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

Summary

There’s a lot to learn when it comes to vector mathematics, and this chapter has only scratched at the surface and plucked out the essential parts relevant to graphics and games. If you get a chance, I would strongly suggest that you review the extra links given throughout. Vector mathematics is a university-level topic. I’ve attempted to reveal the simplicity of the topic and reduce it to simple addition and multiplication operations, but if you feel you haven’t grasped the topic, I’d encourage you to investigate what’s available on Khan Academy (khanacademy.org). In this book, I’m addressing the most relevant aspects of all mathematical topics concerning computer graphics and games, but unfortunately, due to page count, I can’t cover everything.

We started this chapter by looking at the differences between points and vectors, followed by several key vector operations required to manipulate them to move objects in space....