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

Summary

Along with the data structures required for storing and drawing a mesh, affine transformations are a fundamental part of computer graphics. In fact, how OpenGL stores and manipulates them is the crux of all graphics processing.

In this chapter, we’ve examined the five transformations that fit into this special category—translation, scaling, rotation, shearing, and reflection. Of all these, rotation is the most complex. The mathematics of rotations has been a hotly researched topic in computer graphics since its inception, as you too will experience as we progress through the book.

We began by reviewing translation, a functionality we have been using since the creation of the Transform class in our Python project. It, along with scaling, is a very simple mathematical function. We spent a lot of time adding the final touches to the Transform class, completing it with methods to control scaling and rotation.

These newfound skills will assist you in expanding...