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

Placing Textures on Meshes

Materials are the surface treatments given to polygons that make them appear solid. The coloring-in of the polygon plane gives the illusion that it has substance and is more than its surrounding edges. The surface treatment applied interacts with the lighting applied to give the final appearance.

Just like lights, materials have different ambient, diffuse, and specular colors. Each of these interacts with the corresponding lights to determine the final effect seen. For example, white diffuse light shone on a diffuse green cube will reflect the color green. Although white light is hitting the cube, the green color of the cube determines what light gets reflected. White light is when all the color channels for R, G, and B are turned on, hence the (1, 1, 1) value. If the cube is green, then its color is set to (0, 1, 0). Essentially, it’s the channel that the light and the material both have turned on that is reflected. Of course, it is a little more...