6 ms·

Hexagonal Grids (2013)

furyofantares 6y ago
I love this page. I've used this page as a reference, it saved me a lot of time and left me with a stronger understanding as well. It reminds me of old school web. When google first came on the scene I was amazed at how many informational pages from either hobbyists or professionals existed (but which I wasn't finding with older search engines), where someone just decided to put everything they know about some topic into a page in glorious detail.
- hoten 6y ago
  His page about map generation is an invaluable resource for game developers.
- amitp 6y ago
  Yes, old school web! A few of the others I like: https://faculty.evansville.edu/ck6/tcenters/ https://faculty.evansville.edu/ck6/tcenters/ ; http://paulbourke.net/ http://paulbourke.net/ ; https://pomax.github.io/bezierinfo/ https://pomax.github.io/bezierinfo/ ; https://www.fieggen.com/shoelace/ https://www.fieggen.com/shoelace/ ; https://www.wood-database.com/ https://www.wood-database.com/ ; http://www.oftenpaper.net/sierpinski.htm http://www.oftenpaper.net/sierpinski.htm ; https://www.animatedknots.com/ https://www.animatedknots.com/ . There are lots more out there but social media favors new content rather than timeless content. I want to see more pages like that so, following “Be the change that you wish to see in the world”, I am writing informational pages.
swsieber 6y ago
I remember this page. I used it almost a decade ago when implementing a settlers of catan clone for that was going to be the main project for a class curriculum. I was a TA/RA at the time. It's a great page. It was invaluable to me.
- xenihn 6y ago
  Any chance you still have that project/curriculum? Would love to see it.
  - swsieber 6y ago
    I don't think I do. Though it might be hidden on a hardrive somewhere. I didn't do the curriculum so much as the "reference" implementation. This was for BYU CS 340. If you search those on GitHub you can probably find some students' implementations. The whole class was about working as a group and design patterns.
shwestrick 6y ago
Such an invaluable resource! I spent many hours here while helping develop https://hexiconapp.com/ https://hexiconapp.com/. The axial coordinate system, in particular, makes working with hexagons much simpler.
rgovostes 6y ago
See also several past discussions, though none recent: https://hn.algolia.com/?dateRange=all&page=0&prefix=true&query=redblobgames.com%20hexagons&sort=byPopularity&type=story https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...
type_enthusiast 6y ago
This is from 2013, so I guess it comes up every so often (2019: https://news.ycombinator.com/item?id=19184412 https://news.ycombinator.com/item?id=19184412). But, I've had it bookmarked since the first time I saw it come up. It's a great article for anyone who's ever played a hexagonal game or has thought about making a hexagonal game. The source site also has a lot of great stuff on applications of computer science to less-thought-of aspects of game development (by which I mean people usually think of pixel-blasting 3D engines as "game development", but there's a lot more to it)
devsquid 6y ago
This is cool. I recently wrote an A* pathfinding system for a hex based game. Choosing a good coordinate system 100% makes this easier.
- rendall 6y ago
  Which one did you go for?
  - devsquid 6y ago
    I went with what they call the "Axial coordinates". I think the alternative, "Cube coordinates", causes a lot of issues and confusion when writing game logic.
    - rendall 6y ago
      My imagination fails when I attempt to think of a good reason for using the 'offset' coordinates. If someone knows of one, I'd be open to hearing it, but I suspect that it makes things quite tricky
ChrisMarshallNY 6y ago
That’s useful! Thanks for posting it. I don’t need to do this too often, but I like having choices.
xipho 6y ago
This just came up a bit ago in another thread. RBG is so good. Like I did a while back I'll mention that that work is the reason I could write this Ruby svg viz library https://github.com/SpeciesFileGroup/waxy https://github.com/SpeciesFileGroup/waxy and it be a fun, rather than painful process.
Timothee 6y ago
Ah, I wish I had come across this two weeks ago! I've been doodling with Processing and was working on hexagonal Truchet tiles. (basically random tiles that have paths connecting to any random tiles next to it, with hexagons as tiles instead of squares) I ended up having to figure out some of that stuff again, in particular the coordinate system inside each tile so that I could deal with integer coordinates and translate them into the right fraction of the radius. It was fun to figure out what I needed, so I don't regret it :) And I am also planning on doing something with cubes, so this page will come in handy. Thanks for sharing! I love how it covers all aspects of the problem. Result of the tiling: https://twitter.com/_timothee/status/1330315929641570304 https://twitter.com/_timothee/status/1330315929641570304 Diagram of my coordinate system: https://twitter.com/_timothee/status/1327859098642046976 https://twitter.com/_timothee/status/1327859098642046976
- thewebcount 6y ago
  Sweet! I love Truchet Tiles. (Did you know Truchet was a priest in the 18th century?[0]) I see that Apple's Motion has a Truchet tile generator[1], too. [0] https://en.wikipedia.org/wiki/Sébastien_Truchet https://en.wikipedia.org/wiki/Sébastien_Truchet [1] https://support.apple.com/en-afri/guide/motion/motn5d6778a0/mac https://support.apple.com/en-afri/guide/motion/motn5d6778a0/...
taywrobel 6y ago
I almost never use bookmarks any more, but I’ve had this page bookmarked for the better part of a decade now and still refer to it at least once a year, and I don’t even work in game development.
joshu 6y ago
i've used this guide several times. hooray!
Groxx 6y ago
Red Blob Games has quite a few excellent blog posts. I highly recommend checking out the rest of their blog :)
aidenn0 6y ago
FWIW, I strongly prefer square grids for tabletop games. Hexagonal grids give you precise measurements in exactly 6 directions. If you approximate sqrt(2) as 1.5 then square grids give you pretty darn accurate measurements in 8 directions, including 2 pairs of directions that are orthogonal, which is good for rectangular features like buildings. Furthermore the distance between two points can be quickly calculated with (long-side + 1/2 short-side), which is doable in your head, unlike the distance calculation on a hex grid. Lastly, if you divide the circle into a large number of slices and calculate the average error for path distance using hex or squares, among those slices, the average error (compared to pythogorean) is smaller with squares (obviously for small multiples of 6 and small multiples of 8 respectively, one or the other will be preferred).
- jghn 6y ago
  I always found the hex grid useful in Battletech as your facing has an impact on where you get hit and having 6 sides provides more potential combinations of facing.
  - aidenn0 6y ago
    I find 8 facing directions (4 sides, 4 corners) to be sufficient, but I suppose a hexagon gives you 12 (6 sides, 6 corners).
- rrobukef 6y ago
  On the other hand, for movement along the 8 directions the distance is 41% short, for movement along the 4 main directions, the taxicab distance is 41% longer than the actual distance. For a hexagonal grid, the distance is approximated by counting the number of cells of the shortest path. This has <10% relative error (IIRC) from the actual distance.
  - alisonkisk 6y ago
    If you take diagonals to be 1.5, then distances are <10% high. The half-short-side heuristic (sqrt(aa + bb) ~= a + b/2) makes taxicab very close to correct for non-square distance as well.
yudlejoza 6y ago
For a semi-goofy take (CGPGrey) on hexagons: https://youtu.be/thOifuHs6eY https://youtu.be/thOifuHs6eY
- smexxymoose 6y ago
  Came to the comments just for this link
- amitp 6y ago
  Hexagons are bestagons!
- wumms 6y ago
  More hexagons in nature: Image: "Hexagonal formations on the surface of the Salar de Uyuni (Bolivia, 3,656 meters above sea level) [0] as a result of salt crystallization from evaporating water": https://en.wikipedia.org/wiki/Salar_de_Uyuni#/media/File:Salar_Uyuni_au01.jpg https://en.wikipedia.org/wiki/Salar_de_Uyuni#/media/File:Sal... "During the rainy season (December to March) the salt flat gets covered with a layer of water. As the water evaporates under largely still conditions, the salt forms hexagonal shapes (optimal for heat transfer) on its surface known as Bénard cells, an example of the Rayleigh–Bénard convection [1] phenomena." [2] [0] https://en.wikipedia.org/wiki/Salar_de_Uyuni https://en.wikipedia.org/wiki/Salar_de_Uyuni [1] https://en.wikipedia.org/wiki/Rayleigh%E2%80%93B%C3%A9nard_convection https://en.wikipedia.org/wiki/Rayleigh%E2%80%93B%C3%A9nard_c... [2] https://commons.wikimedia.org/wiki/File:20170809_Bolivia_1581_Uyuni_sRGB_(26204506689).jpg https://commons.wikimedia.org/wiki/File:20170809_Bolivia_158...
  - amitp 6y ago
    Also in nature: there is a giant hexagon on Saturn! http://www-cs-students.stanford.edu/~amitp/diagrams/saturn-hexagon/ http://www-cs-students.stanford.edu/~amitp/diagrams/saturn-h...
jsjohnst 6y ago
Surprised they didn’t cover hexagonal ring data structures. Here[0] is a visualization along with the calculations needed to find nearest neighbors. [0] https://www.flickr.com/photos/jeremyjohnstone/3979747216/ https://www.flickr.com/photos/jeremyjohnstone/3979747216/
cookiengineer 6y ago
Every time I see a post of redblobgames, I realize what a treasure this website is. I've been on this website so often, and pointed other people so many times to it... I hope this never gets lost and is archived. If Amit would write a book about gamedev, I'd definitely buy it and add it to my collection.
neilfrndes 6y ago
Uber's H3 geospatial library uses a lot of these concepts. https://eng.uber.com/h3/ https://eng.uber.com/h3/
mrtnmcc 6y ago
In case anyone is doing signal processing on a hexagonal grid, the https://en.wikipedia.org/wiki/Hexagonal_fast_Fourier_transform https://en.wikipedia.org/wiki/Hexagonal_fast_Fourier_transfo... is pretty useful. I work on consumer phased arrays with hexagonal grids, so the HFFT is useful for computing the far-field beam pattern.
wycy 6y ago
This guide was incredibly helpful a few years ago for one of the Advent of Code challenges.
keyle 6y ago
The guides on that website are fantastic. I wrote multiple games using them as reference. Well written, explained clearly and a wealth of information.
swayvil 6y ago
Are you familiar with the kisrhombille grid? https://en.wikipedia.org/wiki/Truncated_trihexagonal_tiling#Kisrhombille_tiling https://en.wikipedia.org/wiki/Truncated_trihexagonal_tiling#... Scaleable like a square grid. 12 directions.
michaericalribo 6y ago
An added challenge is to efficiently construct hex grids by hand——quickly, at the expense of accuracy. I didn’t have access to a printer early in the pandemic, but wanted to put together maps for a tabletop rpg. This is a clever solution: http://www.rdwarf.com/users/wwonko/hex/irregular/ http://www.rdwarf.com/users/wwonko/hex/irregular/ It has the added benefit of being easy to remember
bransonf 6y ago
And if you want something cool to do with this, try implementing Gliński's variant of chess. It’s something I’m dabbling in, but no doubt an order of magnitude more difficult to implement than orthodox chess. The idea of indexing by cubes is so obvious once you discover it, but maybe not as easy to intuit. Same goes for the data structures.
elihu 6y ago
CGP Grey did a video about hexagons recently. I mean, there's only so much you can say about hexagons really, but he manages to cover a lot of ground. https://www.youtube.com/watch?v=thOifuHs6eY https://www.youtube.com/watch?v=thOifuHs6eY
amitp 6y ago
A surprise to be on HN! Tech notes for the curious: I started the page in 2013 based on notes I had been collecting for ~20 years before that. I update this reference page as I come up with better visualizations and explanations. The last major update was in 2018 when I rewrote it from using d3.js to using vue.js. It greatly reduced the amount of code I was writing, and also let me make the page more interactive. I then added lots more (doubled coordinates, links to papers, axes legends, diagonal directions, side by side comparisons) and improved most of the existing sections. In 2019 the changes were minor, rewriting the map storage section and improving performance. In 2020 I improved the cube/hex animation, the pixel-to-hex section, and added Rust sample code. There's lots more I could add to the page[1] but I don't have any specific plans for when I'll get around to it. The page is svg- and js-heavy. I prerender the diagrams on the server (try loading it without js!). Then using IntersectionObserver on each section of the page, I swap the static diagrams and text with interactive versions. This improves load times somewhat, because almost no JS has to run on page load. For printability I process the page with xsltproc, extract all the links, and turn them into footnotes. Try print preview on the page to see these. Unfortunately the diagrams are broken when printing in Chrome (it works in Firefox) so I need to investigate. [1]: https://www.notion.so/redblobgames/f8bc2f44fba94607afa9c06711d23245?v=0766432cb1534ce582ce35b33cbbef7e&p=7d2d4d624bc5483dafbe615d75ab3902 https://www.notion.so/redblobgames/f8bc2f44fba94607afa9c0671...
- privatemonkey 6y ago
  This is a wonderfull source. Very well written. I'm happy to see it on Hacker News. A few years since I used it last. Didn't know you had rewritten it but I see now the updates you've done, especially in interactivity. I'll continue to use this as my main reference point for hex grids, especially now that I've picked up pace on my virtual tabletop project. Good work!! Thanks
- Calloutman 6y ago
  Thanks for the resource. I'm pretty sure I used it for some of my simulations of C60 molecules hexagonal packing, during my physics PhD a few years back.
- simonh 6y ago
dang 6y ago
If curious see also 2019 https://news.ycombinator.com/item?id=19184412 https://news.ycombinator.com/item?id=19184412 2017 https://news.ycombinator.com/item?id=14627711 https://news.ycombinator.com/item?id=14627711 2015 https://news.ycombinator.com/item?id=9537009 https://news.ycombinator.com/item?id=9537009 2015 https://news.ycombinator.com/item?id=8941588 https://news.ycombinator.com/item?id=8941588 Discussed at the time: https://news.ycombinator.com/item?id=5809724 https://news.ycombinator.com/item?id=5809724
payelsarkar28 6y ago
Hi
- payelsarkar28 6y ago
  Hello
goldenkey 6y ago
In case you want to make a hexagonal cellular automata: https://github.com/churchofthought/HexagonalComplexAutomata https://github.com/churchofthought/HexagonalComplexAutomata Or in WebGL: https://github.com/churchofthought/Grautamaton/tree/complex https://github.com/churchofthought/Grautamaton/tree/complex
rcarmo 6y ago
This is an awesome resource I keep going back to now and again for the sheer fun of it. Glad to see it on HN again (it’s well worth reposting occasionally for folk who haven’t seen it yet).
darkwinx 6y ago
this web site is amazing!!
willis936 6y ago
Good stuff. I’m surprised that I have not seen a voxel-based game that leverages a purely 2D render and expects the player to switch between projections to work with the area.

I love this page. I've used this page as a reference, it saved me a lot of time and left me with a stronger understanding as well. It reminds me of old school web. When google first came on the scene I was amazed at how many informational pages from either hobbyists or professionals existed (but which I wasn't finding with older search engines), where someone just decided to put everything they know about some topic into a page in glorious detail.

hoten 6y ago
His page about map generation is an invaluable resource for game developers.
amitp 6y ago
Yes, old school web! A few of the others I like: https://faculty.evansville.edu/ck6/tcenters/ https://faculty.evansville.edu/ck6/tcenters/ ; http://paulbourke.net/ http://paulbourke.net/ ; https://pomax.github.io/bezierinfo/ https://pomax.github.io/bezierinfo/ ; https://www.fieggen.com/shoelace/ https://www.fieggen.com/shoelace/ ; https://www.wood-database.com/ https://www.wood-database.com/ ; http://www.oftenpaper.net/sierpinski.htm http://www.oftenpaper.net/sierpinski.htm ; https://www.animatedknots.com/ https://www.animatedknots.com/ . There are lots more out there but social media favors new content rather than timeless content. I want to see more pages like that so, following “Be the change that you wish to see in the world”, I am writing informational pages.

swsieber 6y ago

I remember this page. I used it almost a decade ago when implementing a settlers of catan clone for that was going to be the main project for a class curriculum. I was a TA/RA at the time. It's a great page. It was invaluable to me.

xenihn 6y ago
Any chance you still have that project/curriculum? Would love to see it.
- swsieber 6y ago
  I don't think I do. Though it might be hidden on a hardrive somewhere. I didn't do the curriculum so much as the "reference" implementation. This was for BYU CS 340. If you search those on GitHub you can probably find some students' implementations. The whole class was about working as a group and design patterns.

shwestrick 6y ago

Such an invaluable resource! I spent many hours here while helping develop https://hexiconapp.com/ https://hexiconapp.com/. The axial coordinate system, in particular, makes working with hexagons much simpler.

rgovostes 6y ago

See also several past discussions, though none recent: https://hn.algolia.com/?dateRange=all&page=0&prefix=true&query=redblobgames.com%20hexagons&sort=byPopularity&type=story https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...

type_enthusiast 6y ago

This is from 2013, so I guess it comes up every so often (2019: https://news.ycombinator.com/item?id=19184412 https://news.ycombinator.com/item?id=19184412). But, I've had it bookmarked since the first time I saw it come up. It's a great article for anyone who's ever played a hexagonal game or has thought about making a hexagonal game. The source site also has a lot of great stuff on applications of computer science to less-thought-of aspects of game development (by which I mean people usually think of pixel-blasting 3D engines as "game development", but there's a lot more to it)

devsquid 6y ago

This is cool. I recently wrote an A* pathfinding system for a hex based game. Choosing a good coordinate system 100% makes this easier.

rendall 6y ago
Which one did you go for?
- devsquid 6y ago
  I went with what they call the "Axial coordinates". I think the alternative, "Cube coordinates", causes a lot of issues and confusion when writing game logic.
  - rendall 6y ago
    My imagination fails when I attempt to think of a good reason for using the 'offset' coordinates. If someone knows of one, I'd be open to hearing it, but I suspect that it makes things quite tricky

ChrisMarshallNY 6y ago

That’s useful! Thanks for posting it. I don’t need to do this too often, but I like having choices.

xipho 6y ago

This just came up a bit ago in another thread. RBG is so good. Like I did a while back I'll mention that that work is the reason I could write this Ruby svg viz library https://github.com/SpeciesFileGroup/waxy https://github.com/SpeciesFileGroup/waxy and it be a fun, rather than painful process.

Timothee 6y ago

Ah, I wish I had come across this two weeks ago! I've been doodling with Processing and was working on hexagonal Truchet tiles. (basically random tiles that have paths connecting to any random tiles next to it, with hexagons as tiles instead of squares) I ended up having to figure out some of that stuff again, in particular the coordinate system inside each tile so that I could deal with integer coordinates and translate them into the right fraction of the radius. It was fun to figure out what I needed, so I don't regret it :) And I am also planning on doing something with cubes, so this page will come in handy. Thanks for sharing! I love how it covers all aspects of the problem. Result of the tiling: https://twitter.com/_timothee/status/1330315929641570304 https://twitter.com/_timothee/status/1330315929641570304 Diagram of my coordinate system: https://twitter.com/_timothee/status/1327859098642046976 https://twitter.com/_timothee/status/1327859098642046976

thewebcount 6y ago
Sweet! I love Truchet Tiles. (Did you know Truchet was a priest in the 18th century?[0]) I see that Apple's Motion has a Truchet tile generator[1], too. [0] https://en.wikipedia.org/wiki/Sébastien_Truchet https://en.wikipedia.org/wiki/Sébastien_Truchet [1] https://support.apple.com/en-afri/guide/motion/motn5d6778a0/mac https://support.apple.com/en-afri/guide/motion/motn5d6778a0/...

taywrobel 6y ago

I almost never use bookmarks any more, but I’ve had this page bookmarked for the better part of a decade now and still refer to it at least once a year, and I don’t even work in game development.

joshu 6y ago

i've used this guide several times. hooray!

Groxx 6y ago

Red Blob Games has quite a few excellent blog posts. I highly recommend checking out the rest of their blog :)

aidenn0 6y ago

FWIW, I strongly prefer square grids for tabletop games. Hexagonal grids give you precise measurements in exactly 6 directions. If you approximate sqrt(2) as 1.5 then square grids give you pretty darn accurate measurements in 8 directions, including 2 pairs of directions that are orthogonal, which is good for rectangular features like buildings. Furthermore the distance between two points can be quickly calculated with (long-side + 1/2 short-side), which is doable in your head, unlike the distance calculation on a hex grid. Lastly, if you divide the circle into a large number of slices and calculate the average error for path distance using hex or squares, among those slices, the average error (compared to pythogorean) is smaller with squares (obviously for small multiples of 6 and small multiples of 8 respectively, one or the other will be preferred).

jghn 6y ago
I always found the hex grid useful in Battletech as your facing has an impact on where you get hit and having 6 sides provides more potential combinations of facing.
- aidenn0 6y ago
  I find 8 facing directions (4 sides, 4 corners) to be sufficient, but I suppose a hexagon gives you 12 (6 sides, 6 corners).
rrobukef 6y ago
On the other hand, for movement along the 8 directions the distance is 41% short, for movement along the 4 main directions, the taxicab distance is 41% longer than the actual distance. For a hexagonal grid, the distance is approximated by counting the number of cells of the shortest path. This has <10% relative error (IIRC) from the actual distance.
- alisonkisk 6y ago
  If you take diagonals to be 1.5, then distances are <10% high. The half-short-side heuristic (sqrt(aa + bb) ~= a + b/2) makes taxicab very close to correct for non-square distance as well.

yudlejoza 6y ago

For a semi-goofy take (CGPGrey) on hexagons: https://youtu.be/thOifuHs6eY https://youtu.be/thOifuHs6eY

smexxymoose 6y ago
Came to the comments just for this link
amitp 6y ago
Hexagons are bestagons!
wumms 6y ago
More hexagons in nature: Image: "Hexagonal formations on the surface of the Salar de Uyuni (Bolivia, 3,656 meters above sea level) [0] as a result of salt crystallization from evaporating water": https://en.wikipedia.org/wiki/Salar_de_Uyuni#/media/File:Salar_Uyuni_au01.jpg https://en.wikipedia.org/wiki/Salar_de_Uyuni#/media/File:Sal... "During the rainy season (December to March) the salt flat gets covered with a layer of water. As the water evaporates under largely still conditions, the salt forms hexagonal shapes (optimal for heat transfer) on its surface known as Bénard cells, an example of the Rayleigh–Bénard convection [1] phenomena." [2] [0] https://en.wikipedia.org/wiki/Salar_de_Uyuni https://en.wikipedia.org/wiki/Salar_de_Uyuni [1] https://en.wikipedia.org/wiki/Rayleigh%E2%80%93B%C3%A9nard_convection https://en.wikipedia.org/wiki/Rayleigh%E2%80%93B%C3%A9nard_c... [2] https://commons.wikimedia.org/wiki/File:20170809_Bolivia_1581_Uyuni_sRGB_(26204506689).jpg https://commons.wikimedia.org/wiki/File:20170809_Bolivia_158...
- amitp 6y ago
  Also in nature: there is a giant hexagon on Saturn! http://www-cs-students.stanford.edu/~amitp/diagrams/saturn-hexagon/ http://www-cs-students.stanford.edu/~amitp/diagrams/saturn-h...

jsjohnst 6y ago

Surprised they didn’t cover hexagonal ring data structures. Here[0] is a visualization along with the calculations needed to find nearest neighbors. [0] https://www.flickr.com/photos/jeremyjohnstone/3979747216/ https://www.flickr.com/photos/jeremyjohnstone/3979747216/

cookiengineer 6y ago

Every time I see a post of redblobgames, I realize what a treasure this website is. I've been on this website so often, and pointed other people so many times to it... I hope this never gets lost and is archived. If Amit would write a book about gamedev, I'd definitely buy it and add it to my collection.

neilfrndes 6y ago

Uber's H3 geospatial library uses a lot of these concepts. https://eng.uber.com/h3/ https://eng.uber.com/h3/

mrtnmcc 6y ago

In case anyone is doing signal processing on a hexagonal grid, the https://en.wikipedia.org/wiki/Hexagonal_fast_Fourier_transform https://en.wikipedia.org/wiki/Hexagonal_fast_Fourier_transfo... is pretty useful. I work on consumer phased arrays with hexagonal grids, so the HFFT is useful for computing the far-field beam pattern.

wycy 6y ago

This guide was incredibly helpful a few years ago for one of the Advent of Code challenges.

keyle 6y ago

The guides on that website are fantastic. I wrote multiple games using them as reference. Well written, explained clearly and a wealth of information.

swayvil 6y ago

Are you familiar with the kisrhombille grid? https://en.wikipedia.org/wiki/Truncated_trihexagonal_tiling#Kisrhombille_tiling https://en.wikipedia.org/wiki/Truncated_trihexagonal_tiling#... Scaleable like a square grid. 12 directions.

michaericalribo 6y ago

An added challenge is to efficiently construct hex grids by hand——quickly, at the expense of accuracy. I didn’t have access to a printer early in the pandemic, but wanted to put together maps for a tabletop rpg. This is a clever solution: http://www.rdwarf.com/users/wwonko/hex/irregular/ http://www.rdwarf.com/users/wwonko/hex/irregular/ It has the added benefit of being easy to remember

bransonf 6y ago

And if you want something cool to do with this, try implementing Gliński's variant of chess. It’s something I’m dabbling in, but no doubt an order of magnitude more difficult to implement than orthodox chess. The idea of indexing by cubes is so obvious once you discover it, but maybe not as easy to intuit. Same goes for the data structures.

elihu 6y ago

CGP Grey did a video about hexagons recently. I mean, there's only so much you can say about hexagons really, but he manages to cover a lot of ground. https://www.youtube.com/watch?v=thOifuHs6eY https://www.youtube.com/watch?v=thOifuHs6eY

amitp 6y ago

A surprise to be on HN! Tech notes for the curious: I started the page in 2013 based on notes I had been collecting for ~20 years before that. I update this reference page as I come up with better visualizations and explanations. The last major update was in 2018 when I rewrote it from using d3.js to using vue.js. It greatly reduced the amount of code I was writing, and also let me make the page more interactive. I then added lots more (doubled coordinates, links to papers, axes legends, diagonal directions, side by side comparisons) and improved most of the existing sections. In 2019 the changes were minor, rewriting the map storage section and improving performance. In 2020 I improved the cube/hex animation, the pixel-to-hex section, and added Rust sample code. There's lots more I could add to the page[1] but I don't have any specific plans for when I'll get around to it. The page is svg- and js-heavy. I prerender the diagrams on the server (try loading it without js!). Then using IntersectionObserver on each section of the page, I swap the static diagrams and text with interactive versions. This improves load times somewhat, because almost no JS has to run on page load. For printability I process the page with xsltproc, extract all the links, and turn them into footnotes. Try print preview on the page to see these. Unfortunately the diagrams are broken when printing in Chrome (it works in Firefox) so I need to investigate. [1]: https://www.notion.so/redblobgames/f8bc2f44fba94607afa9c06711d23245?v=0766432cb1534ce582ce35b33cbbef7e&p=7d2d4d624bc5483dafbe615d75ab3902 https://www.notion.so/redblobgames/f8bc2f44fba94607afa9c0671...

privatemonkey 6y ago
This is a wonderfull source. Very well written. I'm happy to see it on Hacker News. A few years since I used it last. Didn't know you had rewritten it but I see now the updates you've done, especially in interactivity. I'll continue to use this as my main reference point for hex grids, especially now that I've picked up pace on my virtual tabletop project. Good work!! Thanks
Calloutman 6y ago
Thanks for the resource. I'm pretty sure I used it for some of my simulations of C60 molecules hexagonal packing, during my physics PhD a few years back.
simonh 6y ago

dang 6y ago

If curious see also 2019 https://news.ycombinator.com/item?id=19184412 https://news.ycombinator.com/item?id=19184412 2017 https://news.ycombinator.com/item?id=14627711 https://news.ycombinator.com/item?id=14627711 2015 https://news.ycombinator.com/item?id=9537009 https://news.ycombinator.com/item?id=9537009 2015 https://news.ycombinator.com/item?id=8941588 https://news.ycombinator.com/item?id=8941588 Discussed at the time: https://news.ycombinator.com/item?id=5809724 https://news.ycombinator.com/item?id=5809724

payelsarkar28 6y ago

payelsarkar28 6y ago
Hello

goldenkey 6y ago

In case you want to make a hexagonal cellular automata: https://github.com/churchofthought/HexagonalComplexAutomata https://github.com/churchofthought/HexagonalComplexAutomata Or in WebGL: https://github.com/churchofthought/Grautamaton/tree/complex https://github.com/churchofthought/Grautamaton/tree/complex

rcarmo 6y ago

This is an awesome resource I keep going back to now and again for the sheer fun of it. Glad to see it on HN again (it’s well worth reposting occasionally for folk who haven’t seen it yet).

darkwinx 6y ago

this web site is amazing!!

willis936 6y ago

Good stuff. I’m surprised that I have not seen a voxel-based game that leverages a purely 2D render and expects the player to switch between projections to work with the area.