Probability of damage rolls was the first interactive tutorial I wrote on I was just starting to learn how to make diagrams with d3.js and SVG. On that page I also used Bret Victor's Tangle library.

I structured the page in "textbook style", because that's what I was used to. I started with the simplest thing (rolling one die) and worked progressively towards more complicated things (multiple dice, min/max of rolls, discarding rolls, and critical hits). For each scenario, I presented the idea, the code, and then a histogram of the values you'd get from that code.

One of my goals was to structure all of my pages so that I'd first give you the solution you were looking for, and then give you an idea that would change the way you thought about the problem. For the damage rolls page, the problem you're trying to solve is how to set up the rules for the dice so that you get a distribution of values that you like. You fiddle with the rules, look at the distribution, fiddle with the rules again, look at the distribution, and keep fiddling until you get the distribution you want. The big idea was that you should start with a distribution, and then work backwards towards the code. That way you don't have to keep fiddling with parameters.

When I wrote the page, I was just learning how to make diagrams. The level of diagrams on that page took plenty of effort, and I decided not to implement the "work backwards" diagram: letting someone draw a distribution, and then generating corresponding code. It was more complicated than the others and I thought it'd take too much time.

Since then I've gotten better at making diagrams. I decided to attempt the two interactive diagrams I had wanted for that page but hadn't implemented. The first is making the existing non-interactive diagram in section 3 interactive. It shows an arbitrary distribution:

I wanted to make the distribution editable. You should be able to drag the bars up and down to change their size. To do that, I added a mouse drag handler to the bars. Using the x position of the drag, I calculated which column you are over, and set the bar height to the y position of the drag. However, that wasn't enough, because if you made the bar very short, you can no longer get the mouse over it to drag it back up. I added a white <rect> underneath the bars and put the same drag handler on there. That way all the mouse events would be captured. There are probably some things I could do with SVG's pointer-events CSS property without making the rectangle white, but making it white was the easiest thing to do.

Looking back on it, this diagram was fairly easy to implement. It only took an hour. However I think it would've taken far longer back when I originally wrote the page. I barely understood D3, I didn't understand d3 mouse drag, I didn't understand SVG events, and I had been thinking I needed separate drag handles on each bar instead of the much simpler drawing UI pattern. Looking back on that code, I can see how much I've learned since then.

After the first diagram, I showed the code for a four-valued distribution, and then explained how to generalize it to work for any size. That's where the page ended. I added a diagram here to show that it works for any size. I wanted to let you draw any distribution you wanted, and show the code for it:

The "code" is actually a table. It's an array of values, which you pass to a function roll() that I previously gave.

With this diagram, the narrative of the page is complete. First I take you from random number code to random number distributions, for lots of different variants of code. Then I say that you should be choosing distributions first instead of choosing code first. Then I let you draw the distribution you want and show the corresponding code. I'm pretty happy with the way section 3 looks now.


Last year while working on my new introduction to A*, I decided to try something different for me. Usually I focus on the math, algorithms, and techniques, and let the reader figure out the code. However, for the A* page, I wrote a companion guide that shows how to implement A*. It's simple and unoptimized but I hope it's easy to understand, and shows all the tricky bits that I sometimes gloss over on the main page. While going back through my guide to hexagonal grids, I was improving the pseudocode examples on the page and realized I should probably help people who want to write code.

What usually happens is I have an explosion of questions and possibilities. What languages should I use? What grid variants should I support? What display styles should I implement? Dan Cook writes about alternating brainstorming and culling. I was deep in the brainstorming phase, and came up a crazy idea, that I should procedurally generate code, so that I could generate sample code on the page that matched your choice of grid and programming language, and then I decided I'd learn Haxe macros to do this, and run the code generator both on the server and in the browser, and then also procedurally generate unit tests, and …

… a few months later, I realized I had gone down an unnecessarily long route.

What happened?

Implementing the code generator made me realize I could simplify the variants. That part was actually great. I learned a lot by thinking through all the different ways to structure the code, and found simpler ways of thinking about hex grids. As I simplified more and found a better class design, I realized I didn't need most of the code generator after all.

Once I realized this, it killed my motivation. I felt bad that I had spent so much time on something that didn't work out.

I had jumped right into the procedural code generator, because that part sounded like fun. And it was!! One mistake I often make with procedural generators is that I start with a cool process instead of starting with the end goal. I did that here. I should've started with the output I wanted to make, and then figured out how to get there.

The code generator project didn't really work out the way I wanted. I wasn't sure where to go from there. Should I add more languages? Should I add more grid variants? Should I add comments to the output? I realized that I was spiraling back into the brainstorming phase instead of culling. I switched to culling. No, I won't add Rust and Scheme and Haskell output. No, I won't add more grid variants. No, I won't add comments and modules and docstrings and instance methods. Instead, I'll write up what I have and share it.

Telling myself no to all the possible ways this project could go is what helped me get un-stuck. Based on what I learned from this project, I wrote up a guide to implementing hex grids and also made some improvements to the hex grid guide. I also linked to the output of the code generator, so that you can get started with some working, tested code in C++, Python, C#, Java, Haxe, or JavaScript. Time to move on to another project!

Update: [2015-05-14] I added a bit about why I wanted to generate code (to show sample code on the hex grid guide)

Labels: , , ,

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, 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.

Labels: , ,

Popular Posts