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

Summary

An understanding of triangles is essential for those who want to program in the graphics and games domains. They are the foundation of the data structures used to store meshes, as well as the basic drawing components of them. When it comes to mathematics in these realms, they are equally as important. Their trigonometric properties, as you will see in the next chapter, form the basis of vector mathematics.

In this chapter, you explored the fundamental properties of triangles and learned how to calculate the length of a triangle’s sides and angles using the relationships between similar triangles and the trigonometric rules found in right-angled triangles. Following the theory, we applied our knowledge of triangles to load a triangulated mesh into OpenGL and display it.

Now that you have explored the mathematics of triangles, we can start examining vectors.