Math Primer Series: Matrices III: Affine Transformations and Matrices

We’ve seen matrices used as representations of a basis, and we’ve seen them used as linear transformations, but what else can we do with them? So far, we’ve only been able to use matrices to transform vectors from one vector space to another. What about points and vectors in an affine space? There is another…


Math Primer Series: Matrices II: Linear Transformations

In the last installment of the math primer series, we looked at the basics of matrices. Today, we’ll take a look at using matrices for linear transformations, which are one of the most common uses of matrices in games. But, before we dive into linear transformations, let’s take a quick look at what a transformation…


Intro to Physics in Games

I’ve decided to try something a bit different and mix in physics posts while I wrap up the math primer. Many of you might be more interested in the physics, or may already be familiar with the math topics, so this gives me a chance to have something for everyone. Today, we’ll look at some…


Math Primer Series: Matrices I: Introduction and Basics Operations

  Few things are as ubiquitous in game and graphics programming as a matrix. In this installment of the math primer, we take a look at these structures, investigating not only their numerical significance, but also what they represent visually. Next time, we’ll see how to combine them with vectors and with other matrices to…


Barycentric Coordinates and Point in Triangle Tests

  I know it’s been a little while since my last post, and I apologize. I’ll try and keep the posts a little more frequent moving forward. In the last post, we briefly encountered barycentric coordinates and loosely defined them as the coefficients of an affine combination. While that’s true, we can do better. We…


Math Primer Series: Vectors III: Affine Spaces, Linear and Affine Combinations

In this chapter of our primer, we’ll examine affine spaces, and see what affine and linear combinations are. Furthermore, we can use these concepts to define some other related concepts, such as affine and linear dependency. Affine Space An affine space can be thought of as any space containing points and vectors together, which follow…


Math Primer Series: Vectors II: Vector Operations

  In the last installment of this math primer, we looked at the difference between points and vectors. Today, we’ll dive a little bit deeper into vectors, and the specific operations we can perform on them. More importantly, we’ll take a look at the geometric significance of the many operations, and how they can help…


Math Primer Series: Vectors I: Points vs. vectors

Some math and physics libraries contain separate data types to represent points and vectors. I’ve seen many people become confused by this, since more commonly packages use vectors exclusively for everything. What’s going on here? Why have 2 separate types? Well, the answer is quite simple. Strictly speaking, a point is not a vector and…


Math Primer Series: Intro, Notation, and References

This is the first part of a multi-part primer and reference for the math we’ll be using extensively throughout this blog. If you’ve been around game or graphics programming for any length of time, you’re probably at least somewhat familiar with many of these topics. However, you might be a bit rusty or might not…


My First Post

The first post… what should I talk about? I guess a little about me, and a little about what’s coming up in the blog. My name’s Reza Nourai, and I’m a developer on the XNA Game Studio Team. I like video games… a lot! I like to play them, and I like to make them….