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Quaternions

Overview

In computer graphics applications, quaternions are used to represent three-dimensional rotations. They provide some key advantages over the traditional way of defining generic rotational transformations using Euler angles. Quaternions are also extremely useful for interpolating between two orientations in three-dimensional space. Keyframe animations requiring orientation interpolation therefore find a very convenient mathematical tool in quaternions.

This chapter gives an overview of the algebra of quaternions, the geometrical interpretation of quaternion transformations, and quaternion based linear and spherical interpolation functions. A comparison of rotation interpolation methods using Euler angles, angle-axis representations, and quaternions is presented. The extension of quaternions to eight-dimensional dual quaternions and their usefulness in representing general rigid-body transformations are also discussed.

Keywords

  • Euler Angle
  • Unit Quaternion
  • Rotational Transformation
  • Dual Quaternion
  • Dual Number

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Ramakrishnan Mukundan .

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© 2012 Springer-Verlag London Limited

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Mukundan, R. (2012). Quaternions. In: Advanced Methods in Computer Graphics. Springer, London. https://doi.org/10.1007/978-1-4471-2340-8_5

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  • DOI: https://doi.org/10.1007/978-1-4471-2340-8_5

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