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題 名 | Bλ木條曲面於船殼曲面表示之應用=Application of Bλ-Spline Surfaces in Representation of Hull Forms |
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作 者 | 郭真祥; 莊健青; | 書刊名 | 國立臺灣大學工程學刊 |
卷 期 | 76 1999.06[民88.06] |
頁 次 | 頁67-84 |
分類號 | 444.1 |
關鍵詞 | Bλ木條曲線; B木條曲面; Bλ木條曲面; 曲面內插; 局部形狀控制; B-spline surface; Bλ-spline surface; Surface interpolation; Local shape control; |
語 文 | 中文(Chinese) |
中文摘要 | 對於自由形狀曲線的設計,B木條曲線 (B-splines) 為常使用的方法之 一,然而針對給定曲線形狀之情況下,以B木條曲線定義時,常會有不能完全 表達所要求局部曲線幾何特性的情形。Bl 木條曲線是將一B木條曲線段進一步 分割成 l 段,因控制點相對地增加,容許在極小範圍內將控制點移動而不致於 使影響擴大,因此較B木條曲線有更好的局部控制性,可以對同一組資料點依 照要求之幾何特性,如特定之斜率或╱及曲率等產生局部形狀不同的曲線。 將Bl 木條曲線的構想延伸應用於曲面之設計或表示,衍生兩個不同處理的方 式:一為對應於B木條曲面 (B-spline surface) 之B���n木條曲面,即將一B木條 曲面片進一步分割成 (�鈗 ’ �鈅) 個次曲面片,如此可在通過給定之曲面數據點之 要求下,利用增加的控制點調整曲面局部之幾何形狀;另一為覆皮法 (Skinning method),即以B�� 木條曲線依局部幾何特性需要架築一組曲面之橫剖面曲線, 並以該組曲線為該曲面之骨架,由此骨架內插任意位置之橫剖面曲線,類似在此 骨架上覆上一層外皮。本文並以實例顯示此二種方法在船殼曲面設計應用上之結 果。 |
英文摘要 | For the design of free-form curves, a B-spline curve is one of the often used methods. Nevertheless, B-spline curves are not quite suitable for defining a given curve shape, because they can not represent some specified local curve shape very well. B��-spline curves are constructed by dividing a B-spline curve segment into �� sub-segments for improving the drawbacks of the normal B-splines. B��-spline curves have excellent local shape control properties. With a set of given data points, it is possible not only to create a B-spline curve passing all of them but also to specify some geometrical properties such as slopes or curvature at them. Extending the concept of the B��-spline curve for designing or representing surfaces, two methods can be establisched: one is a B��-spline surface which is defined by subdividing a B-spline surface into (lu ’ lv ) sub-patches. In this way, a surface can then be represented not only with given data points on the surface but also with local shape control ability at these points. The other is a so-called skinning method which constructs a surface on the basis of a set of cross-sectional curves defined by the B��-spline curve formulation. The application of these two methods on the representation of hull-forms will be shown in the paper. |
本系統中英文摘要資訊取自各篇刊載內容。