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

Following where light bounces

PBR is based on the actual physics of light rather than the other relatively simple lighting model of Lambert, examined in Chapter 5, Let’s Light It Up! PBR is a concept rather than a specific algorithm and can be achieved using a variety of mathematical models. To understand how PBR works, we need to understand some key fundamentals about the visual way light works.

Light is a ray we can represent with vectors relative to the normal of the surface being hit, as shown in Figure 19.1:

Figure 19.1: An incident and reflection ray

The light coming in from the source is called the incident ray and the light being reflected from the surface is called the reflection ray. According to the law of reflection, the angle of incidence is equal to the angle of reflection. Both rays travel in a straight line, and whether the strength of the incoming ray is the same as the reflected ray depends on what happens at the point of collision...