2b:null 2c:["$","title",null,{"children":"Where am I? | johnx | Observable"}] 31:T5ba,md`Again, longitude is described in degrees of the angle between the radius running from the Prime Meridian to the centre of the Earth and the radius to the position we're measuring. As we move east from 0°, degrees increase up to 180°, and as we move west from 0°, degrees decrease to -180°, until they meet at the antimeridian - the boundary between the Eastern and Western hemispheres in the Pacific Ocean.

_Right: Latitude and longitude, from [Encyclopaedia Britannica](https://www.britannica.com/science/latitude#/media/1/331993/109269)._ ### Finding Longitude Finding longitude requires the navigator to calculate the time difference between their position and a known position. As the Earth rotates 360° every 24 hours, by working out this time difference it is easy to compute how far east or west of the reference point someone is: 360° / 24 hrs = 15° per hour. It takes 4 minutes for the Earth to rotate 1°. > Reliably keeping time on a moving ship is a tricky thing due to motion and changing environmental conditions, explaining the long, interesting history of the quest to build an accurate clock. For more on the history of longitude and John Harrison's efforts to design this clock, we recommend Longitude by Dava Sobel. `32:T41c,md`### Representing Coordinates We've established that we can describe any position on the surface of a sphere as a pair of coordinates that represent the horizontal and vertical angles of a line transecting that position from a reference radius, drawn to the intersection of the equator and the Prime Meridian. If you want more detail, see the [geographic coordinate systems article on Wikipedia](https://en.wikipedia.org/wiki/Geographic_coordinate_system). As with any unit of measurement, there are several ways to represent coordinates. Historically, latitudes and longitudes were represented in **degrees, minutes, seconds**. > ⚠️ Here, 'minute' does not refer to a unit of time, but rather to a fraction of a degree. Referring to the angle measurements, _1°_ is divided into 60 minutes, represented as _60'_, and each minute is divided into 60 seconds, shown as _60"_. Coordinates are represented as _deg° min" sec' N/S, deg° min" sec' E/W_. For example, Big Ben is located at _51°30'02.6"N 0°07'28.6"W_:`33:[{"id":"95600ef673b728dbb8aec95347d32d6c70081d3f1a18296c622f617c2ea1ea00c3bebd070bd1ae484ce66da77f72bdb87738946b9ee63628b8d5e7efeeb2b21e","href":"https://static.observableusercontent.com/files/95600ef673b728dbb8aec95347d32d6c70081d3f1a18296c622f617c2ea1ea00c3bebd070bd1ae484ce66da77f72bdb87738946b9ee63628b8d5e7efeeb2b21e","name":"longitude-latitude-encyclopaedia-britannica.jpg","type":"image/jpeg","lastModified":1619452129264.647,"size":1183406},{"id":"7b6ff41e373e01d7b5b95773e297d40625bd9ccc1936a023a066a7edd8da5eaadec4ab7a565303539e41e001f2e6730f3ee1e259fae4f19dc59e8d6b2f2ec22b","href":"https://static.observableusercontent.com/files/7b6ff41e373e01d7b5b95773e297d40625bd9ccc1936a023a066a7edd8da5eaadec4ab7a565303539e41e001f2e6730f3ee1e259fae4f19dc59e8d6b2f2ec22b","name":"land-50m.json","type":"application/json","lastModified":1619451917326.929,"size":545534},{"id":"44b801d25f3d51690596abba738f56ccf522fedffebd9e8bd5f0972b94a4499ebdbeb732eeb4c9ac278ae459fc3f2889a332c751dca5c62aed1f100b63d50114","href":"https://static.observableusercontent.com/files/44b801d25f3d51690596abba738f56ccf522fedffebd9e8bd5f0972b94a4499ebdbeb732eeb4c9ac278ae459fc3f2889a332c751dca5c62aed1f100b63d50114","name":"geoid.jpg","type":"image/jpeg","lastModified":1619451669946.186,"size":31474},{"id":"b4314b8c320eb24d238cade8b8c0c443cff42c5cba5415bbd448d404f6f0bb6340750786a3001b0471a47fdcdb56af0b5fe2b76bb2aa627cf73fe9b320505fd0","href":"https://static.observableusercontent.com/files/b4314b8c320eb24d238cade8b8c0c443cff42c5cba5415bbd448d404f6f0bb6340750786a3001b0471a47fdcdb56af0b5fe2b76bb2aa627cf73fe9b320505fd0","name":"dutch-boats-in-a-gale.jpg","type":"image/jpeg","lastModified":1619451621070.132,"size":79696}] 2f:{"id":"82b1b335c61f7f79","slug":"where-am-i","title":"Where am I?","thumbnail":"90e5aa78d3bab3883a842be0dfa0ba80dffc65a3e392123429c0113ed6493c60","access_level":"public","create_time":"$D2021-04-26T15:38:53.665Z","update_time":"$D2024-10-04T11:08:37.273Z","view_time":null,"first_public_time":"$D2021-04-27T15:03:59.915Z","fork":false,"stars":4,"starred":false,"owner":{"type":"team","id":"694a515e88970367","login":"johnx25bd","name":"johnx","avatar_url":"https://avatars-next.observableusercontent.com/2913455d7c8937d6db139dd4363a27c3d0ca15eb7cf0dc8a317fbde440d8a165","tier":"starter_2024"},"version":192,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"a7851601ec4f2322","login":"johnx25bd","name":"johnx","avatar_url":"https://avatars-next.observableusercontent.com/2913455d7c8937d6db139dd4363a27c3d0ca15eb7cf0dc8a317fbde440d8a165","tier":null}],"members":[{"type":"individual","id":"a7851601ec4f2322","login":"johnx25bd","name":"johnx","avatar_url":"https://avatars-next.observableusercontent.com/2913455d7c8937d6db139dd4363a27c3d0ca15eb7cf0dc8a317fbde440d8a165","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":{"id":"6debf9a42039b3ad","slug":"a-guide-to-spatial-data","title":"A Guide to Spatial Data","owner":{"id":"694a515e88970367","login":"johnx25bd","name":"johnx"}},"type":"notebook","body":{"title":"Where am I?","cells":[{"id":0,"value":"md`# Where am I?\n\nFor millennia, accurately working out one’s location was one of the most difficult problems humans faced. Knowing where we are is the first step to deciding where we are going. For travellers - and especially mariners, who often had no fixed points of reference to orient themselves by other than the stars - the task of locating one's self was often a matter of life and death.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":3,"value":"md`\n${gale}\n\n_[Dutch Boats in a Gale](https://www.nationalgallery.org.uk/paintings/joseph-mallord-william-turner-dutch-boats-in-a-gale-the-bridgewater-sea-piece), by J.M.W. Turner, 1801, oil on canvas._`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"md`The Earth is round, but it is not a perfect sphere: it is a bit squashed (a shape called an ellipsoid) and lumpy, with mountains, valleys, seamounts and so on. Furthermore, different areas have different densities. The actual shape of the Earth is a [geoid](https://en.wikipedia.org/wiki/Geoid). The planet rotates on its vertical axis. `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"md`${geoid}\n\n_The Earth's geoid with exaggerated height from [SwissTopo](https://www.swisstopo.admin.ch/en/knowledge-facts/surveying-geodesy/geoid.html)._`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"md`### Latitude\n\nImagine a line running through the diameter of a sphere along its vertical axis, connected by a line encircling the horizontal circumference of the sphere (called a meridian). From the centre of the sphere (the midpoint of this diameter line) we can specify any latitude (any position north or south of the equator on the sphere's surface). Latitude is represented as an angle, from 0° (a horizontal line out from the sphere's centre point to the equator) to 90° (a vertical line to the north or south pole).`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"map(equator)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":28,"value":"md`As it turns out, latitude is _relatively_ easy to calculate by measuring the position of either the sun at noon, or the North Star or Southern Cross above the horizon, then doing some trigonometry (adjusting for the time of year). Learn more about working out one's latitude using celestial navigation with this video.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":95,"value":"md`### Longitude\n\nLongitude, on the other hand, is quite a bit trickier to measure. This is because there is no 'east pole' or 'west pole'. Instead, one of the meridians is used as the origin, reference meridian: the 'prime meridian'. There have been several 'prime' meridians [throughout history](https://en.wikipedia.org/wiki/Prime_meridian); the one currently used as the origin in our global reference system runs through Greenwich, UK and the outskirts of Accra, Ghana, dividing the Eastern and Western hemispheres. \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":92,"value":"map(primeMeridian)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":98,"value":"md`_The Prime Meridian in red._`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":103,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":118,"value":"md`\nWith longitude and latitude - the x and y coordinates - we can describe any point on the Earth's surface. \n\n> ⚠️ Notice how this differs from the linguistic convention - usually, we refer to \"latitude and longitude\" when speaking, which breaks from the mathematical convention of ordering coordinates horizontal (x), then vertical (y). This is a constant bugbear for geospatial developers. \n>\n> There is no universally agreed standard for ordering coordinates, so different programming tools / systems represent coordinates inconsistently - some as [x, y], others as [y, x]. If your coordinates aren't showing up or are in the wrong part of the world - the first thing to do is to check the coordinate ordering! More on this [here](https://macwright.com/lonlat/), including which formats, JS APIs and services use which order, from Tom MacWright.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":125,"value":"md`Here is an example point in GeoJSON format. If you look at \\`\\`geometry.coordinates\\`\\` you will find a coordinate pair, ordered \\`\\`[longitude, latitude]\\`\\`. In this case there are no attributes in the properties object.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":127,"value":"point = ({\n type: \"Feature\",\n properties: {},\n geometry: {\n type: \"Point\",\n coordinates: [-1.7578125, 52.05249]\n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":134,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":142,"value":"{\n let container = DOM.element(\"div\", {\n style: `width:${width}px;height:${width / 1.6}px`\n });\n yield container;\n\n osMap(container, {\n center: [51.50069276435504, -0.12460470199584961],\n zoom: 17,\n key: \"f7Kc1U5GO9L0D9RpxPGzA9GfASUdhj2O\",\n style: \"Light\",\n point: [51.50069276435504, -0.12460470199584961]\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":152,"value":"md`This degree-minute-second format can be easy to understand in some contexts, but is not particularly easy for computers to work with. Instead, in computing, coordinates are usually represented in decimal degrees — two float values. \n\nWe can convert between the two formats (degrees, minutes, seconds and decimal degrees) based on the relationships described above. In Python:\n\n\\`\\`\\`python\n\ndef convert_dms_to_decdeg(degrees, minutes, seconds, hemisphere):\n decimal_degrees = degrees + (minutes / 60) + (seconds / 3600)\n\n if hemisphere == \"S\":\n decimal_degrees *= -1\n return decimal_degrees\n\ndms_test = convert_dms_to_decdeg(51, 30, 2.6, \"N\")\nprint(dms_test)\n# 51.0007222222\n\\`\\`\\``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":155,"value":"md`Less frequently, you might find degrees measured in radians. A radian is \"the measure of a central angle subtending an arc equal in length to the radius\" ([dictionary.com](https://www.dictionary.com/browse/radian?s=t)).\n~~~javascript\n// 1 radian == 360 / 2π ≈ 57.2974693618 degrees\n\nvar radians = 1.570797;\nvar decimalDegrees = radians * (360 / (Math.PI * 2));\n\nconsole.log(decimalDegrees);\n// > 90.00003857181117\n\n~~~\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":158,"value":"viewof demoCoords = gbMapCoordinates([-2.679, 54.4248])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":162,"value":"md`| Type | Format | Example | \n| --- | --- |\n| Decimal degrees | \\`[lon, lat]\\` | \\`${JSON.stringify(demoCoords)}\\` |\n| Degrees, minutes, seconds | latitude, longitude | ${decToDMS(demoCoords)} | \n| Radians | \\`(x, y)\\` | \\`[${decDegToRad(demoCoords)\n .map((c) => c.toFixed(5))\n .join()}]\\` |\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":171,"value":"md`There's a quick overview of positioning - how we're able to represent *where* things are on Earth - or in relation to any polyhedron.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":172,"value":"md`**Next read [3D to 2D: Making maps →](https://observablehq.com/@johnx25bd/3d-2d-making-maps)**\n\n**← Or go back to the [table of contents](https://observablehq.com/@johnx25bd/a-guide-to-spatial-data)**`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"md`## Appendices`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":8,"value":"gale = FileAttachment(\"dutch-boats-in-a-gale.jpg\").image()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"geoid = FileAttachment(\"geoid.jpg\").image()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":104,"value":"britannica = FileAttachment(\"longitude-latitude-encyclopaedia-britannica.jpg\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":54,"value":"world = FileAttachment(\"land-50m.json\").json()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":59,"value":"land = topojson.feature(world, world.objects.land)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":71,"value":"graticule = d3.geoGraticule10()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":73,"value":"sphere = ({ type: \"Sphere\" })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":62,"value":"equator = ({\n type: \"MultiLineString\",\n coordinates: [graticule.coordinates[4]]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":67,"value":"latitudes = ({\n type: \"MultiLineString\",\n coordinates: graticule.coordinates.filter((l) => l.length == 3)\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":69,"value":"longitudes = ({\n type: \"MultiLineString\",\n coordinates: graticule.coordinates.filter((l) => l.length > 3)\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":64,"value":"primeMeridian = ({\n type: \"FeatureCollection\",\n features: [\n {\n type: \"Feature\",\n properties: {},\n geometry: {\n type: \"MultiLineString\",\n coordinates: [\n [\n [0, 90],\n [0, 0],\n [0, -90]\n ]\n // [[180, 90], [180, 0], [180, -90]]\n ]\n }\n }\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":82,"value":"height = {\n const [[, y0], [, y1]] = d3.geoPath(orthoProjection).bounds(sphere);\n return y1 - y0;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":87,"value":"rotate = [9, -40]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":42,"value":"md`### Libraries`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":44,"value":"d3 = require(\"https://d3js.org/d3.v4.min.js\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":51,"value":"topojson = require(\"topojson-client@3\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":48,"value":"import {\n formatLatitude,\n formatLongitude,\n outline,\n map as millerMap,\n path as millerPath\n} from \"@d3/graticule-labels\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":149,"value":"html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":31,"value":"md`### Functions`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":146,"value":"import { osMap, gbMapCoordinates } from \"@johnx25bd/os\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":40,"value":"orthoProjection = d3.geoOrthographic()\n// .rotate(rotate)\n// .fitWidth(width, sphere)\n// .precision(0.1)|","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":34,"value":"function map(highlightedMeridian) {\n return html``;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":37,"value":"{\n d3.select(millerMap)\n .append(\"path\")\n .classed(\"equator\", true)\n .attr(\"d\", millerPath(equator));\n\n d3.select(millerMap)\n .append(\"path\")\n .attr(\"d\", millerPath(primeMeridian))\n .classed(\"prime-meridian\", true);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":164,"value":"function decToDMS(decimalCoords) {\n let lng = decimalCoords[0];\n let lat = decimalCoords[1];\n\n let lngDMS = decDegToDMS(lng, true);\n let latDMS = decDegToDMS(lat, false);\n\n return latDMS + \" \" + lngDMS;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":166,"value":"// from https://gist.github.com/mbykovskyy/1c67b0b4ba8da9972488 - thanks @mbykovskyy!\nfunction decDegToDMS(dd, isLng) {\n var dir = dd < 0 ? (isLng ? \"W\" : \"S\") : isLng ? \"E\" : \"N\";\n\n var absDd = Math.abs(dd);\n var deg = absDd | 0;\n var frac = absDd - deg;\n var min = (frac * 60) | 0;\n var sec = frac * 3600 - min * 60;\n // Round it to 2 decimal points.\n sec = Math.round(sec * 100) / 100;\n return deg + \"°\" + min + \"'\" + sec + '\"' + dir;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":168,"value":"function decDegToRad(decimalCoords) {\n return decimalCoords.map((c) => (c * Math.PI) / 180);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W33","stdlib":"1","titling":"auto"}} 30:"$2f:body"