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

Understanding OpenGL’s Matrix Stack

In graphics, the current transformation applied to a point or object is determined by the current model-view-projection (MVP) matrix. This is a culmination of the model matrix, the view matrix, and the projection matrix. We first discussed these matrices as coordinate spaces in Chapter 4, Graphics and Game Engine Components. Each one has a specific use in the graphics pipeline, as is shown in Figure 14.1 (this diagram has been reinserted here from Chapter 4, Graphics and Game Engine Components, for your convenience):

Figure 14.1: The graphics pipeline

The coordinates or points that define a graphics object are stored in a model’s local coordinate system. They define the geometry of the object independently of where it is situated in world space. As we saw in Chapter 4, Graphics and Game Engine Components, a cube can be defined by six points, one for each of the vertices, thus:

cube.vertices = [(0.5, -0.5...