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

Index

As this ebook edition doesn't have fixed pagination, the page numbers below are hyperlinked for reference only, based on the printed edition of this book.

Symbols

2D environment

combining, with 3D environment 120-125

3D coordinates system 73

left-handed system 73, 74

perspective projection 74-76

points, translating 225, 226

projecting, into NDC 76-79

right-handed system 73, 74

3D shapes rotation

reference link 233

3-gon 33

4-gon 33

A

Affine Transformations 223

compounding 254-256

linear equations, moving to matrix operations 252-254

matrix representations, creating 252

albedo 392

ambient lighting 374

using 374, 375

ambient occlusion (AO) 392, 398

angles

relationship with vectors, exploring 172, 173

anti-aliasing 56-58

application programming interface (API) 62

arbitrary axis

rotating around 312-315

arccos 150

arcsin 150

arctan 150

ASCII art

URL 29

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