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

Translating points in 3D

We first encountered OpenGL’s translations and rotations back in Chapter 4, Graphics and Game Engine Components, and then began building a Transform class for our Python project in Chapter 6, Updating and Drawing the Graphics Environment. In this chapter, we will continue working on this class to provide all the functionality of affine transformations, beginning with that of translation.

Whichever affine transformation you are applying, the rule is that the operation is applied to every point to which you want to apply the transformation. In the case of the vertices of a cube, you may have six vertices, as shown in Figure 12.2. This cube is centered around the origin:

Figure 12.2: A cube with each vertex coordinate displayed

To translate the cube—that is, to move it to another location—we must perform the same operation on each of the vertices such that they maintain the integrity of the cube. That means that...