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

Let’s Start Drawing

There’s nothing quite like getting your first graphics application running. There’s a real sense of achievement when you see your ideas for the rearrangements of pixels come together on the screen. My first coding language was BASIC on an Amstrad CPC664 and even though the code was quite laborious, I liked nothing better than to draw shapes and change the colors on the screen.

Computer-drawn images ultimately end up as single pixels (such as the ones drawn in the previous section) with differing colors on a graphics display. To draw all objects pixel by pixel whenever you’d like to create an image would be a long, drawn-out process. It might have been how images were rendered on a screen in the 1950s, but now, with advanced technology, Cartesian coordinate systems, and mathematics, we are able to specify drawing primitives and use these over and over to compose a picture.

In this chapter, you will learn about the most primitive...