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

Defining polygon sides with normals

So far in this book, we’ve calculated normals but not explored their many uses. One of these uses is to dictate which side of a polygon is visible. The same plane that you have been using up to this point has had the normals reversed in Autodesk Maya, a 3D modeling program, for the center polygons, as shown in Figure 11.4:

Figure 11.4: A plane with some normals reversed

The black section in the middle of the plane in Figure 11.4 when rendered would in fact appear as a hole when viewed from one direction and solid from the other. Even though it might look like a hole, that doesn’t mean there aren’t any polygons covering this area. When this plane is drawn with a cube behind it in Python and OpenGL, the hole is evident, as shown in Figure 11.5 (a):

Figure 11.5: A plane with normals reversed viewed from both sides

As can be seen in Figure 11.5, whichever polygons have normals on...