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

Applying the Inverse Square Law

The way that the strength of light gets weaker with distance from the light source is described by the inverse square law. It states that the light intensity gets inversely weaker based on the square of the distance the viewer is away from the light source. Mathematically, we represent it like this:

Just how quickly the light strength falls off with distance will depend on the medium through which the light is traveling. We can calculate the strength of light at a certain distance in the same medium if we know its strength for a previously measured distance. For example, if the light intensity is 10 at a distance of 100 meters from the source, we can calculate the strength that this same light will be at 125 meters, using proportions like this:

This answer makes sense if we think about it as the same light at a further distance being less bright.

The strength of the light being emitted from the light source, as we discussed...