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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.


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

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Correspondence to Ramakrishnan Mukundan .

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Mukundan, R. (2012). Quaternions. In: Advanced Methods in Computer Graphics. Springer, London.

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