本篇論文中，我們介紹一種讓使用者輸入兩個模型就可以透過自動找出最重要視角的輪廓來生成一個從不同視角可以看到不同模型輪廓的線條藝術作品。這種方法不僅能協助初學者找尋三維空間中的線條雕塑；還可以幫助藝術家快速獲得初步的三維空間中的線條雕塑，再進行微調，以節省創作時間。
多數的線條藝術，以單一模型為主，透過線條的彎曲方式與組合來達到從任何視角都可以看出該線條藝術所呈現的物體。還有一種則是多視角線條藝術，是雕塑藝術的一種變形，在兩個特定方向觀看時，同一個線條雕塑會有兩種完全不同的輪廓。而本篇論文則是多視角線條藝術，由於必須對線條在空間中的位置有很好的概念，因此，這類線條藝術作品的數量相對於單一模型的線條藝術較少。
我們提出一種方法，將輸入的兩個三維模型經過前置處理轉換成三維空間中的線條，並透過提出之方法對三維空間中的線條進行刪減，盡量使旋轉過程中，讓觀看者可以產生線條雕塑從一個輪廓逐漸轉變成另一個輪廓的錯覺，最後加入一些限制條件讓線條進行合併，希望能以最少線條產生線條雕塑。

We propose a novel method to generate multiple view line art from two input models to generate a line art that can see the contours of different models from different perspectives by automatically finding out the best-view contour. This method can not only help beginners find the line sculpture in the 3D space but also help the artist quickly obtain the preliminary 3D line sculpture to saving the creation time.
Most of the line art uses the way of bending and combination of lines to achieve the object represented by the line art from any perspective. There is also a multi-view line art, which is a variant of sculpture art. When viewed in two specific directions, the same line sculpture will have two completely different outlines.
We propose a method that converts the two input models into 3D lines through preprocessing and prunes the 3D lines through some methods so that the viewer can generate line sculptures during the rotation. The illusion of gradually changing from one contour to another, and finally adding some constraints to merge the lines, hoping to produce line sculptures with a minimum of lines.

[1] Song Ho Ahn. Opengl frame buffer object (fbo). http://www.songho.ca/opengl/gl_fbo.html, 2012.
[2] Milena Bogdanović. An ilp formulation and genetic algorithm for the maximum degree-bounded connected subgraph problem. Comput. Math. Appl., 59(9):3029–3038, May 2010.
[3] Doug DeCarlo, Adam Finkelstein, Szymon Rusinkiewicz, and Anthony Santella. Suggestive contours for conveying shape. In ACM SIGGRAPH 2003 Papers, SIGGRAPH ’03, pages 848–855, New York, NY, USA, 2003. ACM.
[4] Michael R. Garey and David S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York, NY, USA, 1979.
[5] Imdat Kara and Tolga Bektas. Integer linear programming formulations of multiple salesman problems and its variations. European Journal of Operational Research, 174(3):1449 – 1458, 2006.
[6] Philip Kollmannsberger. Skeleton3d - file exchange - matlab central. https://www. mathworks.com/matlabcentral/fileexchange/43400-skeleton3d, 2018.
[7] Peter Kovesi. Peter’s functions for computer vision. (2017). http://www. peterkovesi.com/matlabfns/, 2017.
[8] Chang Ha Lee, Amitabh Varshney, and David W. Jacobs. Mesh saliency. In ACM SIGGRAPH 2005 Papers, SIGGRAPH ’05, pages 659–666, New York, NY, USA, 2005. ACM.
[9] Lingjie Liu, Duygu Ceylan, Cheng Lin, Wenping Wang, and Niloy J. Mitra. Image-based reconstruction of wire art. ACM Trans. Graph., 36(4):63:1–63:11, July 2017.
[10] Zoran Maksimovic. A new mixed integer linear programming formulation for the maximum degree bounded connected subgraph problem. 99:99–108, 01 2016.
[11] Niloy J. Mitra and Mark Pauly. Shadow art. In ACM SIGGRAPH Asia 2009 Papers, SIGGRAPH Asia ’09, pages 156:1–156:7, New York, NY, USA, 2009. ACM.
[12] Tomohiro Ohgami and Kokichi Sugihara. Realizability of solids from three silhouettes. In Abstracts 24th European Workshop Comput. Geom, pages 233–236, 2008.
[13] Ren Suzuki, Masaki Moriguchi, and Keiko Imai. Generation and optimization of multi-view wire art. Poster presented at the Pacific Graphics, October 2017.