Author: Boris

Constraint-Based Tile Generators

| Boris

Last article, we were comparing WaveFunctionCollapse (WFC), and Model Synthesis (MS). These are both similar procedural generation techniques that work along similar lines. Specifically, they generate a grid of tiles (or pixels), using a set of hard constraints, and some generalized solver technique to find a solution, a set of tiles that satisfies all the constraints provided. Let’s call this overall class of thing constraint-based tile generators.

The techniques have been pretty popular in recent years, and part of that is because it’s actually a very easy concept to experiment with and extend. Many of the more practical examples in the wild include their own extensions, as basic WFC tends to produce levels that look a bit repetitive and structureless.

Today I thought I’d do a review of all the different ways that you can customize this generation technique, showing how WFC and MS are subsets of a greater class. The whole family of such algorithms is much larger and I think there’s a lot of potential still to explore.

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Model Synthesis and Modifying in Blocks

| Boris

I’ve written a lot about Wave Function Collapse. Developed in 2016 by Maxim Gumin, it’s an algorithm for generating tilemaps and pixel textures based on the constraint solving with extra randomization . But did you know most of the key ideas come from a paper written a full decade earlier? Today, we’ll be looking into Model Synthesis, the 2007 PhD dissertation of Paul Merrell, and some of the elaborations he’s designed, particularly Modifying in Blocks.

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Beyond Basic Autotiling

| Boris

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. For example, Godot’s Autotiling system or Tiled’s Terrain brush. 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

| Boris

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

| Boris

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 algorithm. Let’s talk a bit about how those both work.

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Recursive Subdivision Variants

| Boris

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

| Boris

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

| Boris

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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