近幾年來，電腦繪圖已成為人機介面中，最重要的資料顯示方法，並廣泛的運用在各種應用之中。例如計算機輔助設計，醫療方面的影像處理，以及電腦動畫…等等，尤其在3-D 電腦繪圖，3D engine技術的重大突破，使得這些應用可以以低成本的即時3D電腦繪圖技術為基礎。在本篇論文中，我們實作浮點運算CORDIC算術處理器，來執行許多算術運算，並利用這些數學函數的功能來輔助3D engine的設計。

Computer graphics has become one of the important method to display information and has been applied in many applications such as CAD, medical image processing, computer animation, multimedia and virtual reality. These popular applications rely on the low-cost and real-time processing of 3D graphics which become available due to the breakthrough in the hardware design of 3D graphic engine. In this thesis, we implement a CORDIC-based floating-point processor that can compute a wide variety of arithmetic operations and show how it can be applied to the design of 3D engine.

CHAPTER 1 導論 1
1.1 論文架構 1
1.2 研究動機 1
CHAPTER 2 CORDIC相關研究 3
2.1 原始的座標軸數位旋轉計算器原理: 3
2.2 修正長度因子說明: 4
2.3 相關研究成果 6
CHAPTER 3 3D GRAPHICS之原理及硬體設計 13
3.1 3-D繪圖硬體的設計目標 13
3.2 標準3-D繪圖著色管線 15
3.2.1 幾何轉換子系統 (Geometric Subsystem) 17
3.2.2 著色子系統 (Raster Subsystem) 18
3.3 克服 3-D 硬體瓶頸的技術 21
3.3.1 平行化 21
3.3.2 記憶體輸出入系統的改良 24
CHAPTER 4 浮點運算CORDIC及其實作 27
4.1 浮點運算器架構 27
4.2 前置處理單元 31
4.3 內部CORDIC計算器 33
4.4 後置處理單元 34
4.5 CORDIC FPU在MICROSPARC2上的應用 35
4.6 CORDIC FPU與其他FPU的比較 40
4.7 驗證與實驗數據 40
4.7.1 浮點數CORDIC驗證 41
4.7.2 各項實驗數據 41
CHAPTER 5 幾何轉換器 45
5.1 三維幾何轉換矩陣運算 45
5.2 快速矩陣相乘 49
5.3 矩陣相乘方向選擇器 51
5.4 幾何轉換處理器 59
CHAPTER 6 新的快速VECTORING CORDIC 62
6.1 預測VECTORING MODE CORDIC前N/3 個ITERATIONS 64
6.2 預測VECTORING MODE CORDIC後2N/3 個ITERATIONS 68
CHAPTER 7 結論 71

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