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

Updating and drawing objects

Objects in a game or graphics application are entities within the system that possess numerous properties and methods that allow them to exist and interact within their environment.

As shown in Figure 6.2, a typical object possesses many subparts or components:

Figure 6.2: A game object and a few of its components

You can think of components as functionality added to the object, for without the components, the object is nothing except a placeholder. The object may have all or only a subset of the components, as illustrated in Figure 6.2. For example, you might have an object in the environment that only plays a sound. For this, it would only need an audio component, whereas an object representing a game character might have a mesh that defines what it looks like, a render component that tells the game engine how to draw it on the screen, and a transform component that stores its location and orientation in the world.

In...