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

Anti-aliasing

In the previous sections, we worked on producing pixel-by-pixel lines where one pixel was chosen over another in order to create a continual line or circle. If you zoom in on these pixels, however, you will find that they are quite jagged in appearance, as illustrated by the zoomed-in section of a circle shown in Figure 3.10:

Figure 3.10: A zoomed-in section of the Bresenham circle pixels

This effect occurs because of the way that integer values are chosen to represent the drawing. However, when we looked at the actual equations for lines and circles in the The Naïve Way: Drawing a line with brute force and Drawing Circles the Bresenham way sections, it was clear they involved floating-point values and seemed to pass through more than one pixel. To improve the look of these kinds of drawings, a process called anti-aliasing is employed to blur the pixels that are neighbors of the line pixels to fade the edges of the line. Figure 3.11 shows...