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@yelper
Last active June 16, 2018 08:10
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Playing with binned representations
license: cc-by-sa-4.0
height: 1220

A juxtaposed comparison of a hexagonal binning representation, a scatterplot, and a subsampled binning representation with multiple 'data series'. The hexagons try to be smart about attenuation with number of points, and the hexagon's color is a weighted average of colors in Lab space.

To add points, click on the scatterplot and the other plots will update as well. Hold down combinations of Alt and Ctrl to create points of other colors. Add your own data (or clear the data) by changing ptData and calling updateVis().

This block is in-progress -- consider sampling the points within each bin to still show some distribution while keeping faithful to the proportion of classes within.

x y category
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8.45671410877048 0.954304853487182 0
8.41629111947018 0.0844707892858723 0
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!function(){d3.hexbin=function(){function u(n){var r={};return n.forEach(function(n,t){var a=s.call(u,n,t)/o,e=Math.round(a),c=h.call(u,n,t)/i-(1&e?.5:0),f=Math.round(c),l=a-e;if(3*Math.abs(l)>1){var v=c-f,g=f+(f>c?-1:1)/2,m=e+(e>a?-1:1),M=c-g,d=a-m;v*v+l*l>M*M+d*d&&(f=g+(1&e?1:-1)/2,e=m)}var j=f+"-"+e,p=r[j];p?p.push(n):(p=r[j]=[n],p.i=f,p.j=e,p.x=(f+(1&e?.5:0))*i,p.y=e*o)}),d3.values(r)}function a(r){var t=0,u=0;return n.map(function(n){var a=Math.sin(n)*r,e=-Math.cos(n)*r,i=a-t,o=e-u;return t=a,u=e,[i,o]})}var e,i,o,c=1,f=1,h=r,s=t;return u.x=function(n){return arguments.length?(h=n,u):h},u.y=function(n){return arguments.length?(s=n,u):s},u.hexagon=function(n){return arguments.length<1&&(n=e),"m"+a(n).join("l")+"z"},u.centers=function(){for(var n=[],r=0,t=!1,u=0;f+e>r;r+=o,t=!t,++u)for(var a=t?i/2:0,h=0;c+i/2>a;a+=i,++h){var s=[a,r];s.i=h,s.j=u,n.push(s)}return n},u.mesh=function(){var n=a(e).slice(0,4).join("l");return u.centers().map(function(r){return"M"+r+"m"+n}).join("")},u.size=function(n){return arguments.length?(c=+n[0],f=+n[1],u):[c,f]},u.radius=function(n){return arguments.length?(e=+n,i=2*e*Math.sin(Math.PI/3),o=1.5*e,u):e},u.radius(1)};var n=d3.range(0,2*Math.PI,Math.PI/3),r=function(n){return n[0]},t=function(n){return n[1]}}();
<!DOCTYPE html>
<meta charset="utf-8">
<style>
body {
display: flex;
flex-flow: row wrap;
justify-content: space-around;
}
.canvasContainer {
position: relative;
}
.canvasContainer canvas, .canvasContainer svg {
position: absolute;
top: 0;
left: 0;
}
.canvasContainer svg {
z-index: 10;
}
.canvasContainer .hexagons > path {
fill: none;
stroke: #fff;
stroke-width: 1px;
}
.axis text {
font: 10px sans-serif;
}
.axis path,
.axis line {
fill: none;
stroke: #000;
shape-rendering: crispEdges;
}
#scattersvg {
cursor: pointer;
}
</style>
<body>
<script src="//d3js.org/d3.v3.min.js"></script>
<!--<script src="textures.min.js"></script>-->
<script src="d3.hexbin.min.js"></script>
<script>
var margins = {top: 20, right: 20, bottom: 40, left: 20};
var thisClick = function(event) {
if (d3.event.defaultPrevented) return;
var series = 0;
if (d3.event.ctrlKey) series = 2;
if (d3.event.altKey) series++;
var point = d3.mouse(this);
var p = [point[0] - margins.left, point[1] - margins.top, series, ptId++];
ptData.push(p);
updateVis();
};
var width = 320,
height = 300;
var xd = [0, 10];
var yd = [0, 10];
var colors = d3.scale.category10().range().slice(0, 4);
var svgDefs = [
{
name: "bin",
classes: "hexbin",
title: "Weighted Average Binning"
},
{
name: "scatter",
classes: "pts",
title: "Scatterplot"
},
{
name: "binpt",
classes: "hexbin binpts",
title: "Exemplar pts (picked randomly)"
},
{
name: "binclass",
classes: "hexbin binpts",
title: "Exemplar pts (at least one of each class)"
},
{
name: "binoutlier",
classes: "hexbin binpts",
title: "Exemplar pts (explicit outliers as △)"
},
{
name: "binpie",
classes: "hexbin binpies",
title: "Binning with pies"
},
{
name: "binpiesize",
classes: "binpies",
title: "Pie glyphs (size = number)"
},
{
name: "weaving",
classes: "hexbin weaving canvasOverlay",
title: "Color weaving"
},
{
name: "weaving-prop",
classes: "hexbin weaving canvasOverlay",
title: "Color weaving in proportion"
},
{
name: "textures",
classes: "hexbin texture",
title: "Strokes"
}
];
d3.select("body").selectAll('svg')
.data(svgDefs).enter()
.append('svg')
.attr('id', function(d) { return d.name + "svg"; })
.attr('class', function(d) { return d.classes; })
.attr('width', width)
.attr('height', height);
// add a canvas element behind any elements that request them
d3.selectAll("svg.canvasOverlay").each(function() {
var thisSVG = d3.select(this);
var thisID = thisSVG.attr('id');
var thisPrefix = thisID.split("svg")[0];
var thisContainer = d3.select("body").insert("div", "#" + thisID)
.attr("id", thisPrefix + "-container")
.attr('class', 'canvasContainer')
.style('width', width + "px"); // have to define a width for this to be a placeable div
// add the svg
thisSVG.remove();
thisContainer.append(function() {
return thisSVG.node();
});
// then append a canvas element
thisContainer.append('canvas')
.attr('width', width - margins.left - margins.right)
.attr('height', height - margins.top - margins.bottom)
.style('top', margins.top + "px")
.style('left', margins.left + "px");
});
// add click interaction to the scatterplot svg
d3.select("#scattersvg").on('click', thisClick);
width = d3.select("svg").attr('width') - margins.left - margins.right;
height = d3.select("svg").attr('height') - margins.top - margins.bottom;
var x1 = d3.scale.linear()
.domain(xd)
.range([0, width]);
var y1 = d3.scale.linear()
.domain(yd)
.range([height, 0]);
var hexbin = d3.hexbin()
.size([width,height])
.radius(15);
var pie = d3.layout.pie()
.sort(d3.descending);
var arc = d3.svg.arc()
.outerRadius(8)
.innerRadius(0);
svg = d3.selectAll('svg').append('g')
.attr("transform", "translate(" + margins.left + ", " + margins.top + ")");
svg.append('g')
.attr('class', 'xaxis axis')
.attr('transform', 'translate(0,' + height + ')')
.call(d3.svg.axis().orient('bottom').scale(x1));
svg.append('g')
.attr('class', 'yaxis axis')
.call(d3.svg.axis().orient("left").scale(y1));
svg.append('g')
.attr('class', 'svg-label')
.attr('transform', 'translate(0,' + (height + 35) + ')')
.append('text')
.attr('x', width / 2)
.style('text-anchor', 'middle')
.text(function(d) { return d.title; });
// only do this for hexsvgs
var hexsvgs = d3.selectAll('svg.hexbin > g');
hexsvgs.append('clipPath')
.attr('id', 'clip')
.append('rect')
.attr('class', 'mesh')
.attr('width', width)
.attr('height', height);
var hexagon = hexsvgs.append("g")
.attr('clip-path', 'url(#clip)')
.attr("class", "hexagons");
// only do this for ptsvgs
var ptsvgs = d3.selectAll('svg.pts > g');
var points = ptsvgs.append('g').attr('class', 'points')
.attr('clip-path', 'url(#clip)');
var binptsvgs = d3.selectAll('svg.binpts > g');
var binpts_points = binptsvgs.append('g').attr('class', 'points')
.attr('clip-path', 'url(#clip)');
var binpie_pies = d3.selectAll('svg.binpies > g')
.append('g').attr('class', 'pies')
.attr('clip-path', 'url(#clip)');
var bin_lines = d3.selectAll('svg.texture > g')
.append('g').attr('class', 'lines')
.attr('clip-path', 'url(#clip)');
var attenuation = d3.scale.log().range([0,1]);
var ptSize = 3;
var hexagonRadius = 14.5;
// <http://stackoverflow.com/questions/19911514/how-can-i-click-to-add-or-drag-in-d3>
var ptData;
var updateVis = function() {
var pts = points.selectAll('circle.point')
.data(ptData, function(d) { return d[3]; });
pts.exit().remove();
pts.enter().append('circle')
.attr("class", "point")
.attr('r', ptSize)
.attr('cx', function(e) { return e[0]; })
.attr('cy', function(e) { return e[1]; })
.style('fill', function(e) { return colors[e[2]]; });
var hexbins = hexbin(ptData);
attenuation.domain([.1, d3.max(hexbins.map(function(d) { return d.length; }))]);
var hex = hexagon.selectAll("path")
.data(hexbins, function(d) { return d.i + "," + d.j });
var colorBins = 8;
var lightnessScale = d3.scale.quantize()
.range(d3.range(colorBins).map(
d3.scale.linear()
.domain([0, colorBins-1])
.range(["#ffffff", "#000000"])
.interpolate(d3.interpolateLab)))
.domain(attenuation.domain());
hex.exit().remove();
hex.enter().append("path")
.attr("d", hexbin.hexagon(hexagonRadius))
.attr("transform", function(d) { return "translate(" + d.x + "," + d.y + ")"; });
hex.style("fill",
function(d) {
var counts = [0,0,0,0];
d.forEach(function(p) {
counts[p[2]]++;
});
return counts.reduce(function(p, c, i) {
return d3.interpolateLab(p, colors[i])(c / d.length);
}, "white");
})
.style('fill-opacity', function(d) { return attenuation(d.length); });
// try to move all points in binptsvg closer to center of their respective bins
var pp = binpts_points.selectAll('g.binpts')
.data(hexbins, function(d) { return d.i + "," + d.j; });
pp.exit().remove();
var newbin = pp.enter().append('g')
.attr('class', 'binpts')
.attr('id', function(d) { return d.i + "," + d.j});
var newpp = pp.selectAll('circle.point')
.data(function(d) { return d; }, function(d) { return d[3]; });
newpp.exit().remove();
newpp.enter().append('circle')
.attr('class', 'point')
.attr('r', 2)
.attr('cx', function(d) { return d[0]})
.attr('cy', function(d) { return d[1]})
.style('fill', function(d) { return colors[d[2]]; })
.style('stroke', '#333')
.style('stroke-width', '0.5px');
// try moving points closer to the origin of their bins??
newpp.each(function(pData, i) {
pData.remove = false;
pData.selected = false;
var pt = d3.select(this);
// is bin too far from center?
var binCenter = d3.select(pt.node().parentNode).data().map(function(d) { return [d.x, d.y]})[0];
var unitpt = binCenter.map(function(d, i) { return pData[i] - d; });
var dist = Math.sqrt(unitpt.reduce(function(p, d) { return p + Math.pow(d,2); }, 0));
var distThreshold = 10;
if (dist > distThreshold) {
var newPos = unitpt.map(function(d) { return d * distThreshold / dist; });
pt.attr('cx', binCenter[0] + newPos[0])
.attr('cy', binCenter[1] + newPos[1]);
}
});
// diverge here, remove baesd on # points, or # classes
binpts_points.each(function(d, i) {
var thisSVG = d3.select(this);
var thisID = d3.select(thisSVG.node().parentNode.parentNode).attr('id');
var thisPoints = thisSVG.selectAll('g.binpts').selectAll('circle.point');
// reset point state (since it's shared because we set it all at once??)
thisPoints.each(function(d) {
d.remove = false;
d.selected = false;
d.isOutlier = false;
})
var ptThreshold = 7;
if (thisID === 'binclasssvg' || thisID == 'binoutliersvg') {
// try to select one of each class
thisPoints.forEach(function(binData, binID) {
var binPts = d3.selectAll(binData);
var binClasses = d3.set(binPts.data().map(function(d) { return d[2]; })).values();
binClasses.forEach(function(thisClass) {
var thesePoints = binPts.filter(function(d) { return d[2] == thisClass; });
// try to pick the index farthest away from everything else
var thosePoints = binPts.filter(function(d) { return d[2] != thisClass; });
var maxPt;
var maxDist = -Infinity;
// select the point that has the highest distance from everything else
thesePoints.each(function(thisPt) {
var minDist = Infinity;
thosePoints.each(function(thatPt) {
var dist = eucliDist(thisPt, thatPt);
if (dist < minDist) {
minDist = dist;
}
});
if (minDist > maxDist) {
maxDist = minDist;
maxPt = d3.select(this);
}
});
var pickedPt = maxPt.each(function(d, i) {
d.selected = true;
// also mark as outlier if this is the only point of this class in this bin
if (thesePoints.size() == 1)
d.isOutlier = true;
});
});
var shuf = shuffle(d3.range(binPts.data().length));
var order = {};
binPts.data().map(function(d) { return d[3]; })
.forEach(function(d, i) { order[d] = shuf[i]; });
// see if we can highlight any more points
binPts.sort(function(a,b) {
return a.selected ?
(b.selected ? 0 : -1) :
(b.selected ? 1 : order[a[3]] - order[b[3]]);
});
binPts.each(function(curData, curI) {
if (!curData.remove) {
binPts.each(function(d, i) {
if (eucliDist(d, curData) < ptThreshold && i != curI && !d.selected)
d.remove = true;
});
}
});
});
// finally, actually remove the subsampled points
thisPoints.filter(function(d) { return d.remove; }).remove();
// identify points that are single outliers and replace them with crosses
var cross = d3.svg.symbol().type("triangle-up").size(10);
if (thisID == 'binoutliersvg') {
thisPoints.filter(function(d) { return !!d.isOutlier; }).forEach(function(grpOutliers) {
theseOutliers = d3.selectAll(grpOutliers).each(function(d) {
var thisPt = d3.select(this);
d3.select(thisPt.node().parentNode).append('path')
.attr('class', 'outlier')
.attr('transform', 'translate('+thisPt.attr('cx')+','+thisPt.attr('cy')+')')
.attr('d', cross)
.style('fill', colors[d[2]])
.style('stroke', '#333')
.style('stroke-width', '0.5px');
thisPt.style('opacity', '0');
});
});
}
} else if (thisID === 'binptsvg') {
// subsample. just flag points, then remove all that conflict
thisPoints.forEach(function(binData, binID) {
var order = shuffle(d3.range(binData.length));
var binPts = d3.selectAll(binData);
order.forEach(function(i) {
var curPt = d3.select(binData[i]);
var curData = curPt.datum();
// if point has not already been marked to remove, remove its neighbors
if (!curData.remove) {
// select all points except the current one that are within 2px and remove them
binPts.each(function(d, thisI) {
if (eucliDist(d, curData) < ptThreshold && thisI != i)
d.remove = true;
});
}
});
});
// finally, actually remove the subsampled points
thisPoints.filter(function(d) { return d.remove; }).remove();
} else
throw "unimplemented subsampling routing for svg#" + thisID;
});
// deal with pies
var pp = binpie_pies.selectAll('g.binpie')
.data(hexbins, function(d) { return d.i + "," + d.j; })
pp.exit().remove();
var newpies = pp.enter().append('g')
.attr('class', 'binpie')
.attr('id', function(d) { return d.i + "," + d.j; })
.attr('transform', function(d) { return 'translate(' + d.x + "," + d.y + ")"});
var pieScale = d3.scale.pow().exponent(2)
.range([4, 13])
.domain(d3.extent(d3.selectAll(pp[0]).data().map(function(d) { return d.length; })));
pp.each(function(binPts) {
var thisPie = d3.select(this);
var isSize = d3.select(thisPie.node().parentNode.parentNode.parentNode).attr('id') == "binpiesizesvg";
if (isSize)
arc.outerRadius(pieScale(binPts.length));
else
arc.outerRadius(8)
// count the number of classes here
var counts = binPts.reduce(function(p, pt) {
var thisClass = pt[2];
if (!p[thisClass])
p[thisClass] = 1;
else
p[thisClass]++;
return p;
}, Array(4).fill(0));
thisPie.selectAll('.arc').remove();
var arcs = thisPie.selectAll('.arc')
.data(pie(counts))
.enter().append('g')
.attr('class', 'arc');
arcs.append('path')
.attr('d', arc)
.style('fill', function(d, i) {
return colors[i];
})
.style('opacity', function(d) { return isSize ? 1 : attenuation(binPts.length); });
// add white outline
// thisPie.append('circle')
// .attr('r', 9)
// .style('stroke', '#fff')
// // .style('stroke-width', '1.5')
// .style('fill', 'none');
});
d3.selectAll("#binpiesvg .hexagons > path")
.style('fill', function(d) {
return lightnessScale(d.length);
});
// deal with weaving
d3.selectAll("svg.weaving .hexagons > path").style("fill", "none");
d3.selectAll("svg.weaving + canvas").each(function() {
var thisCanvas = d3.select(this);
var thisID = d3.select(thisCanvas.node().parentNode).select("svg").attr('id');
var ctx = thisCanvas.node().getContext("2d");
ctx.clearRect(0, 0, width, height);
// get the generalized hexagon path
var hexAngles = d3.range(0, 2 * Math.PI, Math.PI / 3);
var hexPos = hexAngles.map(function(angle) {
var x = Math.sin(angle) * hexagonRadius;
var y = -Math.cos(angle) * hexagonRadius;
return [x,y];
})
// now, go through each bin, figure out the proportions, then fill in the hexagon
hexbins.forEach(function(binPts) {
// save original transformation (identity)
ctx.save();
// move to the bin center
ctx.translate(binPts.x, binPts.y);
// define the hexagon path
ctx.beginPath();
hexPos.forEach(function(pos, i) {
if (i == 0) ctx.moveTo(pos[0], pos[1]);
else ctx.lineTo(pos[0], pos[1]);
});
ctx.closePath();
ctx.clip();
// round to nearest full pixel
ctx.translate(binPts.x - Math.floor(binPts.x), binPts.y - Math.floor(binPts.y));
// draw rectangle of weaving, clipping will make it a hexagon
var w = Math.ceil(hexagonRadius) * 2;
ctx.translate(-w / 2, -w / 2);
// all pixels to fill; see <http://bl.ocks.org/yelper/aa0860f4d35997a3c94df34764be97b9>
var ptData = binPts.map(function(d) { return d[2]; });
if (thisID != "weavingsvg") {
ptData = ptData.concat(Array(attenuation.domain()[1] - ptData.length).fill(-1));
}
var pixelSize = 1;
for (var i = 0; i < w * w / pixelSize; i++) {
var di = i % ptData.length;
if (di === 0) shuffle(ptData);
var x = i % w;
var y = Math.floor(i / w);
// skip drawing this pixel if we're simulating proportional measurement
if (ptData[di] == -1) continue;
ctx.fillStyle = colors[ptData[di]];
ctx.fillRect(x * pixelSize, y * pixelSize, pixelSize, pixelSize);
}
// restore to origin (0,0)
ctx.restore();
});
});
// add outlines for sparse weaving
d3.selectAll("#weaving-propsvg .hexagons > path")
.attr('d', hexbin.hexagon(Math.ceil(hexagonRadius)))
.style('stroke', "#333")
.style('stroke-width', '1');
// deal with textures (try to be smart about line orientation?)
d3.selectAll("svg.texture").each(function() {
var thisCanvas = d3.select(this);
thisCanvas.selectAll("clipPath#hex")
.data([0]).enter().append('clipPath')
.attr('id', 'hex')
.append('path')
.attr('d', d3.hexbin().radius(13).hexagon());
// blank out background colors
thisCanvas.selectAll('g.hexagons path')
.style('fill', null)
.style('fill-opacity', 0)
.style('stroke', 'black')
.style('stroke-width', 0.5);
// do brain-dead thing and get max of any one class in all
var maxClass = hexbins.reduce(function(p, thishex) {
thiscount = thishex.reduce(
function(p, d) {
p[d[2]]++; return p;
}, Array(4).fill(0));
return p.map(function(d, i) {
return d > thiscount[i] ? d : thiscount[i];
});
}, Array(4).fill(0));
var freq = d3.scale.quantize()
.domain([0, d3.max(maxClass)])
.range(d3.range(1,8));
var angles = d3.range(0, Math.PI, Math.PI / 4);
var ll = bin_lines.selectAll('g.binlines')
.data(hexbins, function(d) { return d.i + "," + d.j; });
ll.exit().remove();
var newlines = ll.enter().append('g')
.attr('class', 'binlines')
.attr('id', function(d) { return d.i + "," + d.j; })
.attr('clip-path', 'url(#hex)')
.attr('transform', function(d) { return 'translate(' + d.x + "," + d.y + ")"; });
ll.each(function(thishex) {
var thisbin = d3.select(this);
var thiscount = thishex.reduce(
function(p, d) {
p[d[2]]++; return p;
}, Array(4).fill(0));
var linegrp = thisbin.selectAll('g.linegrp')
.data(thiscount);
linegrp.enter().append('g')
.attr('class', 'linegrp');
linegrp.each(function(count, i) {
// skip drawing lines if count == 0
if (count == 0) return;
var thisgrp = d3.select(this);
var x = (hexagonRadius + 10)* Math.sin(angles[i]);
var y = (hexagonRadius + 10) * Math.cos(angles[i]);
var numFreq = freq(count);
var stepSize = hexagonRadius / numFreq;
var startAtZero = numFreq % 2 == 1;
for (var k = 0; k < numFreq; k++) {
if (startAtZero) {
var pos = k % 2 == 1 ? -1 : 1;
var shift = Math.ceil(k / 2) * stepSize * pos;
var shiftx = shift * Math.cos(angles[i]);
var shifty = shift * Math.sin(angles[i]);
} else {
var pos = k % 2 == 1 ? -1 : 1;
var shift = (stepSize / 2 * pos) + Math.floor(k / 2) * stepSize * pos;
var shiftx = shift * Math.cos(angles[i]);
var shifty = shift * Math.sin(angles[i]);
}
// var pos = k % 2 == 1 ? -1 : 1;
// var shift = Math.floor(k / 2) * stepSize * pos;
thisgrp.append('line')
.attr({
'x1': x + shiftx,
'x2': -x + shiftx,
'y1': y - shifty,
'y2': -y - shifty
})
.style('stroke', colors[i])
.style('stroke-width', 2);
}
});
// var lines = thisbin.selectAll('line')
// .data(thiscount);
// lines.enter().append('line');
// lines.each(function(count, i) {
// // skip drawing lines if count == 0
// if (count == 0) return;
// var thisline = d3.select(this);
// var x = hexagonRadius * Math.sin(angles[i]);
// var y = hexagonRadius * Math.cos(angles[i]);
// var numFreq = freq(count);
// var stepSize = hexagonRadius / 2 / numFreq;
// for (var k = 0; k < numFreq; k++) {
// var pos = k % 2 == 1 ? -1 : 1;
// var shift = Math.floor(k / 2) * stepSize * pos;
// var thisx = x + shift;
// var thisy = y - shift;
// thisline.attr({
// 'x1': thisx,
// 'x2': -thisx,
// 'y1': thisy,
// 'y2': -thisy
// })
// .style('stroke', colors[i])
// .style('stroke-width', 2);
// }
// });
});
// ll.append('line')
// .attr({
// x1:-15, y1:-15,
// x2: 15, y2: 15
// })
// .style("stroke", 'red')
// .style("stroke-width", 0.5);
});
};
var ptId = 0;
d3.csv("cluster-data.csv", function(d) {
return [x1(+d.x), y1(+d.y), +d.category, ptId++];
}, function(error, rows) {
ptData = rows;
updateVis();
}
);
function eucliDist(pt1, pt2) {
return Math.sqrt(Math.pow(pt1[0] - pt2[0], 2) + Math.pow(pt1[1] - pt2[1], 2));
}
// fisher-yates shuffling
function shuffle(arr) {
var i = arr.length;
var tmp, ri;
while (i !== 0) {
ri = Math.floor(Math.random() * i--);
tmp = arr[i];
arr[i] = arr[ri];
arr[ri] = tmp;
}
return arr;
};
</script>
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