Abstract
The aim of this work is to define quaternion curves and surfaces and their conjugates via operators in Euclidean projective geometric algebra (EPGA). In this space, quaternions were obtained by the geometric product of vector fields. New vector fields, which we call trajectory curves and surfaces, were obtained by using this new quaternion operator. Moreover, dual quaternion curves are determined by a similar method and then their generated motion is studied. Illustrative examples are given.
Publisher
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
Reference24 articles.
1. Vince, J., Imaginary Mathematics for Computer Science, Springer, ISBN-10: 3319946366, 2018. https://doi.org/10.1007/978-3-319-94637-5
2. Argand, J. R., Essai Sur Une Maniere de Representer des Quantites Imaginaires Dans les Constructions Geometriques, 2nd edn. Gauthier-Villars, Paris, 1874.
3. Hamilton, W. R., On quaternions: or a new system of imaginaries in algebra, Phil. Mag.3rd ser., 25(163) (1844), 10-13. doi.org/10.1080/14786444408644923
4. Clifford, W. K., Preliminary sketch of bi-quaternions, Proceedings of the London Mathematical Society, s1–4(1) (1873), 381–395. doi.org/10.1112/plms/s1-4.1.381
5. Study, E., Geometrie der Dynamen, Teubner, Leipzig, 1901.