mint/app/public/js/Highstock-8.0.0/code/modules/venn.src.js

/**
 * @license Highcharts JS v8.0.0 (2019-12-10)
 *
 * (c) 2017-2019 Highsoft AS
 * Authors: Jon Arild Nygard
 *
 * License: www.highcharts.com/license
 */
'use strict';
(function (factory) {
    if (typeof module === 'object' && module.exports) {
        factory['default'] = factory;
        module.exports = factory;
    } else if (typeof define === 'function' && define.amd) {
        define('highcharts/modules/venn', ['highcharts'], function (Highcharts) {
            factory(Highcharts);
            factory.Highcharts = Highcharts;
            return factory;
        });
    } else {
        factory(typeof Highcharts !== 'undefined' ? Highcharts : undefined);
    }
}(function (Highcharts) {
    var _modules = Highcharts ? Highcharts._modules : {};
    function _registerModule(obj, path, args, fn) {
        if (!obj.hasOwnProperty(path)) {
            obj[path] = fn.apply(null, args);
        }
    }
    _registerModule(_modules, 'mixins/draw-point.js', [], function () {
        /* *
         *
         *  !!!!!!! SOURCE GETS TRANSPILED BY TYPESCRIPT. EDIT TS FILE ONLY. !!!!!!!
         *
         * */
        var isFn = function (x) {
            return typeof x === 'function';
        };
        /* eslint-disable no-invalid-this, valid-jsdoc */
        /**
         * Handles the drawing of a component.
         * Can be used for any type of component that reserves the graphic property, and
         * provides a shouldDraw on its context.
         *
         * @private
         * @function draw
         * @param {DrawPointParams} params
         *        Parameters.
         *
         * @todo add type checking.
         * @todo export this function to enable usage
         */
        var draw = function draw(params) {
            var component = this, graphic = component.graphic, animatableAttribs = params.animatableAttribs, onComplete = params.onComplete, css = params.css, renderer = params.renderer;
            if (component.shouldDraw()) {
                if (!graphic) {
                    component.graphic = graphic =
                        renderer[params.shapeType](params.shapeArgs)
                            .add(params.group);
                }
                graphic
                    .css(css)
                    .attr(params.attribs)
                    .animate(animatableAttribs, params.isNew ? false : void 0, onComplete);
            }
            else if (graphic) {
                var destroy = function () {
                    component.graphic = graphic = graphic.destroy();
                    if (isFn(onComplete)) {
                        onComplete();
                    }
                };
                // animate only runs complete callback if something was animated.
                if (Object.keys(animatableAttribs).length) {
                    graphic.animate(animatableAttribs, void 0, function () {
                        destroy();
                    });
                }
                else {
                    destroy();
                }
            }
        };
        /**
         * An extended version of draw customized for points.
         * It calls additional methods that is expected when rendering a point.
         * @private
         * @param {Highcharts.Dictionary<any>} params Parameters
         */
        var drawPoint = function drawPoint(params) {
            var point = this, attribs = params.attribs = params.attribs || {};
            // Assigning class in dot notation does go well in IE8
            // eslint-disable-next-line dot-notation
            attribs['class'] = point.getClassName();
            // Call draw to render component
            draw.call(point, params);
        };

        return drawPoint;
    });
    _registerModule(_modules, 'mixins/geometry.js', [], function () {
        /* *
         *
         *  !!!!!!! SOURCE GETS TRANSPILED BY TYPESCRIPT. EDIT TS FILE ONLY. !!!!!!!
         *
         * */
        /**
         * Calculates the center between a list of points.
         * @private
         * @param {Array<Highcharts.PositionObject>} points
         *        A list of points to calculate the center of.
         * @return {Highcharts.PositionObject}
         *         Calculated center
         */
        var getCenterOfPoints = function getCenterOfPoints(points) {
            var sum = points.reduce(function (sum, point) {
                sum.x += point.x;
                sum.y += point.y;
                return sum;
            }, { x: 0, y: 0 });
            return {
                x: sum.x / points.length,
                y: sum.y / points.length
            };
        };
        /**
         * Calculates the distance between two points based on their x and y
         * coordinates.
         * @private
         * @param {Highcharts.PositionObject} p1
         *        The x and y coordinates of the first point.
         * @param {Highcharts.PositionObject} p2
         *        The x and y coordinates of the second point.
         * @return {number}
         *         Returns the distance between the points.
         */
        var getDistanceBetweenPoints = function getDistanceBetweenPoints(p1, p2) {
            return Math.sqrt(Math.pow(p2.x - p1.x, 2) + Math.pow(p2.y - p1.y, 2));
        };
        /**
         * Calculates the angle between two points.
         * @todo add unit tests.
         * @private
         * @param {Highcharts.PositionObject} p1 The first point.
         * @param {Highcharts.PositionObject} p2 The second point.
         * @return {number} Returns the angle in radians.
         */
        var getAngleBetweenPoints = function getAngleBetweenPoints(p1, p2) {
            return Math.atan2(p2.x - p1.x, p2.y - p1.y);
        };
        var geometry = {
            getAngleBetweenPoints: getAngleBetweenPoints,
            getCenterOfPoints: getCenterOfPoints,
            getDistanceBetweenPoints: getDistanceBetweenPoints
        };

        return geometry;
    });
    _registerModule(_modules, 'mixins/geometry-circles.js', [_modules['mixins/geometry.js']], function (geometry) {
        /* *
         *
         *  !!!!!!! SOURCE GETS TRANSPILED BY TYPESCRIPT. EDIT TS FILE ONLY. !!!!!!!
         *
         * */
        var getAngleBetweenPoints = geometry.getAngleBetweenPoints, getCenterOfPoints = geometry.getCenterOfPoints, getDistanceBetweenPoints = geometry.getDistanceBetweenPoints;
        /**
         * @private
         * @param {number} x
         *        Number to round
         * @param {number} decimals
         *        Number of decimals to round to
         * @return {number}
         *         Rounded number
         */
        function round(x, decimals) {
            var a = Math.pow(10, decimals);
            return Math.round(x * a) / a;
        }
        /**
         * Calculates the area of a circle based on its radius.
         * @private
         * @param {number} r
         *        The radius of the circle.
         * @return {number}
         *         Returns the area of the circle.
         */
        function getAreaOfCircle(r) {
            if (r <= 0) {
                throw new Error('radius of circle must be a positive number.');
            }
            return Math.PI * r * r;
        }
        /**
         * Calculates the area of a circular segment based on the radius of the circle
         * and the height of the segment.
         * See http://mathworld.wolfram.com/CircularSegment.html
         * @private
         * @param {number} r
         *        The radius of the circle.
         * @param {number} h
         *        The height of the circular segment.
         * @return {number}
         *         Returns the area of the circular segment.
         */
        function getCircularSegmentArea(r, h) {
            return r * r * Math.acos(1 - h / r) - (r - h) * Math.sqrt(h * (2 * r - h));
        }
        /**
         * Calculates the area of overlap between two circles based on their radiuses
         * and the distance between them.
         * See http://mathworld.wolfram.com/Circle-CircleIntersection.html
         * @private
         * @param {number} r1
         *        Radius of the first circle.
         * @param {number} r2
         *        Radius of the second circle.
         * @param {number} d
         *        The distance between the two circles.
         * @return {number}
         *         Returns the area of overlap between the two circles.
         */
        function getOverlapBetweenCircles(r1, r2, d) {
            var overlap = 0;
            // If the distance is larger than the sum of the radiuses then the circles
            // does not overlap.
            if (d < r1 + r2) {
                if (d <= Math.abs(r2 - r1)) {
                    // If the circles are completely overlapping, then the overlap
                    // equals the area of the smallest circle.
                    overlap = getAreaOfCircle(r1 < r2 ? r1 : r2);
                }
                else {
                    // Height of first triangle segment.
                    var d1 = (r1 * r1 - r2 * r2 + d * d) / (2 * d), 
                    // Height of second triangle segment.
                    d2 = d - d1;
                    overlap = (getCircularSegmentArea(r1, r1 - d1) +
                        getCircularSegmentArea(r2, r2 - d2));
                }
                // Round the result to two decimals.
                overlap = round(overlap, 14);
            }
            return overlap;
        }
        /**
         * Calculates the intersection points of two circles.
         *
         * NOTE: does not handle floating errors well.
         * @private
         * @param {Highcharts.CircleObject} c1
         *        The first circle.
         * @param {Highcharts.CircleObject} c2
         *        The second sircle.
         * @return {Array<Highcharts.PositionObject>}
         *         Returns the resulting intersection points.
         */
        function getCircleCircleIntersection(c1, c2) {
            var d = getDistanceBetweenPoints(c1, c2), r1 = c1.r, r2 = c2.r;
            var points = [];
            if (d < r1 + r2 && d > Math.abs(r1 - r2)) {
                // If the circles are overlapping, but not completely overlapping, then
                // it exists intersecting points.
                var r1Square = r1 * r1, r2Square = r2 * r2, 
                // d^2 - r^2 + R^2 / 2d
                x = (r1Square - r2Square + d * d) / (2 * d), 
                // y^2 = R^2 - x^2
                y = Math.sqrt(r1Square - x * x), x1 = c1.x, x2 = c2.x, y1 = c1.y, y2 = c2.y, x0 = x1 + x * (x2 - x1) / d, y0 = y1 + x * (y2 - y1) / d, rx = -(y2 - y1) * (y / d), ry = -(x2 - x1) * (y / d);
                points = [
                    { x: round(x0 + rx, 14), y: round(y0 - ry, 14) },
                    { x: round(x0 - rx, 14), y: round(y0 + ry, 14) }
                ];
            }
            return points;
        }
        /**
         * Calculates all the intersection points for between a list of circles.
         * @private
         * @param {Array<Highcharts.CircleObject>} circles
         *        The circles to calculate the points from.
         * @return {Array<Highcharts.GeometryObject>}
         *         Returns a list of intersection points.
         */
        function getCirclesIntersectionPoints(circles) {
            return circles.reduce(function (points, c1, i, arr) {
                var additional = arr.slice(i + 1)
                    .reduce(function (points, c2, j) {
                    var indexes = [i, j + i + 1];
                    return points.concat(getCircleCircleIntersection(c1, c2)
                        .map(function (p) {
                        p.indexes = indexes;
                        return p;
                    }));
                }, []);
                return points.concat(additional);
            }, []);
        }
        /**
         * Tests wether the first circle is completely overlapping the second circle.
         *
         * @private
         * @param {Highcharts.CircleObject} circle1 The first circle.
         * @param {Highcharts.CircleObject} circle2 The The second circle.
         * @return {boolean} Returns true if circle1 is completely overlapping circle2,
         * false if not.
         */
        function isCircle1CompletelyOverlappingCircle2(circle1, circle2) {
            return getDistanceBetweenPoints(circle1, circle2) + circle2.r <
                circle1.r + 1e-10;
        }
        /**
         * Tests wether a point lies within a given circle.
         * @private
         * @param {Highcharts.PositionObject} point
         *        The point to test for.
         * @param {Highcharts.CircleObject} circle
         *        The circle to test if the point is within.
         * @return {boolean}
         *         Returns true if the point is inside, false if outside.
         */
        function isPointInsideCircle(point, circle) {
            return getDistanceBetweenPoints(point, circle) <= circle.r + 1e-10;
        }
        /**
         * Tests wether a point lies within a set of circles.
         * @private
         * @param {Highcharts.PositionObject} point
         *        The point to test.
         * @param {Array<Highcharts.CircleObject>} circles
         *        The list of circles to test against.
         * @return {boolean}
         *         Returns true if the point is inside all the circles, false if not.
         */
        function isPointInsideAllCircles(point, circles) {
            return !circles.some(function (circle) {
                return !isPointInsideCircle(point, circle);
            });
        }
        /**
         * Tests wether a point lies outside a set of circles.
         *
         * TODO: add unit tests.
         * @private
         * @param {Highcharts.PositionObject} point
         *        The point to test.
         * @param {Array<Highcharts.CircleObject>} circles
         *        The list of circles to test against.
         * @return {boolean}
         *         Returns true if the point is outside all the circles, false if not.
         */
        function isPointOutsideAllCircles(point, circles) {
            return !circles.some(function (circle) {
                return isPointInsideCircle(point, circle);
            });
        }
        /**
         * Calculates the points for the polygon of the intersection area between a set
         * of circles.
         *
         * @private
         * @param {Array<Highcharts.CircleObject>} circles
         *        List of circles to calculate polygon of.
         * @return {Array<Highcharts.GeometryObject>} Return list of points in the
         * intersection polygon.
         */
        function getCirclesIntersectionPolygon(circles) {
            return getCirclesIntersectionPoints(circles)
                .filter(function (p) {
                return isPointInsideAllCircles(p, circles);
            });
        }
        /**
         * Calculate the path for the area of overlap between a set of circles.
         * @todo handle cases with only 1 or 0 arcs.
         * @private
         * @param {Array<Highcharts.CircleObject>} circles
         *        List of circles to calculate area of.
         * @return {Highcharts.GeometryIntersectionObject|undefined}
         *         Returns the path for the area of overlap. Returns an empty string if
         *         there are no intersection between all the circles.
         */
        function getAreaOfIntersectionBetweenCircles(circles) {
            var intersectionPoints = getCirclesIntersectionPolygon(circles), result;
            if (intersectionPoints.length > 1) {
                // Calculate the center of the intersection points.
                var center_1 = getCenterOfPoints(intersectionPoints);
                intersectionPoints = intersectionPoints
                    // Calculate the angle between the center and the points.
                    .map(function (p) {
                    p.angle = getAngleBetweenPoints(center_1, p);
                    return p;
                })
                    // Sort the points by the angle to the center.
                    .sort(function (a, b) {
                    return b.angle - a.angle;
                });
                var startPoint = intersectionPoints[intersectionPoints.length - 1];
                var arcs = intersectionPoints
                    .reduce(function (data, p1) {
                    var startPoint = data.startPoint, midPoint = getCenterOfPoints([startPoint, p1]);
                    // Calculate the arc from the intersection points and their
                    // circles.
                    var arc = p1.indexes
                        // Filter out circles that are not included in both
                        // intersection points.
                        .filter(function (index) {
                        return startPoint.indexes.indexOf(index) > -1;
                    })
                        // Iterate the circles of the intersection points and
                        // calculate arcs.
                        .reduce(function (arc, index) {
                        var circle = circles[index], angle1 = getAngleBetweenPoints(circle, p1), angle2 = getAngleBetweenPoints(circle, startPoint), angleDiff = angle2 - angle1 +
                            (angle2 < angle1 ? 2 * Math.PI : 0), angle = angle2 - angleDiff / 2;
                        var width = getDistanceBetweenPoints(midPoint, {
                            x: circle.x + circle.r * Math.sin(angle),
                            y: circle.y + circle.r * Math.cos(angle)
                        });
                        var r = circle.r;
                        // Width can sometimes become to large due to floating
                        // point errors
                        if (width > r * 2) {
                            width = r * 2;
                        }
                        // Get the arc with the smallest width.
                        if (!arc || arc.width > width) {
                            arc = {
                                r: r,
                                largeArc: width > r ? 1 : 0,
                                width: width,
                                x: p1.x,
                                y: p1.y
                            };
                        }
                        // Return the chosen arc.
                        return arc;
                    }, null);
                    // If we find an arc then add it to the list and update p2.
                    if (arc) {
                        var r = arc.r;
                        data.arcs.push(['A', r, r, 0, arc.largeArc, 1, arc.x, arc.y]);
                        data.startPoint = p1;
                    }
                    return data;
                }, {
                    startPoint: startPoint,
                    arcs: []
                }).arcs;
                if (arcs.length === 0) {
                    // empty
                }
                else if (arcs.length === 1) {
                    // empty
                }
                else {
                    arcs.unshift(['M', startPoint.x, startPoint.y]);
                    result = {
                        center: center_1,
                        d: arcs
                    };
                }
            }
            return result;
        }
        var geometryCircles = {
            getAreaOfCircle: getAreaOfCircle,
            getAreaOfIntersectionBetweenCircles: getAreaOfIntersectionBetweenCircles,
            getCircleCircleIntersection: getCircleCircleIntersection,
            getCirclesIntersectionPoints: getCirclesIntersectionPoints,
            getCirclesIntersectionPolygon: getCirclesIntersectionPolygon,
            getCircularSegmentArea: getCircularSegmentArea,
            getOverlapBetweenCircles: getOverlapBetweenCircles,
            isCircle1CompletelyOverlappingCircle2: isCircle1CompletelyOverlappingCircle2,
            isPointInsideCircle: isPointInsideCircle,
            isPointInsideAllCircles: isPointInsideAllCircles,
            isPointOutsideAllCircles: isPointOutsideAllCircles,
            round: round
        };

        return geometryCircles;
    });
    _registerModule(_modules, 'mixins/nelder-mead.js', [], function () {
        /* *
         *
         *  !!!!!!! SOURCE GETS TRANSPILED BY TYPESCRIPT. EDIT TS FILE ONLY. !!!!!!!
         *
         * */
        /* eslint-disable valid-jsdoc */
        var getCentroid = function (simplex) {
            var arr = simplex.slice(0, -1), length = arr.length, result = [], sum = function (data, point) {
                data.sum += point[data.i];
                return data;
            };
            for (var i = 0; i < length; i++) {
                result[i] = arr.reduce(sum, { sum: 0, i: i }).sum / length;
            }
            return result;
        };
        /**
         * Finds an optimal position for a given point.
         * @todo add unit tests.
         * @todo add constraints to optimize the algorithm.
         * @private
         * @param {Highcharts.NelderMeadTestFunction} fn
         *        The function to test a point.
         * @param {Highcharts.NelderMeadPointArray} initial
         *        The initial point to optimize.
         * @return {Highcharts.NelderMeadPointArray}
         *         Returns the opimized position of a point.
         */
        var nelderMead = function nelderMead(fn, initial) {
            var maxIterations = 100, sortByFx = function (a, b) {
                return a.fx - b.fx;
            }, pRef = 1, // Reflection parameter
            pExp = 2, // Expansion parameter
            pCon = -0.5, // Contraction parameter
            pOCon = pCon * pRef, // Outwards contraction parameter
            pShrink = 0.5; // Shrink parameter
            /**
             * @private
             */
            var weightedSum = function weightedSum(weight1, v1, weight2, v2) {
                return v1.map(function (x, i) {
                    return weight1 * x + weight2 * v2[i];
                });
            };
            /**
             * @private
             */
            var getSimplex = function getSimplex(initial) {
                var n = initial.length, simplex = new Array(n + 1);
                // Initial point to the simplex.
                simplex[0] = initial;
                simplex[0].fx = fn(initial);
                // Create a set of extra points based on the initial.
                for (var i = 0; i < n; ++i) {
                    var point = initial.slice();
                    point[i] = point[i] ? point[i] * 1.05 : 0.001;
                    point.fx = fn(point);
                    simplex[i + 1] = point;
                }
                return simplex;
            };
            var updateSimplex = function (simplex, point) {
                point.fx = fn(point);
                simplex[simplex.length - 1] = point;
                return simplex;
            };
            var shrinkSimplex = function (simplex) {
                var best = simplex[0];
                return simplex.map(function (point) {
                    var p = weightedSum(1 - pShrink, best, pShrink, point);
                    p.fx = fn(p);
                    return p;
                });
            };
            var getPoint = function (centroid, worst, a, b) {
                var point = weightedSum(a, centroid, b, worst);
                point.fx = fn(point);
                return point;
            };
            // Create a simplex
            var simplex = getSimplex(initial);
            // Iterate from 0 to max iterations
            for (var i = 0; i < maxIterations; i++) {
                // Sort the simplex
                simplex.sort(sortByFx);
                // Create a centroid from the simplex
                var worst = simplex[simplex.length - 1];
                var centroid = getCentroid(simplex);
                // 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;
                    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];
        };
        var content = {
            getCentroid: getCentroid,
            nelderMead: nelderMead
        };

        return content;
    });
    _registerModule(_modules, 'modules/venn.src.js', [_modules['parts/Globals.js'], _modules['mixins/draw-point.js'], _modules['mixins/geometry.js'], _modules['mixins/geometry-circles.js'], _modules['mixins/nelder-mead.js'], _modules['parts/Utilities.js']], function (H, draw, geometry, GeometryCircleMixin, NelderMeadModule, U) {
        /* *
         *
         *  Experimental Highcharts module which enables visualization of a Venn
         *  diagram.
         *
         *  (c) 2016-2019 Highsoft AS
         *  Authors: Jon Arild Nygard
         *
         *  Layout algorithm by Ben Frederickson:
         *  https://www.benfrederickson.com/better-venn-diagrams/
         *
         *  License: www.highcharts.com/license
         *
         *  !!!!!!! SOURCE GETS TRANSPILED BY TYPESCRIPT. EDIT TS FILE ONLY. !!!!!!!
         *
         * */
        var getAreaOfCircle = GeometryCircleMixin.getAreaOfCircle, getAreaOfIntersectionBetweenCircles = GeometryCircleMixin.getAreaOfIntersectionBetweenCircles, getCircleCircleIntersection = GeometryCircleMixin.getCircleCircleIntersection, getCirclesIntersectionPolygon = GeometryCircleMixin.getCirclesIntersectionPolygon, getOverlapBetweenCirclesByDistance = GeometryCircleMixin.getOverlapBetweenCircles, isCircle1CompletelyOverlappingCircle2 = GeometryCircleMixin.isCircle1CompletelyOverlappingCircle2, isPointInsideAllCircles = GeometryCircleMixin.isPointInsideAllCircles, isPointInsideCircle = GeometryCircleMixin.isPointInsideCircle, isPointOutsideAllCircles = GeometryCircleMixin.isPointOutsideAllCircles;
        // TODO: replace with individual imports
        var nelderMead = NelderMeadModule.nelderMead;
        var animObject = U.animObject, isArray = U.isArray, isNumber = U.isNumber, isObject = U.isObject, isString = U.isString;
        var addEvent = H.addEvent, color = H.Color, extend = H.extend, getCenterOfPoints = geometry.getCenterOfPoints, getDistanceBetweenPoints = geometry.getDistanceBetweenPoints, merge = H.merge, seriesType = H.seriesType, seriesTypes = H.seriesTypes;
        var objectValues = function objectValues(obj) {
            return Object.keys(obj).map(function (x) {
                return obj[x];
            });
        };
        /**
         * Calculates the area of overlap between a list of circles.
         * @private
         * @todo add support for calculating overlap between more than 2 circles.
         * @param {Array<Highcharts.CircleObject>} circles
         * List of circles with their given positions.
         * @return {number}
         * Returns the area of overlap between all the circles.
         */
        var getOverlapBetweenCircles = function getOverlapBetweenCircles(circles) {
            var overlap = 0;
            // When there is only two circles we can find the overlap by using their
            // radiuses and the distance between them.
            if (circles.length === 2) {
                var circle1 = circles[0];
                var circle2 = circles[1];
                overlap = getOverlapBetweenCirclesByDistance(circle1.r, circle2.r, getDistanceBetweenPoints(circle1, circle2));
            }
            return overlap;
        };
        /**
         * Calculates the difference between the desired overlap and the actual overlap
         * between two circles.
         * @private
         * @param {Dictionary<Highcharts.CircleObject>} mapOfIdToCircle
         * Map from id to circle.
         * @param {Array<Highcharts.VennRelationObject>} relations
         * List of relations to calculate the loss of.
         * @return {number}
         * Returns the loss between positions of the circles for the given relations.
         */
        var loss = function loss(mapOfIdToCircle, relations) {
            var precision = 10e10;
            // Iterate all the relations and calculate their individual loss.
            return relations.reduce(function (totalLoss, relation) {
                var loss = 0;
                if (relation.sets.length > 1) {
                    var wantedOverlap = relation.value;
                    // Calculate the actual overlap between the sets.
                    var actualOverlap = getOverlapBetweenCircles(
                    // Get the circles for the given sets.
                    relation.sets.map(function (set) {
                        return mapOfIdToCircle[set];
                    }));
                    var diff = wantedOverlap - actualOverlap;
                    loss = Math.round((diff * diff) * precision) / precision;
                }
                // Add calculated loss to the sum.
                return totalLoss + loss;
            }, 0);
        };
        /**
         * Finds the root of a given function. The root is the input value needed for
         * a function to return 0.
         *
         * See https://en.wikipedia.org/wiki/Bisection_method#Algorithm
         *
         * TODO: Add unit tests.
         *
         * @param {Function} f
         * The function to find the root of.
         * @param {number} a
         * The lowest number in the search range.
         * @param {number} b
         * The highest number in the search range.
         * @param {number} [tolerance=1e-10]
         * The allowed difference between the returned value and root.
         * @param {number} [maxIterations=100]
         * The maximum iterations allowed.
         * @return {number}
         * Root number.
         */
        var bisect = function bisect(f, a, b, tolerance, maxIterations) {
            var fA = f(a), fB = f(b), nMax = maxIterations || 100, tol = tolerance || 1e-10, delta = b - a, n = 1, x, fX;
            if (a >= b) {
                throw new Error('a must be smaller than b.');
            }
            else if (fA * fB > 0) {
                throw new Error('f(a) and f(b) must have opposite signs.');
            }
            if (fA === 0) {
                x = a;
            }
            else if (fB === 0) {
                x = b;
            }
            else {
                while (n++ <= nMax && fX !== 0 && delta > tol) {
                    delta = (b - a) / 2;
                    x = a + delta;
                    fX = f(x);
                    // Update low and high for next search interval.
                    if (fA * fX > 0) {
                        a = x;
                    }
                    else {
                        b = x;
                    }
                }
            }
            return x;
        };
        /**
         * Uses the bisection method to make a best guess of the ideal distance between
         * two circles too get the desired overlap.
         * Currently there is no known formula to calculate the distance from the area
         * of overlap, which makes the bisection method preferred.
         * @private
         * @param {number} r1
         * Radius of the first circle.
         * @param {number} r2
         * Radiues of the second circle.
         * @param {number} overlap
         * The wanted overlap between the two circles.
         * @return {number}
         * Returns the distance needed to get the wanted overlap between the two
         * circles.
         */
        var getDistanceBetweenCirclesByOverlap = function getDistanceBetweenCirclesByOverlap(r1, r2, overlap) {
            var maxDistance = r1 + r2, distance;
            if (overlap <= 0) {
                // If overlap is below or equal to zero, then there is no overlap.
                distance = maxDistance;
            }
            else if (getAreaOfCircle(r1 < r2 ? r1 : r2) <= overlap) {
                // When area of overlap is larger than the area of the smallest circle,
                // then it is completely overlapping.
                distance = 0;
            }
            else {
                distance = bisect(function (x) {
                    var actualOverlap = getOverlapBetweenCirclesByDistance(r1, r2, x);
                    // Return the differance between wanted and actual overlap.
                    return overlap - actualOverlap;
                }, 0, maxDistance);
            }
            return distance;
        };
        var isSet = function (x) {
            return isArray(x.sets) && x.sets.length === 1;
        };
        /**
         * Calculates a margin for a point based on the iternal and external circles.
         * The margin describes if the point is well placed within the internal circles,
         * and away from the external
         * @private
         * @todo add unit tests.
         * @param {Highcharts.PositionObject} point
         * The point to evaluate.
         * @param {Array<Highcharts.CircleObject>} internal
         * The internal circles.
         * @param {Array<Highcharts.CircleObject>} external
         * The external circles.
         * @return {number}
         * Returns the margin.
         */
        var getMarginFromCircles = function getMarginFromCircles(point, internal, external) {
            var margin = internal.reduce(function (margin, circle) {
                var m = circle.r - getDistanceBetweenPoints(point, circle);
                return (m <= margin) ? m : margin;
            }, Number.MAX_VALUE);
            margin = external.reduce(function (margin, circle) {
                var m = getDistanceBetweenPoints(point, circle) - circle.r;
                return (m <= margin) ? m : margin;
            }, margin);
            return margin;
        };
        /**
         * Finds the optimal label position by looking for a position that has a low
         * distance from the internal circles, and as large possible distane to the
         * external circles.
         * @private
         * @todo Optimize the intial position.
         * @todo Add unit tests.
         * @param {Array<Highcharts.CircleObject>} internal
         * Internal circles.
         * @param {Array<Highcharts.CircleObject>} external
         * External circles.
         * @return {Highcharts.PositionObject}
         * Returns the found position.
         */
        var getLabelPosition = function getLabelPosition(internal, external) {
            // Get the best label position within the internal circles.
            var best = internal.reduce(function (best, circle) {
                var d = circle.r / 2;
                // Give a set of points with the circle to evaluate as the best label
                // position.
                return [
                    { x: circle.x, y: circle.y },
                    { x: circle.x + d, y: circle.y },
                    { x: circle.x - d, y: circle.y },
                    { x: circle.x, y: circle.y + d },
                    { x: circle.x, y: circle.y - d }
                ]
                    // Iterate the given points and return the one with the largest
                    // margin.
                    .reduce(function (best, point) {
                    var margin = getMarginFromCircles(point, internal, external);
                    // If the margin better than the current best, then update best.
                    if (best.margin < margin) {
                        best.point = point;
                        best.margin = margin;
                    }
                    return best;
                }, best);
            }, {
                point: void 0,
                margin: -Number.MAX_VALUE
            }).point;
            // Use nelder mead to optimize the initial label position.
            var optimal = nelderMead(function (p) {
                return -(getMarginFromCircles({ x: p[0], y: p[1] }, internal, external));
            }, [best.x, best.y]);
            // Update best to be the point which was found to have the best margin.
            best = {
                x: optimal[0],
                y: optimal[1]
            };
            if (!(isPointInsideAllCircles(best, internal) &&
                isPointOutsideAllCircles(best, external))) {
                // If point was either outside one of the internal, or inside one of the
                // external, then it was invalid and should use a fallback.
                if (internal.length > 1) {
                    best = getCenterOfPoints(getCirclesIntersectionPolygon(internal));
                }
                else {
                    best = {
                        x: internal[0].x,
                        y: internal[0].y
                    };
                }
            }
            // Return the best point.
            return best;
        };
        /**
         * Finds the available width for a label, by taking the label position and
         * finding the largest distance, which is inside all internal circles, and
         * outside all external circles.
         *
         * @private
         * @param {Highcharts.PositionObject} pos
         * The x and y coordinate of the label.
         * @param {Array<Highcharts.CircleObject>} internal
         * Internal circles.
         * @param {Array<Highcharts.CircleObject>} external
         * External circles.
         * @return {number}
         * Returns available width for the label.
         */
        var getLabelWidth = function getLabelWidth(pos, internal, external) {
            var radius = internal.reduce(function (min, circle) {
                return Math.min(circle.r, min);
            }, Infinity), 
            // Filter out external circles that are completely overlapping.
            filteredExternals = external.filter(function (circle) {
                return !isPointInsideCircle(pos, circle);
            });
            var findDistance = function (maxDistance, direction) {
                return bisect(function (x) {
                    var testPos = {
                        x: pos.x + (direction * x),
                        y: pos.y
                    }, isValid = (isPointInsideAllCircles(testPos, internal) &&
                        isPointOutsideAllCircles(testPos, filteredExternals));
                    // If the position is valid, then we want to move towards the max
                    // distance. If not, then we want to  away from the max distance.
                    return -(maxDistance - x) + (isValid ? 0 : Number.MAX_VALUE);
                }, 0, maxDistance);
            };
            // Find the smallest distance of left and right.
            return Math.min(findDistance(radius, -1), findDistance(radius, 1)) * 2;
        };
        /**
         * Calulates data label values for a given relations object.
         *
         * @private
         * @todo add unit tests
         * @param {Highcharts.VennRelationObject} relation A relations object.
         * @param {Array<Highcharts.VennRelationObject>} setRelations The list of
         * relations that is a set.
         * @return {Highcharts.VennLabelValuesObject}
         * Returns an object containing position and width of the label.
         */
        function getLabelValues(relation, setRelations) {
            var sets = relation.sets;
            // Create a list of internal and external circles.
            var data = setRelations.reduce(function (data, set) {
                // If the set exists in this relation, then it is internal,
                // otherwise it will be external.
                var isInternal = sets.indexOf(set.sets[0]) > -1;
                var property = isInternal ? 'internal' : 'external';
                // Add the circle to the list.
                data[property].push(set.circle);
                return data;
            }, {
                internal: [],
                external: []
            });
            // Filter out external circles that are completely overlapping all internal
            data.external = data.external.filter(function (externalCircle) {
                return data.internal.some(function (internalCircle) {
                    return !isCircle1CompletelyOverlappingCircle2(externalCircle, internalCircle);
                });
            });
            // Calulate the label position.
            var position = getLabelPosition(data.internal, data.external);
            // Calculate the label width
            var width = getLabelWidth(position, data.internal, data.external);
            return {
                position: position,
                width: width
            };
        }
        /**
         * Takes an array of relations and adds the properties `totalOverlap` and
         * `overlapping` to each set. The property `totalOverlap` is the sum of value
         * for each relation where this set is included. The property `overlapping` is
         * a map of how much this set is overlapping another set.
         * NOTE: This algorithm ignores relations consisting of more than 2 sets.
         * @private
         * @param {Array<Highcharts.VennRelationObject>} relations
         * The list of relations that should be sorted.
         * @return {Array<Highcharts.VennRelationObject>}
         * Returns the modified input relations with added properties `totalOverlap` and
         * `overlapping`.
         */
        var addOverlapToSets = function addOverlapToSets(relations) {
            // Calculate the amount of overlap per set.
            var mapOfIdToProps = relations
                // Filter out relations consisting of 2 sets.
                .filter(function (relation) {
                return relation.sets.length === 2;
            })
                // Sum up the amount of overlap for each set.
                .reduce(function (map, relation) {
                var sets = relation.sets;
                sets.forEach(function (set, i, arr) {
                    if (!isObject(map[set])) {
                        map[set] = {
                            overlapping: {},
                            totalOverlap: 0
                        };
                    }
                    map[set].totalOverlap += relation.value;
                    map[set].overlapping[arr[1 - i]] = relation.value;
                });
                return map;
            }, {});
            relations
                // Filter out single sets
                .filter(isSet)
                // Extend the set with the calculated properties.
                .forEach(function (set) {
                var properties = mapOfIdToProps[set.sets[0]];
                extend(set, properties);
            });
            // Returns the modified relations.
            return relations;
        };
        /**
         * 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.
         */
        var sortByTotalOverlap = function sortByTotalOverlap(a, b) {
            return b.totalOverlap - a.totalOverlap;
        };
        /**
         * Uses a greedy approach to position all the sets. Works well with a small
         * number of sets, and are in these cases a good choice aesthetically.
         * @private
         * @param {Array<object>} relations List of the overlap between two or more
         * sets, or the size of a single set.
         * @return {Array<object>} List of circles and their calculated positions.
         */
        var layoutGreedyVenn = function layoutGreedyVenn(relations) {
            var positionedSets = [], mapOfIdToCircles = {};
            // Define a circle for each set.
            relations
                .filter(function (relation) {
                return relation.sets.length === 1;
            }).forEach(function (relation) {
                mapOfIdToCircles[relation.sets[0]] = relation.circle = {
                    x: Number.MAX_VALUE,
                    y: Number.MAX_VALUE,
                    r: Math.sqrt(relation.value / Math.PI)
                };
            });
            /**
             * Takes a set and updates the position, and add the set to the list of
             * positioned sets.
             * @private
             * @param {object} set
             * The set to add to its final position.
             * @param {object} coordinates
             * The coordinates to position the set at.
             * @return {void}
             */
            var positionSet = function positionSet(set, coordinates) {
                var circle = set.circle;
                circle.x = coordinates.x;
                circle.y = coordinates.y;
                positionedSets.push(set);
            };
            // Find overlap between sets. Ignore relations with more then 2 sets.
            addOverlapToSets(relations);
            // Sort sets by the sum of their size from large to small.
            var sortedByOverlap = relations
                .filter(isSet)
                .sort(sortByTotalOverlap);
            // Position the most overlapped set at 0,0.
            positionSet(sortedByOverlap.shift(), { x: 0, y: 0 });
            var relationsWithTwoSets = relations.filter(function (x) {
                return x.sets.length === 2;
            });
            // Iterate and position the remaining sets.
            sortedByOverlap.forEach(function (set) {
                var circle = set.circle, radius = circle.r, overlapping = set.overlapping;
                var bestPosition = positionedSets
                    .reduce(function (best, positionedSet, i) {
                    var positionedCircle = positionedSet.circle, overlap = overlapping[positionedSet.sets[0]];
                    // Calculate the distance between the sets to get the correct
                    // overlap
                    var distance = getDistanceBetweenCirclesByOverlap(radius, positionedCircle.r, overlap);
                    // Create a list of possible coordinates calculated from
                    // distance.
                    var possibleCoordinates = [
                        { x: positionedCircle.x + distance, y: positionedCircle.y },
                        { x: positionedCircle.x - distance, y: positionedCircle.y },
                        { x: positionedCircle.x, y: positionedCircle.y + distance },
                        { x: positionedCircle.x, y: positionedCircle.y - distance }
                    ];
                    // If there are more circles overlapping, then add the
                    // intersection points as possible positions.
                    positionedSets.slice(i + 1).forEach(function (positionedSet2) {
                        var positionedCircle2 = positionedSet2.circle, overlap2 = overlapping[positionedSet2.sets[0]], distance2 = getDistanceBetweenCirclesByOverlap(radius, positionedCircle2.r, overlap2);
                        // Add intersections to list of coordinates.
                        possibleCoordinates = possibleCoordinates.concat(getCircleCircleIntersection({
                            x: positionedCircle.x,
                            y: positionedCircle.y,
                            r: distance
                        }, {
                            x: positionedCircle2.x,
                            y: positionedCircle2.y,
                            r: distance2
                        }));
                    });
                    // Iterate all suggested coordinates and find the best one.
                    possibleCoordinates.forEach(function (coordinates) {
                        circle.x = coordinates.x;
                        circle.y = coordinates.y;
                        // Calculate loss for the suggested coordinates.
                        var currentLoss = loss(mapOfIdToCircles, relationsWithTwoSets);
                        // If the loss is better, then use these new coordinates.
                        if (currentLoss < best.loss) {
                            best.loss = currentLoss;
                            best.coordinates = coordinates;
                        }
                    });
                    // Return resulting coordinates.
                    return best;
                }, {
                    loss: Number.MAX_VALUE,
                    coordinates: void 0
                });
                // Add the set to its final position.
                positionSet(set, bestPosition.coordinates);
            });
            // Return the positions of each set.
            return mapOfIdToCircles;
        };
        /**
         * Calculates the positions, and the label values of all the sets in the venn
         * diagram.
         *
         * @private
         * @todo Add support for constrained MDS.
         * @param {Array<Highchats.VennRelationObject>} relations
         * List of the overlap between two or more sets, or the size of a single set.
         * @return {Highcharts.Dictionary<*>}
         * List of circles and their calculated positions.
         */
        function layout(relations) {
            var mapOfIdToShape = {};
            var mapOfIdToLabelValues = {};
            // Calculate best initial positions by using greedy layout.
            if (relations.length > 0) {
                var mapOfIdToCircles_1 = layoutGreedyVenn(relations);
                var setRelations_1 = relations.filter(isSet);
                relations
                    .forEach(function (relation) {
                    var sets = relation.sets;
                    var id = sets.join();
                    // Get shape from map of circles, or calculate intersection.
                    var shape = isSet(relation) ?
                        mapOfIdToCircles_1[id] :
                        getAreaOfIntersectionBetweenCircles(sets.map(function (set) {
                            return mapOfIdToCircles_1[set];
                        }));
                    // Calculate label values if the set has a shape
                    if (shape) {
                        mapOfIdToShape[id] = shape;
                        mapOfIdToLabelValues[id] = getLabelValues(relation, setRelations_1);
                    }
                });
            }
            return { mapOfIdToShape: mapOfIdToShape, mapOfIdToLabelValues: mapOfIdToLabelValues };
        }
        var isValidRelation = function (x) {
            var map = {};
            return (isObject(x) &&
                (isNumber(x.value) && x.value > -1) &&
                (isArray(x.sets) && x.sets.length > 0) &&
                !x.sets.some(function (set) {
                    var invalid = false;
                    if (!map[set] && isString(set)) {
                        map[set] = true;
                    }
                    else {
                        invalid = true;
                    }
                    return invalid;
                }));
        };
        var isValidSet = function (x) {
            return (isValidRelation(x) && isSet(x) && x.value > 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.
         */
        var processVennData = 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 objectValues(mapOfIdToRelation);
        };
        /**
         * Calculates the proper scale to fit the cloud inside the plotting area.
         * @private
         * @todo add unit test
         * @param {number} targetWidth
         * Width of target area.
         * @param {number} targetHeight
         * Height of target area.
         * @param {Highcharts.PolygonBoxObject} field
         * The playing field.
         * @return {Highcharts.Dictionary<number>}
         * Returns the value to scale the playing field up to the size of the target
         * area, and center of x and y.
         */
        var getScale = function getScale(targetWidth, targetHeight, field) {
            var height = field.bottom - field.top, // top is smaller than bottom
            width = field.right - field.left, scaleX = width > 0 ? 1 / width * targetWidth : 1, scaleY = height > 0 ? 1 / height * targetHeight : 1, adjustX = (field.right + field.left) / 2, adjustY = (field.top + field.bottom) / 2, scale = Math.min(scaleX, scaleY);
            return {
                scale: scale,
                centerX: targetWidth / 2 - adjustX * scale,
                centerY: targetHeight / 2 - adjustY * scale
            };
        };
        /**
         * If a circle is outside a give field, then the boundaries of the field is
         * adjusted accordingly. Modifies the field object which is passed as the first
         * parameter.
         * @private
         * @todo NOTE: Copied from wordcloud, can probably be unified.
         * @param {Highcharts.PolygonBoxObject} field
         * The bounding box of a playing field.
         * @param {Highcharts.CircleObject} circle
         * The bounding box for a placed point.
         * @return {Highcharts.PolygonBoxObject}
         * Returns a modified field object.
         */
        var updateFieldBoundaries = function updateFieldBoundaries(field, circle) {
            var left = circle.x - circle.r, right = circle.x + circle.r, bottom = circle.y + circle.r, top = circle.y - circle.r;
            // TODO improve type checking.
            if (!isNumber(field.left) || field.left > left) {
                field.left = left;
            }
            if (!isNumber(field.right) || field.right < right) {
                field.right = right;
            }
            if (!isNumber(field.top) || field.top > top) {
                field.top = top;
            }
            if (!isNumber(field.bottom) || field.bottom < bottom) {
                field.bottom = bottom;
            }
            return field;
        };
        /**
         * A Venn diagram displays all possible logical relations between a collection
         * of different sets. The sets are represented by circles, and the relation
         * between the sets are displayed by the overlap or lack of overlap between
         * them. The venn diagram is a special case of Euler diagrams, which can also
         * be displayed by this series type.
         *
         * @sample {highcharts} highcharts/demo/venn-diagram/
         *         Venn diagram
         * @sample {highcharts} highcharts/demo/euler-diagram/
         *         Euler diagram
         *
         * @extends      plotOptions.scatter
         * @excluding    connectEnds, connectNulls, cropThreshold, dragDrop,
         *               findNearestPointBy, getExtremesFromAll, jitter, label, linecap,
         *               lineWidth, linkedTo, marker, negativeColor, pointInterval,
         *               pointIntervalUnit, pointPlacement, pointStart, softThreshold,
         *               stacking, steps, threshold, xAxis, yAxis, zoneAxis, zones
         * @product      highcharts
         * @requires     modules/venn
         * @optionparent plotOptions.venn
         */
        var vennOptions = {
            borderColor: '#cccccc',
            borderDashStyle: 'solid',
            borderWidth: 1,
            brighten: 0,
            clip: false,
            colorByPoint: true,
            dataLabels: {
                enabled: true,
                verticalAlign: 'middle',
                formatter: function () {
                    return this.point.name;
                }
            },
            /**
             * @ignore-option
             * @private
             */
            inactiveOtherPoints: true,
            marker: false,
            opacity: 0.75,
            showInLegend: false,
            states: {
                /**
                 * @excluding halo
                 */
                hover: {
                    opacity: 1,
                    borderColor: '#333333'
                },
                /**
                 * @excluding halo
                 */
                select: {
                    color: '#cccccc',
                    borderColor: '#000000',
                    animation: false
                }
            },
            tooltip: {
                pointFormat: '{point.name}: {point.value}'
            }
        };
        var vennSeries = {
            isCartesian: false,
            axisTypes: [],
            directTouch: true,
            pointArrayMap: ['value'],
            translate: function () {
                var chart = this.chart;
                this.processedXData = this.xData;
                this.generatePoints();
                // Process the data before passing it into the layout function.
                var relations = processVennData(this.options.data);
                // Calculate the positions of each circle.
                var _a = layout(relations), mapOfIdToShape = _a.mapOfIdToShape, mapOfIdToLabelValues = _a.mapOfIdToLabelValues;
                // Calculate the scale, and center of the plot area.
                var field = Object.keys(mapOfIdToShape)
                    .filter(function (key) {
                    var shape = mapOfIdToShape[key];
                    return shape && isNumber(shape.r);
                })
                    .reduce(function (field, key) {
                    return updateFieldBoundaries(field, mapOfIdToShape[key]);
                }, { top: 0, bottom: 0, left: 0, right: 0 }), scaling = getScale(chart.plotWidth, chart.plotHeight, field), scale = scaling.scale, centerX = scaling.centerX, centerY = scaling.centerY;
                // Iterate all points and calculate and draw their graphics.
                this.points.forEach(function (point) {
                    var sets = isArray(point.sets) ? point.sets : [], id = sets.join(), shape = mapOfIdToShape[id], shapeArgs, dataLabelValues = mapOfIdToLabelValues[id] || {}, dataLabelWidth = dataLabelValues.width, dataLabelPosition = dataLabelValues.position, dlOptions = point.options && point.options.dataLabels;
                    if (shape) {
                        if (shape.r) {
                            shapeArgs = {
                                x: centerX + shape.x * scale,
                                y: centerY + shape.y * scale,
                                r: shape.r * scale
                            };
                        }
                        else if (shape.d) {
                            // TODO: find a better way to handle scaling of a path.
                            var d = shape.d.reduce(function (path, arr) {
                                if (arr[0] === 'M') {
                                    arr[1] = centerX + arr[1] * scale;
                                    arr[2] = centerY + arr[2] * scale;
                                }
                                else if (arr[0] === 'A') {
                                    arr[1] = arr[1] * scale;
                                    arr[2] = arr[2] * scale;
                                    arr[6] = centerX + arr[6] * scale;
                                    arr[7] = centerY + arr[7] * scale;
                                }
                                return path.concat(arr);
                            }, [])
                                .join(' ');
                            shapeArgs = {
                                d: d
                            };
                        }
                        // Scale the position for the data label.
                        if (dataLabelPosition) {
                            dataLabelPosition.x = centerX + dataLabelPosition.x * scale;
                            dataLabelPosition.y = centerY + dataLabelPosition.y * scale;
                        }
                        else {
                            dataLabelPosition = {};
                        }
                        if (isNumber(dataLabelWidth)) {
                            dataLabelWidth = Math.round(dataLabelWidth * scale);
                        }
                    }
                    point.shapeArgs = shapeArgs;
                    // Placement for the data labels
                    if (dataLabelPosition && shapeArgs) {
                        point.plotX = dataLabelPosition.x;
                        point.plotY = dataLabelPosition.y;
                    }
                    // Add width for the data label
                    if (dataLabelWidth && shapeArgs) {
                        point.dlOptions = merge(true, {
                            style: {
                                width: dataLabelWidth
                            }
                        }, isObject(dlOptions) && dlOptions);
                    }
                    // Set name for usage in tooltip and in data label.
                    point.name = point.options.name || sets.join('∩');
                });
            },
            /* eslint-disable valid-jsdoc */
            /**
             * Draw the graphics for each point.
             * @private
             */
            drawPoints: function () {
                var series = this, 
                // Series properties
                chart = series.chart, group = series.group, points = series.points || [], 
                // Chart properties
                renderer = chart.renderer;
                // Iterate all points and calculate and draw their graphics.
                points.forEach(function (point) {
                    var attribs = {
                        zIndex: isArray(point.sets) ? point.sets.length : 0
                    }, shapeArgs = point.shapeArgs;
                    // Add point attribs
                    if (!chart.styledMode) {
                        extend(attribs, series.pointAttribs(point, point.state));
                    }
                    // Draw the point graphic.
                    point.draw({
                        isNew: !point.graphic,
                        animatableAttribs: shapeArgs,
                        attribs: attribs,
                        group: group,
                        renderer: renderer,
                        shapeType: shapeArgs && shapeArgs.d ? 'path' : 'circle'
                    });
                });
            },
            /**
             * Calculates the style attributes for a point. The attributes can vary
             * depending on the state of the point.
             * @private
             * @param {Highcharts.Point} point
             * The point which will get the resulting attributes.
             * @param {string} [state]
             * The state of the point.
             * @return {Highcharts.SVGAttributes}
             * Returns the calculated attributes.
             */
            pointAttribs: function (point, state) {
                var series = this, seriesOptions = series.options || {}, pointOptions = point && point.options || {}, stateOptions = (state && seriesOptions.states[state]) || {}, options = merge(seriesOptions, { color: point && point.color }, pointOptions, stateOptions);
                // Return resulting values for the attributes.
                return {
                    'fill': color(options.color)
                        .setOpacity(options.opacity)
                        .brighten(options.brightness)
                        .get(),
                    'stroke': options.borderColor,
                    'stroke-width': options.borderWidth,
                    'dashstyle': options.borderDashStyle
                };
            },
            /* eslint-enable valid-jsdoc */
            animate: function (init) {
                if (!init) {
                    var series = this, animOptions = animObject(series.options.animation);
                    series.points.forEach(function (point) {
                        var args = point.shapeArgs;
                        if (point.graphic && args) {
                            var attr = {}, animate = {};
                            if (args.d) {
                                // If shape is a path, then animate opacity.
                                attr.opacity = 0.001;
                            }
                            else {
                                // If shape is a circle, then animate radius.
                                attr.r = 0;
                                animate.r = args.r;
                            }
                            point.graphic
                                .attr(attr)
                                .animate(animate, animOptions);
                            // If shape is path, then fade it in after the circles
                            // animation
                            if (args.d) {
                                setTimeout(function () {
                                    if (point && point.graphic) {
                                        point.graphic.animate({
                                            opacity: 1
                                        });
                                    }
                                }, animOptions.duration);
                            }
                        }
                    }, series);
                    series.animate = null;
                }
            },
            utils: {
                addOverlapToSets: addOverlapToSets,
                geometry: geometry,
                geometryCircles: GeometryCircleMixin,
                getLabelWidth: getLabelWidth,
                getMarginFromCircles: getMarginFromCircles,
                getDistanceBetweenCirclesByOverlap: getDistanceBetweenCirclesByOverlap,
                layoutGreedyVenn: layoutGreedyVenn,
                loss: loss,
                nelderMead: NelderMeadModule,
                processVennData: processVennData,
                sortByTotalOverlap: sortByTotalOverlap
            }
        };
        var vennPoint = {
            draw: draw,
            shouldDraw: function () {
                var point = this;
                // Only draw points with single sets.
                return !!point.shapeArgs;
            },
            isValid: function () {
                return isNumber(this.value);
            }
        };
        /**
         * A `venn` series. If the [type](#series.venn.type) option is
         * not specified, it is inherited from [chart.type](#chart.type).
         *
         * @extends   series,plotOptions.venn
         * @excluding connectEnds, connectNulls, cropThreshold, dataParser, dataURL,
         *            findNearestPointBy, getExtremesFromAll, label, linecap, lineWidth,
         *            linkedTo, marker, negativeColor, pointInterval, pointIntervalUnit,
         *            pointPlacement, pointStart, softThreshold, stack, stacking, steps,
         *            threshold, xAxis, yAxis, zoneAxis, zones
         * @product   highcharts
         * @requires  modules/venn
         * @apioption series.venn
         */
        /**
         * @type      {Array<*>}
         * @extends   series.scatter.data
         * @excluding marker, x, y
         * @product   highcharts
         * @apioption series.venn.data
         */
        /**
         * The name of the point. Used in data labels and tooltip. If name is not
         * defined then it will default to the joined values in
         * [sets](#series.venn.sets).
         *
         * @sample {highcharts} highcharts/demo/venn-diagram/
         *         Venn diagram
         * @sample {highcharts} highcharts/demo/euler-diagram/
         *         Euler diagram
         *
         * @type      {number}
         * @since     7.0.0
         * @product   highcharts
         * @apioption series.venn.data.name
         */
        /**
         * The value of the point, resulting in a relative area of the circle, or area
         * of overlap between two sets in the venn or euler diagram.
         *
         * @sample {highcharts} highcharts/demo/venn-diagram/
         *         Venn diagram
         * @sample {highcharts} highcharts/demo/euler-diagram/
         *         Euler diagram
         *
         * @type      {number}
         * @since     7.0.0
         * @product   highcharts
         * @apioption series.venn.data.value
         */
        /**
         * The set or sets the options will be applied to. If a single entry is defined,
         * then it will create a new set. If more than one entry is defined, then it
         * will define the overlap between the sets in the array.
         *
         * @sample {highcharts} highcharts/demo/venn-diagram/
         *         Venn diagram
         * @sample {highcharts} highcharts/demo/euler-diagram/
         *         Euler diagram
         *
         * @type      {Array<string>}
         * @since     7.0.0
         * @product   highcharts
         * @apioption series.venn.data.sets
         */
        /**
         * @excluding halo
         * @apioption series.venn.states.hover
         */
        /**
         * @excluding halo
         * @apioption series.venn.states.select
         */
        /**
         * @private
         * @class
         * @name Highcharts.seriesTypes.venn
         *
         * @augments Highcharts.Series
         */
        seriesType('venn', 'scatter', vennOptions, vennSeries, vennPoint);
        /* eslint-disable no-invalid-this */
        // Modify final series options.
        addEvent(seriesTypes.venn, 'afterSetOptions', function (e) {
            var options = e.options, states = options.states;
            if (this instanceof seriesTypes.venn) {
                // Explicitly disable all halo options.
                Object.keys(states).forEach(function (state) {
                    states[state].halo = false;
                });
            }
        });

    });
    _registerModule(_modules, 'masters/modules/venn.src.js', [], function () {


    });
}));