貝茲曲線是二維電腦圖學與字型外觀構成的重要基本元素，因此在資源有限的嵌入式應用上如何有效率地描繪貝茲曲線是一項重要的課題。在二維圖形填色時需要判斷曲線和掃瞄線的交點位置，才可得到精確的填色結果，本論文首先針對填色需求提出新的可調適前向插分演算法。接著針對曲線的筆觸效果描繪電路提出各種描繪電路架構，評估並比較所有提出的描繪電路架構的運作效率和硬體面積。從評估的結果可發現以查表為基礎的法向量計算方式對於筆觸效果的描繪相對於其他架構將會有最好的運作效率；另一方面，在所須的電路面積上，使用CORDIC計算法向量的描繪電路架構，則有較小的面積。本論文在嵌入式系統開發平台上整合開發標準的二維向量繪圖函式OpenVG與嵌入式Linux，並實作貝茲曲線的描繪電路，用以加速嵌入式平台上的二維向量描繪。

Bezier curve is one of the most fundamental primitives for the modeling of fonts and two-dimensional (2D) computer graphics objects. How to efficiently render the Bezier curve becomes an important task for many embedded applications. This thesis first proposed a novel adaptive curve-rendering algorithm which can determine the coordinates of all the crossing points of the curve and scan-lines with the required accuracy for the graphics fill operation. Next, for the rendering of stroked Bezier curves, this thesis proposed several possible rendering circuit architectures. The performance and gate count of these architectures have been estimated, and compared in this thesis. It has been found that the design based on the table-lookup normal vector calculator can lead to the fastest circuit, while the design based on the Cordic operator represents the most economic design. A basic Bezier curve rendering circuit has been implemented in this thesis, and used to accelerate a prototype OpenVG embedded systems.

摘要 I
Abstract II
Contents III
List of Figure V
List of Table VII
List of Formula VIII
Chapter 1 概論 1
1.1 研究動機 1
1.2 論文大綱 1
Chapter 2 曲線描繪相關研究 3
2.1 貝茲曲線之基本描繪 3
2.1.1 貝茲曲線簡介 3
2.1.2 貝茲曲線相關研究 5
2.1.2.1 Direct Computation 5
2.1.2.2 Forward Difference 6
2.1.2.3 Adaptive Forward Difference 7
2.1.2.4 Subdivision 9
2.2 曲線的筆觸效果之描繪 11
2.2.1 筆觸效果簡介 11
2.2.2 筆觸效果相關研究 12
Chapter 3 具筆觸效果的貝茲曲線描繪電路設計 15
3.1 曲線筆觸外殼之產生 15
3.1.1 切線向量計算 16
3.1.2 切線單位法向量計算與筆觸效果取樣點 17
3.2 完整之曲線描繪電路設計 21
3.2.1 以貝茲曲線定義方程式為基礎的設計 21
3.2.2 以Forward Difference為基礎的設計 22
3.2.3 以Subdivision為基礎的設計 23
3.2.4 避免筆觸效果斷裂的曲線描繪電路 23
Chapter 4 針對填色的貝茲曲線描繪電路設計 35
4.1 填色誤差 35
4.2 以Adaptive Forward Difference為基礎的解決方法 36
Chapter 5 實驗結果 44
5.1 實驗數據評估方法 44
5.2 實驗數據 49
Chapter 6 貝茲曲線描繪軟硬體系統整合應用 54
6.1 二維向量描繪函式庫的移植 54
6.2 二維向量繪圖加速硬體設計 54
6.3 嵌入式平台作業系統與軟硬體的整合 55
6.4 結果呈現 56
Chapter 7 結論與未來目標 58
7.1 結論 58
7.2 未來目標 58
Reference 59

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