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 relationship between angles and vectors

The angles that are made from intersecting two vectors can best be explored by considering how a game character facing one vector should turn to be facing another. In this section, we will explore how such a game character might turn toward the desired object.

At the end of Chapter 8, Reviewing Our Knowledge of Triangles, you added a mesh loading class to your project and used it to display a teapot in the graphics window. How much did you want to turn this teapot around to get a better look at it? Besides translation, rotation is another primary transformation used in graphics. Rotations require angles; these angles are measured between vectors using the principles we explored in Chapter 8.

For example, let’s consider the case shown in Figure 9.7, in which the game character, Chomper, would like to turn and face the jar of Vegemite. A vector is used to represent the direction Chomper is facing, as well as the direction...