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

Transferring processing from the CPU to the GPU

OpenGL pre-dates modern graphics cards as we know them now. It was originally built to work with render farms, which were mostly superseded by modern-day graphics cards. As such, it underwent an API redesign in 2008 with the release of version 3.0, which focused on GPU programming.

You might now be wondering whether what you’ve learned thus far in this book is suddenly out of date! The answer is no. The mathematics is always relevant—it never changes. Up until now, you’ve received a gentle introduction to graphics programming. From here on, it gets more challenging.

If you think about it, the transforms that we’ve performed on an object move the object as a whole, but the equations for the transforms move each vertex individually. It’s just the nature of affine transformations. As discussed in Chapter 12, Mastering Affine Transformations, this means that moving an object is the same as transforming...