Beyond Basic Autotiling

Autotiling is a system for automatically picking which tile to place on the map, based on user input. It’s a fast way to design levels without having to fiddle with every tile indivually to ensure they are all consistent. Autotiling becoming increasingly well supported by game engines.

An exceptionally fancy autotiler, Tilekit

While there’s not a great deal of standardization at the moment, I’d say that 90% of systems at the moment are based on marching squares, which chooses between 16 tiles based on user input at each corner, or blob, which chooses between 47 tiles based on user input on each tile. I’ve written about these and other schemes before.

These approaches do work quite well for quickly whipping up a level, after the initial slog of creating the tiles, but when you start getting into more complex cases, a major shortcoming appears: combinatorial explosion.

Basically, as autotilers chose one tile for each situation, there needs to be a tile ready for any given combination. It’s bad enough creating 47 tiles needed for the blob pattern, but that only handles transitions between two different terrains. If you add a third, you need hundreds of tiles. And even simpler patterns quickly blow up with a few terrains.

Today, we look at a few ways to deal with that.

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Advanced Table Constraints

Previously we considered the Arc Consistency 3 and Arc Consistency 4 algorithms, which are an essential component of many constraint solvers. I’ve been using AC-4 myself for some time, and I naturally got curious as to what other improvements can be made.

Diving it, I discovered there is a huge amount of papers with new innovations are refinements on these two fundamental techniques. I’m going to attempt to summarize them there, and maybe later experiment with them in my own software, but I’m afraid this article is going to be pretty niche.

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Arc Consistency Explained

I’ve been doing a lot of experiments with WaveFunctionCollapse, which as we’ve covered before, is essentially a constraint solver turned into a procedural generator.

The underlying solver WaveFunctionCollapse came with is called Arc Consistency 3, or AC-3 for short. But AC-3 is actually one of a whole family of Arc Consistency algorithms. Today, my solver and most others uses AC-4, a more advanced algorith. Let’s talk a bit about how those both work.

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Recursive Subdivision Variants

You are probably familiar with Recursive Subdivision – also known as Binary Space Partitioning – as a procedural generation technique. Like all the best proc gen, it’s a simple idea, that produces complex output. I’m here to discuss some variants that others have used to produce interesting results.

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Using Unity’s TextGenerator.verts

TextGenerator.verts is meant to give the position information of every character in a given string. This is useful in Unity if you need to align something with exactly where some particular text is occuring, if for some reason you are not already using TextMeshPro.

Older Unity versions created 4 verts for every character, which made life easy. But now many non-rendering characters don’t have verts generated for them, and the relationship between verts and characters is undocumented. I’ve reverse engineered it, as best as I can tell:

int? GetVertForPosition(int position, string text, TextGenerator textGenerator)
{
    var c = 0;
    var vert = 0;
    for (var i = 0; i < position; i++)
    {
        if (textGenerator.characters.Count <= c)
            return null;
        if (!char.IsWhiteSpace(text[i]) && textGenerator.characters[c].charWidth > 0)
            vert += 4;
        if (text[i] != '\n')
            c++;
    }
    return vert;
}

Driven WaveFunctionCollapse

WaveFunctionCollapse (WFC) is a procedural generation technique for creating images and tile-based levels. I’ve discussed it many times before.

As a technique, it has some pros and cons. Pro: it’s almost uncannilly good at stitching together tilesets into interesting arrangements, and is pretty good at copying the style in a supplied sample image. Cons: it becomes bland and repetitive at large scales.

In my software Tessera, I’ve been working on various ways of customizating the generation to work around that con. But I’ve seen another way that turns WFC on its head. Instead of using WFC as a full level generator, we want to decide the overall structure of a level some other way, and then use WFC just for the details.

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Triangle Grids

Ah, the triangle grid. Square grids are virtually ubiquitous, laying out out everything from the pixels in an image to houses in a city block. The hex grid has a decent showing too, particularly in board games. But triangle grids – regular tilings of the 2d plane with equilateral triangles – just don’t seem popular. I’ve seen claims they are useless, or that the maths is hard. But I’m here to prove both of these are wrong: the maths is actually easier than working with hexes, and triangles have all sorts of neat advantages.

I’ve worked out all the maths in my reference code on github, but it’s worth explaining why and how to use these grids.

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