Öz
Kaynakça
- [1] Daniilidis, K.: Hand-eye calibration using dual quaternions. International Journal of Robotics Research. 18, 286-298 (1999).
- [2] Fischer, I.: Dual-number method in kinematics, statics and dynamics. CRC Press (1998).
- [3] Funda, J., Paul, R. P.: A computational analysis of screw transformations in robotics. IEEE Transactions on Robotics and Automation. 6, 348-356 (1990).
- [4] Goldman, R.: Rethinking Quaternions: Theory and Computation. Synthesis Lectures on Computer Graphics and Animation, ed. Brian A. Barsky, No. 13. San Rafael: Morgan & Claypool Publishers (2010).
- [5] Wang, H., Goldman, R.: Surfaces of revolution with moving axes and angles. Graphical Models. 106, 101047 (2019). https://doi.org/10.1016/j.gmod.2019.101047
- [6] Hamilton, W.: Elements of Quaternions. Cambridge University Press. Cambridge, UK (1866).
- [7] Jüttler, B.: Visualization of Moving Objects using Dual Quaternion Curves. Computers and Graphics. 18, 315-326 (1994).
- [8] McCarthy, M.: Introduction to theoretical kinematics. The MIT Press (1990).
- [9] Pressley, A.: Elementary differential geometry. Springer, London (2012).
- [10] Singh, R. R.: Engineering Mathematics. Tata McGraw-Hill (1993).
- [11] Swokowski, E. W.: Calculus with analytic geometry. Prindle, Webe & Schmidt (1983).
- [12] Zatsiorsky, V. M.: Kinematics of Human Motion. Human Kinetics (1998).
Öz
A surface of revolution is a surface that can be generated by rotating a planar curve (the directrix)
around a straight line (the axis) in the same plane. Using the mathematics of quaternions, we provide a parametric
equation of a surface of revolution generated by rotating a directrix about an axis by quaternion multiplication
of the parametric representations of the directrix curve and the line of axis. Then, we describe an algorithm
to determine whether a parametric surface is a surface of revolution, and identify the axis and the directrix.
Examples are provided to illustrate our algorithm.
Anahtar Kelimeler
Surface of revolution quaternion multiplication rotation axis directrix
Kaynakça
- [1] Daniilidis, K.: Hand-eye calibration using dual quaternions. International Journal of Robotics Research. 18, 286-298 (1999).
- [2] Fischer, I.: Dual-number method in kinematics, statics and dynamics. CRC Press (1998).
- [3] Funda, J., Paul, R. P.: A computational analysis of screw transformations in robotics. IEEE Transactions on Robotics and Automation. 6, 348-356 (1990).
- [4] Goldman, R.: Rethinking Quaternions: Theory and Computation. Synthesis Lectures on Computer Graphics and Animation, ed. Brian A. Barsky, No. 13. San Rafael: Morgan & Claypool Publishers (2010).
- [5] Wang, H., Goldman, R.: Surfaces of revolution with moving axes and angles. Graphical Models. 106, 101047 (2019). https://doi.org/10.1016/j.gmod.2019.101047
- [6] Hamilton, W.: Elements of Quaternions. Cambridge University Press. Cambridge, UK (1866).
- [7] Jüttler, B.: Visualization of Moving Objects using Dual Quaternion Curves. Computers and Graphics. 18, 315-326 (1994).
- [8] McCarthy, M.: Introduction to theoretical kinematics. The MIT Press (1990).
- [9] Pressley, A.: Elementary differential geometry. Springer, London (2012).
- [10] Singh, R. R.: Engineering Mathematics. Tata McGraw-Hill (1993).
- [11] Swokowski, E. W.: Calculus with analytic geometry. Prindle, Webe & Schmidt (1983).
- [12] Zatsiorsky, V. M.: Kinematics of Human Motion. Human Kinetics (1998).
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Erken Görünüm Tarihi | 23 Temmuz 2022 |
| Yayımlanma Tarihi | 31 Ekim 2022 |
| Kabul Tarihi | 19 Ekim 2022 |
| Yayımlandığı Sayı | Yıl 2022 Cilt: 15 Sayı: 2 |
