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Spherical Voronoi Diagram

jasondavies.com

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Re: Spherical Voronoi Diagram

#21

Post by Analemma_ »

WillAdams wrote: post #17
kayo_20211030 wrote: post #12

Thanks and very fun. The graphic "The United States of Voronoi" is another reminder of why the mercator projection is so counter-intuitive at times.

The Mercator projection is perfectly suited to its intended use --- maintaining angles for navigation. That it was pushed into other usages was a function of cold war politics (makes Russia seem larger/more intimidating) and needs to be considered in that context. Arguably, every classroom (and home with children) should have a globe.

> That it was pushed into other usages was a function of cold war politics (makes Russia seem larger/more intimidating) and needs to be considered in that context.

Is this actually true, or was it just done "on autopilot" because before universal public education most people using maps of the entire world were navigators for whom Mercator made the most sense?

I don't know, I just hear a lot of conspiracy theories about the dominance of Mercator. If it's not Cold War politics then it's "white supremacists trying to make North America/Europe larger and Africa smaller", and I think laziness and just going with what worked in the past is a more likely explanation.

Re: Spherical Voronoi Diagram

#22

Post by [deleted] »

Analemma_ wrote: post #21
WillAdams wrote: post #17

Earlier quoted context omitted.

The Mercator projection is perfectly suited to its intended use --- maintaining angles for navigation. That it was pushed into other usages was a function of cold war politics (makes Russia seem larger/more intimidating) and needs to be considered in that context. Arguably, every classroom (and home with children) should have a globe.

> That it was pushed into other usages was a function of cold war politics (makes Russia seem larger/more intimidating) and needs to be considered in that context. Is this actually true, or was it just done "on autopilot" because before universal public education most people using maps of the entire world were navigators for whom Mercator made the most sense? I don't know, I just hear a lot of conspiracy theories abo…

[deleted]

Re: Spherical Voronoi Diagram

#23

Post by trial3 »

zokier wrote: post #16

Reminds me of this little map I created some time ago: https://ibb.co/TPVMCR3 My intent was to simplify the shapes of state borders as much as possible while retaining the topological (?) relationship between states. But there is no fancy math behind my map, it's just hand-drawn mess.

i’m amused by Triangle New York

Re: Spherical Voronoi Diagram

#24

Post by markstos »

Voroni is useful for spatial analysis when you want to assign points to a nearest /something/ like airplane positions to the nearest airport.

I used for intersection crash analysis to make sure each crash was assigned to at most intersection. I combined this with a radius around each intersection so crashes too far away were also not attributed to an intersection.

More here: https://mark.stosberg.com/intersection-crash-analysis-with-q...

Re: Spherical Voronoi Diagram

#25

Post by loremium »

hermitcrab wrote: post #4

I remember seeing something similar to https://www.jasondavies.com/maps/voronoi/capitals/ . But the areas were weighted by the populations of the capitals. You ended up with something quite close to real political maps IIRC.

“You don’t choose anything. You’re born into it, man. One side or the other. You play it out.” Miller (the expanse)

Re: Spherical Voronoi Diagram

#26

Post by stephbook »

WillAdams wrote: post #17
kayo_20211030 wrote: post #12

Thanks and very fun. The graphic "The United States of Voronoi" is another reminder of why the mercator projection is so counter-intuitive at times.

The Mercator projection is perfectly suited to its intended use --- maintaining angles for navigation. That it was pushed into other usages was a function of cold war politics (makes Russia seem larger/more intimidating) and needs to be considered in that context. Arguably, every classroom (and home with children) should have a globe.

The Mercator hate is a remnant of the turn of the decade. The unprivileged "global south" is smaller than Greenland!!

Except that Google Maps (yes maps, not Google Earth) has shown a globe for a decade now.

And, of course, pupils do have access to a globe. But somehow, people always frame it as an unfulfilled necessity that perpetuates "global power imbalances" or stuff like that.

Re: Spherical Voronoi Diagram

#27

Post by ghurtado »

zokier wrote: post #16

Reminds me of this little map I created some time ago: https://ibb.co/TPVMCR3 My intent was to simplify the shapes of state borders as much as possible while retaining the topological (?) relationship between states. But there is no fancy math behind my map, it's just hand-drawn mess.

Very "60s movie cartoon credits". I absolutely love it.

(I guess saying "The Incredibles" would have been shorter, but it feels weird to credit them with this style)

Re: Spherical Voronoi Diagram

#28

Post by ghurtado »

srean wrote: post #18
kayo_20211030 wrote: post #12

Thanks and very fun. The graphic "The United States of Voronoi" is another reminder of why the mercator projection is so counter-intuitive at times.

The problem that Mercator was trying to solve and the solution he came up with is super interesting to me. Very neat. It is still not known for sure how he came up with mathematical details of the stretching and spacing of the latitudes. The actual closed form was discovered much later and that too by sheer accident - by looking at log trig tables and noticing they match the Mercator scaling numerically, upto four pl…

> you will have to constantly steer to follow constant bearing paths

Is this why airline routes look like they are "hopping" on a map?

When I was a kid, I thought this was meant to represent the Z axis (so until today)

Re: Spherical Voronoi Diagram

#29

Post by eugmai86 »

Nice visualization. Putting the cells directly on the sphere makes the nearest-neighbor idea much easier to understand.

On a flat map I always have to ask myself how much of what I’m seeing is geometry and how much is projection distortion

Re: Spherical Voronoi Diagram

#30

Post by srean »

ghurtado wrote: post #28
srean wrote: post #18

Earlier quoted context omitted.

The problem that Mercator was trying to solve and the solution he came up with is super interesting to me. Very neat. It is still not known for sure how he came up with mathematical details of the stretching and spacing of the latitudes. The actual closed form was discovered much later and that too by sheer accident - by looking at log trig tables and noticing they match the Mercator scaling numerically, upto four pl…

> you will have to constantly steer to follow constant bearing paths Is this why airline routes look like they are "hopping" on a map? When I was a kid, I thought this was meant to represent the Z axis (so until today)

Very likely no.

Airline routes between touchpoints usually follow great circles, not constant bearing paths. Great circles are shortest paths and also they do not need any steering (modulo crosswinds etc).

The bearing keeps changing along the great circle path though *, this why sailors of earlier vintage preferred constant bearing paths -- easy to be sure that you are on track, just keep the ship pointed at the required angle with respect to North South direction.

In other words, the kid was damn right.

* Except for North South paths and along Equator paths.

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