highcharts
Version:
JavaScript charting framework
1,195 lines (1,190 loc) • 77.3 kB
JavaScript
/**
* @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) {