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研究生：	曾主龍 Tseng, Chu-Lung
論文名稱：	以FPGA實現用於撞球遊戲之圖學光柵演算法 A FPGA Implementation of Graphics Rasterization Algorithms for Pool Games
指導教授：	張名先 Chang, Ming-Xian
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 電腦與通信工程研究所 Institute of Computer & Communication Engineering
論文出版年：	2024
畢業學年度：	112
語文別：	英文
論文頁數：	69
中文關鍵詞：	現場可程式化邏輯閘陣列 (FPGA) 、電腦圖學、3D影像處理、二維碰撞、即時、MVP轉換、光線追踪
外文關鍵詞：	Field-Programmable Gate Array (FPGA), Computer Graphics, 3D Image Processing, 2D Collision, Real-Time, MVP Translation, Ray tracing
相關次數：	點閱：50 下載：2
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電腦圖學已經具有多年的技術演進，在科技的發展當中提供了資訊視覺化的功能。隨著技術的發展，電腦圖學所能產生的圖像愈來愈逼真並能在科技、建模、藝術、娛樂等等領域有著非常大量的應用以及貢獻。本論文使用了電腦圖學的架構來實現基於3D物件顯示開發的撞球電玩遊戲系統。
本篇論文著重研究的問題在於如何應用現場可程式化邏輯閘陣列 (FPGA)讓三維的電腦影像物件繪圖能即時顯示在一個解析度為(640×480)、幀率可達每秒60幀的VGA螢幕，並且能對於這些物件達到操控以及互動藉此來完成一個可供操作並且能視覺化顯示的電玩遊戲。
本論文所提出的系統通過PC端的使用者控制介面透過RS232介面將控制指令傳送至FPGA。在FPGA中將輸入於RAM中的三維物件頂點資訊以及控制指令合併作為輸入參數來執行Model-View-Projection (MVP)轉換，讓三維物件能被投影到二維平面上，並能根據使用者所下達的指令做出對應的運動變化。完成投影的物件資訊將會輸入進著色模組，結合光線追踪技術進行物件的上色並加上遮擋判定，以賦予物件逼真的立體效果。最後將著色的結果利用影像緩衝區來穩定色彩訊號的輸出，便能透過VGA介面來將所有的三維物件以及使用者的控制結果顯示在螢幕中。

Computer graphics has evolved significantly over the years, providing critical visualization capabilities in technological advancements. As technology progresses, the images generated by computer graphics have become increasingly realistic, leading to extensive applications and contributions in fields such as science, modeling, art, and entertainment. This thesis utilizes the framework of computer graphics to develop a billiards game system based on the display of 3D objects.
This thesis presents the development of a system using Field-Programmable Gate Arrays (FPGA) to enable real-time rendering of 3D computer graphics objects on a VGA screen with a resolution of (640×480) and a frame rate of up to 60 frames per second. This system allows for the control and interaction with these objects, culminating in a fully operational and visually interactive video game.
The system proposed in this thesis employs a user control interface on the PC side to send control commands to the FPGA via an RS232 interface. Within the FPGA, the 3D object vertex information stored in RAM and the control commands are combined as input parameters to execute the Model-View-Projection (MVP) transformation. This allows the 3D objects to be projected onto a 2D plane and to move according to user commands. The projected object information is then fed into the shading module, where ray tracing is combined with occlusion determination to render realistic, three-dimensional effects on the objects. Finally, the rendered output is stabilized using a frame buffer, enabling the VGA interface to display all 3D objects and user control results on the screen.

摘要 i
Abstract ii
誌謝 iii
Table of Contents iv
List of Figures vi
Chapter 1 Introduction 1
1. Computer Graphics 1
2. Field Programmable Gate Array (FPGA) 2
3. Project 3D objects into 2D space 4
4. Two-dimensional Collision 6
5. Motivation and Contribution 6
6. Thesis Outline 7
Chapter 2 Overview of Related Work 8
1. 3D Computer Graphic 8
1.1. Polygonal Model 8
1.2. Computer Graphics Pipeline 9
1.3. OBJ Geometry Format 9
2. MVP Transformation 10
2.1. Model Matrix 11
2.2. View Matrix 13
2.3. Projection Matrix 17
3. Barycentric Interpolation, Z-Buffer and Lighting 23
3.1. Barycentric Interpolation 23
3.2. Z-Buffer Algorithm 25
3.3. Lighting 26
4. Elastic Collision 28
Chapter 3 Hardware Architecture of The Proposed System 31
1. Workflow 31
2. The Top-Level Module 32
3. RS232 Interface and Module 34
4. The Movement Module 36
4.1. Introduction 36
4.2. Formula implementation (atan2) 37
5. The Project Module 40
5.1. The projection flow in Projection Module 41
5.2. The light flow in Projection Module 43
6. The Draw Module 43
7. The Frame Buffer Module 47
Chapter 4 Experimental Results 49
1. Research Equipment and Setup 49
2. Graphical User Interface 50
3. Results 51
Chapter 5 Conclusion and Future Works 58
1. Conclusion 58
2. Future Works 58
2.1. Grayscale to RGB color 58
2.2. More Complex Objects 59
2.3. More Complex Lighting Model 59
References 60
                                    

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[2] Haojie Cheng, Chunxiao Xu, Zhenxin Chen, Jiajun Wang, Yibo Chen, and Lingxiao Zhao. A mixed reality framework for interactive realistic volume rendering with dynamic environment illumination. In 2023 IEEE Conference on Virtual Reality and 3D User Interfaces Abstracts and Workshops (VRW), pages 741–742, 2023.
[3] Sarah Fachada, Daniele Bonatto, Mehrdad Teratani, and Gauthier Lafruit. Polynomial image-based rendering for non-lambertian objects. In 2021 International Conference on Visual Communications and Image Processing (VCIP), pages 01–05, 2021.
[4] Yeong-Kang Lai and Yu-Chieh Chung. An efficient and high quality rasterization algorithm and architecture in 3d graphics systems. In 2015 IEEE International Symposium on Circuits and Systems (ISCAS), pages 2537–2540, 2015.
[5] Soumitra Ray, Chandra Deo Rajak, A K Shrivastava, and Biswajit Biswas. Implementation of fpga-based portable count down clock (pcdc). In 2023 3rd International Conference on Range Technology (ICORT), pages 1–6, 2023.
[6] Anshy Singh, Manoj Kumar, and Aditi Saxena. Analysis of computer vision for graphics and animation. In 2023 9th International Conference on Advanced Computing and Communication Systems (ICACCS), volume 1, pages 804–807, 2023.
[7] ZHONGYU TAO. A high-precision alu design of interpolation in rasterization. In 2019 16th International Computer Conference on Wavelet Active Media Technology and Information Processing, pages 63–65, 2019.
[8] Andre Waschk and Jens Krüger. Favr - accelerating direct volume rendering for virtual realitysystems. In 2020 IEEE Visualization Conference (VIS), pages 106–110, 2020.
[9] Freddy Indra Wiryadi and Raymond Kosala. Particle rendering using geometry shader. In 2016 1st International Conference on Game, Game Art, and Gamification (ICGGAG), pages 1–6, 2016.
[10] Zhenjie Xia and Min Li. Research on graphic processing system of visual communication design based on computer big data. In 2023 IEEE International Conference on Control, Electronics and Computer Technology (ICCECT), pages 13–17, 2023.
[11] Rachana Yadav and S Prakash. An analysis of how computer graphics and image processing are used in art design. In 2022 International Conference on Futuristic Technologies (INCOFT), pages 1–5, 2022.
[12] Jan Škoda and Martin Motyčka. Lighting design using ray tracing. In 2018 VII. Lighting Conference of the Visegrad Countries (Lumen V4), pages 1–5, 2018.

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