${tip(s.properties.index)}

43:["$","title",null,{"children":"#30DayMapChallenge 2026, Day 3: Polygons | Xavier Olive | Observable"}] 4b:T61c,md`*On the flat map, hover over a polygon for its numbers.* Out of ${fmtM(stats.landKm2)} of land, **${d3.format(".0%")(stats.movedShare)}** would change country, or ${d3.format(".0%")(stats.movedShareNoAntarctica)} leaving Antarctica aside. **Countries whose capital sits near one edge lose the most.** Moscow is at the western end of Russia, Washington near the east coast of the United States, Beijing in the east of China. ${list(stats.losers.filter((d) => d.name !== "Antarctica").slice(0, 4), (d) => `${d.name} (${fmtM(d.change, true)})`)} lose the most land. Russia keeps ${d3.format(".0%")(byName.get("Russia").keptShare)} of its own. **Their far-away land goes to closer capitals.** Ulaanbaatar takes ${fmtM(stats.took("Mongolia", "Russia"))} of Siberia, so Mongolia grows ${d3.format(".1f")(byName.get("Mongolia").cell / byName.get("Mongolia").real)} times. Astana takes ${fmtM(stats.took("Kazakhstan", "Russia"))} of Russia, Tokyo ${fmtM(stats.took("Japan", "Russia"))} of the Russian Far East. Mexico City takes ${fmtM(stats.took("Mexico", "United States of America"))} of the United States, and Nuuk, in Greenland, ${fmtM(stats.took("Greenland", "Canada"))} of northern Canada and ${fmtM(stats.took("Greenland", "United States of America"))} of Alaska. **Antarctica has no capital, so it gets shared out.** Stanley, in the Falkland Islands, takes the largest piece (${fmtM(stats.took("Falkland Is.", "Antarctica"))}), then Wellington (${fmtM(stats.took("New Zealand", "Antarctica"))}) and Canberra (${fmtM(stats.took("Australia", "Antarctica"))}).`4c:Ta91,// ── The flat map, Equal Earth projection, with hover captions ──── drawMap = () => { const W = 1000; const projection = d3.geoEqualEarth().fitWidth(W, {type: "Sphere"}); const path = d3.geoPath(projection); const H = Math.ceil(path.bounds({type: "Sphere"})[1][1]); const uid = `vor-${Math.random().toString(36).slice(2)}`; const tip = (i) => { const d = stats.rows[i]; const capital = sites.find((s) => s.properties.index === i).properties.capital; return [ `${d.name} (${capital})`, `Real land: ${area(d.real)}`, `Nearest-capital land: ${area(d.cell)}`, `Change: ${d.change >= 0 ? "+" : "−"}${area(Math.abs(d.change))}`, d.real >= 1000 ? `Keeps ${d3.format(".0%")(d.kept / d.real)} of its own land` : null ].filter(Boolean).join("\n"); }; const siteOf = new Map(sites.map((s) => [s.properties.name, s])); const labelled = notable.filter((n) => siteOf.has(n.name)); return svg``; } 4d:T13a5,// ── The same map on a slowly rotating globe (drag to turn it), as a function so the view switch can rebuild it drawGlobe = (invalidation) => { const size = Math.min(width, 640); const context = DOM.context2d(size, size); const maxTilt = 45; // degrees: dragging up/down tilts the globe at most this far const speed = 6; // degrees of longitude per second const projection = d3.geoOrthographic().fitExtent([[8, 8], [size - 8, size - 8]], {type: "Sphere"}); const path = d3.geoPath(projection, context); const graticule = d3.geoGraticule10(); const siteOf = new Map(sites.map((s) => [s.properties.name, s])); const labelled = notable.filter((n) => siteOf.has(n.name)); const container = html`

${context.canvas}

Drag the globe to turn it; it starts rotating again when you let go.

`; const canvas = context.canvas; canvas.style.cursor = "grab"; canvas.style.touchAction = "none"; let lon = -10, tilt = -20; // tilt < 0 shows the northern lands let drag = null; const k = 180 / size; // degrees per pixel: dragging across the globe turns it half a turn canvas.addEventListener("pointerdown", (e) => { drag = {x: e.clientX, y: e.clientY, lon, tilt}; canvas.setPointerCapture(e.pointerId); canvas.style.cursor = "grabbing"; e.preventDefault(); }); canvas.addEventListener("pointermove", (e) => { if (!drag) return; lon = drag.lon + (e.clientX - drag.x) * k; tilt = Math.max(-maxTilt, Math.min(maxTilt, drag.tilt - (e.clientY - drag.y) * k)); }); const release = () => { drag = null; canvas.style.cursor = "grab"; }; canvas.addEventListener("pointerup", release); canvas.addEventListener("pointercancel", release); function draw(lon) { projection.rotate([lon, tilt]); const center = [-lon, -tilt]; context.clearRect(0, 0, size, size); context.beginPath(); path({type: "Sphere"}); context.fillStyle = colors.ocean; context.fill(); context.beginPath(); path(graticule); context.strokeStyle = "rgba(255,255,255,0.6)"; context.lineWidth = 0.5; context.stroke(); // All land orange, then each country's own land inside its polygon in grey context.beginPath(); path(land); context.fillStyle = colors.changed; context.fill(); context.fillStyle = colors.kept; for (const s of sites) { const i = s.properties.index; context.save(); context.beginPath(); path(cells[i]); context.clip(); context.beginPath(); path(countries[i]); context.fill(); context.restore(); } context.beginPath(); path(borders); context.strokeStyle = "rgba(51,48,46,0.45)"; context.lineWidth = 0.4; context.stroke(); // New borders, only over land context.save(); context.beginPath(); path(land); context.clip(); context.beginPath(); path(voronoiEdges); context.strokeStyle = "#fff"; context.lineWidth = 1.2; context.lineJoin = "round"; context.stroke(); context.restore(); context.beginPath(); path({type: "Sphere"}); context.strokeStyle = "rgba(51,48,46,0.5)"; context.lineWidth = 1; context.stroke(); // Capitals and labels on the visible side only const visible = (p) => d3.geoDistance(p, center) < Math.PI / 2 - 0.05; context.fillStyle = "#33302e"; for (const s of sites) { const p = s.geometry.coordinates; if (!visible(p)) continue; const [x, y] = projection(p); context.beginPath(); context.arc(x, y, 1.6, 0, 2 * Math.PI); context.fill(); } context.font = "600 12px system-ui, sans-serif"; context.lineJoin = "round"; for (const n of labelled) { const p = siteOf.get(n.name).geometry.coordinates; if (d3.geoDistance(p, center) > 1.2) continue; // labels hide well before the edge (about 69° from the centre) const [x, y] = projection(p); context.textAlign = n.anchor === "end" ? "right" : "left"; const tx = x + (n.dx ?? 6), ty = y + (n.dy ?? -6); const w = context.measureText(n.label ?? n.name).width; const x0 = n.anchor === "end" ? tx - w : tx, x1 = x0 + w; const r = size / 2 - 8, inside = (px, py) => Math.hypot(px - size / 2, py - size / 2) < r - 2; if (!inside(x0, ty - 10) || !inside(x1, ty - 10) || !inside(x0, ty + 2) || !inside(x1, ty + 2)) continue; // whole label must sit on the globe context.strokeStyle = "#fff"; context.lineWidth = 3; context.strokeText(n.label ?? n.name, tx, ty); context.fillStyle = "#1d1a17"; context.fillText(n.label ?? n.name, tx, ty); context.fillStyle = "#33302e"; } } let last = performance.now(), frame; function tick(now) { if (!drag) lon += ((now - last) / 1000) * speed; // lands move west to east, as the Earth turns last = now; draw(lon); frame = requestAnimationFrame(tick); } draw(lon); frame = requestAnimationFrame(tick); invalidation.then(() => cancelAnimationFrame(frame)); return container; } 4e:Tf33,// ── Who keeps, gains and loses what ────────────────────────────── // Countries are painted on a canvas in an equal-area projection (Equal // Earth), one colour each, so every pixel covers the same area. Each land // pixel is then given to the nearest capital. Coastal pixels count for the // share of the pixel that is land (its alpha); where the browser blends two // countries' colours, the pixel takes the owner of the nearest clean pixel // (see unresolvedShare for what is left). stats = { const w = 1600; const projection = d3.geoEqualEarth().fitWidth(w, {type: "Sphere"}); const h = Math.ceil(d3.geoPath(projection).bounds({type: "Sphere"})[1][1]); const canvas = DOM.canvas(w, h); const context = canvas.getContext("2d", {willReadFrequently: true}); const path = d3.geoPath(projection, context); const random = d3.randomLcg(42); const code = new Map(); countries.forEach((f, i) => { let c; do c = 1 + Math.floor(random() * 0xfffffe); while (code.has(c)); code.set(c, i); context.fillStyle = `#${c.toString(16).padStart(6, "0")}`; context.beginPath(); path(f); context.fill(); }); const km2PerPixel = (4 * Math.PI * 6371.0088 ** 2) / d3.geoPath(projection).area({type: "Sphere"}); const {data} = context.getImageData(0, 0, w, h); // Owner of each pixel: country index, -1 for sea, -2 for a blended pixel const owner = new Int16Array(w * h); for (let j = 0; j < w * h; ++j) { if (data[4 * j + 3] === 0) { owner[j] = -1; continue; } owner[j] = code.get((data[4 * j] << 16) | (data[4 * j + 1] << 8) | data[4 * j + 2]) ?? -2; } // Blended pixels take the owner of the nearest clean pixel (up to 3 px away) const resolved = Int16Array.from(owner); for (let y = 0; y < h; ++y) for (let x = 0; x < w; ++x) { const j = y * w + x; if (owner[j] !== -2) continue; search: for (let r = 1; r <= 3; ++r) for (let dy = -r; dy <= r; ++dy) for (let dx = -r; dx <= r; ++dx) { const xx = x + dx, yy = y + dy; if (xx < 0 || yy < 0 || xx >= w || yy >= h) continue; const o = owner[yy * w + xx]; if (o >= 0) { resolved[j] = o; break search; } } } const n = countries.length; const real = new Float64Array(n), cell = new Float64Array(n), kept = new Float64Array(n); const transfers = new Map(); // "to|from" → km² let painted = 0, unresolved = 0; for (let y = 0; y < h; ++y) for (let x = 0; x < w; ++x) { const j = y * w + x; if (owner[j] === -1) continue; const area = km2PerPixel * data[4 * j + 3] / 255; painted += area; const k = resolved[j]; if (k < 0) { unresolved += area; continue; } const p = projection.invert([x + 0.5, y + 0.5]); const near = sites[voronoi.find(p[0], p[1])].properties.index; real[k] += area; cell[near] += area; if (near === k) kept[k] += area; else { const key = `${near}|${k}`; transfers.set(key, (transfers.get(key) ?? 0) + area); } } const capitalOf = new Map(sites.map((s) => [s.properties.index, s.properties.capital])); const rows = countries.map((f, i) => ({ name: f.properties.name, capital: capitalOf.get(i) ?? "", real: real[i], cell: cell[i], kept: kept[i], change: cell[i] - real[i], keptShare: real[i] ? kept[i] / real[i] : NaN })); const index = new Map(countries.map((f, i) => [f.properties.name, i])); const landKm2 = d3.sum(real); const antarctica = rows[index.get("Antarctica")]; return { rows, landKm2, movedShare: 1 - d3.sum(kept) / landKm2, movedShareNoAntarctica: 1 - d3.sum(kept) / (landKm2 - antarctica.real), unresolvedShare: unresolved / painted, winners: d3.sort(rows, (d) => -d.change), losers: d3.sort(rows, (d) => d.change), took: (to, from) => transfers.get(`${index.get(to)}|${index.get(from)}`) ?? 0 // km² of `from` going to `to` }; }4f:[{"id":"fe3ce34e26bdfcf6536e22bd69bc1aae61e1d6981921a41245d0bdd9e9601ee1c6c141758417c6867d8886209dfa422531b8ef78600af12a0f15520fe63cbf2c","href":"https://static.observableusercontent.com/files/fe3ce34e26bdfcf6536e22bd69bc1aae61e1d6981921a41245d0bdd9e9601ee1c6c141758417c6867d8886209dfa422531b8ef78600af12a0f15520fe63cbf2c","name":"capitals.csv","type":"text/csv","lastModified":1793640103458,"size":10045}] 47:{"id":"7b1c6caabfa99c1a","slug":"30-day-map-challenge-2026-day-3-polygons","title":"#30DayMapChallenge 2026, Day 3: Polygons","thumbnail":"81c1f7abf7d9dd50a3e642c5a986b50daca1abce6268c3f68f621543c75d5228","access_level":"public","create_time":"$D2026-11-02T16:06:11.099Z","update_time":"$D2026-11-02T19:34:55.266Z","view_time":null,"first_public_time":"$D2026-11-03T07:25:23.577Z","has_unpublished_edits":null,"fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"6b95df6ccdd0cd40","login":"xoolive","name":"Xavier Olive","avatar_url":"https://avatars-next.observableusercontent.com/e055a445877c5a8ee2da134a257760536c2d1ee2fcd43f3aaf3f40db54e13733","tier":"starter_2024","bio":"Research scientist. 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That's a Voronoi diagram: one polygon per capital, and the polygons are the new countries.\n\nCapitals come from Natural Earth's populated places, matched to the capital that the world-countries dataset lists for each country: Pretoria for South Africa, Sucre for Bolivia, Naypyidaw for Myanmar. 23 small territories and Antarctica have no capital in these data. They get no polygon, and their land goes to the nearest capital like everyone else's. Orange is land that would change country, grey is land that stays where it is. White lines are the new borders, thin dark lines the real ones, dots the capitals.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2,"value":"viewof view = Inputs.radio(new Map([[\"Rotating globe\", \"globe\"], [\"Flat map, hover for the numbers\", \"map\"]]), {value: \"globe\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"// The view chosen above, drawn by the functions in the code section\nview === \"globe\" ? drawGlobe(invalidation) : drawMap()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3,"value":"$4b","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"Inputs.table(stats.rows.filter((d) => d.real > 0 || d.cell > 0), {\n columns: [\"name\", \"capital\", \"real\", \"cell\", \"change\", \"keptShare\"],\n header: {name: \"Country\", capital: \"Capital\", real: \"Real land (km²)\", cell: \"Nearest-capital land (km²)\", change: \"Change (km²)\", keptShare: \"Own land kept\"},\n format: {real: d3.format(\",.0f\"), cell: d3.format(\",.0f\"), change: d3.format(\"+,.0f\"), keptShare: d3.format(\".0%\")},\n sort: \"change\",\n reverse: true\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"---\n\n*Code*","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"$4c","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":25,"value":"$4d","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"// ── Countries, 1:50m ─────────────────────────────────────────────\n// world-atlas (Natural Earth 1:50m), 241 countries and territories.\nworld = fetch(\"https://cdn.jsdelivr.net/npm/world-atlas@2.0.2/countries-50m.json\").then((r) => r.json())","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"countries = topojson.feature(world, world.objects.countries).features.filter((f) => f.geometry)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":8,"value":"land = topojson.feature(world, world.objects.land)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"borders = topojson.mesh(world, world.objects.countries, (a, b) => a !== b)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"// ── Spherical Voronoi, from d3-geo-voronoi ───────────────────────\ngeoVoronoi = import(\"https://cdn.jsdelivr.net/npm/d3-geo-voronoi@2.1.0/+esm\").then((m) => m.geoVoronoi)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"// ── One site per capital ─────────────────────────────────────────\n// index points back to the country in `countries`.\nsites = {\n const byName = new Map(capitals.map((d) => [d.name, d]));\n return countries.flatMap((f, index) => {\n const c = byName.get(f.properties.name);\n return c ? [{type: \"Feature\", properties: {index, name: f.properties.name, capital: c.capital}, geometry: {type: \"Point\", coordinates: [c.lon, c.lat]}}] : [];\n });\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":21,"value":"// ── Capital cities ───────────────────────────────────────────────\n// 217 of the atlas's 241 countries and territories. The capital is the one\n// listed by world-countries (mledoze, npm world-countries@5.1.0), located\n// with Natural Earth's 1:10m populated places. Kept only when the city lies\n// within the country's bounding box, so Norfolk Island doesn't get Jamaica's\n// Kingston. Astana is renamed from Natural Earth's \"Nur-Sultan\"; North\n// Nicosia is entered by hand. Antarctica and 23 small territories without a\n// capital in these data get no site.\ncapitals = FileAttachment(\"capitals.csv\").csv({typed: true})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"voronoi = geoVoronoi(sites)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"// ── Nearest-capital polygon of each country, in the order of `countries`\n// (undefined for countries without a capital)\ncells = {\n const out = new Array(countries.length);\n for (const c of voronoi.polygons().features) out[c.properties.site.properties.index] = c;\n return out;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"// The new borders: outlines of all polygons\nvoronoiEdges = ({type: \"FeatureCollection\", features: cells.filter(Boolean)})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"$4e","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"byName = new Map(stats.rows.map((d) => [d.name, d]))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":17,"value":"// ── Formatting helpers for the text ──────────────────────────────\nfmtM = (km2, signed = false) => `${(signed ? d3.format(\"+.1f\") : d3.format(\".1f\"))(km2 / 1e6)} million km²`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":22,"value":"// Areas for the hover captions: millions above a million km², three\n// significant digits below, and nothing finer than the ~500 km² pixel\narea = (km2) => km2 >= 1e6 ? `${d3.format(\".1f\")(km2 / 1e6)} million km²`\n : km2 >= 1000 ? `${d3.format(\",.3r\")(km2)} km²`\n : \"under 1,000 km²\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"list = (items, f) => {\n const s = items.map(f);\n return s.length > 1 ? `${s.slice(0, -1).join(\", \")} and ${s.at(-1)}` : s.join(\"\");\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"// ── Countries named on the map, at their capital ─────────────────\nnotable = [\n {name: \"Russia\", label: \"Moscow\"},\n {name: \"Mongolia\", label: \"Ulaanbaatar\"},\n {name: \"Kazakhstan\", label: \"Astana\"},\n {name: \"Japan\", label: \"Tokyo\"},\n {name: \"Mexico\", label: \"Mexico City\", anchor: \"end\", dx: -6},\n {name: \"United States of America\", label: \"Washington\"},\n {name: \"Greenland\", label: \"Nuuk\"},\n {name: \"Falkland Is.\", label: \"Stanley\"},\n {name: \"New Zealand\", label: \"Wellington\"},\n {name: \"Australia\", label: \"Canberra\", anchor: \"end\", dx: -6}\n]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"colors = ({ocean: \"#e8eef2\", kept: \"#cfc8c0\", changed: \"#f28e2b\"})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W4f","stdlib":"2"}} 42:null