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

Getting Started with Python, PyCharm, and Pygame

In this section, we will go through the process of setting up PyCharm and rendering a graphics window on the screen. To do this, follow these steps:

  1. Open PyCharm. The first window will appear as shown in Figure 1.2.
Figure 1.2: The opening PyCharm screen on an Apple Mac (the screen on other platforms will look similar but not the same)

Figure 1.2: The opening PyCharm screen on an Apple Mac (the screen on other platforms will look similar but not the same)

You may want to take some time to look at the Customize section. This will allow you to set up colors, fonts, and other visual components. There are also many different settings and customizations you can make within PyCharm, and if you ever want to explore these, then we recommend a visit to the manual at www.jetbrains.com/help/PyCharm/quick-start-guide.html.

  1. Next, select the New Project button on the Projects page of the startup window. A window like what is shown in Figure 1.3 will appear.
Figure 1.3: PyCharm’s New Project window and settings

Figure 1.3: PyCharm’s New Project window and settings

  1. Next, we need to set up our new project as follows:
    1. For Location (1), create a new folder for your files. Unlike a single source file such as what you might get with a Word document, a Python project can consist of many files. Therefore, instead of specifying a single file name, you must specify a folder. Call it Mathematics.
    2. In the field for Base interpreter (2), ensure that you select the version of Python that you downloaded and installed. It’s possible to have more than one version of Python installed on your machine. This is useful if you are working on different projects for clients as you can set the version when you create a new project.
    3. When you first open the New Project window, the Create a main.py welcome script tickbox (3) will be ticked. We don’t require a default main.py script and therefore you should untick it.
  2. Once the project settings have been entered, click on the Create button.
  3. As shown in Figure 1.4, after PyCharm opens the new project window, it will display a column on the left with the folder structure (1). By clicking on Python Packages at the bottom of the window (2), a new section will be revealed where you can search and install packages. In the search section (3), type Pygame. This will bring up a list of packages below the search area. Select the one at the top that says Pygame, and then on the right, click the Install button (4). Once Pygame has been installed, you can close the packages section (5).
Figure 1.4: The PyCharm interface and package installation window

Figure 1.4: The PyCharm interface and package installation window

Python, PyCharm, and Pygame are now set up, and you are ready to create your first graphics window.

For those new to Python

If you are new to Python but not programming, it is a straightforward language to pick up. To get up to speed quickly, any newbies are encouraged to read over the beginner’s documentation at https://wiki.python.org/moin/BeginnersGuide.