Math Primer Series: Rotation Representations and Quaternions

We saw the power and usefulness of transforms in the previous primer posts, and we’ll be using them quite a bit in our discussions of physics and graphics. One of the first tasks we’ll need to do is determine how to represent our transformations in code. We’re going to be creating, manipulating, and animating these…

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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…

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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…

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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…

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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…

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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…

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