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

Working out a vector’s magnitude

By drawing and working with vectors, it’s obvious to see they have a length. This is something that also distinguishes them from a point. The magnitude or length of a vector is useful for calculating the distance between where it starts and where it ends. For example, in Figure 9.3, we calculated the vector the pirate had to travel to get from a starting location to the treasure. From this vector, we can see the direction of travel, but we can also calculate how far the pirate is from the treasure. A very common operation to perform in graphics when it comes to moving objects is determining how far objects are apart, as well as working with collisions and a multitude of other functions. Therefore, it’s useful to understand how the magnitude is calculated.

To perform this operation, we must go back to Pythagoras theorem and triangles. Essentially, every vector can be made into a right-angled triangle. From there, the vector...