近年來，針對非專業使用者的設計與建模工具的需求不斷增加，其用途也十分廣泛。其中，依造個人喜好客製化傢俱的方式也日益盛行。由於對非專業建模使用者來說，從無到有設計一款客製化三維模型是十分困難的。因此，本篇論文提出一套線上傢俱建模系統來輔助使用者快速且方便地產生出理想中的三維傢俱模型。

本系統使用現有的傢俱模型，經由光場描述符(LightField Descriptor)提取三維模型的特徵並且做相似度計算。藉由得到的相似度資料做力導向佈局(Force-Directed Layout)來呈現彼此之間的相似度，提供使用者快速尋找與選取概略的傢俱模型，並且透過簡易的互動式建模介面來做零件變換。另外，也提供相似零件的建議，以及零件調整工具，方便使用者做零件替換與編輯。最後，產生出使用者理想中的傢俱模型。

本系統共計有兩大貢獻：第一，三維模型相似度之資料視覺化；第二，三維建模的便利性。

In recent years, the demand for design and modeling tools for non-professional users has been increasing. Among them, customizing a furniture according to personal preferences has also become increasingly popular. For non-professional modeling users, it is very difficult to design a customized 3D model from scratch. Therefore, this paper proposes an online
3D furniture modeling system to assist users to quickly and conveniently generate an ideal 3D furniture model.

This system makes use of existing furniture models. We first extract the features of a 3D model via the LightField Descriptor and perform similarity calculation. We then use the feature data to form a Force-Directed Layout to show the similarity among models. Our system allows users to quickly find and select rough furniture models. And through a simple interactive modeling interface to change its components. In addition, our system provides suggestions for similar components, as well as components adjustment tools, so that users can easily replace and edit components. AS a result, an ideal furniture model can be produced.

The system has made two contributions: first, the visualization of the similarity of 3D models; second, the convenience of 3D modeling.

[1] Archive 3d. https://archive3d.net/ (accessed on April. 30, 2020).
[2] Autodesk. https://www.autodesk.com.tw/ (accessed on April. 30, 2020).
[3] Computational geometry algorithms library. https://www.cgal.org/ (accessed on June. 19, 2020).
[4] D3.js - data-driven documents. https://d3js.org/ (accessed on April. 25, 2020).
[5] Ikea客製化書桌/工作桌/電腦桌. https://www.ikea.com.tw/zh/planner/ build-your-own-desk (accessed on April. 22, 2020).
[6] Meshmixer. http://www.meshmixer.com/ (accessed on April. 30, 2020).
[7] Shapenet. https://www.shapenet.org/ (accessed on April. 30, 2020).
[8] Three.js - javascript 3d library. https://threejs.org/ (accessed on April. 26, 2020).
[9] Three.js主體流程以及基本概念. https://p1htmlkernalweb.mybluemix. net/articles/threejs%E4%B8%BB%E4%BD%93%E6%B5%81%E7%A8%8B%E4%BB% A5%E5%8F%8A%E5%9F%BA%E6%9C%AC%E6%A6%82%E5%BF%B5_4021785_csdn.html (accessed on April. 26, 2020).
[10] Dror Aiger, Niloy J. Mitra, and Daniel Cohen-Or. 4-points congruent sets for robust pairwise surface registration. In SIGGRAPH’08: International Conference on Computer Graphics and Interactive Techniques, ACM SIGGRAPH 2008 Papers 2008. Association for Computing Machinery, 2008.
[11] J K Barnes and Piet Hut. A hierarchical o(n log n) force-calculation algorithm. Nature, 324:446–449, 1986.
[12] Paul J. Besl and Neil D. McKay. A Method for Registration of 3-D Shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14:239–256, 1992.
[13] Siddhartha Chaudhuri and Vladlen Koltun. Data-Driven Suggestions for Creativity Support in 3D Modeling. ACM Transactions on Graphics, 29:1–10, 2010.
[14] Ding Yun Chen, Xiao Pei Tian, Yu Te Shen, and Ming Ouhyoung. On Visual Similarity Based 3D Model Retrieval. In Computer Graphics Forum, volume 22, pages 223–232. Blackwell Publishing Ltd, 2003.
[15] Mathias Eitz, Ronald Richter, Tamy Boubekeur, Kristian Hildebrand, and Marc Alexa. Sketch-based shape retrieval. ACM Trans. Graph. (Proc. SIGGRAPH), 31:1–10, 2012.
[16] Thomas Funkhouser, Michael Kazhdan, Philip Shilane, Patrick Min, William Kiefer, Ayellet Tal, Szymon Rusinkiewicz, and David Dobkin. Modeling by example. In ACM SIGGRAPH 2004 Papers, SIGGRAPH 2004, pages 652– 663, 2004.
[17] A. Gershun. The light field. Journal of Mathematics and Physics, 18:51–151, 1939.
[18] Evangelos Kalogerakis, Siddhartha Chaudhuri, Leonidas Guibas, and Vladlen Koltun. Probabilistic reasoning for assembly-based 3D modeling. ACM Transactions on Graphics, 30, 2011.
[19] Evangelos Kalogerakis, Aaron Hertzmann, and Karan Singh. Learning 3D mesh segmentation and labeling. In ACM SIGGRAPH 2010 Papers, SIGGRAPH 2010. Association for Computing Machinery, Inc, 2010.
[20] Vladimir G. Kim, Wilmot Li, Niloy J. Mitra, Siddhartha Chaudhuri, Stephen Di Verdi, and Thomas Funkhouser. Learning part-based templates from large collections of 3D shapes. ACM Transactions on Graphics, 32, 2013.
[21] John D. Lafferty, Andrew McCallum, and Fernando C. N. Pereira. Conditional random fields: Probabilistic models for segmenting and labeling sequence data. In Proceedings of the Eighteenth International Conference on Machine Learning, pages 282––289. Morgan Kaufmann Publishers Inc., 2001.
[22] Jyh Ming Lien and Nancy M. Amato. Approximate convex decomposition of polyhedra. In Proceedings - SPM 2007: ACM Symposium on Solid and Physical Modeling, pages 121–131, 2007.
[23] Peter Liepa. Filling holes in meshes. In Symposium on Geometry Processing, 2003.
[24] David G. Lowe. Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision, 60:91–110, 2004.
[25] Dawei Lu, Huadong Ma, and Huiyuan Fu. Efficient sketch-based 3D shape retrieval via view selection. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), volume 8294 LNCS, pages 396–407. Springer Verlag, 2013.
[26] Ryutarou Ohbuchi, Kunio Osada, Takahiko Furuya, and Tomohisa Banno. Salient local visual features for shape-based 3d model retrieval. In 2008 IEEE International Conference on Shape Modeling and Applications, pages 93–102, 2008.
[27] Ryan Schmidt. Drag, drop, and clone:an interactive interface for surface composition. 2011.
[28] Lior Shapira, Ariel Shamir, and Daniel Cohen-Or. Consistent mesh partitioning and skeletonisation using the shape diameter function. Visual Computer, 24:249–259, 2008.
[29] Andrei Sharf, Marina Blumenkrants, Ariel Shamir, and Daniel Cohen-Or. SnapPaste: An interactive technique for easy mesh composition. Visual Computer, 22:835–844, 2006.
[30] Oana Sidi, Yanir Kleiman, Daniel Cohen-Or, Oliver van Kaick, and Hao Zhang. Unsupervised Co-Segmentation of a Set of Shapes via Descriptor-Space Spectral Clustering. ACM Transactions on Graphics, 30:1–10, 2011.
[31] Johan W.H. Tangelder and Remco C. Veltkamp. A survey of content based 3D shape retrieval methods. Multimedia Tools and Applications, 39:441–471, 2008.
[32] Antonio Torralba, Kevin P. Murphy, and William T. Freeman. Sharing visual features for multiclass and multiview object detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29:854–869, 2007.
[33] Fang Wang, Le Kang, and Yi Li. Sketch-based 3d shape retrieval using convolutional neural networks. 2015.
[34] Kai Xu, Vladimir G. Kim, Qixing Huang, Niloy Mitra, and Evangelos Kalogerakis. Data-driven shape analysis and processing. In SA 2016 - SIGGRAPH ASIA 2016 Courses. Association for Computing Machinery, Inc, 2016.
[35] Kai Xu, Hao Zhang, Daniel Cohen-Or, and Baoquan Chen. Fit and diverse: Set evolution for inspiring 3d shape galleries. ACM Trans. Graph., 31, 2012.
[36] Kai Xu, Hanlin Zheng, Ligang Liu, Daniel Cohen-Or, Hao Zhang, Yueshan Xiong, and Kai Xu. Photo-Inspired Model-Driven 3D Object Modeling. ACM Transactions on Graphics, 30:1–10, 2011.
[37] Yizhou Yu, Kun Zhou, Dong Xuz, Xiaohan Shi, Hujun Bao, Baining Guo, and Heung Yeung Shum. Mesh editing with poisson-based gradient field manipulation. In ACM SIGGRAPH 2004 Papers, SIGGRAPH 2004, pages 644–651, 2004.
[38] Dengsheng Zhang and Guojun Lu. An integrated approach to shape based image retrieval. 2008.