|
contracted = getPoint(centroid, worst, 1 - pOCon, pOCon);
|
|
if (contracted.fx < reflected.fx) {
|
|
simplex = updateSimplex(simplex, contracted);
|
|
}
|
|
else {
|
|
simplex = shrinkSimplex(simplex);
|
|
}
|
|
}
|
|
}
|
|
else {
|
|
simplex = updateSimplex(simplex, reflected);
|
|
}
|
|
}
|
|
return simplex[0];
|
|
}
|
|
/**
|
|
* Prepares the venn data so that it is usable for the layout function.
|
|
* Filter out sets, or intersections that includes sets, that are missing in
|
|
* the data or has (value < 1). Adds missing relations between sets in the
|
|
* data as value = 0.
|
|
* @private
|
|
* @param {Array<object>} data The raw input data.
|
|
* @return {Array<object>} Returns an array of valid venn data.
|
|
*/
|
|
function processVennData(data) {
|
|
var d = isArray(data) ? data : [];
|
|
var validSets = d
|
|
.reduce(function (arr, x) {
|
|
// Check if x is a valid set, and that it is not an duplicate.
|
|
if (isValidSet(x) && arr.indexOf(x.sets[0]) === -1) {
|
|
arr.push(x.sets[0]);
|
|
}
|
|
return arr;
|
|
}, [])
|
|
.sort();
|
|
var mapOfIdToRelation = d.reduce(function (mapOfIdToRelation, relation) {
|
|
if (isValidRelation(relation) &&
|
|
!relation.sets.some(function (set) {
|
|
return validSets.indexOf(set) === -1;
|
|
})) {
|
|
mapOfIdToRelation[relation.sets.sort().join()] =
|
|
relation;
|
|
}
|
|
return mapOfIdToRelation;
|
|
}, {});
|
|
validSets.reduce(function (combinations, set, i, arr) {
|
|
var remaining = arr.slice(i + 1);
|
|
remaining.forEach(function (set2) {
|
|
combinations.push(set + ',' + set2);
|
|
});
|
|
return combinations;
|
|
}, []).forEach(function (combination) {
|
|
if (!mapOfIdToRelation[combination]) {
|
|
var obj = {
|
|
sets: combination.split(','),
|
|
value: 0
|
|
};
|
|
mapOfIdToRelation[combination] = obj;
|
|
}
|
|
});
|
|
// Transform map into array.
|
|
return Object
|
|
.keys(mapOfIdToRelation)
|
|
.map(function (id) {
|
|
return mapOfIdToRelation[id];
|
|
});
|
|
}
|
|
/**
|
|
* Takes two sets and finds the one with the largest total overlap.
|
|
* @private
|
|
* @param {Object} a
|
|
* The first set to compare.
|
|
* @param {Object} b
|
|
* The second set to compare.
|
|
* @return {number}
|
|
* Returns 0 if a and b are equal, <0 if a is greater, >0 if b is greater.
|
|
*/
|
|
function sortByTotalOverlap(a, b) {
|
|
return b.totalOverlap - a.totalOverlap;
|
|
}
|
|
/* *
|
|
*
|
|
* Default Export
|
|
*
|
|
* */
|
|
var VennUtils = {
|
|
geometry: GU,
|
|
geometryCircles: CU,
|
|
addOverlapToSets: addOverlapToSets,
|
|
getCentroid: getCentroid,
|
|
getDistanceBetweenCirclesByOverlap: getDistanceBetweenCirclesByOverlap,
|
|
getLabelWidth: getLabelWidth,
|
|
getMarginFromCircles: getMarginFromCircles,
|
|
isSet: isSet,
|
|
layoutGreedyVenn: layoutGreedyVenn,
|
|
loss: loss,
|
|
nelderMead: nelderMead,
|
|
processVennData: processVennData,
|
|
sortByTotalOverlap: sortByTotalOverlap
|
|
};
|
|
export default VennUtils;
|