In the previous post, we introduced vectors, and showed some very elementary uses for them. We presented them as a simple and convenient way to pack a number (3, in our case) of scalar values into a single object. Now, we’ll consider their geometrical representation, which will help you grasp them more intuitively. For simplification’s sake, we’ll use two-dimensional vectors for all our examples, but the same extends to 3D vectors.

If you don’t already use vectors (and I mean vectors in the MATHEMATICAL sense, not in the “dynamic array” sense that languages like C++ or Java use), this is probably going to be the single most useful piece of math you can learn for writing games. It’s easy, efficient, and makes your code much shorter. In fact, provided that you’re using a language that supports definition of operators for user-defined types (like, say, C++ or Haskell), using vectors is going to be extremely intuitive and simple.

Here comes a harsh fact of life: game programming requires mathematics. One could say that programming IS, in a way, math, but you don’t really need to know math to write the vast majority of programs. Most of the time, you don’t need it to write parsers, to interact with databases, to validate data. Games, however, very often rely on mathematics. If you want objects to move across your world realistically, or if you want to draw things on the screen following certain geometric patterns, or if you want to check for collision between certain shapes, you need math.

But don’t despair! Even though I say “math”, what you ACTUALLY need is geometry. Luckily for us, geometry is probably the easiest part of mathematics! Now, I’m not saying that discrete mathematics, algebra and calculus are useless for writing games (or other sorts of programs), but geometry is the bread and butter of video game programmers.

An interesting thing that I did notice is that, despite my previous assertion, many game programmers do not actually know much geometry! This means that they’ll often do things in extremely laborious, buggy and verbose ways, when it could very easily be done with some basic grasp of geometry. For example, if you want to place several objects along an arc of circle, you COULD do it through trial and error, or place it in an image editing program (like Photoshop) and copying the coordinates, but it will be much easier if you simply use a parametric equation.

So I intend to write a few posts to explain, as clearly as I can, some topics that are important to game programming. These are the topics that I intend to cover:

• Vectors
• Parametric Equations
• Vector bases
• Basic Trigonometry
• Matrices
• Complex Numbers
• Quaternions

While there are many basic and in-depth tutorials of all of the above topics on the Internet, explanations as to why the matter to game programmers and how to use them seem to be scarce, or left as an exercise to the reader. My goal is to make those topics easy to understand and put into use.

Hello, my name is Rodrigo Monteiro, and this is my shining, brand-new blog. I have been a hobbist game designer and programmer for over a decade now, and have recently moved into the realm of professional game development. I am also creator of the “Aegisub” subtitling program, which is the de facto standard for anime subtitling, used by the vast majority of fansubbing groups worldwide. I intend to write thoughts and tutorials on game design, programming, and my recent musings with the development of games on functional languages (e.g. Haskell).