Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/1482
標題: 不可展曲面攤平方法之探討
Reasearch about Flattening Methods for Non-Developable Surfaces
作者: 吳鴻昆
Kun, Wu Hong
關鍵字: undevelopable surfaces;不可展曲面;flattening;B-spline surface;strip;guide strip;攤平;B-spline曲面;細長片;引導細長片
出版社: 機械工程學系
摘要: 
本文之目的是在不考量曲面厚度、力學行為與材料性質之條件限制下,以幾何處理觀點,針對不可展曲面之攤平技術及演算法則,經由分析探討後應用於處理參數曲面建構之不可展曲面整理成曲面攤平的工作流程。讓需要曲面模型之攤平圖案的從事者能應用簡易的工作流程完成相關工作。
整個過程是首先以B-spline曲面建構不可展曲面模型,並且利用建構B-spline曲面的各條B-spline曲線執行曲面的三角網格化。在曲面攤平執行前,依據曲面的攤平特性中測地曲率的定義計算各條B-spline曲線的測地曲率值。曲面攤平執行時,選取全部B-spline曲線中測地曲率較小者之曲線鄰接的三角網格綴面為引導細長片,再以引導細長片的測地曲率值計算攤開方位。然後使用旋轉矩陣的正交轉換定理對細長片作曲面攤平運算。
此外,為了檢驗曲面攤平的結果。藉由計算攤平前後之圖樣的面積差及周長差,使用幾何指標作攤平圖樣的評估。對於曲面攤平後產生的裂縫或重疊現象是採取原處修正方式,將裂縫或重疊往閉合方向作修正。
經由選擇引導細長片和決定攤開方位比無決定引導細長片和攤開方位的曲面攤平方式,能夠產生多樣化的曲面攤平圖樣。且使用細長片比使用單個三角網格綴面作旋轉矩陣的正交轉換,所需要進行曲面攤平的運算次數少。因此其整體曲面攤平的運算效率會較高。

Taking only geometric processing into consideration, the objective of this research is to develop procedural steps for flattening undevelopable surfaces.
Using the B-spline surface as the surface constructing model, the model is triangulated for further flattening process according to the geodesic curvatures of the B-spline curves on the B-spline surface.
In the flattening process, the adjacent triangular patch along the curve with the smallest geodesic curvature is selected as the guide strip. Using the geodesic curvature of the guide strip to calculate the flattening direction, the surface on the guide strip is flattened by using the theorem of orthogonality property of rotation matrices.
The differences of areas and perimeter lengths before and after the flattening process are used as the criterions for examining the results of flattening. The gaps and overlappings produced after flattening are amended by moving the boundaries toward the closings.
More of diversified patterns are generated by using the selection of guide strip and determination of directions of unfolding than not using. And less flattening calculations are needed by using the guide strip than using triangular patches to make orthogonality transformation of rotation matrices. The overall computations of this proposed procedure is efficient for surface flattening.
URI: http://hdl.handle.net/11455/1482
Appears in Collections:機械工程學系所

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