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

Working with the View Matrix

The view matrix takes the world space coordinates produced by the modelview matrix and transforms them into the camera or eye space. The eye space assumes the origin of this space to be at the position of the camera or viewer’s eye. As we saw in Chapter 4, Graphics and Game Engine Components, the eye space can either be a frustum (a pyramid with the top cut off for perspective views) or orthogonal (a rectangular prism for parallel views). The view matrix can take translation and rotations like the modelview matrix, but instead of transforming individual objects, it transforms everything in the world. That’s because it’s basically the equivalent of moving a camera around in the world, and then determining what the world will look like through that camera.

Unlike the modelview matrix, which can be loaded after an OpenGL call to glGetDoublev( GL_MODELVIEW_MATRIX), the view matrix sets a special matrix mode. The view matrix is multiplied...