An insight into the evolution of rotation operator to quaternion’s. Computer graphics perspective

• Autorzy: Sami Saad Bin , Tariq Humera

Identyfikatory

DOI

10.17512/jamcm.2019.1.07

• Języki publikacji: EN

Abstrakty

EN

Rotations are an integral part of various computational techniques and mechanics. The objective in this paper is twofold: first to have a classical insight into the history of quaternions, a problem that Hamilton faced for over a decade and secondly to look at into its applications from computer graphics perspective. Thorough revision of quaternion algebra and its use case as a rotation operator has been presented. A quaternion simulation algorithm has been written and practiced to generate simulation results. Results show that though quaternions supersede Euler angles technically but are tricky to use and control for e.g. when same quaternion is applied on a different vector axis, the particle is not able to reach its initial position and an incomplete rotation effect has been recorded and observed.

Słowa kluczowe

EN

rotation; affine; transformation OpenGL; visualization

PL

rotacja; operacja afiniczna; grafika komputerowa; operator obrotu; wizualizacja

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2019
• Tom: Vol. 18, nr 1
• Strony: 77--87
• Opis fizyczny: Bibliogr. 12 poz., rys., tab.

Twórcy

autor

Sami Saad Bin

• Department of Computer Science, University of Karachi Karachi, Pakistan

autor

Tariq Humera

• Department of Computer Science, University of Karachi Karachi, Pakistan

Bibliografia

• [1] Hill, F.S. (1999). Computer Graphics using Open GL (Second Edition). Prentice Hall.
• [2] Paeth, A.W. (1995). Graphics Gems V. Academic Press.
• [3] Shriener, D., Sellers, G., Kessinish, J., & Licea, K.B. (2013). Open GL Programming Guide: The Official Guide to Learning. (Eighth Edition). Addison Wesley.
• [4] Gellert, W., Kiistner, H., Hellwich, M., & Kastner, H. (1975). The VNR Concise Encyclopedia of Mathematics. Van Nostrand Reinhold.
• [5] Pletinckx, D. (1989). Quaternion calculus as a basic tool in computer graphics. The Visual Computer, 5(1), 2-13.
• [6] Pavllo, D., Feichtenhofer, C., Auli, M., & Grangier, D. (2019). Modeling Human Motion with Quaternion-based Neural Networks. Pre print arXiv.
• [7] Wei-Hsu, H. et al. (2019). Quaternion-based head pose estimation with multiregression loss. IEEE Transactions on Multimedia, 21(4), 1035-1046.
• [8] Familton, J.C. (2015). Quaternions: A History Of Complex Noncommutative Rotation Groups In Theoretical Physics. Pre print arXiv.
• [9] Van Der Waerden, B.L. (1976). Hamilton’s discovery of quaternions. Mathematics Magazine, 49(5), 227-234.
• [10] Vince, J. (2011). Quaternions for Computer Graphics. London: Springer-Verlag.
• [11] Kuipers, J.B. (1999). Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace, and Virtual Reality. Princeton University Press.
• [12] Nielson, F., & River, C. (2005). Visual Computing: Geometry, Graphics and Vision. Charler Medial Press.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).