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Last active Jul 10, 2017
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Encircle Scatterplot with alpha shapes
license: gpl-3.0
border: no
height: 960

Using alpha shapes to group or "encircle" sets of points.

It's not fast, but it's fun.

DISCLAIMER: this code is quite hackish, don't copy it blindly.

TODO: buffer the shapes so that they nicely enclose dots as ggplot2's geom_encircle function does.


The scatterplot matrix visualizations pairwise correlations for multi-dimensional data; each cell in the matrix is a scatterplot. This example uses Anderson's data of iris flowers on the Gaspé Peninsula. Scatterplot matrix design invented by J. A. Hartigan; see also R and GGobi. Data on Iris flowers collected by Edgar Anderson and published by Ronald Fisher.

S Forked from mbostock’s Scatterplot Matrix Brushing.

sepal length sepal width petal length petal width species
5.1 3.5 1.4 0.2 setosa
4.9 3.0 1.4 0.2 setosa
4.7 3.2 1.3 0.2 setosa
4.6 3.1 1.5 0.2 setosa
5.0 3.6 1.4 0.2 setosa
5.4 3.9 1.7 0.4 setosa
4.6 3.4 1.4 0.3 setosa
5.0 3.4 1.5 0.2 setosa
4.4 2.9 1.4 0.2 setosa
4.9 3.1 1.5 0.1 setosa
5.4 3.7 1.5 0.2 setosa
4.8 3.4 1.6 0.2 setosa
4.8 3.0 1.4 0.1 setosa
4.3 3.0 1.1 0.1 setosa
5.8 4.0 1.2 0.2 setosa
5.7 4.4 1.5 0.4 setosa
5.4 3.9 1.3 0.4 setosa
5.1 3.5 1.4 0.3 setosa
5.7 3.8 1.7 0.3 setosa
5.1 3.8 1.5 0.3 setosa
5.4 3.4 1.7 0.2 setosa
5.1 3.7 1.5 0.4 setosa
4.6 3.6 1.0 0.2 setosa
5.1 3.3 1.7 0.5 setosa
4.8 3.4 1.9 0.2 setosa
5.0 3.0 1.6 0.2 setosa
5.0 3.4 1.6 0.4 setosa
5.2 3.5 1.5 0.2 setosa
5.2 3.4 1.4 0.2 setosa
4.7 3.2 1.6 0.2 setosa
4.8 3.1 1.6 0.2 setosa
5.4 3.4 1.5 0.4 setosa
5.2 4.1 1.5 0.1 setosa
5.5 4.2 1.4 0.2 setosa
4.9 3.1 1.5 0.2 setosa
5.0 3.2 1.2 0.2 setosa
5.5 3.5 1.3 0.2 setosa
4.9 3.6 1.4 0.1 setosa
4.4 3.0 1.3 0.2 setosa
5.1 3.4 1.5 0.2 setosa
5.0 3.5 1.3 0.3 setosa
4.5 2.3 1.3 0.3 setosa
4.4 3.2 1.3 0.2 setosa
5.0 3.5 1.6 0.6 setosa
5.1 3.8 1.9 0.4 setosa
4.8 3.0 1.4 0.3 setosa
5.1 3.8 1.6 0.2 setosa
4.6 3.2 1.4 0.2 setosa
5.3 3.7 1.5 0.2 setosa
5.0 3.3 1.4 0.2 setosa
7.0 3.2 4.7 1.4 versicolor
6.4 3.2 4.5 1.5 versicolor
6.9 3.1 4.9 1.5 versicolor
5.5 2.3 4.0 1.3 versicolor
6.5 2.8 4.6 1.5 versicolor
5.7 2.8 4.5 1.3 versicolor
6.3 3.3 4.7 1.6 versicolor
4.9 2.4 3.3 1.0 versicolor
6.6 2.9 4.6 1.3 versicolor
5.2 2.7 3.9 1.4 versicolor
5.0 2.0 3.5 1.0 versicolor
5.9 3.0 4.2 1.5 versicolor
6.0 2.2 4.0 1.0 versicolor
6.1 2.9 4.7 1.4 versicolor
5.6 2.9 3.6 1.3 versicolor
6.7 3.1 4.4 1.4 versicolor
5.6 3.0 4.5 1.5 versicolor
5.8 2.7 4.1 1.0 versicolor
6.2 2.2 4.5 1.5 versicolor
5.6 2.5 3.9 1.1 versicolor
5.9 3.2 4.8 1.8 versicolor
6.1 2.8 4.0 1.3 versicolor
6.3 2.5 4.9 1.5 versicolor
6.1 2.8 4.7 1.2 versicolor
6.4 2.9 4.3 1.3 versicolor
6.6 3.0 4.4 1.4 versicolor
6.8 2.8 4.8 1.4 versicolor
6.7 3.0 5.0 1.7 versicolor
6.0 2.9 4.5 1.5 versicolor
5.7 2.6 3.5 1.0 versicolor
5.5 2.4 3.8 1.1 versicolor
5.5 2.4 3.7 1.0 versicolor
5.8 2.7 3.9 1.2 versicolor
6.0 2.7 5.1 1.6 versicolor
5.4 3.0 4.5 1.5 versicolor
6.0 3.4 4.5 1.6 versicolor
6.7 3.1 4.7 1.5 versicolor
6.3 2.3 4.4 1.3 versicolor
5.6 3.0 4.1 1.3 versicolor
5.5 2.5 4.0 1.3 versicolor
5.5 2.6 4.4 1.2 versicolor
6.1 3.0 4.6 1.4 versicolor
5.8 2.6 4.0 1.2 versicolor
5.0 2.3 3.3 1.0 versicolor
5.6 2.7 4.2 1.3 versicolor
5.7 3.0 4.2 1.2 versicolor
5.7 2.9 4.2 1.3 versicolor
6.2 2.9 4.3 1.3 versicolor
5.1 2.5 3.0 1.1 versicolor
5.7 2.8 4.1 1.3 versicolor
6.3 3.3 6.0 2.5 virginica
5.8 2.7 5.1 1.9 virginica
7.1 3.0 5.9 2.1 virginica
6.3 2.9 5.6 1.8 virginica
6.5 3.0 5.8 2.2 virginica
7.6 3.0 6.6 2.1 virginica
4.9 2.5 4.5 1.7 virginica
7.3 2.9 6.3 1.8 virginica
6.7 2.5 5.8 1.8 virginica
7.2 3.6 6.1 2.5 virginica
6.5 3.2 5.1 2.0 virginica
6.4 2.7 5.3 1.9 virginica
6.8 3.0 5.5 2.1 virginica
5.7 2.5 5.0 2.0 virginica
5.8 2.8 5.1 2.4 virginica
6.4 3.2 5.3 2.3 virginica
6.5 3.0 5.5 1.8 virginica
7.7 3.8 6.7 2.2 virginica
7.7 2.6 6.9 2.3 virginica
6.0 2.2 5.0 1.5 virginica
6.9 3.2 5.7 2.3 virginica
5.6 2.8 4.9 2.0 virginica
7.7 2.8 6.7 2.0 virginica
6.3 2.7 4.9 1.8 virginica
6.7 3.3 5.7 2.1 virginica
7.2 3.2 6.0 1.8 virginica
6.2 2.8 4.8 1.8 virginica
6.1 3.0 4.9 1.8 virginica
6.4 2.8 5.6 2.1 virginica
7.2 3.0 5.8 1.6 virginica
7.4 2.8 6.1 1.9 virginica
7.9 3.8 6.4 2.0 virginica
6.4 2.8 5.6 2.2 virginica
6.3 2.8 5.1 1.5 virginica
6.1 2.6 5.6 1.4 virginica
7.7 3.0 6.1 2.3 virginica
6.3 3.4 5.6 2.4 virginica
6.4 3.1 5.5 1.8 virginica
6.0 3.0 4.8 1.8 virginica
6.9 3.1 5.4 2.1 virginica
6.7 3.1 5.6 2.4 virginica
6.9 3.1 5.1 2.3 virginica
5.8 2.7 5.1 1.9 virginica
6.8 3.2 5.9 2.3 virginica
6.7 3.3 5.7 2.5 virginica
6.7 3.0 5.2 2.3 virginica
6.3 2.5 5.0 1.9 virginica
6.5 3.0 5.2 2.0 virginica
6.2 3.4 5.4 2.3 virginica
5.9 3.0 5.1 1.8 virginica
<!DOCTYPE html>
<meta charset="utf-8">
<style>
svg {
font: 10px sans-serif;
padding: 10px;
}
.axis,
.frame {
shape-rendering: crispEdges;
}
.axis line {
stroke: #ddd;
}
.axis path {
display: none;
}
.cell text {
font-weight: bold;
text-transform: capitalize;
fill: black;
}
.frame {
fill: none;
stroke: #aaa;
}
circle {
fill-opacity: .7;
}
circle.hidden {
fill: #ccc !important;
}
.extent {
fill: #000;
fill-opacity: .125;
stroke: #fff;
}
.contour {
stroke-width: 1.5;
}
</style>
<body>
<script src="https://d3js.org/d3.v4.min.js"></script>
<script src="https://d3js.org/d3-hexbin.v0.2.min.js"></script>
<script>
// Computes boundaries of connected triangles, given an array of triangles.
// Jason Davies - http://bl.ocks.org/jasondavies/1554783
function boundary(mesh) {
console.log(mesh)
var counts = {},
edges = {},
r,
result = [];
// Traverse the edges of all triangles and discard any edges that appear twice.
mesh.forEach(function(triangle) {
for (var i = 0; i < 3; i++) {
var edge = [triangle[i], triangle[(i + 1) % 3]].sort(ascendingCoords).map(String);
(edges[edge[0]] = (edges[edge[0]] || [])).push(edge[1]);
(edges[edge[1]] = (edges[edge[1]] || [])).push(edge[0]);
var k = edge.join(":");
if (counts[k]) delete counts[k];
else counts[k] = 1;
}
});
while (1) {
var k = null;
// Pick an arbitrary starting point on a boundary.
for (k in counts) break;
if (k == null) break;
result.push(r = k.split(":").map(function(d) { return d.split(",").map(Number); }));
delete counts[k];
var q = r[1];
while (q[0] !== r[0][0] || q[1] !== r[0][1]) {
var p = q,
qs = edges[p.join(",")],
n = qs.length;
for (var i = 0; i < n; i++) {
q = qs[i].split(",").map(Number);
var edge = [p, q].sort(ascendingCoords).join(":");
if (counts[edge]) {
delete counts[edge];
r.push(q);
break;
}
}
}
}
return result;
}
function ascendingCoords(a, b) {
return a[0] === b[0] ? b[1] - a[1] : b[0] - a[0];
}
function alphashape(sites, alpha){
var dsq = function(a,b) {
var dx = a[0]-b[0], dy = a[1]-b[1];
return dx*dx+dy*dy;
},
asq = alpha*alpha,
sites2 =
d3.hexbin().radius(3)(sites)
.map(d => [d.x + 0.01 * (Math.random() - Math.random()), d.y + 0.01 * (Math.random() - Math.random())])
,
mesh = d3.voronoi()
.triangles(sites2)
.filter(function(t) {
return dsq(t[0],t[1]) < asq && dsq(t[0],t[2]) < asq && dsq(t[1],t[2]) < asq;
});
//mesh = mesh.map(d => d.map(e => e.map((Math.round))))
return boundary(mesh);
}
function encircle_path(points) {
var a = alphashape(points, 60);
return a.map(d => d ? "M" + d.join(',') : null)
}
var width = 960,
size = 230,
padding = 20;
var x = d3.scaleLinear()
.range([padding / 2, size - padding / 2]);
var y = d3.scaleLinear()
.range([size - padding / 2, padding / 2]);
var xAxis = d3.axisBottom()
.scale(x)
.ticks(6);
var yAxis = d3.axisLeft()
.scale(y)
.ticks(6);
var color = d3.scaleOrdinal(d3.schemeCategory10);
d3.csv("flowers.csv", function(error, data) {
if (error) throw error;
var domainByTrait = {},
traits = d3.keys(data[0]).filter(function(d) { return d !== "species"; }),
n = traits.length;
traits.forEach(function(trait) {
domainByTrait[trait] = d3.extent(data, function(d) { return d[trait]; });
});
xAxis.tickSize(size * n);
yAxis.tickSize(-size * n);
var brush = d3.brush()
.on("start", brushstart)
.on("brush", brushmove)
.on("end", brushend)
.extent([[0,0],[size,size]]);
var svg = d3.select("body").append("svg")
.attr("width", size * n + padding)
.attr("height", size * n + padding)
.append("g")
.attr("transform", "translate(" + padding + "," + padding / 2 + ")");
svg.selectAll(".x.axis")
.data(traits)
.enter().append("g")
.attr("class", "x axis")
.attr("transform", function(d, i) { return "translate(" + (n - i - 1) * size + ",0)"; })
.each(function(d) { x.domain(domainByTrait[d]); d3.select(this).call(xAxis); });
svg.selectAll(".y.axis")
.data(traits)
.enter().append("g")
.attr("class", "y axis")
.attr("transform", function(d, i) { return "translate(0," + i * size + ")"; })
.each(function(d) { y.domain(domainByTrait[d]); d3.select(this).call(yAxis); });
var cell = svg.selectAll(".cell")
.data(cross(traits, traits))
.enter().append("g")
.attr("class", "cell")
.attr("transform", function(d) { return "translate(" + (n - d.i - 1) * size + "," + d.j * size + ")"; })
.each(plot);
// Titles for the diagonal.
cell.filter(function(d) { return d.i === d.j; }).append("text")
.attr("x", padding)
.attr("y", padding)
.attr("dy", ".71em")
.text(function(d) { return d.x; });
cell.call(brush);
function plot(p) {
var cell = d3.select(this);
x.domain(domainByTrait[p.x]);
y.domain(domainByTrait[p.y]);
cell.append("rect")
.attr("class", "frame")
.attr("x", padding / 2)
.attr("y", padding / 2)
.attr("width", size - padding)
.attr("height", size - padding);
cell.selectAll("circle")
.data(data)
.enter().append("circle")
.attr("cx", function(d) { return x(d[p.x]); })
.attr("cy", function(d) { return y(d[p.y]); })
.attr("r", 4)
.style("fill", function(d) { return color(d.species); });
var contours = d3.nest().key(d => d.species).entries(data)
.map(d => {
d.path = encircle_path(d.values.map(d => [x(d[p.x]) + Math.random(), y(d[p.y])]));
return d;
})
cell.selectAll("path.contour")
.data(contours, d => d.key)
.enter()
.append('path')
.classed("contour", true)
.attr('d', d => d.path)
.attr('stroke', d => color(d.key))
.attr('fill', d => color(d.key))
.attr('fill-opacity', 0.3)
}
var brushCell;
// Clear the previously-active brush, if any.
function brushstart(p) {
if (brushCell !== this) {
d3.select(brushCell).call(brush.move, null);
brushCell = this;
x.domain(domainByTrait[p.x]);
y.domain(domainByTrait[p.y]);
}
}
// Highlight the selected circles.
function brushmove(p) {
var e = d3.brushSelection(this);
svg.selectAll("circle").classed("hidden", function(d) {
return !e
? false
: (
e[0][0] > x(+d[p.x]) || x(+d[p.x]) > e[1][0]
|| e[0][1] > y(+d[p.y]) || y(+d[p.y]) > e[1][1]
);
});
var con = cell.selectAll("path.contour")
.data((d,i,e) => {
var c = d3.select(e[i]).selectAll('circle:not(.hidden)');
var p = d3.select(e[i]).data()[0];
x.domain(domainByTrait[p.x]);
y.domain(domainByTrait[p.y]);
return d3.nest()
.key(d => d.species)
.entries(c.data())
.map(d => {
d.path = encircle_path(d.values.map(d => [x(d[p.x]) + Math.random(), y(d[p.y])]));
return d;
})
}, d => d.key)
.attr('d', d => d.path)
x.domain(domainByTrait[p.x]);
y.domain(domainByTrait[p.y]);
con.exit().attr('d', null)
}
// If the brush is empty, select all circles.
function brushend() {
var e = d3.brushSelection(this);
if (e === null) svg.selectAll(".hidden").classed("hidden", false);
}
});
function cross(a, b) {
var c = [], n = a.length, m = b.length, i, j;
for (i = -1; ++i < n;) for (j = -1; ++j < m;) c.push({x: a[i], i: i, y: b[j], j: j});
return c;
}
</script>
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