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@veltman
Last active September 12, 2020 15:07
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Triangulation morphing #2
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<style>
path {
stroke: #666;
fill: #ccc;
}
</style>
</head>
<body>
<svg width="960" height="500"></svg>
<script src="https://cdnjs.cloudflare.com/ajax/libs/d3/4.2.3/d3.min.js"></script>
<script src="https://unpkg.com/earcut@2.1.1/dist/earcut.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/topojson/1.6.20/topojson.min.js"></script>
<script>
var svg = d3.select("svg"),
width = +svg.attr("width"),
height = +svg.attr("height");
d3.json("us.topo.json", function(err, us){
var states = topojson.feature(us, us.objects.states).features.map(function(d){
return d.geometry.coordinates[0];
});
d3.shuffle(states);
morph(states);
});
function morph(states) {
var source = states.shift(),
destination = states[0],
multi = subdivide(source);
states.push(source);
d3.queue(1)
.defer(tween, [source], multi)
.defer(tween, multi, [destination])
.await(function(err){
if (err) throw err;
morph(states);
});
}
function tween(fr, to, cb) {
var pairs;
if (to.length === 1) {
pairs = getTweenablePairs(fr, triangulate(to[0], fr.length))
} else {
pairs = getTweenablePairs(triangulate(fr[0], to.length), to, true);
}
svg.call(updatePaths, pairs)
.selectAll("path")
.transition()
.delay(fr.length > 1 ? 0 : 400)
.duration(2500)
.style("fill", function(d, i){
return fr.length > 1 ? "#ccc" : d3.interpolateCool(i / pairs.length);
})
.attrTween("d", function(d, i){
return d3.interpolateString(join(d[0]), join(d[1]));
})
.on("end", function(){
if (to.length === 1) {
svg.call(updatePaths, to)
.selectAll("path")
.attr("d", join);
}
setTimeout(cb, 0);
})
}
function updatePaths(sel, pairs) {
var paths = sel.selectAll("path")
.data(pairs);
paths.enter().append("path");
paths.exit().remove();
}
function triangulate(ring, numPieces) {
var vertices = ring.reduce(function(arr, point){
return arr.concat(point);
}, []),
cuts = earcut(vertices),
triangles = [],
topology;
for (var i = 0, l = cuts.length; i < l; i += 3) {
// Save each triangle as segments [a, b], [b, c], [c, a]
triangles.push([
[cuts[i], cuts[i + 1]],
[cuts[i + 1], cuts[i + 2]],
[cuts[i + 2], cuts[i]]
]);
}
topology = createTopology(triangles, ring);
return collapse(topology, numPieces);
}
// Merge polygons into neighbors one at a time until only numPieces remain
function collapse(topology, numPieces) {
var geometries = topology.objects.triangles.geometries,
bisector = d3.bisector(function(d) { return d.area; }).left;
while (geometries.length > numPieces) {
mergeSmallestFeature();
}
return topojson.feature(topology, topology.objects.triangles).features.map(function(f){
return f.geometry.coordinates[0];
});
// Shuffle just for fun
function mergeSmallestFeature() {
var smallest = geometries[0],
neighborIndex = d3.shuffle(topojson.neighbors(geometries)[0])[0],
neighbor = geometries[neighborIndex],
merged = topojson.mergeArcs(topology, [smallest, neighbor]);
// MultiPolygon -> Polygon
merged.area = smallest.area + neighbor.area;
merged.type = "Polygon";
merged.arcs = merged.arcs[0];
// Delete smallest and its chosen neighbor
geometries.splice(neighborIndex, 1);
geometries.shift();
// Add new merged shape in sorted order
geometries.splice(bisector(geometries, merged.area), 0, merged);
}
}
function createTopology(triangles, points) {
var arcIndices = {},
topology = {
type: "Topology",
objects: {
triangles: {
"type": "GeometryCollection",
"geometries": []
}
},
arcs: []
};
triangles.forEach(function(triangle){
var geometry = [];
triangle.forEach(function(arc, i){
var slug = arc[0] < arc[1] ? arc.join(",") : arc[1] + "," + arc[0],
coordinates = arc.map(function(pointIndex){
return points[pointIndex];
});
if (slug in arcIndices) {
geometry.push(~arcIndices[slug]);
} else {
geometry.push(arcIndices[slug] = topology.arcs.length);
topology.arcs.push(coordinates);
}
});
topology.objects.triangles.geometries.push({
type: "Polygon",
area: Math.abs(d3.polygonArea(triangle.map(function(d){
return points[d[0]];
}))),
arcs: [
geometry
]
});
});
// Sort smallest first
topology.objects.triangles.geometries.sort(function(a, b){
return a.area - b.area;
});
return topology;
}
function getTweenablePairs(start, end, out) {
// Rearrange order of polygons for least movement
if (out) {
start = closestCentroids(start, end);
} else {
end = closestCentroids(end, start);
}
return start.map(function(a, i){
return align(a.slice(0), end[i].slice(0));
});
}
function align(a, b) {
// Matching rotation
if (d3.polygonArea(a) * d3.polygonArea(b) < 0) {
a.reverse();
}
// Smooth out by bisecting long triangulation cuts
bisectSegments(a, 25);
bisectSegments(b, 25);
// Same number of points on each ring
if (a.length < b.length) {
addPoints(a, b.length - a.length);
} else if (b.length < a.length) {
addPoints(b, a.length - b.length);
}
// Wind the first to minimize sum-of-squares distance to the second
return [wind(a, b), b];
}
function addPoints(ring, numPoints) {
var desiredLength = ring.length + numPoints,
step = d3.polygonLength(ring) / numPoints;
var i = 0,
cursor = 0,
insertAt = step / 2;
while (ring.length < desiredLength) {
var a = ring[i],
b = ring[(i + 1) % ring.length];
var segment = distanceBetween(a, b);
if (insertAt <= cursor + segment) {
ring.splice(i + 1, 0, pointBetween(a, b, (insertAt - cursor) / segment));
insertAt += step;
continue;
}
cursor += segment;
i++;
}
}
// Find best winding for first ring of pair
function wind(ring, vs) {
var len = ring.length,
min = Infinity,
bestOffset,
sum;
for (var offset = 0; offset < len; offset++) {
var sum = d3.sum(vs.map(function(p, i){
var distance = distanceBetween(ring[(offset + i) % len], p);
return distance * distance;
}));
if (sum < min) {
min = sum;
bestOffset = offset;
}
}
return ring.slice(bestOffset).concat(ring.slice(0, bestOffset));
}
// Find ordering of first set that minimizes squared distance between centroid pairs
// Could loosely optimize instead of trying every permutation (would probably have to with 10+ pieces)
function closestCentroids(start, end) {
var min = Infinity,
best,
distances = start.map(function(p1){
return end.map(function(p2){
var distance = distanceBetween(d3.polygonCentroid(p1), d3.polygonCentroid(p2));
return distance * distance;
});
});
function permute(arr, order, sum) {
var cur,
distance,
order = order || [],
sum = sum || 0;
for (var i = 0; i < arr.length; i++) {
cur = arr.splice(i, 1);
distance = distances[cur[0]][order.length];
if (arr.length) {
permute(arr.slice(), order.concat(cur), sum + distance);
arr.splice(i, 0, cur[0]);
} else if (sum + distance < min) {
min = sum + distance;
best = order.concat(cur);
}
}
}
permute(d3.range(start.length));
return best.map(function(i){
return start[i];
});
}
// Bisect any segment longer than x with an extra point
function bisectSegments(ring, threshold) {
for (var i = 0; i < ring.length - 1; i++) {
while (distanceBetween(ring[i], ring[i + 1]) > threshold) {
ring.splice(i + 1, 0, pointBetween(ring[i], ring[i + 1], 0.5));
}
}
}
function distanceBetween(a, b) {
var dx = a[0] - b[0],
dy = a[1] - b[1];
return Math.sqrt(dx * dx + dy * dy);
}
function pointBetween(a, b, pct) {
return [
a[0] + (b[0] - a[0]) * pct,
a[1] + (b[1] - a[1]) * pct
];
}
// Join a ring or array of rings into a path string
function join(geom) {
if (typeof geom[0][0] !== "number") {
return geom.map(join).join(" ");
}
return "M" + geom.join("L") + "Z";
}
// Given a full-sized ring, return 2 - 6 smaller clones in a dice pattern
function subdivide(ring) {
var numClones = 2 + Math.floor(Math.random() * 5),
bounds = getBounds(ring);
return d3.range(numClones).map(function(d){
var x0,
x1,
y0,
y1;
if (numClones === 2) {
x0 = d ? width / 2 : 0;
x1 = x0 + width / 2;
y0 = 0;
y1 = height;
} else if (numClones === 3) {
x0 = d * width / 3;
x1 = x0 + width / 3;
y0 = d * height / 3;
y1 = y0 + height / 3;
} else if (numClones === 4) {
x0 = (d % 2) * width / 2;
x1 = x0 + width / 2;
y0 = d < 2 ? 0 : height / 2;
y1 = y0 + height / 2;
} else if (numClones === 5) {
x0 = (d < 2 ? 0 : d === 2 ? 1 : 2) * width / 3;
x1 = x0 + width / 3;
y0 = [0, 1, 0.5, 0, 1][d] * height / 2;
y1 = y0 + height / 2;
} else {
x0 = (d % 3) * width / 3;
x1 = x0 + width / 3;
y0 = d < 3 ? 0 : height / 2;
y1 = y0 + height / 2;
}
return ring.map(fitExtent([[x0 + 5, y0 + 5], [x1 - 5, y1 - 5]], bounds));
});
}
// Raw fitExtent to avoid some projection stream kinks
function fitExtent(extent, bounds) {
var w = extent[1][0] - extent[0][0],
h = extent[1][1] - extent[0][1],
dx = bounds[1][0] - bounds[0][0],
dy = bounds[1][1] - bounds[0][1],
k = 1 / Math.max(dx / w, dy / h),
x = extent[0][0] - k * bounds[0][0] + (w - dx * k) / 2,
y = extent[0][1] - k * bounds[0][1] + (h - dy * k) / 2;
return function(point) {
return [
x + k * point[0],
y + k * point[1]
];
};
}
function getBounds(ring) {
var x0 = y0 = Infinity,
x1 = y1 = -Infinity;
ring.forEach(function(point){
if (point[0] < x0) x0 = point[0];
if (point[0] > x1) x1 = point[0];
if (point[1] < y0) y0 = point[1];
if (point[1] > y1) y1 = point[1];
});
return [
[x0, y0],
[x1, y1]
];
}
</script>
Display the source blob
Display the rendered blob
Raw
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