Flexible and Cost-Effective Spherical to Cartesian Coordinate Conversion Using 3-D CORDIC Algorithm on FPGA

Authors

  • Nadia M. Salem, Sami I. Serhan, Khawla M. Al-Tarawneh, Ra’fat Al-Msie’deen

Keywords:

Cartesian, CORDIC, Cosine, FPGA, Sine, Spherical, VHDL

Abstract

In computer science, transforming spherical coordinates into Cartesian coordinates is an important mathematical operation. The CORDIC (Coordinate Rotation Digital Computer) iterative algorithm can perform this operation, as well as trigonometric functions and vector rotations, using only simple arithmetic operations like addition, subtraction, and bit-shifting. This research paper presents hardware architecture for a 3-D CORDIC processor using Quartus II 7.1 ALTERA software, which enables easy modifications and design changes due to its regularity and simplicity. The proposed 3-D CORDIC model is evaluated by comparing the calculated results with the simulated results to determine its accuracy. The results were satisfaction and the proposed model could be suitable for numerous real-time applications.

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References

Volder, Jack E. (1959)."The CORDIC Trigonometric Computing Technique." IRE Transactions on Electronic Computers, Vol. EC-8, no. 3, 1959, pp. 330-334.

Volder, J. E. (2000). “The Birth of CORDIC”. Journal of VLSI Signal Processing, 25, 101-105. https://doi.org/10.1023/A:1008191618576.

Duprat, J., & Muller, J. (1993). “The CORDIC algorithm: new results for fast VLSI implementation”. IEEE Transactions on Computers, 42(2), 168-178.

Li, Huan, and Yan Xin. (2010). "Modified CORDIC algorithm and its implementation based on FPGA." 2010 Third International Conference on Intelligent Networks and Intelligent Systems.(pp. 618-621). IEEE.

Bhuria, S., & Muralidhar, P. (2010, November). FPGA implementation of sine and cosine value generators using Cordic Algorithm for Satellite Attitude Determination and calculators. In 2010 International Conference on Power, Control and Embedded Systems (pp. 1-5). IEEE.‏

Kumar, P. A. (2019, March). FPGA implementation of the trigonometric functions using the CORDIC algorithm. In 2019 5th International Conference on Advanced Computing & Communication Systems (ICACCS) (pp. 894-900). IEEE.‏

Mazenc, Mazenc, C., Merrheim, X., & Muller, J. M. (1993). Computing Functions cos-1and sin-1Using CORDIC. IEEE Transactions on Computers, 42(1), 118-122

‏Sadiku, Matthew N. O. (2001),"Coordinate Systems and Transformation." Chapter 2 in Elements of Electromagnetics, third edition, Oxford University Press, pp. 23-51.

Walther, J. S. (1971, May). A unified algorithm for elementary functions. In Proceedings of the May 18-20, 1971, spring joint computer conference (pp. 379-385)

Neji, N., Boudabous, A., Kharrat, W., & Masmoudi, N. (2011, March). Architecture and FPGA implementation of the CORDIC algorithm for fingerprints recognition systems. In Eighth International Multi-Conference on Systems, Signals & Devices (pp. 1-5). IEEE.‏

Gopikiran, G., & Thilagavathy, R. (2011, July). FPGA implementation of floatingpoint rotation mode CORDIC algorithm. In 2011 International Conference on Signal Processing, Communication, Computing and Networking Technologies (pp. 506-508).

Andraka, R. (1998, March). A survey of CORDIC algorithms for FPGA based computers. In Proceedings of the 1998 ACM/SIGDA sixth international symposium on Field programmable gate arrays (pp. 191-200).‏

Lakshmi, B., & Dhar, A. S. (2010). CORDIC Architectures: A Survey. Hindawi Publishing Corporation VLSI Design, 2010, Article ID 794891, 19 pages. doi:10.1155/2010/794891.

Lang, T., Lang, T., & Antelo, E. (2005). High-throughput CORDIC-based geometry operations for 3D computer graphics. IEEE Transactions on Computers, 54(3), 347-361.‏

Li, J. H., Wang, G. C., Chen, Y., Zhang, M., & Li, P. (2012). A VLSI Design of Image Rotation for Real Time 2-D Barcode Identification. Applied Mechanics and Materials, 198, 357-360.‏

Sergiyenko, A., Moroz, L., Mychuda, L., & Samotyj, V. (2021, September). FPGA implementation of CORDIC algorithms for sine and cosine floating-point calculations. In 2021 11th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS) (Vol. 1, pp. 383-386). IEEE.

Nair, H., & Chalil, A. (2022, March). FPGA Implementation of Area and Speed Efficient CORDIC Algorithm. In 2022 6th International Conference on Computing Methodologies and Communication (ICCMC) (pp. 512-518). IEEE.‏

Paz, P., & Garrido, M. (2023). CORDIC-Based Computation of Arcsine and Arccosine Functions on FPGA. IEEE Transactions on Circuits and Systems II: Express Briefs.‏ doi: 10.1109/TCSII.2023.3262353.

Wang, J., Peng, Z., Zhan, Y., Li, Y., Yu, G., Chong, K. S., & Wang, C. (2022). A high-accuracy and energy-efficient CORDIC based izhikevich neuron with error suppression and compensation. IEEE Transactions on Biomedical Circuits and Systems, 16(5), 807-821.‏

Chen, K. T., Fan, K., Han, X., & Baba, T. (2015). A CORDIC algorithm with improved rotation strategy for embedded applications. Journal of Industrial and Intelligent Information, 3(4), 274-279.

Weijun Zhang (2001)." VHDL Tutorial: Learn by Example," University of California, Retrieved April,1,2023,from http://esd.cs.ucr.edu/labs/tutorial/.

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Published

12.06.2024

How to Cite

Nadia M. Salem. (2024). Flexible and Cost-Effective Spherical to Cartesian Coordinate Conversion Using 3-D CORDIC Algorithm on FPGA. International Journal of Intelligent Systems and Applications in Engineering, 12(4), 815 –. Retrieved from https://ijisae.org/index.php/IJISAE/article/view/6302

Issue

Vol. 12 No. 4 (2024)

Section

Research Article

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