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

By now, I am sure you are gaining an appreciation of the importance of vectors, and just how important it is for graphics and game developers to have a firm grasp of them both conceptually and practically. Trust me, this chapter won’t be the last time you see them. The mathematical concepts we explored in this chapter might appear to cover the same ground over and over concerning calculating points and vectors, but this should only convince you further how important these methods are.

Lines are far more complex than they first seem. Although most straight geometrical elements are called lines in a general, collective sense, the differences between vectors, lines, line segments, and rays are clear. Each has its place in graphics development in data structures and drawing, though we can apply many of the same mathematical calculations to any of them. Is it any wonder that many of these are stored in the same data structure of pygame.Vector3?

We started this chapter...