31:T411,Icosahedral = { const context = DOM.context2d(width, height); const warp = geoWarp(projection, context, image); if(image_choice=="Mercator projection") warp(mercator_square, image); else if(image_choice=="Mollweide projection") warp(mollweide, image); else if(image_choice=="Equirectangular projection (I)") warp(equirectangular_I, image); else if(image_choice=="Equirectangular projection (II)") warp(equirectangular_II, image); else if(image_choice=="Equirectangular projection (III)") warp(equirectangular_III, image); else if(image_choice=="Equirectangular projection (IV)") warp(equirectangular_IV, image); else if(image_choice=="Equirectangular projection (V)") warp(equirectangular_V, image); else if(image_choice=="Equirectangular projection (VI)") warp(equirectangular_VI, image); const path = d3.geoPath(projection, context); context.lineWidth = lineWidth; context.strokeStyle = "#ccc"; context.beginPath(), path(land), context.stroke(); return context.canvas; }32:T94d,function geoWarp(targetProjection, context, image) { /* * geoWarp is designed to have a similar interface to geoPath -- it takes a * projection and a context, and returns a function. The function can be used * to paint an image onto a canvas context, much like how a path function can * be used to paint GeoJSON geometries. */ return function(sourceProjection, image) { const bounds = d3.geoPath(targetProjection).bounds(sphere); const sourceContext = DOM.canvas(image.width, image.height).getContext("2d"); sourceContext.drawImage(image, 0, 0, image.width, image.height); const source = sourceContext.getImageData(0, 0, image.width, image.height) const sourceData = source.data; const target = context.getImageData(0, 0, width, height); const targetData = target.data; // make a "cheat sheet" by projecting the sphere and filling it; we can use the resulting image data // to decide whether to invert or not. const cheatSheetContext = DOM.context2d(width, height); cheatSheetContext.beginPath(); d3.geoPath(targetProjection, cheatSheetContext)(sphere); cheatSheetContext.fill(); const cheatSheetImageData = cheatSheetContext.getImageData(0, 0, width, height); const cheatSheetData = cheatSheetImageData.data; for (var y = 0; y < target.height; y += 1) { for (var x = 0; x < target.width; x += 1) { let i = (y * target.width + x) * 4; // compute `i` early so we can use it for the cheat sheet const cheatPixelAlpha = cheatSheetData[i + 3]; // if any cheat pixel isn't black, it hasn't been filled when we projected the sphere, so skip it. if (cheatPixelAlpha === 0) { continue; } const p = [x, y]; const s = targetProjection.invert(p); if (!s) continue; const [λ, φ] = s; if (λ > 180 || λ < -180 || φ > 90 || φ < -90) continue; const q = sourceProjection([λ, φ]); const u = Math.round(q[0]), v = Math.round(q[1]); let j = (v * image.width + u) * 4; targetData[i] = sourceData[j]; targetData[++i] = sourceData[++j]; targetData[++i] = sourceData[++j]; targetData[++i] = 255; } } context.putImageData(target, 0, 0); } }33:[{"id":"d724951b4623e39a896974d85dd1b119d5a4230d0533b3bf7d2cf9a4ae77ab400d2e571fdb3fcfa4093dc74880c3a991a66fbf25a3a7a2a88dd50340322dab3f","href":"https://static.observableusercontent.com/files/d724951b4623e39a896974d85dd1b119d5a4230d0533b3bf7d2cf9a4ae77ab400d2e571fdb3fcfa4093dc74880c3a991a66fbf25a3a7a2a88dd50340322dab3f","name":"Icosahedral_from_Mollweide.png","type":"image/png","lastModified":1704835910264.46,"size":249342},{"id":"4fa7099ae3244cb6d6341049303313a0e7111ed902e422391d860102baf972da441adf2515703ad49de87b08149e8261219176ac087a05f5c8f34a08448bee87","href":"https://static.observableusercontent.com/files/4fa7099ae3244cb6d6341049303313a0e7111ed902e422391d860102baf972da441adf2515703ad49de87b08149e8261219176ac087a05f5c8f34a08448bee87","name":"110m.json","type":"application/json","lastModified":1704836888727.472,"size":102116},{"id":"b77b64d1a34b249164ae8ed893a4514e1211b2b58cf413d57334c9bccf665df29cad1f82233be57c5bbcbc98849b96d3879b67d2b2b7c52ded65f123fd08fe69","href":"https://static.observableusercontent.com/files/b77b64d1a34b249164ae8ed893a4514e1211b2b58cf413d57334c9bccf665df29cad1f82233be57c5bbcbc98849b96d3879b67d2b2b7c52ded65f123fd08fe69","name":"Equirectangular_projection.jpg","type":"image/jpeg","lastModified":1704916576586.58,"size":238676},{"id":"e222b7e2827a31623785ad5007c6a0fba999d8e42e6bba28e0042977905d99556660f9168028f4cc8b7f042d5fbc5ea35c9073162096ac9e1ffe5ac5533c4932","href":"https://static.observableusercontent.com/files/e222b7e2827a31623785ad5007c6a0fba999d8e42e6bba28e0042977905d99556660f9168028f4cc8b7f042d5fbc5ea35c9073162096ac9e1ffe5ac5533c4932","name":"Equirectangular_BlackMarble.jpg","type":"image/jpeg","lastModified":1705099706944.188,"size":558208},{"id":"c142213c1d861168c0a9341d82ff3109b55aab49c033d527706498c4e51e10511cb1295b9c3bc3cede01b9b0d9f77dd9b5840b48345094402b2926e6551f0257","href":"https://static.observableusercontent.com/files/c142213c1d861168c0a9341d82ff3109b55aab49c033d527706498c4e51e10511cb1295b9c3bc3cede01b9b0d9f77dd9b5840b48345094402b2926e6551f0257","name":"Equirectangular_perpetual_ocean.jpg","type":"image/jpeg","lastModified":1705101146162.595,"size":631215},{"id":"13a5c58798880a2590d8b1d5cbe463825e3a57888b580ff9e963bfba7619ca745283ccd541de67d8e1cb53f8ecf5796d872d8f356c8d46bb435e344ec45f95b5","href":"https://static.observableusercontent.com/files/13a5c58798880a2590d8b1d5cbe463825e3a57888b580ff9e963bfba7619ca745283ccd541de67d8e1cb53f8ecf5796d872d8f356c8d46bb435e344ec45f95b5","name":"Mollweide_projection.jpg","type":"image/jpeg","lastModified":1704831521069.827,"size":317145},{"id":"7eebc7dbe24b8081349cd480758d31d59882c58b535f6cff9404c93038e5e591798e0a8c52d588091bd141f0c51e1e1470e008067d668a6b7d7a1cd55969cb36","href":"https://static.observableusercontent.com/files/7eebc7dbe24b8081349cd480758d31d59882c58b535f6cff9404c93038e5e591798e0a8c52d588091bd141f0c51e1e1470e008067d668a6b7d7a1cd55969cb36","name":"Icosahedral_from_Mercator.png","type":"image/png","lastModified":1704836018823.821,"size":254877},{"id":"5a25660c4f0f5e7643605d773f8ebaf4bbc75e3422d52af43278cfe30f554342db2a08095282345f4bcf06d439a267779b39b1aa14f869c859142031960bc4cc","href":"https://static.observableusercontent.com/files/5a25660c4f0f5e7643605d773f8ebaf4bbc75e3422d52af43278cfe30f554342db2a08095282345f4bcf06d439a267779b39b1aa14f869c859142031960bc4cc","name":"Mercator_projection_(square).jpg","type":"image/jpeg","lastModified":1704836732323.025,"size":362704},{"id":"d668df1b9ca572bdf8197a4ae23ddee9c647a1c6ad2565e43859978d3f80a949b2c1dcd59e910e686bb195c5c971ae4915f04391449140ff4bcb91131ece2725","href":"https://static.observableusercontent.com/files/d668df1b9ca572bdf8197a4ae23ddee9c647a1c6ad2565e43859978d3f80a949b2c1dcd59e910e686bb195c5c971ae4915f04391449140ff4bcb91131ece2725","name":"Icosahedral_raster_projection.png","type":"image/png","lastModified":1704838886204.911,"size":3771161},{"id":"9565f79c1bf2bb403a081e7f7a6e65bd64874961d592057f4f0065e35bd794eeababc915c7c26a7f9c821d9eda9f6c4bbac7c717f6f0400f66bdcfc6ab3ae11f","href":"https://static.observableusercontent.com/files/9565f79c1bf2bb403a081e7f7a6e65bd64874961d592057f4f0065e35bd794eeababc915c7c26a7f9c821d9eda9f6c4bbac7c717f6f0400f66bdcfc6ab3ae11f","name":"Icosahedral_from_Equirectangular.png","type":"image/png","lastModified":1704917328164.138,"size":216475},{"id":"c6832927df2be84799a2842626e5d64235490cbb30a86ddcbe527eabd4058c06bf25150207981425e3b1ce52cf23382fc3bd9d852b7bca0197b74cb85f02f648","href":"https://static.observableusercontent.com/files/c6832927df2be84799a2842626e5d64235490cbb30a86ddcbe527eabd4058c06bf25150207981425e3b1ce52cf23382fc3bd9d852b7bca0197b74cb85f02f648","name":"Equirectangular_projection_march2004.jpg","type":"image/jpeg","lastModified":1704918158279.239,"size":237005},{"id":"52f15d71d695e01d50a68c493095ab6e1f4292364bb65d4d518b9c5be94f2603a66c23846ffa4549eff73c213f8cfdd8894e939ed7820729d6a3587986411165","href":"https://static.observableusercontent.com/files/52f15d71d695e01d50a68c493095ab6e1f4292364bb65d4d518b9c5be94f2603a66c23846ffa4549eff73c213f8cfdd8894e939ed7820729d6a3587986411165","name":"Icosahedral_from_Equirectangular_march2004.png","type":"image/png","lastModified":1704918672278.961,"size":215482},{"id":"f00e342ebeeedfa4bb9fa2ac7bff1c4f030ec61bb7885b61b8903e6fb5c8b1ba0fca6771a4a58e8d499ac51b88410314fc462892c00a205480ec5f2f9733d553","href":"https://static.observableusercontent.com/files/f00e342ebeeedfa4bb9fa2ac7bff1c4f030ec61bb7885b61b8903e6fb5c8b1ba0fca6771a4a58e8d499ac51b88410314fc462892c00a205480ec5f2f9733d553","name":"Equirectangular_projection_bathymetry_January2004.jpg","type":"image/jpeg","lastModified":1704920308387.678,"size":391161},{"id":"aef45243d754352830fbea14f6b784e053ddb52e7bb166857ba9331e46f95041b26eec87276e0e3adef209a5dbe70132a009445d471729353afce58b3a74d6d8","href":"https://static.observableusercontent.com/files/aef45243d754352830fbea14f6b784e053ddb52e7bb166857ba9331e46f95041b26eec87276e0e3adef209a5dbe70132a009445d471729353afce58b3a74d6d8","name":"Icosahedral_from_Equirectangular_bathymetry_january2004 .png","type":"image/png","lastModified":1704921832517.788,"size":395712},{"id":"69828cee77726ef459338636a12831f904b3869d82fb30b9afa635353222769103de20074de008a66ab3cd6db130c2d156f94f663ca3ad78b2e9b18fb7416846","href":"https://static.observableusercontent.com/files/69828cee77726ef459338636a12831f904b3869d82fb30b9afa635353222769103de20074de008a66ab3cd6db130c2d156f94f663ca3ad78b2e9b18fb7416846","name":"Icosahedral_from_Equirectangular_IV.png","type":"image/png","lastModified":1705008913762.719,"size":416222},{"id":"c34660099e4973d834ac126c44ce43383fa27876d579377eea59f9260c37f06dd350ccf8a1e9c12e487e468aa89591bd5766d91e88ca3a8217e5b7a17e38952c","href":"https://static.observableusercontent.com/files/c34660099e4973d834ac126c44ce43383fa27876d579377eea59f9260c37f06dd350ccf8a1e9c12e487e468aa89591bd5766d91e88ca3a8217e5b7a17e38952c","name":"Equirectangular-projection-topographic.jpg","type":"image/jpeg","lastModified":1705010386551.603,"size":538556},{"id":"2f5a835ac758089be02e4f2170831e8b9c0e4c6c43e3e47df37d8da65ded3ed3ea4d9e38a76e83f0cd06a6b0c569ccbda5e9efe1974097d212522932b91f641e","href":"https://static.observableusercontent.com/files/2f5a835ac758089be02e4f2170831e8b9c0e4c6c43e3e47df37d8da65ded3ed3ea4d9e38a76e83f0cd06a6b0c569ccbda5e9efe1974097d212522932b91f641e","name":"Icosahedral_from_Black_marble.png","type":"image/png","lastModified":1705100222586.152,"size":177013},{"id":"c8994e8faab0e1c679997cda8627fa93626982345e88366893b1b865aad30682c71273af1bdd6d2f1d057be16d6ffccd03239c622966b57f3746196073545702","href":"https://static.observableusercontent.com/files/c8994e8faab0e1c679997cda8627fa93626982345e88366893b1b865aad30682c71273af1bdd6d2f1d057be16d6ffccd03239c622966b57f3746196073545702","name":"Icosahedral_from_perpetual_ocean.png","type":"image/png","lastModified":1705101755843.85,"size":445850}] 2f:{"title":"Icosahedral raster reprojection","cells":[{"id":0,"value":"md`# Icosahedral raster reprojection\n\nThis is a fork from [Jake Low](https://observablehq.com/@jake-low)'s notebook on ***raster reprojection***.\n\n⚠ Rasterisation takes time ⏳ because it has to perform the icosahedral reprojection. Try first with small images... You can also check the final results (PNG images) by clicking on the \"Files\" pane (paper clip 📎).\n`\n ","pinned":false,"hidden":false,"mode":"ojs"},{"id":952,"value":"viewof width = Inputs.select(new Map([[\" 🏃🏻‍♂️ Fast (100 px)\", 100], [\"Rather fast (200 px)\", 200], [\"Rather slow (300 px)\", 300], [\"Slow (400 px)\", 400], [\" ⏳ Very slow (600 px)\", 600], [\" 🐌 Really slow (800 px)\", 800], [\" ❄ Be extremely patient (1100 px)\", 1100], [\" ❄❄❄ Try if you dare (2000 px)\", 2000]]), {value: 200, label: \"Rasterisation speed (Image size)\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":768,"value":"viewof image_choice = Inputs.select([\"Mollweide projection\", \"Mercator projection\", \"Equirectangular projection (I)\", \"Equirectangular projection (II)\", \"Equirectangular projection (III)\", \"Equirectangular projection (IV)\", \"Equirectangular projection (V)\", \"Equirectangular projection (VI)\"], {value: \"Equirectangular projection (I)\", label: \"Starting projection\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":50,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":753,"value":"⮤ Icosahedral raster reprojection from the ${image_choice}.","pinned":false,"hidden":false,"mode":"html"},{"id":777,"value":"

\n⮦ Mollweide projection of the world.","pinned":false,"hidden":false,"mode":"html"},{"id":774,"value":"mollweide_projection = FileAttachment(\"Mollweide_projection.jpg\").image()","pinned":false,"hidden":false,"mode":"ojs"},{"id":803,"value":"\n⮦ Mercador projection (Miller cylindrical projection) of the world between 85°S and 85°N.","pinned":false,"hidden":false,"mode":"html"},{"id":598,"value":"mercator_projection = FileAttachment(\"Mercator_projection_(square).jpg\").image()","pinned":false,"hidden":false,"mode":"ojs"},{"id":896,"value":"\n⮦ Equirectangular projections of the world [Source: Visible Earth, NASA].","pinned":false,"hidden":false,"mode":"html"},{"id":893,"value":"Equirectangular_projection_I = FileAttachment(\"Equirectangular_projection.jpg\").image()","pinned":false,"hidden":false,"mode":"ojs"},{"id":911,"value":"Equirectangular_projection_march2004 = FileAttachment(\"Equirectangular_projection_march2004.jpg\").image()","pinned":false,"hidden":false,"mode":"ojs"},{"id":929,"value":"Equirectangular_projection_bathymetry_january2004 = FileAttachment(\"Equirectangular_projection_bathymetry_January2004.jpg\").image()","pinned":false,"hidden":false,"mode":"ojs"},{"id":1117,"value":"equirectangular_blackmarble = FileAttachment(\"Equirectangular_BlackMarble.jpg\").image()","pinned":false,"hidden":false,"mode":"ojs"},{"id":1098,"value":"\n⮦ Perpetual Ocean [Source: NASA Scientific Visualization Studio].","pinned":false,"hidden":false,"mode":"html"},{"id":1127,"value":"equirectangular_perpetual_ocean = FileAttachment(\"Equirectangular_perpetual_ocean.jpg\").image()","pinned":false,"hidden":false,"mode":"ojs"},{"id":1130,"value":"\n⮦ Another equirectangular projection of the world [Source: Wikimedia].","pinned":false,"hidden":false,"mode":"html"},{"id":1096,"value":"equirectangularProjectionTopographicWorld = FileAttachment(\"Equirectangular-projection-topographic.jpg\").image()","pinned":false,"hidden":false,"mode":"ojs"},{"id":747,"value":"md`-----\n### Appendix`","pinned":false,"hidden":false,"mode":"ojs"},{"id":841,"value":"image = {\n if(image_choice==\"Mercator projection\")\n return mercator_projection\n else if (image_choice==\"Mollweide projection\")\n return mollweide_projection\n else if (image_choice==\"Equirectangular projection (I)\")\n return Equirectangular_projection_I\n else if (image_choice==\"Equirectangular projection (II)\")\n return Equirectangular_projection_march2004\n else if (image_choice==\"Equirectangular projection (III)\")\n return Equirectangular_projection_bathymetry_january2004\n else if (image_choice==\"Equirectangular projection (IV)\")\n return equirectangularProjectionTopographicWorld\n else if (image_choice==\"Equirectangular projection (V)\")\n return equirectangular_blackmarble\n else if (image_choice==\"Equirectangular projection (VI)\")\n return equirectangular_perpetual_ocean\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1035,"value":"rotate = [-80.2, 28, -85.6]","pinned":false,"hidden":false,"mode":"ojs"},{"id":322,"value":"projection = d3.geoIcosahedral() \n .parents([-1, 0, 1, 11, 3, 0, 7, 1, 7, 8, 9, 10, 11, 12, 13, 6, 8, 10, 19, 15])\n .angle(-60)\n .rotate(rotate)\n .fitSize([width, height], sphere)\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":65,"value":"mercator_square = d3.geoMercator()\n.fitExtent([[0, 0], [mercator_projection.width, mercator_projection.height]], sphere)","pinned":false,"hidden":false,"mode":"ojs"},{"id":903,"value":"equirectangular_I = d3.geoEquirectangular()\n.fitExtent([[0, 0], [Equirectangular_projection_I.width, Equirectangular_projection_I.height]], sphere)","pinned":false,"hidden":false,"mode":"ojs"},{"id":914,"value":"equirectangular_II = d3.geoEquirectangular()\n.fitExtent([[0, 0], [Equirectangular_projection_march2004.width, Equirectangular_projection_march2004.height]], sphere)","pinned":false,"hidden":false,"mode":"ojs"},{"id":933,"value":"equirectangular_III = d3.geoEquirectangular()\n.fitExtent([[0, 0], [Equirectangular_projection_bathymetry_january2004.width, Equirectangular_projection_bathymetry_january2004.height]], sphere)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1103,"value":"equirectangular_IV = d3.geoEquirectangular()\n.fitExtent([[0, 0], [equirectangularProjectionTopographicWorld.width, equirectangularProjectionTopographicWorld.height]], sphere)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1123,"value":"equirectangular_V = d3.geoEquirectangular()\n.fitExtent([[0, 0], [equirectangular_blackmarble.width, equirectangular_blackmarble.height]], sphere)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1136,"value":"equirectangular_VI = d3.geoEquirectangular()\n.fitExtent([[0, 0], [equirectangular_perpetual_ocean.width, equirectangular_perpetual_ocean.height]], sphere)","pinned":false,"hidden":false,"mode":"ojs"},{"id":784,"value":"mollweide = d3.geoMollweide()\n .fitExtent([[0, 0], [mollweide_projection.width, mollweide_projection.height]], sphere)","pinned":false,"hidden":false,"mode":"ojs"},{"id":389,"value":"height = width / 1.6","pinned":false,"hidden":false,"mode":"ojs"},{"id":520,"value":"lineWidth = 0.4 + width / 1000","pinned":false,"hidden":false,"mode":"ojs"},{"id":22,"value":"land = topojson.feature(world, world.objects.land)","pinned":false,"hidden":false,"mode":"ojs"},{"id":20,"value":"sphere = ({ type: \"Sphere\" })","pinned":false,"hidden":false,"mode":"ojs"},{"id":879,"value":"world = FileAttachment(\"110m.json\").json()","pinned":false,"hidden":false,"mode":"ojs"},{"id":18,"value":"topojson = require(\"topojson-client@3\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":105,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":7,"value":"d3 = require(\"d3-fetch\", \"d3-geo\", \"d3-geo-projection\", \"d3-geo-polygon\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":724,"value":"stylesheet = html`\n(Images are sized to display properly on wide screens.)\n\n`","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W33","stdlib":"1","titling":"auto"}