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

Vertex and Fragment Shading

The rendering of the models we’ve achieved thus far has used OpenGL’s deprecated API calls along with mathematics calculated on the CPU by Python to draw, texture, and light images on the screen. If you have tried to render models with many vertices using the current project, you’ll have noticed how slow the methods become as the vertex count increases. Even the original teapot model from Chapter 8, Reviewing Our Knowledge of Triangles, starts to slow down the application.

To speed up rendering, a graphics card (GPU) can be used to process vertices and pixels in parallel. To move the logic and algorithms we’ve written thus far onto the GPU, we must first learn how to write shader programs that are compiled and executed on the GPU.

To this end, in this chapter, we will cover the following topics:

  • Understanding shaders
  • Transferring processing from the CPU to the GPU
  • Processing pixel by pixel

As we refactor...