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

Mastering Affine Transformations

Throughout the book so far, you’ll have gained an appreciation for the variety of methods used to move, rotate, and scale vectors and points. To move a mesh from one location in space to another requires each vertex in that mesh to be moved, and then the mesh is redrawn. This movement (formally called a translation) is just one of a set of special point and vector manipulator methods called affine transformations.

Affine transformations are important in computer graphics primarily, as they allow for the manipulation of a set of vertices without losing the integrity of the form. By this, I mean that any lines and planes in a mesh retain their relative parallelism and ratios. This might sound a little abstract, so let’s illustrate it with an example. Consider the diagram in Figure 12.1:

Figure 12.1: An affine transformation of a cube

Figure 12.1 shows an original cube in (a) made up of six sides and eight vertices...