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

Manipulating the Light and Texture of Triangles

We started drawing triangles back in Chapter 2, Let’s Start Drawing, and added lighting and texturing in Chapter 5, Let’s Light It Up! Now that we’ve covered normals in Chapter 10, Getting Acquainted with Lines, Rays, and Normals, it’s time to put it all together to take a look at how these special vectors are used to manipulate and affect the appearance of triangles.

Normals can belong to vertices and mesh faces. Besides being used to specify which side of a polygon should be rendered, they are also used to calculate how light falls across the surface of a polygon. In this chapter, we will begin by improving on the normal drawing technique discussed in Chapter 10, Getting Acquainted with Lines, Rays, and Normals, and use more vector calculations on triangles to find the center of a triangle and draw the normal from that point. This will allow you to draw normals on any mesh in your project, not just cubes...