Hex grids: more on coordinate names #

Two years ago when I wrote my hex grid guide, I had to come up with some names of grid types and coordinates. There were several to choose from, and I ended up picking Cube, Axial, Offset for the grid types, and x/y/z, q/r for the coordinates. For the last few months I've been working on a procedural generator that creates various types of hex grid libraries. The guide is focused on theory, but actually making hex grid libraries made me think about implementation. This project made me realize the naming conventions I've used are a bit confusing.

Here's what I had done for the theory post: I picked names based on whether it's a 3d cartesian coordinate system or a 2d hex coordinate system. The world space 3d cartesian coordinates are a rotation of the 3d cube-hex coordinates, so they're related geometrically.


However, in practice, I don't think about them that way. I think about the world and screen coordinates as being different from Cube. World and screen coordinates are "pixel" and Cube is "grid". Axial and Offset coordinates are also different, as they use different axes, and the kinds of operations you can do on the two are different. Cube and Axial are essentially the same though. In some of my projects using Axial coordinates, I calculate a third "s" coordinate, which is "y" from Cube coordinates. I think of the systems like this:


My choice of names seems to be the worst combination:

  1. I use the same names for world/screen cartesian coordinates and Cube, even though they're different.
  2. I use the same names for Axial and Offset, even though they're different.
  3. I use different names for Cube and Axial, even though they're the same.

Of these, #1 bothers me the most. In past projects I've found it best to name the grid coordinates and the world/screen coordinates differently. I end up with more bugs when I use the same names for two different systems. Problem #2 is minor, because most people aren't using both Axial and Offset in the same project. Problem #3 complicates things. If they had the same name, then you'd no longer have to treat them separately. You can compute the third coordinate when you need to, or store it all the time if you prefer. Axial vs. Cube becomes "no big deal" instead of being a separate system you have to think about.

Of course, if I had known all of this when I started, I would've done things differently. The question is, what do I want to do now? Do I keep the current system because it's the same as what the last 2 years of readers have seen, or do I switch to a less error-prone naming scheme, because it helps the next 20 years of readers? If I switch, how do I support the last 2 years of readers? Do I point to archive.org, which has an older version of the page, or do I host my own second version? If I host my own, do I backport future bug fixes, improvements, and new diagrams to that version?

Trying to decide what to do about this change reminds me that I've made lots of other changes. How should I handle all the other changes I've made over the years?

  • I've switched treating pointy vs flat as a 30° rotation to a 90° rotation and then to an x/y axis flip. The x/y axis flip is more consistent with the pseudocode I give, but the 30° rotation is more consistent with the diagrams. I'm still unsure of what to do with this.
  • I've switched the inconsistent naming of "3-axis" + Cube, "2-axis" + Axial to only use Cube and Axial.
  • I've switched pixel-to-hex from showing lots of different ways to one recommendation and then listing the others on a separate page. I want to avoid a "paradox of choice" problem. This change also made me start thinking of the page as recommendations instead of a catalog of every approach I've seen.
  • I've switched field of view from one suboptimal algorithm to another suboptimal algorithm. The newer one is simpler and slower but works on all maps instead of only specific shaped maps.
  • I've switched the Axial coordinate axes to be consistent with Cube axes. I had previously claimed that the axes were different from Cube, but I was wrong about that, and didn't realize it for months.
  • I've added an explanation of how hex-to-pixel and pixel-to-hex are related. They're both matrix multiplies, and the matrices are inverses of each other.
  • I've switched the line drawing algorithm to one that mostly worked to one that always works, and is simpler. I later switched the pseudocode from something long and custom to something short and simple.
  • I've switched the pathfinding explanation from "go look at this other page and figure it out" to "here's a diagram, but then go look at this other page".
  • I've made the pathfinding, field of view, and movement range diagrams consistent in their interaction and appearance.
  • I've made many of the maps editable, including on touch devices.
  • I've added a visual explanation of the six constraints needed to make a hexagonal region.
  • I've switched the code for coordinate conversions from pure pseudocode to code that might actually have a chance of working in a real programming language, given precedence rules and integer arithmetic rules. For example, "1/2" evaluates to 0 in many languages, so I instead write "1.0/2".
  • I've fixed lots of bugs in diagrams and pseudocode.

I also have to balance this with what it will do to the likelihood of me updating the page. If it's a lot of work to update the page, I'm less likely to do it.

My plan right now is to rename offset coordinate fields q,r to col,row, but to leave alone the names of the offset coordinate systems (even-q, odd-q, even-r, odd-r). Those field names aren't used in many places on the page. I don't yet know what to do about Cube coordinates x,y,z. They show up in far more places on the page. Merging Cube and Axial would simplify things, and be even more a step towards this page becoming a recommendation page instead of a catalog of techniques. I have mixed feelings about that.

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