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@mbostock mbostock/.block
Last active Feb 9, 2016

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Line Simplification
license: gpl-3.0
(function() {
d3.simplify = function() {
var projection = d3.geo.albers();
function simplify(feature) {
if (feature.type !== "MultiPolygon") throw new Error("not yet supported");
var heap = minHeap(),
maxArea = 0,
triangle;
feature.coordinates = feature.coordinates.map(function(polygon) {
return polygon.map(function(lineString) {
var points = lineString.map(projection),
triangles = [];
if (points.some(function(p) { return p == null; })) return null;
for (var i = 1, n = lineString.length - 1; i < n; ++i) {
triangle = points.slice(i - 1, i + 2);
if (triangle[1][2] = area(triangle)) {
triangles.push(triangle);
heap.push(triangle);
}
}
for (var i = 0, n = triangles.length; i < n; ++i) {
triangle = triangles[i];
triangle.previous = triangles[i - 1];
triangle.next = triangles[i + 1];
}
return points;
}).filter(function(polygon) {
return polygon != null;
});
});
while (triangle = heap.pop()) {
// If the area of the current point is less than that of the previous point
// to be eliminated, use the latter’s area instead. This ensures that the
// current point cannot be eliminated without eliminating previously-
// eliminated points.
if (triangle[1][2] < maxArea) triangle[1][2] = maxArea;
else maxArea = triangle[1][2];
if (triangle.previous) {
triangle.previous.next = triangle.next;
triangle.previous[2] = triangle[2];
update(triangle.previous);
} else {
triangle[0][2] = triangle[1][2];
}
if (triangle.next) {
triangle.next.previous = triangle.previous;
triangle.next[0] = triangle[0];
update(triangle.next);
} else {
triangle[2][2] = triangle[1][2];
}
}
function update(triangle) {
heap.remove(triangle);
triangle[1][2] = area(triangle);
heap.push(triangle);
}
return feature;
}
simplify.projection = function(_) {
if (!arguments.length) return projection;
projection = _;
return simplify;
};
return simplify;
};
function compare(a, b) {
return a[1][2] - b[1][2];
}
function area(t) {
return Math.abs((t[0][0] - t[2][0]) * (t[1][1] - t[0][1]) - (t[0][0] - t[1][0]) * (t[2][1] - t[0][1]));
}
function minHeap() {
var heap = {},
array = [];
heap.push = function() {
for (var i = 0, n = arguments.length; i < n; ++i) {
var object = arguments[i];
up(object.index = array.push(object) - 1);
}
return array.length;
};
heap.pop = function() {
var removed = array[0],
object = array.pop();
if (array.length) {
array[object.index = 0] = object;
down(0);
}
return removed;
};
heap.remove = function(removed) {
var i = removed.index,
object = array.pop();
if (i !== array.length) {
array[object.index = i] = object;
(compare(object, removed) < 0 ? up : down)(i);
}
return i;
};
function up(i) {
var object = array[i];
while (i > 0) {
var up = ((i + 1) >> 1) - 1,
parent = array[up];
if (compare(object, parent) >= 0) break;
array[parent.index = i] = parent;
array[object.index = i = up] = object;
}
}
function down(i) {
var object = array[i];
while (true) {
var right = (i + 1) << 1,
left = right - 1,
down = i,
child = array[down];
if (left < array.length && compare(array[left], child) < 0) child = array[down = left];
if (right < array.length && compare(array[right], child) < 0) child = array[down = right];
if (down === i) break;
array[child.index = i] = child;
array[object.index = i = down] = object;
}
}
return heap;
}
})();
<!DOCTYPE html>
<meta charset="utf-8">
<style>
#chart .background {
fill: none;
pointer-events: all;
}
#chart text {
font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;
font-size: 32px;
pointer-events: none;
}
#chart path {
fill: #eee;
stroke: #000;
pointer-events: none;
}
</style>
<div id="chart"></div>
<script src="//d3js.org/d3.v3.min.js"></script>
<script src="//d3js.org/topojson.v1.min.js"></script>
<script src="readme-simplify.js"></script>
<script>
var width = 960,
height = 600,
minArea = 1,
formatArea = d3.format(".2r"),
formatPercent = d3.format(".2%");
var svg = d3.select("#chart").append("svg")
.attr("width", width)
.attr("height", height);
var shape = svg.append("path");
var text = svg.append("text")
.attr("x", width / 2)
.attr("y", height / 2)
.attr("dy", ".35em")
.attr("text-anchor", "middle");
var path = d3.geo.path()
.projection(null);
var simplify = d3.simplify()
.projection(d3.geo.albersUsa()
.scale(1280)
.translate([width / 2, height / 2]));
d3.json("/mbostock/raw/4090846/us-land.json", function(error, us) {
if (error) throw error;
us = topojson.feature(us, us.objects.land).geometry;
var m = us.coordinates.reduce(function(m, polygon) {
return m + polygon.reduce(function(m, lineString) {
return m + lineString.length;
}, 0);
}, 0);
simplify(us);
animation();
function animation() {
svg.transition()
.duration(7500)
.tween("precision", function() {
var area = d3.interpolate(.1, 100);
return function(t) {
minArea = area(t);
render();
};
})
.transition()
.duration(7500)
.tween("precision", function() {
var area = d3.interpolate(100, .1);
return function(t) {
minArea = area(t);
render();
};
})
.transition()
.duration(2500)
.each("end", animation);
}
function render() {
var n = 0;
shape.attr("d", path({
type: "MultiPolygon",
coordinates: us.coordinates.map(function(polygon) {
return polygon.map(function(lineString) {
return lineString.filter(function(point) {
return point[2] >= minArea && ++n;
});
});
})
}));
text.text(formatArea(minArea) + "px² / " + formatPercent(n / m));
}
});
d3.select(self.frameElement).style("height", height + "px");
</script>
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