whitesource
Version:
whitesource node module
772 lines (657 loc) • 29.6 kB
JavaScript
/*
* D3 Venn Diagram Code by Ben Fred
* Released under MIT license
* Examples and source code available on GitHub:
* https://github.com/benfred/venn.js
* */
(function(venn) {
"use strict";
/** given a list of set objects, and their corresponding overlaps.
updates the (x, y, radius) attribute on each set such that their positions
roughly correspond to the desired overlaps */
venn.venn = function(sets, overlaps, parameters) {
parameters = parameters || {};
parameters.maxIterations = parameters.maxIterations || 500;
var lossFunction = parameters.lossFunction || venn.lossFunction;
var initialLayout = parameters.layoutFunction || venn.greedyLayout;
// initial layout is done greedily
sets = initialLayout(sets, overlaps);
// transform x/y coordinates to a vector to optimize
var initial = new Array(2*sets.length);
for (var i = 0; i < sets.length; ++i) {
initial[2 * i] = sets[i].x;
initial[2 * i + 1] = sets[i].y;
}
// optimize initial layout from our loss function
var totalFunctionCalls = 0;
var solution = venn.fmin(
function(values) {
totalFunctionCalls += 1;
var current = new Array(sets.length);
for (var i = 0; i < sets.length; ++i) {
current[i] = {x: values[2 * i],
y: values[2 * i + 1],
radius : sets[i].radius,
size : sets[i].size};
}
return lossFunction(current, overlaps);
},
initial,
parameters);
// transform solution vector back to x/y points
var positions = solution.solution;
for (i = 0; i < sets.length; ++i) {
sets[i].x = positions[2 * i];
sets[i].y = positions[2 * i + 1];
}
return sets;
};
/** Returns the distance necessary for two circles of radius r1 + r2 to
have the overlap area 'overlap' */
venn.distanceFromIntersectArea = function(r1, r2, overlap) {
// handle complete overlapped circles
if (Math.min(r1, r2) * Math.min(r1,r2) * Math.PI <= overlap) {
return Math.abs(r1 - r2);
}
return venn.bisect(function(distance) {
return circleIntersection.circleOverlap(r1, r2, distance) - overlap;
}, 0, r1 + r2);
};
/// gets a matrix of euclidean distances between all sets in venn diagram
venn.getDistanceMatrix = function(sets, overlaps) {
// initialize an empty distance matrix between all the points
var distances = [];
for (var i = 0; i < sets.length; ++i) {
distances.push([]);
for (var j = 0; j < sets.length; ++j) {
distances[i].push(0);
}
}
// compute distances between all the points
for (var i = 0; i < overlaps.length; ++i) {
var current = overlaps[i];
if (current.sets.length !== 2) {
continue;
}
var left = current.sets[0],
right = current.sets[1],
r1 = Math.sqrt(sets[left].size / Math.PI),
r2 = Math.sqrt(sets[right].size / Math.PI),
distance = venn.distanceFromIntersectArea(r1, r2, current.size);
distances[left][right] = distances[right][left] = distance;
}
return distances;
};
/** Lays out a Venn diagram greedily, going from most overlapped sets to
least overlapped, attempting to position each new set such that the
overlapping areas to already positioned sets are basically right */
venn.greedyLayout = function(sets, overlaps) {
// give each set a default position + radius
var setOverlaps = {};
for (var i = 0; i < sets.length; ++i) {
setOverlaps[i] = [];
sets[i].radius = Math.sqrt(sets[i].size / Math.PI);
sets[i].x = sets[i].y = 0;
}
// map each set to a list of all the other sets that overlap it
for (i = 0; i < overlaps.length; ++i) {
var current = overlaps[i];
if (current.sets.length !== 2) {
continue;
}
var left = current.sets[0], right = current.sets[1];
setOverlaps[left].push ({set:right, size:current.size});
setOverlaps[right].push({set:left, size:current.size});
}
// get list of most overlapped sets
var mostOverlapped = [];
for (var set in setOverlaps) {
if (setOverlaps.hasOwnProperty(set)) {
var size = 0;
for (i = 0; i < setOverlaps[set].length; ++i) {
size += setOverlaps[set][i].size;
}
mostOverlapped.push({set: set, size:size});
}
}
// sort by size desc
function sortOrder(a,b) {
return b.size - a.size;
}
mostOverlapped.sort(sortOrder);
// keep track of what sets have been laid out
var positioned = {};
function isPositioned(element) {
return element.set in positioned;
}
// adds a point to the output
function positionSet(point, index) {
sets[index].x = point.x;
sets[index].y = point.y;
positioned[index] = true;
}
// add most overlapped set at (0,0)
positionSet({x: 0, y: 0}, mostOverlapped[0].set);
// get distances between all points
var distances = venn.getDistanceMatrix(sets, overlaps);
for (i = 1; i < mostOverlapped.length; ++i) {
var setIndex = mostOverlapped[i].set,
set = sets[setIndex],
overlap = setOverlaps[setIndex].filter(isPositioned);
overlap.sort(sortOrder);
if (overlap.length === 0) {
throw "Need overlap information for set " + JSON.stringify( set );
}
var points = [];
for (var j = 0; j < overlap.length; ++j) {
// get appropriate distance from most overlapped already added set
var p1 = sets[overlap[j].set],
d1 = distances[setIndex][overlap[j].set];
// sample positions at 90 degrees for maximum aesthetics
points.push({x : p1.x + d1, y : p1.y});
points.push({x : p1.x - d1, y : p1.y});
points.push({y : p1.y + d1, x : p1.x});
points.push({y : p1.y - d1, x : p1.x});
// if we have at least 2 overlaps, then figure out where the
// set should be positioned analytically and try those too
for (var k = j + 1; k < overlap.length; ++k) {
var p2 = sets[overlap[k].set],
d2 = distances[setIndex][overlap[k].set];
var extraPoints = circleIntersection.circleCircleIntersection(
{ x: p1.x, y: p1.y, radius: d1},
{ x: p2.x, y: p2.y, radius: d2});
for (var l = 0; l < extraPoints.length; ++l) {
points.push(extraPoints[l]);
}
}
}
// we have some candidate positions for the set, examine loss
// at each position to figure out where to put it at
var bestLoss = 1e50, bestPoint = points[0];
for (var j = 0; j < points.length; ++j) {
sets[setIndex].x = points[j].x;
sets[setIndex].y = points[j].y;
var loss = venn.lossFunction(sets, overlaps);
if (loss < bestLoss) {
bestLoss = loss;
bestPoint = points[j];
}
}
positionSet(bestPoint, setIndex);
}
return sets;
};
/// Uses multidimensional scaling to approximate a first layout here
venn.classicMDSLayout = function(sets, overlaps) {
// get the distance matrix
var distances = venn.getDistanceMatrix(sets, overlaps);
// get positions for each set
var positions = mds.classic(distances);
// translate back to (x,y,radius) coordinates
for (var i = 0; i < sets.length; ++i) {
sets[i].x = positions[i][0];
sets[i].y = positions[i][1];
sets[i].radius = Math.sqrt(sets[i].size / Math.PI);
}
return sets;
};
/** Given a bunch of sets, and the desired overlaps between these sets - computes
the distance from the actual overlaps to the desired overlaps. Note that
this method ignores overlaps of more than 2 circles */
venn.lossFunction = function(sets, overlaps) {
var output = 0;
function getCircles(indices) {
return indices.map(function(i) { return sets[i]; });
}
for (var i = 0; i < overlaps.length; ++i) {
var area = overlaps[i], overlap;
if (area.sets.length == 2) {
var left = sets[area.sets[0]],
right = sets[area.sets[1]];
overlap = circleIntersection.circleOverlap(left.radius, right.radius,
circleIntersection.distance(left, right));
} else {
overlap = circleIntersection.intersectionArea(getCircles(area.sets));
}
output += (overlap - area.size) * (overlap - area.size);
}
return output;
};
/** Scales a solution from venn.venn or venn.greedyLayout such that it fits in
a rectangle of width/height - with padding around the borders. */
venn.scaleSolution = function(solution, width, height, padding) {
var minMax = function(d) {
var hi = Math.max.apply(null, solution.map(
function(c) { return c[d] + c.radius; } )),
lo = Math.min.apply(null, solution.map(
function(c) { return c[d] - c.radius;} ));
return {max:hi, min:lo};
};
width -= 2*padding;
height -= 2*padding;
var xRange = minMax('x'),
yRange = minMax('y'),
xScaling = width / (xRange.max - xRange.min),
yScaling = height / (yRange.max - yRange.min),
scaling = Math.min(yScaling, xScaling);
for (var i = 0; i < solution.length; ++i) {
var set = solution[i];
set.radius = scaling * set.radius;
set.x = padding + (set.x - xRange.min) * scaling;
set.y = padding + (set.y - yRange.min) * scaling;
}
solution.scaling = scaling;
return solution;
};
function weightedSum(a, b) {
var ret = new Array(a[1].length || 0);
for (var j = 0; j < ret.length; ++j) {
ret[j] = a[0] * a[1][j] + b[0] * b[1][j];
}
return ret;
}
function centerVennDiagram( diagram, width, height, padding ) {
var diagramBoundaries;
var allowedWidth = width - ( 2 * ( padding || 0 ) );
var allowedHeight = height - ( 2 * ( padding || 0 ) );
var scale;
var transformX, transformY;
var transform = "";
if ( diagram ) {
diagramBoundaries = diagram[ 0 ][ 0 ].getBBox();
if ( diagramBoundaries && width && height ) {
// See if we need to scale to fit the width/height
if ( diagramBoundaries.width > allowedWidth ) {
scale = allowedWidth / diagramBoundaries.width;
}
if ( diagramBoundaries.height > allowedHeight ) {
if ( !scale || ( allowedHeight / diagramBoundaries.height ) < scale ) {
scale = allowedHeight / diagramBoundaries.height;
}
}
if ( scale ) {
transform = "scale(" + scale + ")";
}
else {
scale = 1;
}
transformX = Math.floor( ( allowedWidth - ( diagramBoundaries.width * scale ) ) / 2 );
transformY = Math.floor( ( allowedHeight - ( diagramBoundaries.height * scale ) ) / 2 );
diagram.attr( "transform", "translate(" + transformX + "," + transformY + ") " + transform );
}
}
}
/** finds the zeros of a function, given two starting points (which must
* have opposite signs */
venn.bisect = function(f, a, b, parameters) {
parameters = parameters || {};
var maxIterations = parameters.maxIterations || 100,
tolerance = parameters.tolerance || 1e-10,
fA = f(a),
fB = f(b),
delta = b - a;
if (fA * fB > 0) {
throw "Initial bisect points must have opposite signs";
}
if (fA == 0) return a;
if (fB == 0) return b;
for (var i = 0; i < maxIterations; ++i) {
delta /= 2;
var mid = a + delta,
fMid = f(mid);
if (fMid * fA >= 0) {
a = mid;
}
if ((Math.abs(delta) < tolerance) || (fMid == 0)) {
return mid;
}
}
return a + delta;
}
/** minimizes a function using the downhill simplex method */
venn.fmin = function(f, x0, parameters) {
parameters = parameters || {};
var maxIterations = parameters.maxIterations || x0.length * 200,
nonZeroDelta = parameters.nonZeroDelta || 1.1,
zeroDelta = parameters.zeroDelta || 0.001,
minErrorDelta = parameters.minErrorDelta || 1e-5,
rho = parameters.rho || 1,
chi = parameters.chi || 2,
psi = parameters.psi || -0.5,
sigma = parameters.sigma || 0.5,
callback = parameters.callback;
// initialize simplex.
var N = x0.length,
simplex = new Array(N + 1);
simplex[0] = x0;
simplex[0].fx = f(x0);
for (var i = 0; i < N; ++i) {
var point = x0.slice();
point[i] = point[i] ? point[i] * nonZeroDelta : zeroDelta;
simplex[i+1] = point;
simplex[i+1].fx = f(point);
}
var sortOrder = function(a, b) { return a.fx - b.fx; };
for (var iteration = 0; iteration < maxIterations; ++iteration) {
simplex.sort(sortOrder);
if (callback) {
callback(simplex);
}
if (Math.abs(simplex[0].fx - simplex[N].fx) < minErrorDelta) {
break;
}
// compute the centroid of all but the worst point in the simplex
var centroid = new Array(N);
for (i = 0; i < N; ++i) {
centroid[i] = 0;
for (var j = 0; j < N; ++j) {
centroid[i] += simplex[j][i];
}
centroid[i] /= N;
}
// reflect the worst point past the centroid and compute loss at reflected
// point
var worst = simplex[N];
var reflected = weightedSum([1+rho, centroid], [-rho, worst]);
reflected.fx = f(reflected);
var replacement = reflected;
// if the reflected point is the best seen, then possibly expand
if (reflected.fx <= simplex[0].fx) {
var expanded = weightedSum([1+chi, centroid], [-chi, worst]);
expanded.fx = f(expanded);
if (expanded.fx < reflected.fx) {
replacement = expanded;
}
}
// if the reflected point is worse than the second worst, we need to
// contract
else if (reflected.fx >= simplex[N-1].fx) {
var shouldReduce = false;
var contracted;
if (reflected.fx <= worst.fx) {
// do an inside contraction
contracted = weightedSum([1+psi, centroid], [-psi, worst]);
contracted.fx = f(contracted);
if (contracted.fx < worst.fx) {
replacement = contracted;
} else {
shouldReduce = true;
}
} else {
// do an outside contraction
contracted = weightedSum([1-psi * rho, centroid], [psi*rho, worst]);
contracted.fx = f(contracted);
if (contracted.fx <= reflected.fx) {
replacement = contracted;
} else {
shouldReduce = true;
}
}
if (shouldReduce) {
// do reduction. doesn't actually happen that often
for (i = 1; i < simplex.length; ++i) {
simplex[i] = weightedSum([1 - sigma, simplex[0]],
[sigma - 1, simplex[i]]);
simplex[i].fx = f(simplex[i]);
}
}
}
simplex[N] = replacement;
}
simplex.sort(sortOrder);
return {f : simplex[0].fx,
solution : simplex[0]};
};
venn.drawD3Diagram = function(element, dataset, width, height, parameters) {
parameters = parameters || {};
var colours = d3.scale.category10(),
circleFillColours = parameters.circleFillColours || colours,
circleStrokeColours = parameters.circleStrokeColours || circleFillColours,
circleStrokeWidth = parameters.circleStrokeWidth || function(i) { return 0; },
textFillColours = parameters.textFillColours || colours,
textStrokeColours = parameters.textStrokeColours || textFillColours,
nodeOpacity = parameters.opacity || 0.3,
padding = parameters.padding || 6;
dataset = venn.scaleSolution(dataset, width, height, padding);
var svg = element.append("svg")
.attr("width", width)
.attr("height", height);
var diagram = svg.append( "g" );
var nodes = diagram.selectAll("circle")
.data(dataset)
.enter()
.append("g");
var circles = nodes.append("circle")
.attr("r", function(d) { return d.radius; })
.style("fill-opacity", nodeOpacity)
.attr("cx", function(d) { return d.x; })
.attr("cy", function(d) { return d.y; })
.style("stroke", function(d, i) { return circleStrokeColours(i); })
.style("stroke-width", function(d, i) { return circleStrokeWidth(i); })
.style("fill", function(d, i) { return circleFillColours(i); });
var text = nodes.append("text")
.attr("x", function(d) { return d.x; })
.attr("y", function(d) { return d.y; })
.attr("text-anchor", "middle")
.attr("dy", "0.35em")
.style("stroke", function(d, i) { return textStrokeColours(i); })
.style("fill", function(d, i) { return textFillColours(i); })
.text(function(d) { return d.label; });
centerVennDiagram( diagram, width, height, padding );
return {'svg' : svg,
'nodes' : nodes,
'circles' : circles,
'text' : text };
};
venn.updateD3Diagram = function(element, dataset) {
var svg = element.select("svg"),
width = parseInt(svg.attr('width'), 10),
height = parseInt(svg.attr('height'), 10);
dataset = venn.scaleSolution(dataset, width, height, 6);
element.selectAll("circle")
.data(dataset)
.transition()
.duration(400)
.attr("cx", function(d) { return d.x; })
.attr("cy", function(d) { return d.y; })
.attr("r", function(d) { return d.radius; });
element.selectAll("text")
.data(dataset)
.transition()
.duration(400)
.attr("x", function(d) { return d.x; })
.attr("y", function(d) { return d.y; });
};
}(window.venn = window.venn || {}));
(function(circleIntersection) {
"use strict";
var SMALL = 1e-10;
/** Returns the intersection area of a bunch of circles (where each circle
is an object having an x,y and radius property) */
circleIntersection.intersectionArea = function(circles, stats) {
// get all the intersection points of the circles
var intersectionPoints = getIntersectionPoints(circles);
// filter out points that aren't included in all the circles
var innerPoints = intersectionPoints.filter(function (p) {
return circleIntersection.containedInCircles(p, circles);
});
var arcArea = 0, polygonArea = 0, arcs = [], i;
// if we have intersection points that are within all the circles,
// then figure out the area contained by them
if (innerPoints.length > 1) {
// sort the points by angle from the center of the polygon, which lets
// us just iterate over points to get the edges
var center = circleIntersection.getCenter(innerPoints);
for (i = 0; i < innerPoints.length; ++i ) {
var p = innerPoints[i];
p.angle = Math.atan2(p.x - center.x, p.y - center.y);
}
innerPoints.sort(function(a,b) { return b.angle - a.angle;});
// iterate over all points, get arc between the points
// and update the areas
var p2 = innerPoints[innerPoints.length - 1];
for (i = 0; i < innerPoints.length; ++i) {
var p1 = innerPoints[i];
// polygon area updates easily ...
polygonArea += (p2.x + p1.x) * (p1.y - p2.y);
// updating the arc area is a little more involved
var midPoint = {x : (p1.x + p2.x) / 2,
y : (p1.y + p2.y) / 2},
arc = null;
for (var j = 0; j < p1.parentIndex.length; ++j) {
if (p2.parentIndex.indexOf(p1.parentIndex[j]) > -1) {
// figure out the angle halfway between the two points
// on the current circle
var circle = circles[p1.parentIndex[j]],
a1 = Math.atan2(p1.x - circle.x, p1.y - circle.y),
a2 = Math.atan2(p2.x - circle.x, p2.y - circle.y);
var angleDiff = (a2 - a1);
if (angleDiff < 0) {
angleDiff += 2*Math.PI;
}
// and use that angle to figure out the width of the
// arc
var a = a2 - angleDiff/2,
width = circleIntersection.distance(midPoint, {
x : circle.x + circle.radius * Math.sin(a),
y : circle.y + circle.radius * Math.cos(a)
});
// pick the circle whose arc has the smallest width
if ((arc === null) || (arc.width > width)) {
arc = { circle : circle,
width : width,
p1 : p1,
p2 : p2};
}
}
}
arcs.push(arc);
arcArea += circleIntersection.circleArea(arc.circle.radius, arc.width);
p2 = p1;
}
} else {
// no intersection points, is either disjoint - or is completely
// overlapped. figure out which by examining the smallest circle
var smallest = circles[0];
for (i = 1; i < circles.length; ++i) {
if (circles[i].radius < smallest.radius) {
smallest = circles[i];
}
}
// make sure the smallest circle is completely contained in all
// the other circles
var disjoint = false;
for (i = 0; i < circles.length; ++i) {
if (circleIntersection.distance(circles[i], smallest) > Math.abs(smallest.radius - circles[i].radius)) {
disjoint = true;
break;
}
}
if (disjoint) {
arcArea = polygonArea = 0;
} else {
arcArea = smallest.radius * smallest.radius * Math.PI;
arcs.push({circle : smallest,
p1: { x: smallest.x, y : smallest.y + smallest.radius},
p2: { x: smallest.x - SMALL, y : smallest.y + smallest.radius},
width : smallest.radius * 2 });
}
}
polygonArea /= 2;
if (stats) {
stats.area = arcArea + polygonArea;
stats.arcArea = arcArea;
stats.polygonArea = polygonArea;
stats.arcs = arcs;
stats.innerPoints = innerPoints;
stats.intersectionPoints = intersectionPoints;
}
return arcArea + polygonArea;
};
/** returns whether a point is contained by all of a list of circles */
circleIntersection.containedInCircles = function(point, circles) {
for (var i = 0; i < circles.length; ++i) {
if (circleIntersection.distance(point, circles[i]) > circles[i].radius + SMALL) {
return false;
}
}
return true;
};
/** Gets all intersection points between a bunch of circles */
function getIntersectionPoints(circles) {
var ret = [];
for (var i = 0; i < circles.length; ++i) {
for (var j = i + 1; j < circles.length; ++j) {
var intersect = circleIntersection.circleCircleIntersection(circles[i],
circles[j]);
for (var k = 0; k < intersect.length; ++k) {
var p = intersect[k];
p.parentIndex = [i,j];
ret.push(p);
}
}
}
return ret;
}
circleIntersection.circleIntegral = function(r, x) {
var y = Math.sqrt(r * r - x * x);
return x * y + r * r * Math.atan2(x, y);
};
/** Returns the area of a circle of radius r - up to width */
circleIntersection.circleArea = function(r, width) {
return circleIntersection.circleIntegral(r, width - r) - circleIntersection.circleIntegral(r, -r);
};
/** euclidean distance between two points */
circleIntersection.distance = function(p1, p2) {
return Math.sqrt((p1.x - p2.x) * (p1.x - p2.x) +
(p1.y - p2.y) * (p1.y - p2.y));
};
/** Returns the overlap area of two circles of radius r1 and r2 - that
have their centers separated by distance d. Simpler faster
circle intersection for only two circles */
circleIntersection.circleOverlap = function(r1, r2, d) {
// no overlap
if (d >= r1 + r2) {
return 0;
}
// completely overlapped
if (d <= Math.abs(r1 - r2)) {
return Math.PI * Math.min(r1, r2) * Math.min(r1, r2);
}
var w1 = r1 - (d * d - r2 * r2 + r1 * r1) / (2 * d),
w2 = r2 - (d * d - r1 * r1 + r2 * r2) / (2 * d);
return circleIntersection.circleArea(r1, w1) + circleIntersection.circleArea(r2, w2);
};
/** Given two circles (containing a x/y/radius attributes),
returns the intersecting points if possible.
note: doesn't handle cases where there are infinitely many
intersection points (circles are equivalent):, or only one intersection point*/
circleIntersection.circleCircleIntersection = function(p1, p2) {
var d = circleIntersection.distance(p1, p2),
r1 = p1.radius,
r2 = p2.radius;
// if to far away, or self contained - can't be done
if ((d >= (r1 + r2)) || (d <= Math.abs(r1 - r2))) {
return [];
}
var a = (r1 * r1 - r2 * r2 + d * d) / (2 * d),
h = Math.sqrt(r1 * r1 - a * a),
x0 = p1.x + a * (p2.x - p1.x) / d,
y0 = p1.y + a * (p2.y - p1.y) / d,
rx = -(p2.y - p1.y) * (h / d),
ry = -(p2.x - p1.x) * (h / d);
return [{ x: x0 + rx, y : y0 - ry },
{ x: x0 - rx, y : y0 + ry }];
};
/** Returns the center of a bunch of points */
circleIntersection.getCenter = function(points) {
var center = { x: 0, y: 0};
for (var i =0; i < points.length; ++i ) {
center.x += points[i].x;
center.y += points[i].y;
}
center.x /= points.length;
center.y /= points.length;
return center;
};
}(window.circleIntersection = window.circleIntersection || {}));