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 Bidirectional Reflectance

Besides ordinary reflectance and scattering, PBR also integrates a bidirectional reflectance distribution function (BRDF), which considers how a specular reflection will fall off or how fuzzy it appears around the edges. It is a function that considers the four factors of the incident ray, the vector to the viewer, the surface normal, and radiance (how well the surface reflects light). In fact, the Lambert (diffuse) and Phong (specular) models we considered in Chapter 18, Customizing the Render Pipeline, are examples of BRDFs. The BRDF for Phong, which calculates specular lighting that can be added to the diffuse of Lambert for a final effect, can be stated as the following:

In this formula, R is the vector of reflection of the incoming light, E is the vector from the point of contact to the viewer’s eye, and p is the specular power. All vectors involved in calculating reflections are shown in Figure 19.4:

Figure...