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

Understanding shaders

In graphics, a shader is a special program used to determine how a virtual object is drawn on the screen. It calculates the color of each pixel based on the geometry of an object, the color or texture of the object, and the light falling on the object’s surface. Shaders are written in a shading language. There are three general types of shaders—fragment, vertex, and geometry. These shaders allow graphics programmers to intercept the render pipeline shown in Figure 17.1:

Figure 17.1: The render pipeline

The process of rasterization is how 3D virtual objects get drawn onto the screen as pixels. It starts out as a 3D mesh or model with vertices, normals, UVs, and tangents. The vertex processor (1 in Figure 17.1) computes the normalized coordinate-space positions of the vertices and associated values, taking them from model coordinates and converting them into screen coordinates. The mathematics for this process was revealed...