Motions on curves and surfaces using geometric algebra
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Date
2022
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Publisher
Ankara Üniversitesi
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.
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Keywords
Geometric algebra, curves, surfaces, quaternions, rotation matrices, homothetic motions