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World Airports Voronoi (2014)
- nmg 8y agoThis is gorgeous. For me it recalls Fuller's Dymaxion map. He would be cheering if he had this in his web browser.
- reacweb 8y agoThis gives a lot of importance to small airports in small islands. Big international airports are surrounded by other smaller airports. They are associated with a tiny surface. I can not see how this representation may be of any use for airports.
- acjohnson55 8y agoIt doesn't seem to me that it's designed to be "useful" as much as just interesting.
- jypepin 8y agoI guess that would be useful in a case where you'd want a representation with an importance that is reversely proportional to the airport importance.
- schreiaj 8y agoAbility to divert in an emergency?
- perilunar 8y agoAbsolutely. It's a map of closest airport for any location on earth. You could do different versions of this for different classes of plane (e.g. select a minimum runway length).
- mikeash 8y agoThis has a big influence on which routes a plane can fly. You can’t be more than a certain distance from a usable airport at any time during the flight to mitigate the risk of engine failure resulting in an off-airport landing/crash. See: https://en.m.wikipedia.org/wiki/ETOPS https://en.m.wikipedia.org/wiki/ETOPS
- isostatic 8y agoAnd diversion airports of course vary with things like weather
- amelius 8y agoWhat would happen if distance over sea is penalized by a certain factor? Is there an extension of Voronoi diagrams that addresses this issue?
- emblaegh 8y agoVoronoi diagrams work for any definition of `distance` that may suit your needs. So weighting by airport size and/or sea distance is pretty trivial.
- amelius 8y agoI don't think it's that simple if the definition of distance is a function of position.
- deleted 8y ago[deleted]
- Marazan 8y agoYeah I'm pretty sure that whilst the 'mid' points on Delauny triangulation would be correctly scalped the edges of the Voronoi diagram would be wrong?
- _verandaguy 8y agoA different approach: you can distort the map underneath, similarly to those maps that scale regions as a function of population rather than actual geographic area.
- joakleaf 8y agoI wonder what happens if you "give weight" to each point relative to size of the airport (measured e.g. by number of take-offs/landings per year)?
- deleted 8y ago[deleted]
- deleted 8y ago[deleted]
- sunnyam 8y agoSince Voronoi is a distance based measure, I'm not sure it would look any different. However, if airports were removed by weight, that would be quite interesting - to get a similar view but only for major airports
- catbird 8y agoThen you get a "weighted Voronoi diagram," haha. If the weights are multiplicative, the edges between adjacent cells become circular arcs. It looks cool, but it's much more difficult to generate and analyze. For instance, the region belonging to a generating point is no longer guaranteed to be convex, and may even have holes or be in multiple disconnected pieces. Weighted Voronoi diagrams show up sometimes in multi-agent systems where agents have different speeds, e.g. pursuit-evasion problems, or in facility placement (where to build a new store/warehouse, etc).
- Zeebrommer 8y agoThere must be a correlation with population density
- Demiurge 8y agoIt doesn't look like it. You can have different size airports serving vastly different volumes. It looks like the spacial distance is first factor, and then municipal boundaries. The boundaries are historical and can be based on population.
- jschulenklopper 8y agoYou misread the intention of the parent's comment. It's not that population _is_ taken into account (your interpretation), but that is _should be_ taken into account.
- Demiurge 8y agoHmm, could be, but how can you definitively determine that? :)
- iandioch 8y agoI did a similar visualisation a few months ago, but less polished, for my own curiosity: https://twitter.com/iandioch/status/968938231550107649 https://twitter.com/iandioch/status/968938231550107649
- pandem 8y agoDoesn't work on my mobile (OnePlus5t) without requesting desktop site
- daef 8y agoThis is awesome. Now I'd love to be able to visualize which aiports are flown to/from the one under the mouse... Where can one get this data?
- megaman22 8y agoVoronoi diagrams are so fun. I messed around for months with them after I saw Amit Patel's procedural map generator that used them. http://www-cs-students.stanford.edu/~amitp/game-programming/polygon-map-generation/ http://www-cs-students.stanford.edu/~amitp/game-programming/... Fortune's Algorithm is pretty simple, but it's tricky to get right, particularly if you're also maintaining the information in a form that lets you do something useful with it besides spitting out the points of the Voronoi centers. https://en.wikipedia.org/wiki/Fortune%27s_algorithm https://en.wikipedia.org/wiki/Fortune%27s_algorithm
- OskarS 8y agoI also consider Voronoi diagrams fun, and in my life I've implemented three different algorithms for generating 2D Voronoi diagrams (or Delaunay triangulations, which are the duals of Voronoi diagrams): 1. Fortune's algorithm [0] 2. The Bowyer-Watson algorithm for generating the Delaunay triangulation incrementally [1] 3. Quickhull (which generates the 3D convex hull of points, which is the 2D delaunay triangulation of points). [2] Of these, Quickhull is the simplest, and Bowyer-Watson is by far the hardest. Bowyer-Watson seems very simple, but there are demons hiding in that algorithm, and almost every implementation you can find online is incorrect (for instance, this one [3]). You can tell that these implementations of Bowyer-Watson are incorrect, because every Delaunay triangulation contains the convex hull of the points, and it's easy to tell when they don't. In fact, even the description in Computational Geometry: Algorithms and Applications (a standard textbook) is subtly wrong. The reason Bowyer-Watson is hard is this: it's an incremental algorithm where you add the points one-by-one to an already constructed Delaunay triangulation, you make sure all edges are flipped right, and at the end you have the full triangulation. However: you have to have a triangle to start with. In order for the algorithm to work, this initial "super-triangle", has to contain all the points in the set, and also be made up of points that are not contained in any circumcircle of any combination of three points in the set. However: if three points are colinear (or very close, which it is almost guaranteed some points are going to be), the circumcircle of those three points is MASSIVE (essentially "infinite", covering the entire half-plane). But the super-triangle points still have to be outside of it. This means that the super-triangle points have to be essentially "symbolic" points (not normal points with coordinates, but special magic points), and you have to hard-code special rules for them. It is extremely difficult to implement these rules correctly. Fortune's algorithm is on the surface more complex, but there's less goblins hiding in that algorithm. There's some tricky data-structure stuff, but it's not too bad. Quickhull is fairly straight-forward, and is the algorithm I would recommend if you want to give this whole Voronoi adventure a go (also has the benefit of giving you a 3D convex hull algorithm, which you can have all sorts of fun with!). [0]: https://en.wikipedia.org/wiki/Fortune%27s_algorithm https://en.wikipedia.org/wiki/Fortune%27s_algorithm [1]: https://en.wikipedia.org/wiki/Bowyer%E2%80%93Watson_algorithm https://en.wikipedia.org/wiki/Bowyer%E2%80%93Watson_algorith... [2]: https://en.wikipedia.org/wiki/Quickhull https://en.wikipedia.org/wiki/Quickhull (this description is for the 2D version, but the 3D version is similar) [3]: https://cdn.rawgit.com/axelboc/voronoi-delaunay/v2.1/index.htm https://cdn.rawgit.com/axelboc/voronoi-delaunay/v2.1/index.h...
- mattlondon 8y agoI cant see Baltra Airport in the Galapagos Islands (https://goo.gl/maps/x9PW5i4VWMH2 https://goo.gl/maps/x9PW5i4VWMH2) - it is "near" the most remote Mataveri Airport on Easter Island and may skew the most remote result to another airport? I guess not all airports are included (e.g there is one I've flown into as a tourist to the antarctic peninsula that is missing (https://goo.gl/maps/u54LnTDYb8N2 https://goo.gl/maps/u54LnTDYb8N2) Great visualisation though :)
- perilunar 8y agoYeah, he mentions that: "There are in fact airports on Antarctica, but they are not classed as medium or large, and do not have scheduled services according to this dataset." The list of airports in Antarctica is surprising long, but most of them are ice or snow and probably need to be remade each year. Some are hard to impossible to see on google maps, but many are quite visible. https://en.wikipedia.org/wiki/List_of_airports_in_Antarctica https://en.wikipedia.org/wiki/List_of_airports_in_Antarctica
- harry-wood 8y agoIt says "2,980 large and medium airports with scheduled services from OurAirports.": http://ourairports.com/data/ http://ourairports.com/data/
- M_Bakhtiari 8y agoThere are obviously more airports in the world than this. What are the criteria for inclusion in the visualization?
- calebegg 8y agoIt's at the very top of the description, just below the globe. "2,980 large and medium airports with scheduled services from OurAirports."
- SiempreViernes 8y agoInclusion by http://ourairports.com/data/ http://ourairports.com/data/ in the categories "medium" or "large". > 2,980 large and medium airports with scheduled services from OurAirports.
- NKosmatos 8y agoNice one, actually all Voronoi diagrams are cool. If only there was a webpage/software where someone could click/select points on a map (or even better enter coordinates) and a user Voronoi diagram would be created ;-)
- burfog 8y agoVoronoi diagrams of Penrose tilings are extra cool. There are six at the bottom of this page: http://www.josleys.com/show_gallery.php?galid=284 http://www.josleys.com/show_gallery.php?galid=284 I'd love to see it as real tiles. The nicest looking might be pearly-white granite or quartzite, with pink granite for the pentagons. Adding grey into the mix, I think a floor could be done without same-color adjacent tiles. I wonder where I could buy this.
- MetallicCloud 8y agoThis does the job nicely http://alexbeutel.com/webgl/voronoi.html http://alexbeutel.com/webgl/voronoi.html
- NKosmatos 8y agoYes, thank you. Looks nice, clean is operational and configurable and with ~80% of the functionality I had in mind. I'm sure that with a few tweaks and a map as background/layer it would be perfect. Strange that there isn't something like this around, would be useful for finding the nearest Starbucks, Pizza Hut, drugstore, whatever... If only I/we could have some extra time for all those side projects :-(
- NKosmatos 8y agoJust so that other people don't have to search: http://lpetrich.org/Science/GeometryDemo/GeometryDemo_GMap.html http://lpetrich.org/Science/GeometryDemo/GeometryDemo_GMap.h... and a very good tutorial: https://chriszetter.com/blog/2014/06/15/building-a-voronoi-map-with-d3-and-leaflet/ https://chriszetter.com/blog/2014/06/15/building-a-voronoi-m... on how the UK supermarkets Voronoi map was made: https://chriszetter.com/voronoi-map/examples/uk-supermarkets/ https://chriszetter.com/voronoi-map/examples/uk-supermarkets... also have a look at (code included): http://bl.ocks.org/shimizu/5610671 http://bl.ocks.org/shimizu/5610671
- elicash 8y agoThis is my favorite instance of a voronoi diagram: https://imgur.com/a/zjNWL https://imgur.com/a/zjNWL I actually wrote into the Reese's company to find out what that was happening to their giant cups, and got no reply unfortunately.
- mumrah 8y agoI would guess they have injectors for the filling at the centers of those cells. A Voronoi edge is equidistant from the two points it bisects, so it kind of makes sense that this would happen naturally if the filling is injected at a constant rate.
- drostie 8y agoI'd guess more likely that they are chocolate nozzles -- it seems more straightforward to me to produce a precise chocolate "cup", pour or place the filling inside of it, then pipe a chocolate "lid" onto the cup. Presumably the multiple nozzles of chocolate would help it to settle flatter faster. Edit: there's a video on Facebook that covers the whole process in a minute. My hunch is partly right: the wrapper and chocolate cup are indeed completed first, then a circle of peanut butter is indeed placed in, then the thing is shaken to encourage that peanut butter to fill the space uniformly. However the chocolate "lid" is just plopped on as one wide dollop from a hose, and then blown out across the cup with compressed air: so the Voronoi cells probably come either from this blowing phase, or else the hose has some sort of "spreader" inside of it or so.
- glup 8y agoInteresting to compare with ETOPS (good maps: gc.kls2.com) which governs how far away from acceptable alternate airports a commercial plane can be. It corresponds to safe flying time with a single functional engine. So a lot of the area in some of the larger Voronoi regions, especially in the Southern Hemisphere, is actually unreachable by any commercial flight from the closest airport.
- JoeMalt 8y agoIt's worth noting that ETOPS only applies to 2-engine aircraft; a 4-engine aircraft can travel outside the ETOPS-permitted areas as long as it has enough fuel.
- detaro 8y agoDepends on the jurisdiction, the FAA applies the same rules to 4-engine aircraft that are carrying passengers now.
- glup 8y agoe.g. http://boeing.mediaroom.com/2015-03-18-Boeing-747-8-Intercontinental-Receives-FAA-Approval-for-330-Minute-ETOPS http://boeing.mediaroom.com/2015-03-18-Boeing-747-8-Intercon...
- rimliu 8y agoAnd ETOPS was one of the reason for the trijets. Just recently watched: https://www.youtube.com/watch?v=gxnptDPy47M https://www.youtube.com/watch?v=gxnptDPy47M about this.
- madeofpalk 8y agoWhen people say "ETPOS" these days, it's understood that they're talking about the maximum distance an aircraft of any size can fly from an airport - various regulators still apply such restrictions on aircraft with more than two aircrafts.
- coin 8y ago
- tzahola 8y agoI assume it's using the great circle distance metric. I wonder how it would look like if the metric was "shortest land/sea travel time".
- weeksie 8y agoI've flown in and out of Mataveri and I know it sounds superstitious or whatever, but I felt that isolation. It's amazing to me that the Polynesians were able to colonize so widely. Also, I love Voronoi diagrams. I ran across them many moons ago when I was building a wayfinding application and was looking for ways to generate map meshes—this was not that—but I thought they were super interesting.
- tclancy 8y agoI am in love with the so-so reviews they happily places on the homepage of the airport: https://www.mataverinternational.com/ https://www.mataverinternational.com/ - "It's a small airport with just one place to eat and a few store to buy stuff." Truth in advertising lives!
- mattlondon 8y agoWhat I thought was curious about this airport was that yes, it is indeed very small and very basic (the departure lounge included outdoor seating overlooking the tarmac - a small waist-high fence separating you from the apron), but the flights in and out were on brand new 787s! Easter Island really does feel very remote though. Even though the 787s are jam-packed with tourists, you're flying due-west from Chile for 6 hours to a tiny spec in the middle of the pacific. The in-flight map was mostly just entirely blank the whole time since the island itself is so tiny it didn't really show up! In the museum there they had some really interesting exhibits about how the original inhabitants used interesting navigation aids to find land - e.g. looking for the directions birds were flying or sea-turtles were swimming, or the sea swell etc. Fascinating stuff. https://en.wikipedia.org/wiki/Polynesian_navigation#Navigational_techniques https://en.wikipedia.org/wiki/Polynesian_navigation#Navigati...
- snag 8y ago787 can land because the airstrip there is really long (more than 3Kms according to wikipedia. This airport was chosen by NASA at some point as an emergency landing stop for the shuttle, and paid for it's extension. https://en.wikipedia.org/wiki/Mataveri_International_Airport https://en.wikipedia.org/wiki/Mataveri_International_Airport
- cozzyd 8y agoCome on now what about Willy Field or the South Pole skiway? The USAP kind of has a schedule...
- djsumdog 8y agoIf you want to know more about those Antarctic airstrips, there's a great Wendover video on them: https://www.youtube.com/watch?v=-s3j-ptJD10 https://www.youtube.com/watch?v=-s3j-ptJD10 Most of them are just hard packed ice.
- jtlienwis 8y agoI did some work on Voronoi a few years ago. I made an overlay in Voronoi transparent colored cells that would show for example where the nearest convenience store was to a given location in the city and this would overlay the regular map of the city. I was going to try to sell these to the convenience store as they always had a map of the city they were in somewhere in each store. An improvement would be to run a google map from each store to each house and actually use the mileage to the store the store. This would account for rivers etc that would block the shortest path. There is probably an idea for a startup somewhere there....
- jtlienwis 8y agoWhen I did work on Voronoi, i used the Mathematica built in function. I would get the gps coordinants from Google maps and use them as input. The output put into a google function that could make rectangular colored transparent regions on the map. But this was all 2d.
- kruhft 8y ago#whut? (headline)
- davidw 8y agoInteresting - was looking at some of the larger area ones in the US and learned that Santa Fe has a tiny airport - smaller than the one here near Bend, Oregon in Redmond. Seems Bend is bigger than Santa Fe for that matter... didn't realize that. Which means that the Albuquerque one ends up as the largest, it looks like, followed (eyeballing it) by Elko?
- gpetukhov 8y agoIt's also a (population density) x (per capita income) map.
- evrydayhustling 8y agoI bet the vertices are correct, but shouldn't the lines in between them look like curves? They are projected solutions for the points that are equidistant by great circle distance to two airports, so I think they should themselves be great circle arcs.
- lisper 8y agoThey are great-circle arcs, but the presentation is a projected sphere, so the lines in the center will look straight because you're looking down on the curved part. Zoom out and look at the lines near the edges.
- evrydayhustling 8y agoThanks, you are totally right. Was zoomed in too far.
- lisper 8y agoThis diagram is oddly selective about which airports it includes. It has some class D airports (Modesto, Santa Maria) but not others (Palo Alto, El Monte, Fullerton). There is no pattern that I can discern other than eliminating airports that are too close to each other, which kind of defeats the purpose of this exercise.
- rando444 8y agoI noticed they included most all the tiny regional airports in Iceland, but left out ones like Kulusuk in Greenland, which receives international air traffic.
- lisper 8y agoReceiving international traffic is actually not a good measure of an airport's significance. Grand View International (WN23), for example, receives international traffic (from Canada), but has only a single 1700-foot grass runway. (It's also private.)
- chx 8y agoLHPR does a lot of business for Audi, 33 000 passengers a year between the Hungarian factory and the Ingolstadt parent plant in Germany and also some cargo as well. There are charters as well. So it receives international air traffic, alright but there are no scheduled flights simply because the area airports have no capacity problems. With three capitals -- Vienna, Budapest and Bratislava -- all within an hours drive in an imaginary scenario where those would be congested it would be booming but this is not London.
- runarberg 8y agoThat is weird indeed. Especially since there are regular scheduled flights from the Reykjavík airport[1] to Kulusuk. Reykjavík airport is included, along with most airports that have scheduled flights from there (like Ísafjörður and Egilsstaðir) but not Kulusuk. [1]: not to be confused with the larger Keflavík international airport that handles almost all international flights to Iceland
- 8y ago
- pdelbarba 8y agoThis is interesting because normally I'd assume this would just follow population density (Europe, the NA, Japan, see xkcd.com/1138) but India and China barely have any airports relative to their populations. That's a lot of traveling just to get to an airport.
- cardiffspaceman 8y agoI've been grinding on an observation about the distribution of people on Earth. It can be reduced to the observation that the city of Ushuaia, AR at 55 degrees south is the most southerly city (FWIW the other two contenders for that title are near Ushuaia), while the city of Copenhagen, DK at 55 degrees north is definitely not the most northerly city. Although there is a great deal of land below the Antarctic Circle, there are only research stations there. There isn't as much land above the Arctic Circle, but civilians live above it.
- alexbeloi 8y agoThat's really interesting. Do you think it could be related to the effect of map projection biases? Is that a thing dates far enough back to affect settlement decisions?
- cardiffspaceman 8y agoI haven't done the research but if you look at the kinds of groups that are settled above the Arctic Circle and how they got there, vs how a group would have got to Antarctica, it may just boil down to accessibility. Whalers eventually patrolled Antarctica's seas but, if they tried to farm its shores they didn't get very far. The Polynesian settlers of the South Seas are hard to beat for navigation ability, but one imagines that either the seas were not worth crossing, or the lands were not worth populating, to those navigators. On the other hand, Greenland and Iceland have at times supported Europeans and their agriculture. Antarctica was not well bounded on maps until the Wilkes expedition and others in the 1830's.
- toomanybeersies 8y agoA lot of the subantarctic islands have similar weather to the Faroe Islands in the North Sea. However, the Polynesians were not cold weather people, and the subantarctic islands are extremely remote. It was hard enough as it was for the Polynesians to settle New Zealand, I can't imagine them settling any further south.
- 8y ago
- zeristor 8y agoAm I missing something, there are a number of airports in Antartica, I assume that none of these are commercial though: https://en.wikipedia.org/wiki/List_of_airports_in_Antarctica https://en.wikipedia.org/wiki/List_of_airports_in_Antarctica
- Mogzol 8y agoFrom the bottom of the page: "There are in fact airports on Antarctica, but they are not classed as medium or large, and do not have scheduled services according to this dataset."
- tolger 8y agoAs someone who studied Voronoi diagrams in college, I find this really fascinating. It's a really cool way of visualizing the data.
- dang 8y agoDiscussed from 2015: https://news.ycombinator.com/item?id=10161326 https://news.ycombinator.com/item?id=10161326. (Posted in 2014 too but there weren't really comments: https://news.ycombinator.com/item?id=7557438 https://news.ycombinator.com/item?id=7557438)
- deleted 8y ago[deleted]
- callumprentice 8y agohttp://voronoi.surge.sh/ http://voronoi.surge.sh/ Recently, I was working on a WebGL version that renders all 54,000+ airports and got it working again today after seeing this.It's quite pretty and runs well but needs some love.
- ericnyamu12345 8y agowow.check out this cool forum http://mawazo.byethost7.com/index.php http://mawazo.byethost7.com/index.php