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

Line Plotting Pixel by Pixel

It’s difficult to appreciate what goes on mathematically behind the scenes of high-level drawing methods, such as those used by Pygame methods, unless you’ve written a program to plot objects pixel by pixel – because when it comes down to it, this is how the methods produce their rendered results. To that end, we are going to explore a little deeper the techniques involved in drawing a line pixel by pixel onto the screen. At first, you might assume this is quite a simple thing to do, but you’ll soon discover that it’s quite complex.

As we progress through the content, it will become clear why special algorithms are required to draw mathematical constructs such as lines on a pixel display. The algorithm we are going to explore is also a key technique that can be used for various other graphics and game-related functions wherever straight-line calculations are needed.

Once you’ve completed this chapter, you...