Motions on curves and surfaces using geometric algebra

Year 2022, Volume: 71 Issue: 1, 39 - 50, 30.03.2022

Selahattin Aslan , Yusuf Yaylı

https://doi.org/10.31801/cfsuasmas.878766

Cited By: 3

Abstract

Geometric algebra is a useful tool to overcome some problems in kinematics. Thus, the geometric algebra has attracted the attention of many researchers. In this paper, quaternion operators on curves and surfaces in Euclidean 3-space are defined by using geometric algebra. These operators generate the curves or the surfaces from the points, curves or surfaces. Using quaternion operators, we obtain motions that have orbits along the generated curve or surface. Also, these motions are expressed as 1-parameter or 2-parameter homothetic motions.

Keywords

Geometric algebra, curves, surfaces, quaternions, rotation matrices, homothetic motions

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