頁籤選單縮合
題名 | 具較少線段數之NURBS曲線線性近似方法=Linear Approximation of NURBS Curves with Effective Data Reduction |
---|---|
作 者 | 施浚龍; 吳明勳; 葉長茂; 李敏智; | 書刊名 | 工程應用技術學刊 |
卷期 | 2:2 2014.08[民103.08] |
頁次 | 頁134-142 |
分類號 | 448.945 |
關鍵詞 | NURBS曲線; 線性近似; Bézier曲線; 凸殼; NURBS curves; Linear approximation; Bézier curves; Convex hul; |
語文 | 中文(Chinese) |
中文摘要 | 在CG及CAD/CAM的應用領域裡,計算自由曲線之線性近似是一項非常重要且基本的幾何操作。本研究的目的即在發展一演算法,來計算NURBS曲線之較少線段數的線性近似。這個方法的最大優點是,當我們在對一個未満足近似裕度的Bézier曲線執行分割(subdividing)操作的同時,亦能利用分割後的兩個子Bézier控制多邊形,去建構一個「較緊凸殼」(tighter convex hull)來重新計算父Bézier曲線的線性近似誤差,並利用它來重新檢驗原先分割的必要性。由於以較緊凸殼所得到之誤差會更準確,因此,使用它來作為分割與否的判斷依據,將可有效地避免一些不必要的分割動作,進而達到降低NURBS曲線線性近似資料量的目的。最後值得一提的是,由於本文所提出的方法,完全僅使用線性的幾何運算,因此該方法會是十分強健且有效率的。 |
英文摘要 | Computing linear approximation of freeform curves is a very important and fundamental geometric operation in areas of CG and CAD/CAM. In this paper, a new algorithm for computing linear approximation of NURBS curves with fewer straight line segments is presented. The main advantage of the method is that a tighter convex hull of a Bézier curve, which does not satisfy a prescribed tolerance of linear approximation, can be constructed while the curve is subdivided. In effect, the tighter convex hull is formed by a union of the two newly generated sub-Bézier control polygons, and then it can be used in reexamining the linear approximation error of the progenitor Bézier curve to check if the initial subdivision is necessary or not. Since the estimation of linear approximation error with tighter convex hull is more accurate, unnecessary subdivisions can be avoided effectively. As a result, the output data of the linear approximation operation can be further reduced. In addition, since all of the geometric computations involved are linear, the proposed method is very robust and efficient. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。