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

Improving camera orientations

Regardless of the direction the camera is facing, when flying around in a 3D environment, being able to yaw around the world’s up axis is far less disorientating than yawing at an unexpected angle, no matter how mathematically correct it may be. Rolling around the forward-facing vector of the camera is however intuitive as it is the way the viewer is facing. Many first-person player controllers are set up to rotate around the world's up axis and the camera-forward axis as shown in Figure 15.5. It prevents the camera tipping accidentally upside down and experiencing gimbal lock.

Figure 15.5: Intuitive camera flying rotation axes

To instigate rotations using these axes, we need to be able to switch between local and world space. In this instance we want to rotate the camera in world space (where it yaws around the up axis) and roll around the local z axis, which is the axis that indicates the direction the camera is...