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

Coloring and texturing mesh faces

Thus far, in our OpenGL project, we have implemented simple white mesh rendering. Now, it’s time to add the functionality of coloring and texturing polygons and pixels. The logic is similar to that of vertex coloring and UV mapping, as discussed in Chapter 5, Let’s Light It Up! Though now, when using shaders to do the rendering, the colors are added vertex by vertex and pixel by pixel.

A color is allocated to a vertex via the vertex shader and then passed to the fragment shader. The color for each vertex will specify the color of the pixel representing the vertex, but not the colors in between. Take, for example, the close-up of our teapot model in Figure 18.1:

Figure 18.1: Polygons colored using vertex colors

The colors for each vector are indicated by (a), (b), and (c). This means the fragment shader must interpret what the value for each pixel between the vertices will be. As you can see from Figure 18.1...