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

Understanding 3D Coordinate Systems in OpenGL

There are two alignments in which 3D coordinates can be defined: the left-handed system and the right-handed system. Each is used to define the direction in which rotations around the axes occur and can be visualized using the thumb and first two fingers on the respective hands (see Figure 4.11). For both systems, the thumb is used to represent the z axis; the direction in which the fingers wrap into a fist is the direction of a positive rotation:

Figure 4.11: The right-hand and left-hand rules of 3D axis orientation

For a detailed elucidation, you are encouraged to read the following web page:

https://en.wikipedia.org/wiki/Right-hand_rule

In OpenGL, eye coordinates are defined using the right-handed system, meaning that the positive z axis protrudes out of the screen (toward the eye) whereas traditionally in DirectX, the z axis is positive in the opposite direction. Other 3D software packages seem to have...