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Canal Surfaces with Quaternions

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Abstract

Quaternions are more usable than three Euler angles in the three dimensional Euclidean space. Thus, many laws in different fields can be given by the quaternions. In this study, we show that canal surfaces and tube surfaces can be obtained by the quaternion product and by the matrix representation. Also, we show that the equation of canal surface given by the different frames of its spine curve can be obtained by the same unit quaternion. In addition, these surfaces are obtained by the homothetic motion. Then, we give some results.

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Authors and Affiliations

  1. Department of Mathematics, Ankara University, 06100, Ankara, Turkey

    Selahattin Aslan & Yusuf Yaylı

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  1. Selahattin Aslan
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  2. Yusuf Yaylı
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Correspondence to Selahattin Aslan.

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Aslan, S., Yaylı, Y. Canal Surfaces with Quaternions. Adv. Appl. Clifford Algebras 26, 31–38 (2016). https://doi.org/10.1007/s00006-015-0602-5

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