Mathematics for Game Programming and Computer Graphics

A comprehensive guide to learning fundamental 3D mathematical principles used in games and computer graphics by example

Key Features
Get acquainted with the essential mathematics needed to describe, simulate, and render 3D creations
Construct and manipulate 3D animated environments using Python, Pygame, and PyOpenGL
Develop vertex and fragment shaders in OpenGL shader language to speed up rendering
Book Description
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.

What you will learn
Get up and running with Python, Pycharm, Pygame, and PyOpenGL
Experiment with different graphics API drawing commands
Review basic trigonometry and how it's important in 3D environments
Apply vectors and matrices to move, orient, and scale 3D objects
Render 3D objects with textures, colors, shading, and lighting
Work with vertex shaders for faster GPU-based rendering
Who this book is for
This book is for programmers who want to enhance their 3D mathematics skills relating to computer graphics and computer games. Knowledge of high school–level mathematics and a working understanding in an object-orientated language is needed to grasp the contents present in this book.

Table of Contents
Hello Graphics Window: You're on your way
Let's Start Drawing
Line Plotting Pixel by Pixel
Graphics and Game Engine Components
Let's Light it Up!
Updating and Drawing the Graphics Environment
Interactions with the Keyboard and Mouse for Dynamic Graphics Programs
Reviewing Our Knowledge of Triangles
Practicing Vector Essentials
Getting acquainted with Lines, Rays and Normals
Manipulating the Light and Texture of Triangles
Mastering Affine Transformations
Understanding the Importance of Matrices
Working with coordinate Spaces
Navigating the view space
Rotating with Quaternions
Vertex and fragment shading
Customizing the Render Pipeline
Rendering Visual Realism Like a Pro