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

Displaying Mesh Triangle Normals

We will begin this chapter by adding some extra functionality to the normal drawing in Chapter 10, Getting Acquainted with Lines, Rays, and Normals. At the time, we restricted the drawing of these normals to the center of the cube being drawn. This technique won’t work with more complicated meshes. More ideally, it would work better if each normal for a plane were emitted from the center point of the triangle, which is called the centroid. The centroid can be found using the medians of the vectors that make up its sides. Take, for example, the triangle in Figure 11.1:

Figure 11.1: The centroid of a triangle

The centroid can be found by finding a point halfway along any of the sides, connecting that point with the opposite corner, and then moving along the vector from the corner to the halfway point by two-thirds. In this example, that means if you find the vector from corner A to B and then travel halfway along it to...