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

Practicing Vector Essentials

If there’s one thing you must learn to conquer in the domain of programming graphics (besides triangles), it is vector mathematics. I may have mentioned this before, but that’s how important it is! As you will start to see in this chapter and then throughout the rest of this book, you can’t do anything in this domain without a solid understanding of them.

This understanding began in Chapter 8, Reviewing Our Knowledge of Triangles, with the introduction of trigonometry. Vectors are used in everything from defining meshes as the positions of vertices, edges that run between vertices, UV values, and more to moving objects to rendering pixels on the screen. They are extremely versatile, as are their mathematical principles.

This chapter will begin by examining the similarities and differences between the concepts of points and vectors to help you distinguish between the two since, mathematically, they are very similar. We will then...