本研究提出並實現一個基於FPGA的即時3D機器人顯示系統，以硬體化的方式實作3D繪圖流程，包含模型轉換(Model Transformation)、視角轉換 (View Transformation)、投影轉換(Projection Transformation)、遮擋判斷(Occlusion Handling) 與著色(Shading)。本系統使用Cyclone IV FPGA為開發平台，並輸出640×480 @ 60 Hz VGA訊號，以達成即時顯示需求。
在設計方法上，系統採用多階段管線化與運算資源共享，並利用線性近似法實現三角函數運算，有效降低邏輯資源消耗，同時滿足即時運算之時序要求。為提升互動性，本研究開發一個Python圖形化介面(GUI)，使用者可透過RS-232串列介面控制機器人模型之各個部位的旋轉角度，並立即在VGA畫面上呈現對應動作。
實驗結果顯示，本系統能在有限的FPGA硬體資源下完成即時3D機器人圖形的顯示與控制，其中邏輯元素使用率約68%，記憶體使用率達80%。此結果驗證了設計架構在高資源壓力下仍能維持正確性與即時性。此成果不僅展示了 FPGA 在硬體圖形加速上的潛力，也可作為未來即時 3D 圖形處理與嵌入式視覺應用之參考基礎。

This study proposes and implements an FPGA-based real-time 3D robot display system, in which the 3D graphics pipeline is realized in hardware. The implemented pipeline includes Model Transformation, View Transformation, Projection Transformation, Occlusion Handling, and Shading. The system is built on a Cyclone IV FPGA and outputs 640×480 @ 60 Hz VGA signals to achieve real-time display.
In terms of design methodology, the system adopts a multi-stage pipelined architecture and resource sharing, while trigonometric functions are implemented using a piecewise linear approximation. This approach effectively reduces logic element usage while still meeting timing requirements for real-time computation. To enhance interactivity, a Python-based graphical user interface (GUI) was developed. Through the RS-232 serial interface, users can control the rotation angles of different robot body parts, and the corresponding movements are immediately displayed on the VGA screen.
Experimental results show that the proposed system achieves real-time 3D robot rendering and control under limited FPGA hardware resources, with approximately 68% of logic elements and 80% of memory bits utilized. These results verify that the proposed architecture maintains correctness and real-time performance under high resource utilization. The outcome demonstrates the potential of FPGAs in hardware-accelerated graphics processing and can serve as a reference for future research on real-time 3D graphics and embedded visualization applications.

[1] D. G. Bailey and C. T. Johnston, “Algorithm transformation for fpga implementation”, 2010 Fifth IEEE International Symposium on Electronic Design, Test & Applications, pages 77–81, 2010.
[2] L. Cao, J. Chen and J. Li, “Working principle and application analysis of UART”, Proceedings of the 2023 IEEE 2nd International Conference on Electrical Engineering, Big Data and Algorithms (EEBDA), pages 255–259, 2023.
[3] H. Cheng, C. Xu, Z. Chen, J. Wang, Y. Chen, and L. Zhao. “A mixed reality framework for interactive realistic volume rendering with dynamic environment illumination”, 2023 IEEE Conference on Virtual Reality and 3D User Interfaces Abstracts and Workshops (VRW), pages 741–742, 2023.
[4] A. Chinchanikar, P. H. Chandankhede and A. Titarmare, “VGA controller design & implementation on FPGA”, Proceedings of the 2023 4th IEEE Global Conference for Advancement in Technology (GCAT), pages 1203–1207, 2023.
[5] D. J. Eck, “Introduction to computer graphics”, FreeTechBooks, pages 55–227, 2023.
[6] J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, “Computer Graphics: Principles and Practice”, 2nd ed. Reading, MA: Addison-Wesley, 1996.
[7] R. Goel, M. Schütz, P. J. Narayanan and B. Kerbl, “Real-time decompression and rasterization of massive point clouds”, Proceedings of the ACM on Computer Graphics and Interactive Techniques, pages 1–15, 2024.
[8] S. Juneja, A. Kaur, N. Sehgal, Sudha, and A. Prabhakar. “Emerging trends and technologies in graphics rendering pipeline”, 2025 International Conference on Networks and Cryptology (NETCRYPT), pages 1–6, 2025.
[9] LearnOpenGL CN, “Coordinate System”, LearnOpenGL CN, Available:https://learnopenglcn.github.io/01%20Getting%20started/08%20Coordinate %20Systems/, [Accessed: Aug. 23, 2025].
[10] Mirabilis Design, "Working applications of FPGA", Mirabilis Design. Available: https://www.mirabilisdesign.com/working-applications-of-fpga/, [Accessed: Aug. 22, 2025].
[11] V. Skala, “Barycentric coordinates computation in homogeneous coordinates”, Computers & Graphics, pages 120–127, 2008.
[12] K. Song, J. Zhu, Z. Wang and L. Yan, “Parallel depth buffer algorithm based on a ternary optical computer”, Applied Optics, pages 6811–6822, 2022.
[13] Terasic Technology Inc., "DE2-115 User Manual", Terasic Technology Inc, pages 8-13, 2012.
[14] F. Wang, K. Yu, and L. Yang, “Computer graphics algorithm demonstration system”, Procedia Computer Science, pages 736–744, 2023.
[15] X. Xu, X. Wu, Z. Chen, R. Chen, Y. Xu, and L. Wang, “A survey of ray tracing rendering of large-scale scenes”, Journal of Computer-Aided Design & Computer Graphics, pages 1155–1170, 2024.