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@mbostock /.block
Last active Feb 9, 2016

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Adaptive Resampling
license: gpl-3.0

Adaptive resampling recursively subdivides input polygons, applying the Douglas–Peucker perpendicular distance check to determine whether additional samples are needed.

<!DOCTYPE html>
<meta charset="utf-8">
<style>
.sphere,
.graticule {
fill: none;
stroke: #aaa;
}
.sphere {
stroke-width: 1.5px;
}
.point circle,
.equator {
fill: none;
stroke: red;
stroke-width: 2px;
}
.resample circle {
fill: none;
stroke: black;
stroke-width: 2px;
}
.resample line {
fill: none;
stroke: black;
stroke-width: 4px;
stroke-linecap: round;
}
</style>
<body>
<script src="//d3js.org/d3.v3.min.js"></script>
<script>
var width = 960,
height = 500;
var projection = d3.geo.equirectangular()
.scale(145)
.rotate([0, 0, 89])
.translate([width / 2, height / 2])
.precision(.3);
var coordinates = [[-180, 0], [-90, 0], [0, 0], [90, 0], [180, 0]],
resampled = coordinates;
var stages = d3.range(8).map(function() {
var result = resample(resampled);
resampled = result.after;
result.before = result.before.map(projection);
result.after = result.after.map(projection);
resampled.forEach(function(d, i) { result.after[i].resampled = d.resampled; });
return result;
});
var path = d3.geo.path()
.projection(projection);
var graticule = d3.geo.graticule();
var svg = d3.select("body").append("svg")
.attr("width", width)
.attr("height", height);
svg.append("path")
.datum(graticule)
.attr("class", "graticule")
.attr("d", path);
svg.append("path")
.datum({type: "Sphere"})
.attr("class", "sphere")
.attr("d", path);
var equator = svg.append("path")
.attr("class", "equator");
var point = svg.append("g")
.attr("class", "point")
.selectAll("g");
animation();
function animation() {
var transition = svg,
start = Date.now();
point = point.remove().data([]);
stages.forEach(function(stage, i) {
setTimeout(function() {
equator
.attr("d", "M" + stage.before.join("L"))
.transition()
.delay(500)
.duration(500)
.attr("d", "M" + stage.after.join("L"));
point = point.data(stage.after, function(d) { return d; });
point.exit().remove();
var pointEnter = point.enter().append("g");
point.classed("resample", function(d) { return d.resampled; });
pointEnter.append("circle")
.attr("transform", function(d) { return "translate(" + d + ")"; })
.attr("r", 0)
.transition()
.attr("r", 4.5);
pointEnter.filter(function(d) { return d.resampled; }).append("line")
.attr("x1", function(d) { return d[0]; })
.attr("y1", function(d) { return d[1]; })
.attr("x2", function(d) { return d[0]; })
.attr("y2", function(d) { return d[1] + 1e-3; }) // force caps
.transition()
.duration(500)
.attr("x2", function(d) { return d.resampled[0]; })
.attr("y2", function(d) { return d.resampled[1]; })
.transition()
.attr("x2", function(d) { return d[0]; })
.attr("y2", function(d) { return d[1] + 1e-3; }); // force caps
}, i * 1250);
});
setTimeout(animation, stages.length * 1250);
}
function resample(coordinates) {
var i = 0, n = coordinates.length, before = [], after = [];
while (++i < n) {
var c0 = coordinates[i - 1].slice(),
c1 = coordinates[i].slice(),
p0 = projection(c0),
p1 = projection(c1),
x10 = p1[0] - p0[0],
y10 = p1[1] - p0[1],
d1 = x10 * x10 + y10 * y10;
before.push(c0);
after.push(c0);
if (d1 > 4 * .1) { // linear distance check
var c2 = d3.geo.interpolate(c0, c1)(.5),
p2 = projection(c2),
x20 = p2[0] - p0[0],
y20 = p2[1] - p0[1],
dz = y10 * x20 - x10 * y20;
if (dz * dz / d1 > .1) { // perpendicular distance check
var t = (x20 * x10 + y20 * y10) / d1;
before.push(projection.invert(c2.resampled = [p0[0] + t * x10, p0[1] + t * y10]));
after.push(c2);
}
}
}
if (n) before.push(c1), after.push(c1);
return {before: before, after: after};
}
</script>
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