
World Airports Voronoi (2014) - JoelSanchez
https://www.jasondavies.com/maps/voronoi/airports/
======
lisper
This 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.

~~~
jasondavies
This is probably the most frequently asked question! The data is from here:
[http://ourairports.com/data/](http://ourairports.com/data/)

I had to limit the number of airports displayed for performance reasons. I
filtered the airport data so that only those airports with scheduled services
and which are denoted "large" or "medium" are included (according to
OurAirports), bringing the number down to 2,980.

~~~
handelaar
Suppose that'll explain why there are at least three airports included in
Ireland that have no scheduled services at all: the data's from nearly a
decade ago

~~~
jasondavies
Interesting. The data is from 2014, which is when I created the visualisation.
Perhaps I should auto-update it every so often!

~~~
handelaar
Most recent item on "recent changes" was five years old in 2014. Galway
Airport's certainly been shut for a lot longer than that.

------
elicash
This 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
I 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
I'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.

~~~
barrkel
I wasn't aware there was anything below the chocolate-like surface, so I
understood you to be saying the same thing as grandparent.

~~~
binarymax
Which country are you in? If you like chocolate and peanut butter (and sugar),
I recommend trying a Reese's cup :)

~~~
barrkel
I am in the UK, and I cannot eat nuts.

~~~
binarymax
Well you're not missing out that much. USA chocolate isn't nearly as good as
UK chocolate.

------
iandioch
I 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)

------
glup
Interesting 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
It'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
Depends on the jurisdiction, the FAA applies the same rules to 4-engine
aircraft that are carrying passengers now.

~~~
glup
e.g.
[http://boeing.mediaroom.com/2015-03-18-Boeing-747-8-Intercon...](http://boeing.mediaroom.com/2015-03-18-Boeing-747-8-Intercontinental-
Receives-FAA-Approval-for-330-Minute-ETOPS)

------
megaman22
Voronoi 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/...](http://www-
cs-students.stanford.edu/~amitp/game-programming/polygon-map-generation/)

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
I 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_algorith...](https://en.wikipedia.org/wiki/Bowyer%E2%80%93Watson_algorithm)

[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.h...](https://cdn.rawgit.com/axelboc/voronoi-
delaunay/v2.1/index.htm)

~~~
bovermyer
I spent a couple weekends trying to implement Voronoi via Fortune's algorithm
in PHP, since there is no existing library for generating them.

I couldn't get past the point of creating a seemingly random mass of
intersecting lines. My math knowledge is lacking (I'm not good at groking
geometry for some reason), so I wasn't sure what was wrong or how to approach
fixing it.

Maybe I should give Quickhull a go. I think I understand what it's doing.

~~~
megaman22
When I did it, I basically had to break down to the point of making a WinForms
app that I could step through the algorithm iteration by iteration, drawing
out the beach-line and and all the circles and edges as it progressed; I had
to have that visualization to see that it was correct.

~~~
bovermyer
This sounds like a good way for me to understand it. I'll have to try this.
Thanks!

------
joakleaf
I 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)?

~~~
catbird
Then 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).

------
weeksie
I'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
I 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
What 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#Navigati...](https://en.wikipedia.org/wiki/Polynesian_navigation#Navigational_techniques)

~~~
snag
787 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)

------
dang
Discussed 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))

------
mattlondon
I 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
Yeah, 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)

------
NKosmatos
Nice 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 ;-)

~~~
MetallicCloud
This does the job nicely
[http://alexbeutel.com/webgl/voronoi.html](http://alexbeutel.com/webgl/voronoi.html)

~~~
NKosmatos
Yes, 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
Just so that other people don't have to search:
[http://lpetrich.org/Science/GeometryDemo/GeometryDemo_GMap.h...](http://lpetrich.org/Science/GeometryDemo/GeometryDemo_GMap.html)

and a very good tutorial: [https://chriszetter.com/blog/2014/06/15/building-a-
voronoi-m...](https://chriszetter.com/blog/2014/06/15/building-a-voronoi-map-
with-d3-and-leaflet/)

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)

------
jtlienwis
I 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....

------
cardiffspaceman
I'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
That'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
I 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
A 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.

------
djsumdog
If 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.

------
tolger
As someone who studied Voronoi diagrams in college, I find this really
fascinating. It's a really cool way of visualizing the data.

------
davidw
Interesting - 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?

------
callumprentice
[http://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.

------
jtlienwis
When 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.

------
evrydayhustling
I 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
They 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
Thanks, you are totally right. Was zoomed in too far.

------
cozzyd
Come on now what about Willy Field or the South Pole skiway? The USAP kind of
has a schedule...

------
tzahola
I 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".

------
daef
This 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?

~~~
aw3c2
[https://openflights.org/data.html](https://openflights.org/data.html)

~~~
daef
awesome, ty!

------
amelius
What would happen if distance over sea is penalized by a certain factor? Is
there an extension of Voronoi diagrams that addresses this issue?

~~~
emblaegh
Voronoi 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
I don't think it's that simple if the definition of distance is a function of
position.

~~~
Marazan
Yeah 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?

------
Zeebrommer
There must be a correlation with population density

~~~
Demiurge
It 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
You 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
Hmm, could be, but how can you definitively determine that? :)

------
nmg
This is gorgeous. For me it recalls Fuller's Dymaxion map.

He would be cheering if he had this in his web browser.

------
zeristor
Am 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
From 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."

------
gpetukhov
It's also a (population density) x (per capita income) map.

------
pdelbarba
This 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.

------
kruhft
#whut? (headline)

------
pandem
Doesn't work on my mobile (OnePlus5t) without requesting desktop site

------
M_Bakhtiari
There are obviously more airports in the world than this. What are the
criteria for inclusion in the visualization?

~~~
SiempreViernes
Inclusion 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.

------
reacweb
This 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.

~~~
schreiaj
Ability to divert in an emergency?

~~~
perilunar
Absolutely. 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
This 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
And diversion airports of course vary with things like weather

