Book Image

Mathematics for Game Programming and Computer Graphics

By : Penny de Byl
5 (1)
Book Image

Mathematics for Game Programming and Computer Graphics

5 (1)
By: Penny de Byl

Overview of this book

Mathematics is an essential skill when it comes to graphics and game development, particularly if you want to understand the generation of real-time computer graphics and the manipulation of objects and environments in a detailed way. Python, together with Pygame and PyOpenGL, provides you with the opportunity to explore these features under the hood, revealing how computers generate and manipulate 3D environments. Mathematics for Game Programming and Computer Graphics is an exhaustive guide to getting “back to the basics” of mathematics, using a series of problem-based, practical exercises to explore ideas around drawing graphic lines and shapes, applying vectors and vertices, constructing and rendering meshes, and working with vertex shaders. By leveraging Python, Pygame, and PyOpenGL, you’ll be able to create your own mathematics-based engine and API that will be used throughout to build applications. By the end of this graphics focussed book, you’ll have gained a thorough understanding of how essential mathematics is for creating, rendering, and manipulating 3D virtual environments and know the secrets behind today’s top graphics and game engines.
Table of Contents (26 chapters)
1
Part 1 – Essential Tools
9
Part 2 – Essential Trigonometry
14
Part 3 – Essential Transformations
20
Part 4 – Essential Rendering Techniques

Rotating with Quaternions

If you can’t remember me saying it before, you’ll be sure to hear me say it numerous times throughout this chapter: quaternions are an advanced mathematical construct. They are so advanced I don’t expect you to fully comprehend them by the end of this chapter. However, what I want you to take away is a healthy appreciation for what they do with respect to solving the gimbal lock issue we discussed in Chapter 15, Navigating the View Space.

Besides their usefulness in calculating 3D rotations, quaternions are useful in numerous fields, including computer vision, crystallographic texture analysis, and quantum mechanics. Conceptually, quaternions live in a 4D space through the addition of another dimension to those of the x, y, and z axes used by Euler angles.

In this chapter, we will start with an overview of quaternions and delve into the benefits of their 4D structure. This will reveal how they can be used to replace operations...