"Game Development" Posts

• 2026-08-31

  Order-Dependent Triangulations

  I’ve spent a lot of time working on procedural asset generation code over the last ten years or so, and procedural mesh generation has been a large focus of that work. I researched and reinvented many algorithms over the course of this time, but one of the most valuable concepts I’ve stumbled into is not an algorithm at all, but rather the realization that the order of the elements in your data structures can matter just as much as what’s actually in them. I think many people are aware that this is true for things like binary searches, but I’ve found that it’s a useful tool in an even wider range of applications. Today, I’ll be talking about the applications of this concept to generating triangulations.

• 2026-07-15

  Reverse Engineering Tears of the Kingdom's Object Rotation System

  Tears of the Kingdom, the long awaited followup to Breath of the Wild, was lauded at it release for its intuitive and powerful construction system. I played Tears of the Kingdom, and while I did enjoy playing around with the build system, I couldn’t help feeling like something was strange. The problem that was on my mind the whole time was the fact that you could seemingly rotate objects in the build system by 45 degrees around 2 different axes in any order you chose, but you would only ever end up reaching a small number of possible orientations. Mathematically, this actually shouldn’t be possible.

• 2026-06-30

  Aiming Projectiles

  Shooting is a very common mechanic in video games; however, unless your projectiles are entirely hitscan, meaning that the player instantly hits whatever they are aiming at when pulling the trigger, aiming projectiles is unexpectedly non-trivial from a mathematical perspective. For players, this is part of the fun, and their aim is more driven by physics intuition and muscle memory. But for AI-controlled characters, this is a real problem, and there are a number of factors that can potentially make it even more complicated. In this post, I will be discussing the solutions for the most common category of projectile aiming problems in video games.

• 2026-05-01

  Corner Place

  The puzzles I’ve posted so far have been easy-to-describe as “like sudoku, but…”. But, as I’ve done more research into the mathematics underlying these types of puzzle systems, I’ve come to realize that the “sudoku-like”ness of these puzzles is captured entirely by the concept of the “Latin square”. And, in doing further research into Latin squares, I found a neat kind of puzzle that seems very underexplored.

• 2026-04-24

  Puzzle Rankings

  The site currently has a few daily puzzle games running: Pair Place and Triple Place. Today, I’m introducing a ranking server that will let you see how well you performed compared to other players on each daily puzzle.

• 2026-01-01

  Triple Place

  A few months ago, I started posting a daily puzzle called Pair Place. Pair Place arose naturally as a math problem during some research, but I naturally started to wonder if there were any basic generalizations of it that could serve as variations on the same puzzle concept. The first such generalization of Pair Place is the subject of today’s post: Triple Place.

• 2025-10-01

  Pair Place

  I thought that it might be a good challenge to try to introduce and keep up-to-date a daily puzzle on the site for as long as I can manage. So, starting today, I will be uploading a daily puzzle for a puzzle system I’ve been investigating, which has some similarities to sudoku.