An FPGA-oriented fully parallel algorithm for multiplying dual quaternions

• Autorzy: Cariow A. , Cariowa G. , Witczak M.
• Języki publikacji: EN

Abstrakty

EN

This paper presents a low multiplicative complexity fully parallel algorithm for multiplying two dual quaternions. The “pen-and-paper” multiplication of two dual quaternions requires 64 real multiplications and 56 real additions. More effective solutions still do not exist. We show how to compute a product of two dual quaternions with 24 real multiplications and 64 real additions. During synthesis of the discussed algorithm we use the fact that the product of two dual quaternions can be represented as a matrix–vector product. The matrix multiplicand that participates in the product calculating has unique structural properties that allow performing its advantageous factorization. Namely this factorization leads to significant reducing of the multiplicative complexity of dual quaternion multiplication. We show that by using this approach, the computational process of calculating dual quaternion product can be structured so that eventually requires only half the number of multipliers compared to the direct implementation of matrix-vector multiplication.

Słowa kluczowe

EN

dual quaternion product; fast algorithms; hardware complexity reduction; FPGA

• Wydawca: Wydawnictwo PAK
• Czasopismo: Measurement Automation Monitoring
• Rocznik: 2015
• Tom: Vol. 61, No. 7
• Strony: 370--372
• Opis fizyczny: Bibliogr 10 poz., rys., tab., wzory

Twórcy

autor

Cariow A.

• West Pomeranian University of Technology, Szczecin, 49 Żołnierska St., 71-210 Szczecin

autor

Cariowa G.

• West Pomeranian University of Technology, Szczecin, 49 Żołnierska St., 71-210 Szczecin

autor

Witczak M.

• West Pomeranian University of Technology, Szczecin, 49 Żołnierska St., 71-210 Szczecin

Bibliografia

• [1] Pennestrì E., Valentini P. P.: Dual quaternions as a tool for rigid body motion analysis: a tutorial with an application to biomechanics. Archive of Mechanical Engineering, vol. LVII, No 2, pp. 187–205. 2010.
• [2] Jiang F., Wang H.-N, Huang Ch. S.: Algorithm for Relative Position and Attitude of Formation Flying Satellites Based on Dual Quaternion. Chinese Space Science and Technology, v32(3): pp. 20-26. 2012.
• [3] Feng X., Wan W.: Real time skeletal animation with dual quaternion. Journal of Theoretical and Applied Information Technology. v. 49, no.1, pp. 356-362, 2013.
• [4] Pham H. L, Perdereau V., Adorno B.V., and Fraisse P.: Position and orientation control of robot manipulators using dual quaternion feedback. IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan, China. 18-22 October 210, pp. 658–663. 2010.
• [5] Torsello A.: Point Invariance of the Screw Tension Minimizer. Università Ca’Foscari Venezia, Dipartimento di Scienze Ambientali Informatica e Statistica, Technical Report Series, Rapporto di Ricerca DAIS-2011-2, pp. 1-7, 2011.
• [6] Kavan L., Collins S., Žára J. J., and O’Sullivan C.: Geometric skinning with approximate dual quaternion blending. ACM Trans. Graph., 27(4):105, pp. 2442-2443, 2008.
• [7] Torsello A., Rodolà E., and Albarelli A.: Multiview Registration via Graph Diffusion of Dual Quaternions. IEEE Conference on Computer Vision and Pattern Recognition, 20-25 June 2011, pp. 2441-2448, 2011.
• [8] Mukundan R.: Advanced Methods in Computer Graphics: With examples in OpenGL. Springer-Verlag London Limited, 2012.
• [9] Kenwright B.: Dual-Quaternions: From Classical Mechanics to Computer Graphics and Beyond, 1-11, Source:www.xbdev.net
• [10] Ţariov A.: Algorytmiczne aspekty racjonalizacji obliczeń w cyfrowym przetwarzaniu sygnałów, Wydawnictwo Zachodniopomorskiego Uniwersytetu Technologicznego, 2011.