29:null 2a:["$","title",null,{"children":"Map Projection Morphing | Christophe Yamahata | Observable"}] 2f:T674,# Map Projection Morphing *This notebook is a fork of Mike Bostock’s Projection Transitions. It adds the Mercator projection and focuses on equal-area projections. Watch how the continents change size and shape as the map morphs from one projection to another. In particular, check out the Strebe 1995 and Strebe Asymmetric 2011, both implemented here in D3 from Strebe's own descriptions.* --- ### Mercator vs Equal-Area Projections On 4 September 2026, the United Nations General Assembly adopted the “Correct the Map” resolution that encourages governments, educational institutions, international organizations, and technology companies to use **Equal Earth** or other equal-area projections whenever the relative size of continents matters, rather than the widely used **Mercator** projection. The same day, France announced that its Ministry for Europe and Foreign Affairs would abandon Mercator for its diplomatic maps and adopt **Eckert IV** instead. Like Equal Earth, Eckert IV is equal-area, but the two give continents a slightly different look. 30:Ta75,projectionTitle = { const prevProj = this?.projectionValue; const currentVal = typeof projection === "object" && projection !== null ? (projection.value ?? projection[0]) : projection; const prevVal = typeof prevProj === "object" && prevProj !== null ? (prevProj.value ?? prevProj[0]) : prevProj; const currentName = projections.find((p) => p.value === currentVal)?.name ?? String(currentVal ?? ""); const prevName = projections.find((p) => p.value === prevVal)?.name ?? String(prevVal ?? ""); const isSingle = typeof selectedProjections !== "undefined" && selectedProjections?.length === 1; if (isSingle) { const staticEl = html`

${currentName}

`; staticEl.projectionValue = currentVal; return staticEl; } const hasChanged = Boolean(prevVal) && prevVal !== currentVal; if (!hasChanged && this) { if (this.activeAnimations) { this.activeAnimations.forEach((anim) => { if (!isRunning) anim.pause(); else anim.play(); }); } return this; } const el = html`

${hasChanged ? html`

${prevName}

` : ""}

${currentName}

`; const oldEl = el.querySelector(".old-title"); const newEl = el.querySelector(".new-title"); const animDuration = 400; const animOptions = { duration: animDuration, easing: "cubic-bezier(0.65, 0, 0.35, 1)", fill: "forwards" }; const animations = []; if (oldEl) { animations.push(oldEl.animate([ { offset: 0, opacity: 1, transform: "translateY(0)" }, { offset: 0.35, opacity: 1, transform: "translateY(0)" }, { offset: 1, opacity: 0, transform: "translateY(-1.5rem)" } ], animOptions)); } if (hasChanged && newEl) { animations.push(newEl.animate([ { opacity: 0, transform: "translateY(1.5rem)" }, { opacity: 1, transform: "translateY(0)" } ], animOptions)); } animations.forEach((anim) => { if (!isRunning) anim.pause(); else anim.play(); }); el.projectionValue = currentVal; el.activeAnimations = animations; return el; }31:T65a,viewof centralMeridianControls = { const prevFixed = this ? this.value?.fixedAngle : []; const prevAngle = this ? this.value?.viewpointAngle : 11; const fixedInput = Inputs.checkbox(["Fixed Angle"], { value: prevFixed }); const angleInput = Inputs.range([-180, 180], { value: prevAngle, step: 1, label: htl.html`Central
Meridian (°)` }); function updateState() { const isFixed = fixedInput.value.length > 0; const rangeEl = angleInput.querySelector("input[type='range']"); const numberEl = angleInput.querySelector("input[type='number']"); if (rangeEl) rangeEl.disabled = !isFixed; if (numberEl) numberEl.disabled = !isFixed; fixedInput.style.opacity = isRunning ? "1" : "0.1"; fixedInput.style.pointerEvents = isRunning ? "auto" : "none"; angleInput.style.opacity = isFixed && isRunning ? "1" : "0.1"; angleInput.style.pointerEvents = isFixed && isRunning ? "auto" : "none"; } updateState(); fixedInput.addEventListener("input", updateState); const container = htl.html`

${fixedInput} ${angleInput}

`; container.value = { fixedAngle: fixedInput.value, viewpointAngle: angleInput.value }; const dispatch = () => { container.value = { fixedAngle: fixedInput.value, viewpointAngle: angleInput.value }; container.dispatchEvent(new CustomEvent("input", { bubbles: true })); }; fixedInput.addEventListener("input", dispatch); angleInput.addEventListener("input", dispatch); return container; }32:T821,viewof running = { let isPlaying = true; // Render SVG icons as real HTML/SVG DOM elements const playIcon = () => html``; const pauseIcon = () => html``; const iconContainer = html`${pauseIcon()}`; const labelContainer = html`Pause`; const btn = html``; // Hover and click feedback btn.onmouseover = () => { btn.style.backgroundColor = "#e4e4e7"; btn.style.borderColor = "#a1a1aa"; }; btn.onmouseout = () => { btn.style.backgroundColor = "#f4f4f5"; btn.style.borderColor = "#d4d4d8"; }; btn.onmousedown = () => { btn.style.transform = "scale(0.96)"; }; btn.onmouseup = () => { btn.style.transform = "scale(1)"; }; btn.value = isPlaying; btn.onclick = (event) => { event.stopPropagation(); isPlaying = !isPlaying; if (isPlaying) { iconContainer.replaceChildren(pauseIcon()); labelContainer.textContent = "Pause"; btn.style.color = "#333333"; } else { iconContainer.replaceChildren(playIcon()); labelContainer.textContent = "Play"; btn.style.color = "#2563eb"; } btn.value = isPlaying; btn.dispatchEvent(new CustomEvent("input")); }; return btn; }33:T5e5, --- ### About the Map Projections - **Mercator** preserves local angles and shapes, which is why navigators use it. The price is area: it inflates land toward the poles, so Greenland looks as large as Africa, which is actually about 14 times bigger. - **Equal-area projections** (Equal Earth, Eckert IV, and the other equal-area projections in this notebook) all keep the relative sizes of regions correct. They differ in how they distort shape, and where. - **Strebe 1995**, by Daniel Strebe, is built by a technique called *substitute deprojection*: an Eckert IV map, scaled to fit inside a Mollweide map, is deprojected to the sphere as if it were a Mollweide, then projected back to the plane with Hammer. Every step preserves area, so the result is equal-area. The result is symmetric and, when centred near 11°E, pushes most of the distortion into the Pacific, away from the big land masses. - **Strebe Asymmetric 2011** keeps the Strebe 1995 projection for the northern hemisphere and reshapes the southern one (using the sinusoidal and McBryde-Thomas II projections) to substantially improve Australia and New Zealand, at the cost of a top-bottom asymmetry.34:T47c,viewof display_inspect = { const el = htl.html`

Variables & Functions

⇣ Check to inspect the script

`; const checkbox = el.querySelector("input"); const spacer = el.querySelector("div"); function update() { const show = checkbox.checked; document.querySelectorAll(".observablehq--inspect").forEach(node => { if (el.contains(node)) return; node.style.display = show ? "" : "none"; }); spacer.style.height = show ? "0" : "20vh"; } checkbox.addEventListener("change", update); // Keep watching the DOM for new inspectors const observer = new MutationObserver(update); observer.observe(document.body, { childList: true, subtree: true }); // Initial state update(); // Clean up when the cell is re-run invalidation.then(() => observer.disconnect()); return el; }35:[{"id":"5667cf6ea53cdbed31600d60556314bcefb28a3bbd66abb351464ab8cf0665cc3a4d508f73841f6ffa78ec215f8ee8acf29e09b8429409b30a3c7e4a18cc2f7f","href":"https://static.observableusercontent.com/files/5667cf6ea53cdbed31600d60556314bcefb28a3bbd66abb351464ab8cf0665cc3a4d508f73841f6ffa78ec215f8ee8acf29e09b8429409b30a3c7e4a18cc2f7f","name":"world-110m_withlakes.topo.json","type":"application/json","lastModified":1789912681276,"size":92469}] 2d:{"id":"513413375cdab407","slug":"map-projection-morphing","title":"Map Projection Morphing","thumbnail":"b1d7364da611544eafcb7b101c4a7f5ae82a653b0076518adda52016b2e819cf","access_level":"public","create_time":"$D2026-09-19T15:37:09.123Z","update_time":"$D2026-09-21T19:37:53.937Z","view_time":null,"first_public_time":"$D2026-09-19T17:10:46.644Z","has_unpublished_edits":null,"fork":{"id":"816a5e069fcbf8ae","slug":"projection-transitions","title":"Projection Transitions","owner":{"id":"863951e3ebe4c0ae","login":"d3","name":"D3"}},"stars":0,"starred":false,"owner":{"type":"team","id":"dd67891d326bcfb1","login":"christophe-yamahata","name":"Christophe Yamahata","avatar_url":"https://avatars-next.observableusercontent.com/8256ac716aa8395babba412b2835913d186874fa4190df57a4a28f2e60129876","tier":"starter_2024"},"version":1496,"publish_version":1496,"role":null,"authored":false,"authors":[{"type":"individual","id":"06f083eba60f5a76","login":"christophe-yamahata","name":"Christophe Yamahata","avatar_url":"https://avatars-next.observableusercontent.com/8256ac716aa8395babba412b2835913d186874fa4190df57a4a28f2e60129876","tier":null}],"members":[{"type":"team","id":"dd67891d326bcfb1","login":"christophe-yamahata","name":"Christophe Yamahata","avatar_url":"https://avatars-next.observableusercontent.com/8256ac716aa8395babba412b2835913d186874fa4190df57a4a28f2e60129876","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":true,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":{"id":"5ea5ed43fe2a637d","slug":"maps","title":"Maps","owner":{"id":"dd67891d326bcfb1","login":"christophe-yamahata","name":"Christophe Yamahata"}},"type":"notebook","body":{"title":"Map Projection Morphing","cells":[{"id":0,"value":"$2f","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":356,"value":"$30","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"viewof context = {\n const context = DOM.context2d(width, height);\n context.canvas.style.display = \"block\";\n context.canvas.style.maxWidth = \"100%\";\n context.canvas.value = context;\n return context.canvas;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":366,"value":"viewof selectedProjections = {\n\n const initial = projections.filter(p => p.name === \"Mercator\" || p.name === \"Equal Earth\" || p.name === \"Eckert IV\" || p.name === \"Strebe 1995\" || p.name === \"Strebe Asymmetric 2011\");\n\n const form = Inputs.checkbox(projections, {\n label: \"Active Projections\",\n format: p => p.name,\n value: initial\n });\n\n let previousValue = form.value;\n\n form.addEventListener(\"input\", (event) => {\n if (form.value.length < 1) {\n event.stopPropagation();\n\n form.value = previousValue;\n form.dispatchEvent(new Event(\"input\"));\n } else {\n previousValue = form.value;\n }\n });\n\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":367,"value":"viewof duration = Inputs.radio([200, 800, 1400], {\n value: 800,\n label: \"Display Time\",\n format: x => {\n switch (x) {\n case 200: return \"Short\";\n case 800: return \"Medium\";\n case 1400: return \"Long\";\n default: return `${x} ms`;\n }\n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":371,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":376,"value":"\nviewof showCountries = {\n const prevValue = this ? this.value : [];\n\n const checkbox = Inputs.checkbox([\"Display Countries\"], {\n value: prevValue\n });\n\n function updateState() {\n checkbox.style.opacity = isRunning ? \"1\" : \"0.1\";\n checkbox.style.pointerEvents = isRunning ? \"auto\" : \"none\";\n }\n\n updateState();\n\n const container = htl.html`

\n ${checkbox}\n

`;\n\n container.value = checkbox.value;\n\n checkbox.addEventListener(\"input\", () => {\n updateState();\n container.value = checkbox.value;\n container.dispatchEvent(new CustomEvent(\"input\", { bubbles: true }));\n });\n\n return container;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":359,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":385,"value":"$33","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":354,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":373,"value":"isRunning = running === true || running === \"true\";","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":372,"value":"isFixed = centralMeridianControls.fixedAngle.includes(\"Fixed Angle\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":364,"value":"mutable projectionIndex = 0","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"projection = {\n while (true) {\n const safeIndex = (mutable projectionIndex) % selectedProjections.length;\n yield selectedProjections[safeIndex].value;\n let elapsed = 0;\n\n while (elapsed < duration) {\n await new Promise((resolve) => setTimeout(resolve, 50));\n if (isRunning) {\n elapsed += 50;\n }\n }\n mutable projectionIndex = (safeIndex + 1) % selectedProjections.length;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":109,"value":"function render(projection) {\n const padding = 10;\n\n projection.fitExtent(\n [[padding, padding], [width - padding, height - padding]],\n outline\n );\n\n const path = d3.geoPath(projection, context);\n context.clearRect(0, 0, width, height);\n context.save();\n context.beginPath(), path(outline), context.clip(), context.fillStyle = \"#fff\", context.fillRect(0, 0, width, height);\n context.beginPath(), path(graticule), context.strokeStyle = \"#ccc\", context.stroke();\n context.beginPath(), path(land), context.fillStyle = \"#000\", context.fill();\n context.beginPath(), path(lakes), context.fillStyle = \"#C7EDF3\", context.fill();\n if (showCountries && showCountries.length > 0) {\n context.beginPath();\n path(countryBorders);\n context.strokeStyle = \"#A19D92\";\n context.lineWidth = 0.5;\n context.stroke();\n }\n context.restore();\n context.beginPath(), path(outline), context.strokeStyle = \"#000\", context.stroke();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":365,"value":"mutable angle = 0","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":38,"value":"update = {\n const r0 = mutable previousProjection;\n const r1 = projection;\n\n mutable previousProjection = r1;\n\n const interpolate = (r0 && r0 !== r1)\n ? interpolateProjection(r0, r1)\n : interpolateProjection(r1, r1);\n\n let lastTime = performance.now();\n\n const transitionDuration = 600;\n let morphProgress = 0;\n\n while (true) {\n const now = performance.now();\n const dt = now - lastTime;\n lastTime = now;\n\n if (morphProgress < transitionDuration) {\n morphProgress = Math.min(transitionDuration, morphProgress + dt);\n }\n\n if (isFixed) {\n mutable angle = -centralMeridianControls.viewpointAngle;\n } else if (isRunning) {\n mutable angle = (mutable angle + dt * 0.015) % 360;\n }\n\n const tProgress = morphProgress / transitionDuration;\n const t = Math.min(1, ease(tProgress));\n\n if(isRunning){\n render(interpolate(t).rotate([mutable angle, 0]));\n }\n\n yield;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":347,"value":"mutable previousProjection = null","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":68,"value":"function interpolateProjection(raw0, raw1) {\n const {scale: scale0, translate: translate0} = fit(raw0);\n const {scale: scale1, translate: translate1} = fit(raw1);\n return t => d3.geoProjection((x, y) => lerp2(raw0(x, y), raw1(x, y), t))\n .scale(lerp1(scale0, scale1, t))\n .translate(lerp2(translate0, translate1, t))\n .precision(0.1);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":343,"value":"function lerp1(x0, x1, t) {\n return (1 - t) * x0 + t * x1;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":342,"value":"function lerp2([x0, y0], [x1, y1], t) {\n return [(1 - t) * x0 + t * x1, (1 - t) * y0 + t * y1];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":292,"value":"function fit(raw) {\n const p = d3.geoProjection(raw)\n .fitExtent(\n [[0.5, 0.5], [width - 0.5, height - 0.5]],\n outline\n );\n\n return {\n scale: p.scale(),\n translate: p.translate()\n };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":113,"value":"ease = d3.easeCubicInOut","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":28,"value":"width = 700","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"height = 700","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":21,"value":"outline = ({type: \"Sphere\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"graticule = d3.geoGraticule10()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"world = FileAttachment(\"world-110m_withlakes.topo.json\").json()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"land = topojson.feature(world, world.objects.land)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":375,"value":"lakes = topojson.feature(world, world.objects.lakes)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":374,"value":"countries = topojson.feature(world, world.objects.countries)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":377,"value":"countryBorders = topojson.mesh(world, world.objects.countries, (a, b) => a !== b)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"import * as topojson from \"npm:topojson-client@3\"","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":344,"value":"import * as d3geo from \"npm:d3-geo@2\"","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":345,"value":"import * as d3projection from \"npm:d3-geo-projection@3\"","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":346,"value":"import * as d3ease from \"npm:d3-ease@2\"","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"d3 = ({\n ...d3geo,\n ...d3projection,\n ...d3ease\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":351,"value":"mercatorRaw = (lambda, phi) => {\n const degrees = phi * 180 / Math.PI;\n const clamped = Math.max(-85, Math.min(85, degrees));\n const radians = clamped * Math.PI / 180;\n\n return [\n lambda,\n Math.log(Math.tan(Math.PI / 4 + radians / 2))\n ];\n};","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":379,"value":"eckertIVScaled = (lambda, phi, s = 1.35) => {\n const [x, y] = d3.geoEckert4Raw(lambda, phi);\n return [x * s, y / s];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":380,"value":"mollweideToHammer = (xe, ye, s = 1.35) => {\n const r = Math.sqrt(Math.max(0, 2 - ye * ye));\n const lambdaP = Math.PI * xe / (4 * r);\n const sinPhiP = (2 * Math.asin(Math.SQRT2 * ye / 2) + r * ye) / Math.PI;\n const phiP = Math.asin(Math.max(-1, Math.min(1, sinPhiP)));\n const D = Math.sqrt(2 / (1 + Math.cos(phiP) * Math.cos(lambdaP)));\n return [(2 * D / s) * Math.cos(phiP) * Math.sin(lambdaP), s * D * Math.sin(phiP)];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":369,"value":"strebe1995Raw = (lambda, phi) => mollweideToHammer(...eckertIVScaled(lambda, phi))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":383,"value":"McBrydeThomasII = (lambda, phi) => {\n const C1 = 0.45503, C2 = 1.36509, C3 = 1.41546, CX = 0.22248, CY = 1.44492;\n const k = C3 * Math.sin(phi);\n for (let i = 0; i < 10; ++i) {\n const t = phi / C2;\n const V = (C1 * Math.sin(t) + Math.sin(phi) - k) / (Math.cos(t) / 3 + Math.cos(phi));\n phi -= V;\n if (Math.abs(V) < 1e-10) break;\n }\n const t = phi / C2;\n return [CX * lambda * (1 + 3 * Math.cos(phi) / Math.cos(t)), CY * Math.sin(t)];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":378,"value":"strebe2011Raw = (lambda, phi) => {\n const [x, y] = strebe1995Raw(lambda, phi);\n const gamma = 1.6\n if (phi >= 0) return [x, y];\n\n const x1 = gamma * x, y1 = y / gamma;\n const phiS = y1, lambdaS = x1 / Math.cos(phiS);\n const mbtIIEquatorScale = McBrydeThomasII(1, 0)[0];\n const [x2, y2] = McBrydeThomasII(lambdaS, phiS);\n const ratio = 1 / mbtIIEquatorScale;\n return [x2 * ratio / gamma, y2 * gamma / ratio];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":169,"value":"projections = [\n {name: \"Mercator\", value: mercatorRaw},\n {name: \"Equal Earth\", value: d3.geoEqualEarthRaw},\n {name: \"Eckert IV\", value: d3.geoEckert4Raw},\n {name: \"Tobler hyperelliptical\", value: d3.geoHyperellipticalRaw(0, 2.5, 1.183136)},\n {name: \"Mollweide\", value: d3.geoMollweideRaw},\n {name: \"Hammer\", value: d3.geoHammerRaw(2,2)},\n {name: \"Goode’s homolosine\", value: d3.geoHomolosineRaw},\n {name: \"Boggs eumorphic\", value: d3.geoBoggsRaw},\n {name: \"Sinusoidal\", value: d3.geoSinusoidalRaw},\n {name: \"Bonne\", value: d3.geoBonneRaw(Math.PI / 4)},\n {name: \"Werner\", value: d3.geoBonneRaw(Math.PI / 2)},\n {name: \"Bottomley\", value: d3.geoBottomleyRaw(0.5)},\n {name: \"Eckert VI\", value: d3.geoEckert6Raw},\n {name: \"McBryde-Thomas II\", value: McBrydeThomasII},\n {name: \"Strebe 1995\", value: strebe1995Raw},\n {name: \"Strebe Asymmetric 2011\", value: strebe2011Raw},\n {name: \"Eckert II\", value: d3.geoEckert2Raw},\n {name: \"Hobo-Dyer\", value: d3.geoCylindricalEqualAreaRaw(37.5 * Math.PI / 180)}\n]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W35","stdlib":"2","titling":"auto"}} 2e:"$2d:body"