You're reading from C++ Game Animation Programming - Second Edition

Product typeBook

Published inDec 2023

Reading LevelN/a

PublisherPackt

ISBN-139781803246529

Edition2nd Edition

Languages

C++

Tools

OpenGL

Concepts

Animation

Authors (2):

Michael Dunsky

Gabor Szauer

View More author details

Exploring vector rotation

Let us start with the most basic rotation we will have in the code, the natural-feeling rotation around the three axes in a three-dimensional cartesian space.

The Euler rotations

In the 18th century, the German mathematician Leonhard Euler (1707-1783) discovered the rule that a composition of two rotations in three-dimensional space is again a rotation, and these rotations differ only by the rotation axis.

We still use this rotation theorem today, to rotate objects around in virtual worlds. The final rotation of a three-dimensional object is a composition of rotations around the x, y, and z axis in three-dimensional cartesian space:

Figure 7.5: The three-dimensional cartesian space, plus the x, y, and z rotation axes

The rotations themselves are defined by the sine and cosine of the rotation angle:

Figure 7.6: Definition of the sine and the cosine of an angle <?AID d835?><?AID df4b?>

Figure 7.6: Definition of the sine and the cosine of an angle <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi mathvariant="bold-italic">φ</mml:mi></mml:math>

We are using the inverse of...

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C++ Game Animation Programming - Second Edition

Published in: Dec 2023Publisher: PacktISBN-13: 9781803246529

Authors (2)

Michael Dunsky

Michael Dunsky is an educated electronics technician, game developer, and console porting programmer with more than 20 years of programming experience. He started at the age of 14 with BASIC, adding on his way Assembly language, C, C++, Java, Python, VHDL, OpenGL, GLSL, and Vulkan to his portfolio. During his career, he also gained extensive knowledge in virtual machines, server operation, infrastructure automation, and other DevOps topics. Michael holds a Master of Science degree in Computer Science from the FernUniversität in Hagen, focused on computer graphics, parallel programming and software systems.
Read more about Michael Dunsky

Gabor Szauer

Gabor Szauer has been making games since 2010. He graduated from Full Sail University in 2010 with a bachelor's degree in game development. Gabor maintains an active Twitter presence, and maintains a programming-oriented game development blog. Gabor's previously published books are Game Physics Programming Cookbook and Lua Quick Start Guide, both published by Packt.
Read more about Gabor Szauer

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