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

Exploring the OpenGL Graphics Pipeline

In software, an engine is an application that takes all the hard work out of creating an application by providing an application programming interface (API) specific to the task. Unity3D, for example, is a game engine. It’s a tool for creating games and empowers the programmer by removing the need to write low-level code.

An engine consists of several modules dedicated to tasks, as shown in Figure 4.1:

Figure 4.1: Typical components of a game engine

A mainstream graphics application needs to possess all the fundamental abilities to display and move graphics elements (such as the ones we examined in Chapter 2, Let’s Start Drawing) in either 2D or 3D, with most 3D engines able to display 2D simply by removing the z axis. These elements work together to take a 2D or 3D model through the graphics pipeline where it is transformed from a set of vertices into an image that appears on the screen. The graphics...