29:null 2a:["$","title",null,{"children":"Strebe 1995 & Strebe Asymmetric 2011 Projections | Christophe Yamahata | Observable"}] 2f:T5c2,Strebe_Map = { const context = DOM.context2d(width, height); const path = d3.geoPath(activeProjection, context); let rasterCanvas = null; for (const canvasBuffer of geoWarp(activeProjection, image, context)) { rasterCanvas = canvasBuffer; context.clearRect(0, 0, width, height); context.save(); context.beginPath(); path({ type: "Sphere" }); context.clip(); if (rasterCanvas) { context.drawImage(rasterCanvas, 0, 0); } context.restore(); yield context.canvas; } context.clearRect(0, 0, width, height); context.save(); context.beginPath(); path({ type: "Sphere" }); context.clip(); if (rasterCanvas) { context.drawImage(rasterCanvas, 0, 0); } context.restore(); if (showLayers.includes("Land")) { context.beginPath(), path(land), context.lineWidth = 0.7, context.strokeStyle = "rgba(50, 50, 40, 0.9)", context.stroke(); } if (showLayers.includes("Countries")) { context.beginPath(), path(countryBorders), context.lineWidth = 0.8, context.strokeStyle = "rgba(50, 50, 40, 0.9)", context.stroke(); } if (showLayers.includes("Graticule")) { context.beginPath(), path(graticule), context.lineWidth = 0.5; context.strokeStyle = "rgba(100, 100, 50, 0.7)", context.stroke(); } if (showLayers.includes("Sphere")) { context.beginPath(), path({ type: "Sphere" }), context.lineWidth = 1, context.strokeStyle = "#999", context.stroke(); } return context.canvas; }30: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; }31:T4f5,image = { const loaders = { satellite: () => FileAttachment("Equirectangular_projection.jpg").image(), topography: () => FileAttachment("Equirectangular-projection-topographic.jpg").image(), topography_USGS_NASA: () => FileAttachment("Equirectangular-projection-topographic_USGS_NASA.jpg").image(), black_marble: () => FileAttachment("Equirectangular_BlackMarble.jpg").image(), bathymetry: () => FileAttachment("Equirectangular_projection_bathymetry_January2004.jpg").image(), perpetual_ocean: () => FileAttachment("Equirectangular_perpetual_ocean.jpg").image(), earth_clouds: () => FileAttachment("Equirectangular-earth-clouds_NASA-GSFC.jpg").image(), GPW2020: () => FileAttachment("population_density_GPW_2020.jpg").image(), vegetation_SPOT4: () => FileAttachment("VGT_S10_19980401.jpg").image(), anthropocene_2012: () => FileAttachment("global_transportation_system_globaia_2012.jpg").image(), aerosol_GEOSFP: () => FileAttachment("Equirectangular-atmosphere_NASA-GEOS_FP_2018235.jpg").image(), AI_vintage: () => FileAttachment("Gemini_Generated_Image.png").image(), }; const load = loaders[selectedImageFile]; if (!load) return null; const img = await load(); img.style.display = 'none'; return img; }32:T801,geoWarp = function*(targetProjection, image, context) { if (!image || !image.complete) return; const w = context.canvas.width; const h = context.canvas.height; const sw = image.naturalWidth || image.width; const sh = image.naturalHeight || image.height; const srcCanvas = document.createElement("canvas"); srcCanvas.width = sw; srcCanvas.height = sh; const srcCtx = srcCanvas.getContext("2d"); srcCtx.drawImage(image, 0, 0); const srcData = srcCtx.getImageData(0, 0, sw, sh).data; // Offscreen target buffer to allow proper context clipping const targetCanvas = document.createElement("canvas"); targetCanvas.width = w; targetCanvas.height = h; const targetCtx = targetCanvas.getContext("2d"); const output = targetCtx.createImageData(w, h); const outData = output.data; const step = 1; for (let y = 0; y < h; y += step) { for (let x = 0; x < w; x += step) { const lonlat = targetProjection.invert([x, y]); if (!lonlat || !Number.isFinite(lonlat[0]) || !Number.isFinite(lonlat[1])) { continue; } const lon = lonlat[0]; const lat = lonlat[1]; if (lon < -180 || lon > 180 || lat < -90 || lat > 90) { continue; } const sx = Math.floor(((lon + 180) / 360) * sw); const sy = Math.floor(((90 - lat) / 180) * sh); if (sx >= 0 && sx < sw && sy >= 0 && sy < sh) { const srcIdx = (sy * sw + sx) * 4; for (let dy = 0; dy < step && y + dy < h; dy++) { for (let dx = 0; dx < step && x + dx < w; dx++) { const outIdx = ((y + dy) * w + (x + dx)) * 4; outData[outIdx] = srcData[srcIdx]; outData[outIdx + 1] = srcData[srcIdx + 1]; outData[outIdx + 2] = srcData[srcIdx + 2]; outData[outIdx + 3] = srcData[srcIdx + 3]; } } } } if (y % 16 === 0) { targetCtx.putImageData(output, 0, 0); yield targetCanvas; } } targetCtx.putImageData(output, 0, 0); yield targetCanvas; }33:[{"id":"accbaf5f78510ca74433f98b1f529d03e6182a00b8d29697e3156aceb96023630f6d8ce42fdcde1c02931e5f36cd0baeb8315217b8e269ff0195a6778bbc5ef6","href":"https://static.observableusercontent.com/files/accbaf5f78510ca74433f98b1f529d03e6182a00b8d29697e3156aceb96023630f6d8ce42fdcde1c02931e5f36cd0baeb8315217b8e269ff0195a6778bbc5ef6","name":"Equirectangular_projection.jpg","type":"image/jpeg","lastModified":1789993843276,"size":238676},{"id":"44e844e68240a35718846eaa5c217d541e4b6bb7245848fe5d6bb90c2cd759a804f3c56dbf681049dd53b6cb26d9911f18210beb1859ea5307fb3e087141a576","href":"https://static.observableusercontent.com/files/44e844e68240a35718846eaa5c217d541e4b6bb7245848fe5d6bb90c2cd759a804f3c56dbf681049dd53b6cb26d9911f18210beb1859ea5307fb3e087141a576","name":"world-50m.json","type":"application/json","lastModified":1789912634275,"size":744301},{"id":"ac7d57ad6c36dfecda04bd16f982fbc396c95e9fed53535131914b421cfe8f460b30ed874972ef496b536ac1f59a1a241e0ceb234136c54861cfc1f7895373b6","href":"https://static.observableusercontent.com/files/ac7d57ad6c36dfecda04bd16f982fbc396c95e9fed53535131914b421cfe8f460b30ed874972ef496b536ac1f59a1a241e0ceb234136c54861cfc1f7895373b6","name":"Equirectangular_perpetual_ocean.jpg","type":"image/jpeg","lastModified":1790003810097,"size":631215},{"id":"9aea9b926c5f7708ca1f13bc3ebef480acf1ea101ca65b3c75f7b67dc21182409ad8f26f327ab576bf25476a51d07ef41334bb187a1b25892922af6aae1fdb00","href":"https://static.observableusercontent.com/files/9aea9b926c5f7708ca1f13bc3ebef480acf1ea101ca65b3c75f7b67dc21182409ad8f26f327ab576bf25476a51d07ef41334bb187a1b25892922af6aae1fdb00","name":"Equirectangular_BlackMarble.jpg","type":"image/jpeg","lastModified":1789993834288,"size":558208},{"id":"01cc9d627ca5ad285ec80ed7bff9e4e00bb5057a457b99f8939a30e83f5a5700d3c4514307f5c31e1bbf89c5fcd3eca9b57a3ab5441c97cd22532a566a8ed357","href":"https://static.observableusercontent.com/files/01cc9d627ca5ad285ec80ed7bff9e4e00bb5057a457b99f8939a30e83f5a5700d3c4514307f5c31e1bbf89c5fcd3eca9b57a3ab5441c97cd22532a566a8ed357","name":"Equirectangular_projection_bathymetry_January2004.jpg","type":"image/jpeg","lastModified":1790005926795,"size":391161},{"id":"cd2820667ec3cf5915f9e4343c123d02152fbbf2ea9d5c05a1f863a8b48c57b48e6dd302fb971523f4bd045056c1c8f5fd1771102f810cc30f9872879409f401","href":"https://static.observableusercontent.com/files/cd2820667ec3cf5915f9e4343c123d02152fbbf2ea9d5c05a1f863a8b48c57b48e6dd302fb971523f4bd045056c1c8f5fd1771102f810cc30f9872879409f401","name":"Equirectangular-projection-topographic.jpg","type":"image/jpeg","lastModified":1790006343029,"size":538556},{"id":"96e0546bf80f69f43dea6f96fb3ddd89915f73d3d5e39dbc0a98cd6eca40c149cc81fe36fc547a5a426e479c2feb0583882fdbcd464bfd3a63349dff4f9b7e7b","href":"https://static.observableusercontent.com/files/96e0546bf80f69f43dea6f96fb3ddd89915f73d3d5e39dbc0a98cd6eca40c149cc81fe36fc547a5a426e479c2feb0583882fdbcd464bfd3a63349dff4f9b7e7b","name":"Equirectangular-projection-topographic_USGS_NASA.jpg","type":"image/jpeg","lastModified":1790104725571,"size":557102},{"id":"bbed0503502991f502d6e18116ac4fa2a438837971185074852f076da20daa0a3afd99cb24030ef43d8ace26bfaaf3e1fa2a977d60f9f4314e2624d9328db9ed","href":"https://static.observableusercontent.com/files/bbed0503502991f502d6e18116ac4fa2a438837971185074852f076da20daa0a3afd99cb24030ef43d8ace26bfaaf3e1fa2a977d60f9f4314e2624d9328db9ed","name":"Equirectangular-earth-clouds_NASA-GSFC.jpg","type":"image/jpeg","lastModified":1790105171761,"size":519577},{"id":"efe4c265afa46c85b1fd672947b3de57a6a3d3f21d6a8b38c463b330c6c560cdb70139a463fadbe473fe7d83aa183bbb9cbc765b310c09258a00cf519c4a8cd8","href":"https://static.observableusercontent.com/files/efe4c265afa46c85b1fd672947b3de57a6a3d3f21d6a8b38c463b330c6c560cdb70139a463fadbe473fe7d83aa183bbb9cbc765b310c09258a00cf519c4a8cd8","name":"Equirectangular-atmosphere_NASA-GEOS_FP_2018235.jpg","type":"image/jpeg","lastModified":1790107171807,"size":198785},{"id":"b4428018be9835d0cd5ec1adc48c4a5c14bc3bb0eb1b76ac04b7a957a76aef9cefef8c765e847fd7f5b1978d48b9688b0ceaa9e5e0c7f0209474fd88526ff571","href":"https://static.observableusercontent.com/files/b4428018be9835d0cd5ec1adc48c4a5c14bc3bb0eb1b76ac04b7a957a76aef9cefef8c765e847fd7f5b1978d48b9688b0ceaa9e5e0c7f0209474fd88526ff571","name":"Gemini_Generated_Image.png","type":"image/png","lastModified":1790118354171,"size":4566323},{"id":"cd03eebfb63d1a854d3997af2aa35b7596a67ba1dca1c8f26f905f4b1c2f445973e75b8a6d2a2a789eb39d249e2944580d0761299f4c7c86dac99bf6d9e13e3e","href":"https://static.observableusercontent.com/files/cd03eebfb63d1a854d3997af2aa35b7596a67ba1dca1c8f26f905f4b1c2f445973e75b8a6d2a2a789eb39d249e2944580d0761299f4c7c86dac99bf6d9e13e3e","name":"population_density_GPW_2020.jpg","type":"image/jpeg","lastModified":1790190486847,"size":270041},{"id":"a33db369672fb9d97712664d7580cc0d6da33241bc4fcdcc1a7300f715a181e540970fc10584ce6365729c63f951e3db96e48877c7e09578b761ca25a806d99c","href":"https://static.observableusercontent.com/files/a33db369672fb9d97712664d7580cc0d6da33241bc4fcdcc1a7300f715a181e540970fc10584ce6365729c63f951e3db96e48877c7e09578b761ca25a806d99c","name":"VGT_S10_19980401.jpg","type":"image/jpeg","lastModified":1790192524366,"size":264658},{"id":"f1b9099ffc35e673daa73d6282a449714b0ec923f90eb506dab0acf560353d30c07c98d436e35804826984d8681a6ca56ff9ad6f2505ae64a49f198c33617805","href":"https://static.observableusercontent.com/files/f1b9099ffc35e673daa73d6282a449714b0ec923f90eb506dab0acf560353d30c07c98d436e35804826984d8681a6ca56ff9ad6f2505ae64a49f198c33617805","name":"global_transportation_system_globaia_2012.jpg","type":"image/jpeg","lastModified":1790195989919,"size":417777}] 2d:{"id":"3db547baefe9d76d","slug":"strebe-1995-and-strebe-asymmetric-2011-projections","title":"Strebe 1995 & Strebe Asymmetric 2011 Projections","thumbnail":"ac596fb7eb912ad21c9122b198ecf7e5b9c2076e2be79c06f8ba8f8b4ad8ed1f","access_level":"public","create_time":"$D2026-09-21T12:13:20.577Z","update_time":"$D2026-09-23T21:03:33.636Z","view_time":null,"first_public_time":"$D2026-09-21T16:19:40.661Z","has_unpublished_edits":null,"fork":false,"stars":1,"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":767,"publish_version":767,"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":"Strebe 1995 & Strebe Asymmetric 2011 Projections","cells":[{"id":1,"value":"# Strebe 1995 & Strebe Asymmetric 2011 Projections\n\nThe **Strebe 1995** equal-area map projection, proposed 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.\n\n**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.\n\n---","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":42,"value":"viewof projectionChoice = Inputs.select(\n [\"Strebe 1995\", \"Strebe Asymmetric 2011\"],\n { label: \"Projection\", value: \"Strebe Asymmetric 2011\" }\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":44,"value":"viewof centralMeridian = {\n const input = Inputs.range([-180, 179], {\n value: 11,\n step: 1,\n label: htl.html`Central
Meridian (°)`\n });\n\n const ewSpan = document.createElement(\"span\");\n ewSpan.style.marginLeft = \"10px\";\n ewSpan.style.fontFamily = \"sans-serif\";\n ewSpan.style.fontSize = \"0.9em\";\n ewSpan.style.color = \"#555\";\n ewSpan.style.verticalAlign = \"middle\";\n\n const updateLabel = (val) => {\n ewSpan.innerHTML = `${Math.abs(val)}°${val >= 0 ? 'E' : 'W'}`;\n };\n\n updateLabel(input.value);\n input.addEventListener(\"input\", () => updateLabel(input.value));\n\n input.appendChild(ewSpan);\n\n return input;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"viewof showLayers = Inputs.checkbox(\n [\"Land\", \"Countries\", \"Graticule\", \"Sphere\"],\n { value: [\"Land\", \"Countries\", \"Graticule\", \"Sphere\"], label: \"Visible Layers\" }\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":32,"value":"viewof selectedImageFile = Inputs.select(\n new Map([\n [\"Topography\", \"topography\"],\n [\"Topography (USGS/NASA)\", \"topography_USGS_NASA\"],\n [\"Satellite world map\", \"satellite\"],\n [\"Bathymetry\", \"bathymetry\"],\n [\"Vegetation (April 1998, SPOT-4)\", \"vegetation_SPOT4\"],\n [\"Earth with clouds (NASA/GSFC)\", \"earth_clouds\"],\n [\"Perpetual ocean (NASA/GSFC)\", \"perpetual_ocean\"],\n [\"Black marble\", \"black_marble\"],\n [\"Anthropocene (globaïa, 2012)\", \"anthropocene_2012\"],\n [\"Population density (GPW 2020)\", \"GPW2020\"],\n [\"Aerosol (2018 model, NASA / GEOS FP)\", \"aerosol_GEOSFP\"],\n [\"AI-generated vintage map\", \"AI_vintage\"]\n ]),\n { value: \"topography\", label: \"World Map\" }\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"viewof width = Inputs.range([200, 1200], { value: 800, step: 100, label: \"Map Width\" })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":17,"value":"$2f","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":34,"value":"{\n const container = html`\n
\n

\n \n

\n Save the generated map in PNG format. \n

\n \n `;\n\n container.querySelector(\"#save-png\").onclick = () => {\n const canvas = Strebe_Map;\n if (!canvas) return;\n\n canvas.toBlob(blob => {\n const url = URL.createObjectURL(blob);\n const a = document.createElement(\"a\");\n a.href = url;\n a.download = (projectionChoice === \"Strebe 1995\" ? \"Strebe1995_\" : \"Strebe2011_\") + selectedImageFile + \"_\"+ width + \"x\" + height+ \".png\";\n a.click();\n URL.revokeObjectURL(url);\n }, \"image/png\");\n };\n\n return container;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"$30","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"import * as d3geo from \"npm:d3-geo@2\"","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"import * as d3projection from \"npm:d3-geo-projection@3\"","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":43,"value":"activeProjection = {\n const proj = projectionChoice === \"Strebe 1995\" ? strebe1995Raw : strebe2011Raw;\n\n return d3.geoProjection(proj)\n .rotate([-centralMeridian, 0, 0])\n .fitExtent([[10, 10], [width - 10, height - 10]], { type: \"Sphere\" })\n .precision(0.1);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":33,"value":"$31","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"height = 0.65*width","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2,"value":"d3 = ({\n ...d3geo,\n ...d3projection,\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"graticule = d3.geoGraticule10()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"world = FileAttachment(\"world-50m.json\").json()","pinned":false,"hidden":false,"mode":"ojs","author":"$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":"$undefined"},{"id":28,"value":"countries = topojson.feature(world, world.objects.countries)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":29,"value":"countryBorders = topojson.mesh(world, world.objects.countries, (a, b) => a !== b)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"sourceProjection = {\n const sw = image.naturalWidth || image.width;\n const sh = image.naturalHeight || image.height;\n\n return d3.geoEquirectangular()\n .fitExtent([[0, 0], [sw, sh]], { type: \"Sphere\" });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":8,"value":"mollweideToHammer = (xe, ye, s = 1.35) => {\n const r = Math.sqrt(Math.max(0, 2 - ye * ye));\n const lambdaP = Math.PI * xe / (4 * r);\n const sinPhiP = (2 * Math.asin(Math.SQRT2 * ye / 2) + r * ye) / Math.PI;\n const phiP = Math.asin(Math.max(-1, Math.min(1, sinPhiP)));\n const D = Math.sqrt(2 / (1 + Math.cos(phiP) * Math.cos(lambdaP)));\n return [(2 * D / s) * Math.cos(phiP) * Math.sin(lambdaP), s * D * Math.sin(phiP)];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"mollweideToHammerInvert = (x, y, s = 1.35) => {\n\n const X = x * s / 2;\n const Y = y / s;\n\n const q = X * X + Y * Y;\n\n if (!Number.isFinite(q) || q > 4 + 1e-10) {\n return [NaN, NaN];\n }\n\n const z = Math.sqrt(Math.max(0, 1 - q / 4));\n\n const sinPhiP = Math.max(-1, Math.min(1, Y * z));\n const phiP = Math.asin(sinPhiP);\n\n const lambdaP = Math.atan2(\n X * z,\n 2 * z * z - 1\n );\n\n const target = sinPhiP;\n\n let lo = -Math.SQRT2;\n let hi = Math.SQRT2;\n\n for (let i = 0; i < 50; i++) {\n const ye = (lo + hi) / 2;\n\n const r = Math.sqrt(\n Math.max(0, 2 - ye * ye)\n );\n\n const value =\n (\n 2 * Math.asin(Math.SQRT2 * ye / 2) +\n r * ye\n ) / Math.PI;\n\n if (value < target) {\n lo = ye;\n } else {\n hi = ye;\n }\n }\n\n const ye = (lo + hi) / 2;\n\n const r = Math.sqrt(\n Math.max(0, 2 - ye * ye)\n );\n\n const xe =\n r < 1e-12\n ? 0\n : (4 * r * lambdaP) / Math.PI;\n\n return [xe, ye];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":21,"value":"eckertIVScaled = (lambda, phi, s = 1.35) => {\n const [x, y] = d3.geoEckert4Raw(lambda, phi);\n return [x * s, y / s];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"strebe1995Raw = {\n const s = 1.35;\n\n const forward = (lambda, phi) => {\n const [xe0, ye0] = d3.geoEckert4Raw(lambda, phi);\n const xe = xe0 * s;\n const ye = ye0 / s;\n return mollweideToHammer(xe, ye, s);\n };\n\n forward.invert = (x, y) => {\n if (!Number.isFinite(x) || !Number.isFinite(y)) return null;\n\n const [xe, ye] = mollweideToHammerInvert(x, y, s);\n if (!Number.isFinite(xe) || !Number.isFinite(ye)) return null;\n\n const xe0 = xe / s;\n const ye0 = ye * s;\n\n const result = d3.geoEckert4Raw.invert(xe0, ye0);\n if (!result || !Number.isFinite(result[0]) || !Number.isFinite(result[1])) {\n return null;\n }\n\n return result;\n };\n\n return forward;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":36,"value":"McBrydeThomasII = (lambda, phi) => {\n const C1 = 0.45503, C2 = 1.36509, C3 = 1.41546, CX = 0.22248, CY = 1.44492;\n const k = C3 * Math.sin(phi);\n for (let i = 0; i < 10; ++i) {\n const t = phi / C2;\n const V = (C1 * Math.sin(t) + Math.sin(phi) - k) / (Math.cos(t) / 3 + Math.cos(phi));\n phi -= V;\n if (Math.abs(V) < 1e-10) break;\n }\n const t = phi / C2;\n return [CX * lambda * (1 + 3 * Math.cos(phi) / Math.cos(t)), CY * Math.sin(t)];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":41,"value":"McBrydeThomasII.invert = (x, y) => {\n const C1 = 0.45503, C2 = 1.36509, C3 = 1.41546, CX = 0.22248, CY = 1.44492;\n const v = y / CY;\n\n if (v < -1 || v > 1) return null;\n\n const theta = C2 * Math.asin(v);\n const sinPhi = (C1 * Math.sin(theta / C2) + Math.sin(theta)) / C3;\n\n if (sinPhi < -1 - 1e-12 || sinPhi > 1 + 1e-12) {\n return null;\n }\n\n const phi = Math.asin(Math.max(-1, Math.min(1, sinPhi)));\n const denom = CX * ( 1 + 3 * Math.cos(theta) / Math.cos(theta / C2) );\n\n if (Math.abs(denom) < 1e-12) return null;\n\n const lambda = x / denom;\n\n return [lambda, phi];\n};","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":37,"value":"strebe2011Raw = function(lambda, phi) {\n const [x, y] = strebe1995Raw(lambda, phi);\n const gamma = 1.6\n if (phi >= 0) return [x, y];\n\n const x1 = gamma * x, y1 = y / gamma;\n const phiS = y1, lambdaS = x1 / Math.cos(phiS);\n const mbtIIEquatorScale = McBrydeThomasII(1, 0)[0];\n const [x2, y2] = McBrydeThomasII(lambdaS, phiS);\n const ratio = 1 / mbtIIEquatorScale;\n return [x2 * ratio / gamma, y2 * gamma / ratio];\n}\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":39,"value":"strebe2011Raw.invert = function(X, Y) {\n if (Y >= 0) {\n return strebe1995Raw.invert(X, Y);\n }\n\n const gamma = 1.6;\n\n const mbtIIEquatorScale = McBrydeThomasII(1, 0)[0];\n const ratio = 1 / mbtIIEquatorScale;\n\n const x2 = X * gamma / ratio;\n const y2 = Y * ratio / gamma;\n\n const result = McBrydeThomasII.invert(x2, y2);\n\n if (!result) return null;\n\n const [lambdaS, phiS] = result;\n\n const x1 = lambdaS * Math.cos(phiS);\n const y1 = phiS;\n\n //\n const x = x1 / gamma;\n const y = y1 * gamma;\n\n return strebe1995Raw.invert(x, y);\n};","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W33","stdlib":"2","titling":"auto"}} 2e:"$2d:body"