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

Part 2 – Essential Trigonometry

This part will take you through the fundamental mathematical skills that underpin the majority of techniques used in graphics and games. As you will discover, graphics applications don’t function without the use of triangles and vectors; therefore, a thorough understanding of these constructs is essential for any graphic or games programmer. As you work through this part, the mathematics principles in geometry and trigonometry will be revealed and integrated into the project to set up the environment for not only drawing and lighting 3D objects but also adding the functionality that will animate them.

In this part, we cover the following chapters:

  • Chapter 8, Reviewing Our Knowledge of Triangles
  • Chapter 9, Practicing Vectors Essentials
  • Chapter 10, Getting Acquainted with Lines, Rays, and Normals
  • Chapter 11, Manipulating the Light and Texture of Triangles