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

Rotations would have to be the single most cause of headaches for programmers working in 3D environments. By now you will have an appreciation for the complexity of their mathematics. It’s often not until you start using the mathematics that you find out what can go wrong. Only then can you really understand how the errors occur and what you can do to fix them. The issues that affect first-person controller rotations also impact the navigation systems of virtual moving objects such as simulated aircraft and spaceships.

In this chapter, we have explored the mathematics required to move and rotate a virtual camera. This knowledge will allow you to position and angle a camera anywhere in the world to view the objects being rendered. Though the use of several key presses, the camera in your project will now be able to move and rotate. This is essential understanding for any graphics or game programmer, as is being able to eye ball a transformation matrix and have an awareness...