Following my article on triangle grids, I’ve been doing a lot more thinking about periodic grids. Here’s three neat things.

Continue reading# Tutorial

# 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.

Continue reading# Lock and Key Dungeons

Lock and key dungeons are, well, video game levels with locks preventing progress, and collectable keys that let you proceed.

The concept is a lot broader than it sounds. Locks/keys aren’t necessary physical objects, but anything that works in a similar way, which can often be quite abstract.

Once you are familiar with the pattern, **you begin spotting it everywhere**. It’s most prominent in puzzle games and metroidvanias, but it’s applicable to any game which has an authored progression path.

In this article, we’ll look at lock and key dungeons, then how to analyse and design them.

Continue reading# Compressed Sparse Fibers Explained

I was browsing the Apache Arrow docs and spotted a term unfamiliar to me. Intrguied, I discovered that **Compressed Sparse Fibers **are a new technique for representing sparse tensors in memory. After reading up a bit, I thought I’d share with you what I’ve learnt. The technique is so new (well, 2015..) it is not mentioned on Wikipedia, and I found virtually nothing elsewhere. There’s a very limited number of ways to handle sparse data, so it’s always interesting to see a new one.

Don’t worry, I’d also never heard of a sparse tensor before, so I’m going to explain things right from the beginning, assuming you have a basic CS background, and don’t mind me going a little quickly.

Continue reading# Wave Function Collapse Explained

*A simple guide to constraint solving*

Since developing DeBroglie and Tessera, I’ve had a lot of requests to explain what it is, how it works. The generation can often seem quite magical, but actually the rules underlying it are quite simple.

So, what is the Wave Function Collapse algorithm (WFC)? Well, it’s an algorithm developed by Maxim Gumin for generating tile based images based off simple configuration or sample images. If you’ve come here hoping to learn about quantum physics, you are going to be disappointed.

WFC is capable of a lot of stuff – just browse Maxim’s examples, or check out #wavefunctioncollapse on twitter, or see my youtube video.

WFC is explained briefly in Maxim’s README, but I felt it needed a fuller explanation from first principals. It is a slight twist on a much more broad concept – constraint programming. So much of this article is going to **explain constraint programming, and we’ll get back to WFC at the end**.

# Wave Function Collapse tips and tricks

I’ve been experimenting a lot with constraint-based procedural generation these days. Specifically the Wave Function Collapse algorithm (WFC). I’ve even made my own open source library, and unity asset.

WFC is a very flexible algorithm, particularly with the enhancements I’ve designed, but at the same time, I’ve found it’s quite hard to actually get it to produce *practical *levels useful for computer games. The key difficulty is WFC doesn’t have any global structure to it, all it does it make the output generation look like the input locally, i.e. when viewing small rectangles of output at a time.

In this article, I share what I’ve learned to take your constraint based generators to the next level.

Continue reading# Messing with Unity’s GUIDs

I recently released an addon in the Unity asset store. It’s actually two addons: Tessera Pro is a fully featured copy, with complete source code, and Tessera which has cut down features, and you just get a precompiled .dll.

I quickly discovered a big problem – if you upgrade from Tessera to Tessera Pro, then all your scenes become broken. You get this error, which is likely familiar to veteran Unity developers.

I’ll go into what’s happening in general, and how I dealt with it.

Continue reading# Dual Contouring Tutorial

# Marching Cubes 3d Tutorial

In the first article I showed how the Marching Cubes algorithm works in 2d.

In this tutorial, I cover how it can be extended to 3d.

Continue reading

# Marching Cubes Tutorial

In Minecraft, you can dig in any direction – removing a block at a time with well defined edges. But other games manage to destruct terrain smoothly, without all the blockiness of Minecraft.

The following tutorial in Marching Cubes, a technique for achieving destructible terrain, and more generally, creating a smooth boundary mesh to something solid. In this series, we’ll cover 2d in this first article, follwed by 3d in the next , and Dual Contouring in the third. This last is a more advanced technique for achieving the same effect.