A comprehensive guide to learning fundamental 3D mathematical principles used in games and computer graphics by example Key Features Get acquainted with the essential mathematics needed to describe, simulate, and render 3D creations Construct and manipulate 3D animated environments using Python, Pygame, and PyOpenGL Develop vertex and fragment shaders in OpenGL shader language to speed up rendering Book Description 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. What you will learn Get up and running with Python, Pycharm, Pygame, and PyOpenGL Experiment with different graphics API drawing commands Review basic trigonometry and how it's important in 3D environments Apply vectors and matrices to move, orient, and scale 3D objects Render 3D objects with textures, colors, shading, and lighting Work with vertex shaders for faster GPU-based rendering Who this book is for This book is for programmers who want to enhance their 3D mathematics skills relating to computer graphics and computer games. Knowledge of high school–level mathematics and a working understanding in an object-orientated language is needed to grasp the contents present in this book. Table of Contents Hello Graphics Window: You're on your way Let's Start Drawing Line Plotting Pixel by Pixel Graphics and Game Engine Components Let's Light it Up! Updating and Drawing the Graphics Environment Interactions with the Keyboard and Mouse for Dynamic Graphics Programs Reviewing Our Knowledge of Triangles Practicing Vector Essentials Getting acquainted with Lines, Rays and Normals Manipulating the Light and Texture of Triangles Mastering Affine Transformations Understanding the Importance of Matrices Working with coordinate Spaces Navigating the view space Rotating with Quaternions Vertex and fragment shading Customizing the Render Pipeline Rendering Visual Realism Like a Pro I can't begin to tell you how many pleasurable hours of study and recreation they have afforded me! I have pored over them in cars, restaurants, at work, at home... and even at a Little League game when my son wasn't in the line-up. –Charles Long If you think you're a really good programmer... read [Knuth's] Art of Computer Programming... You should definitely send me a resume if you can read the whole thing. –Bill Gates It's always a pleasure when a problem is hard enough that you have to get the Knuths off the shelf. I find that merely opening one has a very useful terrorizing effect on computers. –Jonathan Laventhol This first volume in the series begins with basic programming concepts and techniques, then focuses more particularly on information structures–the representation of information inside a computer, the structural relationships between data elements and how to deal with them efficiently. Elementary applications are given to simulation, numerical methods, symbolic computing, software and system design. Dozens of simple and important algorithms and techniques have been added to those of the previous edition. The section on mathematical preliminaries has been extensively revised to match present trends in research.