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

Calculating angles with sine, cosine, and tangent

The length of the hypotenuse and the other two sides can be determined using the triangle’s angles and the sine, cosine, and tangent operations. The sides of a right-angled triangle, apart from the hypotenuse, can be labeled as Opposite and Adjacent based on their positions in the triangle relative to the relevant angle, as shown in Figure 8.8:

Figure 8.8: The adjacent and opposite triangle sides for

Note that for these rules, either angle can be used. If the angle at the other end of the hypotenuse (other than what is shown in Figure 8.8) is used, then the labels for Opposite and Adjacent change positions.

The relationship between the sides and hypotenuse that represent the trigonometric function of sine is as follows:

The relationship for the trigonometric function of cosine is as follows:

The relationship for the trigonometric function of tangent is as follows:

Working with...