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

Using quaternions for smooth rotations

Spherical Linear Interpolation, or SLERP for short, uses mathematics to rotate from the position of one quaternion to the position of another quaternion. Figure 7.10 shows an example of SLERP. The red line is the path for the interpolation between the quaternions with orientations <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:msub><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math> and .

Figure 7.10: Spherical Linear Interpolation between two quaternions

Doing the same transition with Euler angles works in one dimension. But for a full three-dimensional path between two quaternions, there is no simple mathematical solution to go from one combined rotation to another while maintaining a steady path in all the directions of the movement.

Note

Rotating from orientation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:msub><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math> and has a second solution: the other way around the circle, starting on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:msub><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math> and going “downward.” It is not guaranteed that Spherical Linear Interpolation will use the shortest path between two quaternions; this must be checked in the implementation...

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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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