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

Drawing Models with Meshes

A model is an object drawn by the graphics engine. It contains a list of vertices that define its structure in terms of polygons. The collection of these connected polygons is known as a mesh. Each polygon inhabits a plane—this means that it is flat. A basic model with elementary shading appears faceted, such as that shown in Figure 4.4. This flat nature is hidden using differing materials, as we will discuss shortly:

Figure 4.4: A basic polygon mesh showing the flatness of each polygon

A polygon mesh is stored internally as a list of vertices and triangles. Triangles are chosen to represent each polygon over that of a square, as triangles require less storage and are faster to manipulate as they have one less vertex.

A typical data structure to hold a mesh is illustrated in the following diagram:

Figure 4.5: A vertex and triangle array used to define the triangles of a square

The example given stores...