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

Understanding the Importance of Matrices

Matrices are an advanced mathematical concept that you will find everywhere throughout computer games and graphics. Their power comes from their ability to store affine transformations and apply them through multiplication. An understanding of their inherent structure and mathematical operations will provide you with a deep appreciation of the methods underpinning all graphics and game engines.

In this chapter, we will cover the following topics:

  • Defining matrices
  • Performing Operations on matrices
  • Creating matrix representations of affine transformations
  • Combining transformation matrices for complex maneuvers

We will begin by defining matrices and working through all the mathematical operations that can be performed on them. Then, we will examine how the affine transformations presented in Chapter 12, Mastering Affine Transformations, can be achieved through matrix operations. This will involve clarifying the benefits...