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

Getting Acquainted with Lines, Rays, and Normals

Since we covered vectors in the previous chapter, it’s time to jump into exploring the mathematics of lines, rays, and normals. All three can be defined by vectors and on the surface, all appear to be the same and yet they have very specific and differing uses in graphics. Fortunately, their similarities concerning geometric structure allow them to be defined and manipulated by the same equations, as you will discover in this chapter.

The one thing lines, rays, and normals have in common is that they are all straight. This makes them very useful in graphics for defining space, direction, the edges of meshes, distance, collisions, reflections, and much more. The line construct is one of the fundamental drawing operations in graphics, as we covered in Chapter 1, Hello Graphics Window: You're On Your Way, and Chapter 2, Let’s Start Drawing.

In this chapter, we will cover the essential knowledge you need to define...