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

Navigating the View Space

One of the most common uses of transformations in computer games is the movement of the camera viewing the scene. While the camera can be considered as another 3D object in the environment with respect to its movement and orientation, its current transformation is also used as the view matrix by which all virtual objects in the world are affected.

The transformations presented in this chapter for moving and rotating the camera within its environment are the exact same operations that would be performed on any object in the environment.

In this chapter we will explore:

  • Flying maneuvers
  • Understanding and fixing compound rotation quirks
  • Improving camera orientations

By the end of this chapter, you will have a greater appreciation of the complexity of 3D rotations and the issues that arise from using them in mathematical operations to combine multiple orientations. The knowledge herein you will use over and over again as you work...