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

Turning on the lights

When it comes to lighting in shaders, there’s a lot of hands-on mathematics. No longer can we rely on nice, neat OpenGL function calls in our main code. Instead, we must calculate the color of a pixel and consider the lighting in the fragment shader.

In the previous section, when you completed the exercise and loaded the granny model with the texture, it was unlit. It displayed the colors as they appear in the PNG texture file. To include lighting effects, we must determine how the light will influence the original color of the pixel taken from the texture. Over the years, a gradual improvement has been made to lighting models, which is evident if you take a look at the quality of computer graphics from 20 years ago up until now.

In this section, we will examine some popular lighting models and apply the mathematics to our fragment shader to light up the model.

Ambient lighting

Ambient lighting is lighting in a scene that has no apparent source...