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

In this chapter, we’ve taken a bit of time to focus on how rendering is performed and examined the rendering pipeline and camera setups. A thorough understanding of how these affect the positions and projections of objects in the environment is critical to your understanding of the structure of a 3D environment and the relative locations of drawn artifacts. In addition, considerable time has been spent on elucidating the calculations involved in taking a world vertex position and projecting it onto the screen. The process is not as straightforward as it might first seem, but with a knowledge of basic trigonometry and mathematics, the formulae have been derived.

One common issue that I find when developing these types of applications is just knowing how to debug the code when it seems to be running without syntax errors but nothing appears on the screen. Most often, the issue is that the camera cannot see the object. Therefore, if you can visualize in your mind where...