Surface modeling and flattening for products fabricated by slightly-extensible planar materials.

• Other Authors: Zhang, Yunbo.
• Format: Others
• Language: English; Chinese
• Published: 2012
• Subjects: Engineering design > Mathematical models; Surfaces
• Online Access: http://library.cuhk.edu.hk/record=b5549626; http://repository.lib.cuhk.edu.hk/en/item/cuhk-328170

近些年來，計算機輔助造型技術廣泛應用於工業設計領域。對於那些產品設計於三維空間，但是產品加工要使用二維材料的工業，一個急遞解決的問題是對於一件三維設計，如何找到對應的二維裁片。而且，得到的二維裁片應該可以在微小的拉伸下折疊使之還原其原始三綠的形狀。除此之外，工業界還有一些額外的要求例如在特徵線和邊界上的長度控制。為了解決上述問題，我們提出了一些解決方法。 === 關於長度的曲面攤平技術對於生成以可微小拉伸材料製成的二維裁片，是一項非常關鍵的技術。王昌凌教授於2007 年研發了WireWarping 攤平技街，可以在保持邊界和特徵線長度不變的情況下將三維模型攤平得到二維裁片。然而，在攤平過程中，嚴格地保證所有的邊界和特徵長度不變通常會導致得到的二維裁片誤差很大，尤其是當要攤平的三維模型非常不可展的時候。為解決上述問題，我們提出一種新的，可靠而又靈活的新攤平方法--WireWarping++。其基本思想是:我們首先將所有特徵線劃分為彈性特徵線和剛性特徵線。在攤平過程中，只有剛性特徵線的長度需要嚴格保證，而彈性特徵線的長度可以在給定的範圍內變化。為了實現這一功能，我們構架了一個多層優化體系，可以在保證剛性特徵線長度不變的前提下，在一定範圍內改變彈性特徵線的長度，從而使得到的二維裁片形狀最優。除此以外，我們也開發了一套拓撲處理的算法，可以處理那些使得計算不穩定的特徵線網絡拓撲結構。最終的實驗結果證明，我們的WireWarping++方法可以有效地獲得形狀更優的二維裁片，並擁有穩定的性能 === 除了曲面攤平技街，另外一項可以得到二維裁片的技街是可展曲回處理技街。可展曲面處理技術可以將輸入的三維模型處理成可展曲面，而可展曲面可以被無誤差地攤平到二維裁片。現有的方法要么只能處理簡單形狀的模型，要么處理得到的形狀與處理前的相差太遠。 === 為了解決上述困難，我們首先嘗試一種局部可展曲面處理方法。不同於現有的基於全局優化的方法，我們的局部可展曲面處理方法基於可控的拉普拉斯漸變，一個一個地調整頂點的位置。局部可展曲面處理方法的計算速度非常的快。基於此項特性，我們開發了一種實時交互工具去處理輸入的模型。這種工具可以迅速、有效地改進被處理模型的可展度;與王昌凌教授2007 年開發的FL-mesh 方法比，我們的局部處理方法可以得到更接近原始模型形狀的可展曲面。 === 為了進一步得到接近原始模型形狀的可展曲面，我們開發了一種擬合算法，可以擬合出接近原始模型形狀的可展曲面。其中，構成可展曲面的材料僅允許輕微拉伸，而且在擬合過程中，可展曲面與原始模型形狀的誤差被優化，同時可展曲面上的應變得到控制。我們首先提出一種新的曲面造型工具，通過進行一系列接近等量度變形使一個可展曲面的形狀變得更接近原始模型。其次，為了得到更好的擬合結果和克服拓撲死鎖，我們提出了一種隨機形狀擾動的方法來生成不同的初始形狀。最後，為了使我們的方法有可伸縮性，我們提出一套由粗疏到細密擬合的框架，可以處理網格非常細密的模型，而且處理後的模型可以保持原始模型的邊界形狀。 === 除了對輕微可拉伸材料製成的產品進行建模，我們希望將我們的研究拓展到對有壓力產品的建模。我們提出了基於實驗的建模方法，包括以下兩個方面的工作1 )為了建立長度變化--壓力而進行的材料測試2) 長度控制的攤平。目前，我們獲得了一些初步結果。 === In those industries whose products are designed in 3D but fabricated by planar materials, a challenge work is to find out a 2D pattern for a given 3D design, and the 2D pattern should be warped back to the 3D shape with slight extension. Constraints coming from industries like length control on feature curves and boundary interpolation are needed to be enforced. To solve the aforementioned problems, we have proposed several approaches. === Length-aware surface flattening is very useful for generating 2D patterns made of slightly-extensible materials. WireWarping method presented by Wang, 2008 is exploited to generate 2D patterns with invariant lengths of feature and boundary curves. However, strict length constraints on all feature curves sometimes cause large distortions on 2D patterns, especially for those 3D surfaces which are highly non-developable. Then, we present a flexible and robust extension of Wire Warping by introducing a new type of feature curves named elastic feature, which brings flexibility to shape control of the resultant 2D patterns. On these new feature curves, instead of strictly preserving the exact lengths, only the ranges of their lengths are controlled. To achieve this function, a multi-loop shape control optimization framework is proposed to find out the optimized 2D shape among all possible flattening results with different length variations on those elastic feature curves, while the lengths of other feature curves are kept unchanged. Besides, we also present a topology processing algorithm on the network of feature curves to eliminate cases that lead to numerical singularity. The new proposed method is named as WireWarping++. Experimental results show that the WireWarping++ can successfully flatten surface patches into 2D patterns with more flexible shape control and more robust numerical performance. === As an alternative to surface flattening, flattenable surface processing approaches try to process an input model into a flattenable surface where flattenable surface is a polygonal mesh surface that can be unfolded into a planar patch without stretching any polygon. Prior approaches result in either a flattenable surface that could be quite different from the input shape or a (discrete) developable surface has relative simple shape. === To overcome the aforementioned shortages, our first attempt is a local flattenable processing approach. In stead of processing the input model by a global optimization, the local approach adjusts the positions of vertices one by one via a controllable Laplacian evolution. The computation speed of local approach is quite fast so that we develop an interactive tool based on it. The interactive tool can improve the flattenability of the processed model efficiently meanwhile having better shape approximation compared with the result obtained by FL-mesh processing proposed by Wang, 2007. === To achieve a flattenable surface with good shape approximation to the input model, we also proposed a new method for computing a slightly stretched flattenable mesh surface M from a piece wise-linear surface patch P in 3D, where the shape approximation error between M and P is minimized and the strain of stretching on M is controlled. Firstly, we introduce a new surface modeling method to conduct a sequence of nearly isometric deformations to morph a flattenable mesh surface to a new shape which has a better approximation of the input surface. Secondly, in order to get better initial surfaces for fitting and overcome topological obstacles, a shape perturbation scheme is investigated to obtain the optimal surface fitting result. Lastly, to improve the scalability of our optimal surface fitting algorithm, a coarse-to-fine fitting framework is exploited so that very dense flattenable mesh surfaces can be modeled and boundaries of the input surfaces can be interpolated. === Besides modeling on products fabricated by slightly-extensible materials, we also try to extend our work to modeling on compression garment. A calibration based method is proposed consist two aspects: 1) a material testing for establishing the relationship between length change and compression; 2) a length control flattening. Some preliminary results are presented. === Detailed summary in vernacular field only. === Detailed summary in vernacular field only. === Detailed summary in vernacular field only. === Detailed summary in vernacular field only. === Detailed summary in vernacular field only. === Detailed summary in vernacular field only. === Zhang, Yunbo. === Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. === Includes bibliographical references (leaves 148-161). === Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. === Abstract also in Chinese. === Abstract --- p.1 === Chinese Abstract --- p.4 === Acknowledgements --- p.6 === List of Figures --- p.10 === List of Tables --- p.12 === Chapter 1 --- Introduction --- p.1 === Chapter 1.1 --- Motivation. --- p.1 === Chapter 1.2 --- Problems and Methodology. --- p.3 === Chapter 1.2.1 --- Surface Flat tening with Length Control --- p.4 === Chapter 1.2.2 --- Modeling on Flattenable Surfaces --- p.5 === Chapter 1.2.2.1 --- A Local Flat tenable Processing Approach --- p.6 === Chapter 1.2.2.2 --- Optimal Fitting of Strain-cont rolled Flattenable Mesh Surfaces --- p.6 === Chapter 1.2.3 --- Modeling on Compression Garment --- p.7 === Chapter 1.3 --- Thesis Organization --- p.7 === Chapter 2 --- Literature Review --- p.11 === Chapter 2.1 --- Developable Parametric Surfaces --- p.11 === Chapter 2.2 --- Discrete Developable Surface Modeling --- p.12 === Chapter 2.3 --- Mesh Parameterization and Surface Flattening --- p.13 === Chapter 2.4 --- Cloth Simulation --- p.16 === Chapter 2.5 --- Multi-resolution Techniques --- p.16 === Chapter 3 --- Robust and Flexible Surface Flattening with Length Control --- p.18 === Chapter 3.1 --- Const rained Optimizat ion based Surface Flattening --- p.20 === Chapter 3.1.1 --- Length Preserved WireWarping --- p.21 === Chapter 3.1.2 --- Multi-loop Optimization Framework --- p.23 === Chapter 3.1.3 --- Shape Error Function --- p.27 === Chapter 3.2 --- Topology Processing --- p.29 === Chapter 3.2.1 --- Processing on Hinged Feature Curves --- p.30 === Chapter 3.2.2 --- Connecting Separate Boundary Loops --- p.32 === Chapter 3.3 --- Metrics --- p.8 === Chapter 3.4 --- Experimental Results --- p.33 === Chapter 3.5 --- Ot her Applications --- p.34 === Chapter 3.6 --- Angle Constraints on Female Jeans-pants Design --- p.39 === Chapter 3.7 --- Summary --- p.40 === Chapter 4 --- Flattenable Mesh Processing : A Local Approach --- p.42 === Chapter 4.1 --- Problem Definitions --- p.43 === Chapter 4.2 --- Controllable Laplacian Evolution --- p.44 === Chapter 4.2.1 --- Laplacian Operator. --- p.45 === Chapter 4.2.2 --- Analys is on Laplacian Operator --- p.45 === Chapter 4.2.3 --- Localized Energy Function --- p.46 === Chapter 4.2.4 --- Numerical Solution --- p.48 === Chapter 4.3 --- Interactive Tool --- p.49 === Chapter 4.4 --- Summary and Limit ation --- p.50 === Chapter 5 --- Optimal Fitting of St rain-Cont rolled Flattenable Mesh Surfaces --- p.55 === Chapter 5.1 --- Introduction --- p.55 === Chapter 5.2 --- Toolbox --- p.56 === Chapter 5.2.1 --- FL-mesh Processing --- p.56 === Chapter 5.2.2 --- Inextensible Cloth Simulation --- p.57 === Chapter 5.2.3 --- Least-square Mesh --- p.59 === Chapter 5.2.4 --- Spring-mass System --- p.59 === Chapter 5.3 --- Optimal Shape Approximation --- p.61 === Chapter 5.3.1 --- Isometric Surface Fitting --- p.62 === Chapter 5.3.1.1 --- Nearly Isometric Deformation --- p.63 === Chapter 5.3.1.2 --- Surface Fitting --- p.64 === Chapter 5.3.1.3 --- Problem of Numerical Singularity --- p.66 === Chapter 5.3.2 --- Shape Perturbation for Optimal Fitting --- p.68 === Chapter 5.3.3 --- Relaxation for Accurate Strain Control --- p.71 === Chapter 5.4 --- Multi-scale Surface Fitting. --- p.72 === Chapter 5.4.1 --- Coarsening, Local update and Relaxation --- p.74 === Chapter 5.4.2 --- Boundary Constraints of Interpolation --- p.78 === Chapter 5.4.2.1 --- Propert ies of Isometric Deformation --- p.78 === Chapter 5.4.2.2 --- Existence of Solution --- p.80 === Chapter 5.4.2.3 --- Boundary Triangulation --- p.81 === Chapter 5.4.2.4 --- Optimal Boundary Coarsening --- p.83 === Chapter 5.5 --- Results --- p.85 === Chapter 5.6 --- Summary --- p.87 === Chapter 6 --- Towards Compression Garment --- p.89 === Chapter 6.1 --- Problem Formulation --- p.90 === Chapter 6.2 --- Testing on Elastic Materials --- p.92 === Chapter 6.2.1 --- Test ing Overview --- p.92 === Chapter 6.2.2 --- Quad Load Test --- p.92 === Chapter 6.2.3 --- Geometric Models --- p.9 === Chapter 6.2.4 --- Pressure Sensors --- p.94 === Chapter 6.2.5 --- Test -bed --- p.95 === Chapter 6.2.6 --- Data Analysis --- p.99 === Chapter 6.2.6.1 --- Results for Ellipsoid --- p.100 === Chapter 6.2.6.2 --- Results for Cone wit hout Head --- p.102 === Chapter 6.2.6.3 --- Results for Cylinder --- p.105 === Chapter 6.2.7 --- Summary --- p.107 === Chapter 6.3 --- Compression Generation via Length Control --- p.108 === Chapter 6.4 --- Summary and Discussion --- p.111 === Chapter 7 --- Conclusion and Discuss ion --- p.114 === Chapter 7.1 --- Summary --- p.114 === Chapter 7.2 --- Fut ure Work --- p.117 === Chapter A --- Appendix A: Work on An Wet suit Design system --- p.119 === Chapter A.1 --- Introduction --- p.119 === Chapter A.1.1 --- Tools Expect ed by Designers --- p.120 === Chapter A.1.2 --- Existing Met hods --- p.121 === Chapter A.1.3 --- Conventional Fabricat ion of User Customized Products --- p.124 === Chapter A.2 --- System Overview --- p.124 === Chapter A.3 --- System Implement at ion --- p.127 === Chapter A.3.1 --- Styling Design and Its Transformation --- p.127 === Chapter A.3.2 --- Trimming --- p.129 === Chapter A.3.3 --- Unfolding with Length-Preserved Feature Curves --- p.130 === Chapter A.3.4 --- Discrete Developable Mesh Processing --- p.133 === Chapter A.3.5 --- Map-guided Layout Arrangement --- p.135 === Chapter A.4 --- Result s and Applications --- p.137 === Chapter A.5 --- User Experience --- p.142 === Chapter A.6 --- Summary --- p.146 === Bibliography --- p.148