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

Summary

A lot of mathematical concepts were covered in this chapter that focused on matrices. Besides understanding vectors, a solid knowledge of matrices (especially 4 x 4) is an essential skill to have as a graphics programmer since they underpin the majority of the mathematics found in graphics and game engines. Once you appreciate the beauty of their simplicity and power, you’ll become more and more comfortable with their use.

In this chapter, we have only scratched the surface of using matrices in graphics. After learning how the addition operation that’s used in translations can be transformed into a 4 x 4 matrix, and integrated with scaling and rotation to perform compound transformations in 3D, we took a brief look at the ModelView Matrix in OpenGL using the project code created thus far. However, the way we currently perform the transformations is restricted to the same order as how glTranslate(), glRotate(), and glScale() are used in the existing code.

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