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研究生：	吳戈飛 Wu, Ge-Fei
論文名稱：	基於等高線生成表面的線藝術 The wire art of generating surface based on lines of equal elevation
指導教授：	李同益 Lee, Tong-Yee
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 資訊工程學系 Department of Computer Science and Information Engineering
論文出版年：	2020
畢業學年度：	108
語文別：	英文
論文頁數：	66
中文關鍵詞：	線藝術、等高線、繞行方式、模型生成
外文關鍵詞：	wire line art, lines of equal elevations, detour sequence, Model generation
相關次數：	點閱：78 下載：0
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本篇文章中,我們將介紹了一個利用三維模型產生線藝術 (wire line art) 的方法。我們的方法通過將重複的圖元以使用者指定的頂點作為中心點，等測地距離（geodesic distance）等角度地放置，從而生成等距離等角度重複風格的線藝術結果預覽,並通過局部最佳化產生繞行順序的建議。首先我們以三維的網格模型(3D mesh model)作為輸入，從使用者指定的頂點(one selected vertex)生成等高線組(lines of equal elevations or contours)，對於條等高線上的每個頂點我們用累積長度(cumulative length)為依據計算其位於等高線上的的角度 (angles)，并使用頂點擴張(spanning from one selected vertex) 的方式來確定等高線與等高線之間的上下對應關係。接著我們根據以一張黑白的圖片作為圖元，通過像素級(pixel sampling)的採樣得到一個對應的圖（graph）。之後我們使用此圖的節點等角度地放置圖在上下對應的兩個等高線之間。對於特殊情況等高線與其對應的下一條等高線為一對多關係時，不能直接將圖放置在等高線之間，需要通過等高線和其下一條等高線的形狀相似程度（IS-Match）來重新分配等高線之間的表面，之後才能將圖放置於重新分配後的表面。為了使表面細節看起來更貼近原三維模型表面我們使用在等高線等角度點之間的測地線作為測算放置圖上的節點止於三維模型表面的基礎。最後，我們將圖的節點放置與表面所產生的結果藉由圖的連接關係來進行三維空間上的連接，產生線藝術(wire line art)。此外，我們使用帶有限制的最佳化來計算最佳的節點連接順序, 從而給使用者提供手工製作此模型的繞線方式(detour sequence)的建議。

In this article, we will introduce a method to generate wire line art using a 3D model. Our method uses the fixed point specified by the user as the center point of the repeated element, and places them at the same angle and the geodesic distance, thereby generating a preview of the line art results in the same distance and equal angle repeating style. Also we produces recommendations for the detour sequence by local optimization.

First, we take a 3D mesh model as input and generate the line of equal-elevations group from the one vertices selected by the user. For each vertex on the equal-elevations line, we use the cumulative length as the basis to calculate the angle on the contour and use the method of vertex expansion. To determine the upper and lower correspondence between lines of equal elevation. Next,we use a grayscale picture as a element Image, and get a corresponding graph through pixel sampling. Then we use the nodes of this graph to equiangularly place the graph between two adjacent level isoline.For special cases, when the iosline and its corresponding next iosline have a one-to-many relationship, we cannot directly place the graph between the contour lines. We need to redistribute the contour lines through the similarity of the contour line and the next contour line which calculated by IS-Match.After that, the graph can be placed on the redistributed surface.In order to make the surface details look closer to the surface of the original 3D model, we use the geodesic line between the contours and equiangular points as the basis for calculating the nodes on the placement map to stop on the surface of the 3D model.In order to make the surface details look closer to the original 3D model surface, we use the projection path between contours and equiangular points as the basis for measuring and placing the nodes of graph on the 3D model surface.

Finally, we place the nodes of the graph on the surface and use the connection relationship of the graph to connect the three-dimensional space to produce wire line art. In addition, we use limited optimization to calculate the best node connection sequence, so as to provide users with suggestions for the wire line placement method of this model by hand.

摘要 .................................................................................................. I 
Abstract ........................................................................................... II 
誌謝 ................................................................................................ IV 
Table of Contents............................................................................. V 
List of Figures ................................................................................. VII 
Chapter 1 Introduction .................................................................... 1 
1 Motivation ............................................................................... 1 
2 Contribution ............................................................................ 4 
Chapter 2 Related Work .................................................................. 5 
1 Line art generated from pictures .............................................. 5 
2 Multiple-View Line art generated from pictures ..................... 6 
3 Finding geodesic line: ............................................................. 7 
4 Use elements to fill the surface of the 3D model ..................... 8 
5 Shape similarity: ................................................................... 10 
Chapter 3 Method ......................................................................... 10 
1 Overview ............................................................................... 11 
2 Create Equal-elevations Lines ............................................... 13 
2.1 Geodesic Polar Map ........................................................ 13 
2.2 Creating lines of equal elevations .................................... 16 
2.3 Equal-elevations Lines Correspondence .......................... 18 
2.4 Calculate angle of point in equal-elevations .................... 21 
3 Processing elements image .................................................... 25 
3.1 preprocessing ................................................................... 25 
3.2 Use pixel elements to generate images ............................ 26 
3.3 Sampling of graph ........................................................... 27 
3.4 Horizontal matching of endpoints .................................... 31 
3.5 Vertical matching of endpoints ........................................ 32 
4 Assign divergence surface ..................................................... 34 
4.1Cut the current contour line as a sub-line segment ........... 35 
4.2 IS Match....................................................................... 36 
5 Place elements between contour lines ................................... 39 
5.1 Non-divergent contour dividing interval .......................... 39 
5.2 Division of divergent contours ........................................ 40 
5.3 Place the nodes of elements on the surface of the model . 42 
5.4 Generate a path graph ...................................................... 48 
6 Generate 3D model ............................................................... 48 
7 Suggestion for the detour sequence ....................................... 49 
Chapter 4 Results and Discussion .................................................. 55 
1 Implementation environment. ............................................... 55 
2 Results and evaluation ........................................................... 56 
3 Limitation.............................................................................. 63 
Chapter 5 Conclusion ..................................................................... 64 
Chapter 6 References .................................................................... 65 
 
                                    

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2025-09-01公開

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