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

Customizing the Render Pipeline

In Chapter 5, Let’s Light It Up!, we discussed adding color, textures, and lights to a scene. In our project, we colored vertices, applied textures, and turned on lights with single OpenGL calls.

Now in this chapter we will investigate how the color of all pixels is calculated through the use of shaders. When working with shaders, all the mathematics is revealed. With a few modifications to your project, by the end of this chapter you will be using shaders for the following purposes:

  • Coloring and texturing mesh faces
  • Turning on the lights

We will begin by grabbing the UV values that come with the OBJ model file and passing these values and a texture to a vertex and fragment shader for processing. This will allow us to color a model using an external image. Following this, because a plain image on a model will look rather flat, we’ll examine the fundamental lighting models that have been traditionally used to emulate...