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

Part 3 – Essential Transformations

In this part, you will learn how to manipulate graphical elements primarily through translation, rotation, and scaling. This content makes use of the knowledge obtained in Part 2, Essential Trigonometry, by applying vector and triangle mathematics to solve the problem of moving, scaling, and rotating objects in a 3D environment. Of most importance to your success as a graphics programmer is the thorough examination of matrices and quaternions that will explain why graphics and game engines always work with 4D values. In addition, the perplexing set of coordinate spaces that are a large part of transforming a model’s 3D vertices into pixels on the screen will be demystified and built into the project.

In this part, we cover the following chapters: