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

Reviewing Our Knowledge of Triangles

If there’s one area of mathematics that you want to focus on during your educational journey through graphics and games programming, make sure it is vector mathematics. I cannot stress enough how important having a thorough knowledge of this area is to your success in developing your skills in this domain. Trigonometry, which examines the relationships between side lengths and angles in triangles, underpins many of the vector functions. As such, we will be exploring the magic of triangles herein.

Initially, for me, vectors and triangles were taught as separate ideas. It wasn’t until I started using vectors in my game programming that it suddenly became clear how understanding triangles was such a big part of understanding vectors. Also, vectors are just an extension of the mathematics of triangles.

Triangles would have to be one of the most interesting and useful geometrical shapes. Mathematically, their properties are fundamental...