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

Measuring time

Time is used in graphics to control animations – these are any moving objects or changing images. It’s also useful for determining the frame rate at which your application is running. There are numerous useful functions for this in the Pygame API, and you can read the details here: https://www.pygame.org/docs/ref/time.html. The frame rate is expressed in frames per second (FPS), and this is an important measurement as it specifies how fast the main loop takes to execute. It’s important to keep the loop running at the same rate for the entire application to ensure smooth performance and animations. If the loop changes speed, then the experience becomes jittery.

Currently, in our code, the frame rate will be as fast as your computer can run it. However, it might not be consistent, as your operating system processes other things in the background. To see just how fast your computer is running the main loop, try removing the following from the code...