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 and fixing compound rotation quirks

In the previous section, you had the chance to experiment with moving the camera around in its 3D environment so you could explore looking at the environment from different angles. While moving the camera is elementary, adding rotations seems to introduce undesired results. In this section, you will discover the source of these issues and look at how to fix them.

Imagine you are holding a camera and looking through it toward the horizon. Now bend down at the hip by 90 degrees so that the camera is looking straight at the ground. Next, rotate your upper body 90 degrees upward to the left. You might be thinking along the steps shown in Figure 15.3. First rotating around the x axis turns the camera to face downward making its y axis horizontal and then a rotation around the y axis will face the camera sideways and result in the x axis sitting horizontally. In performing these orientations, we assume each axis can move independently...