本研究旨在發展一套正顎手術術前齒列矯正輔助工具軟體，開發專用軟體模擬術前排牙目標，提供配合的矯正科醫師齒列矯正規劃參考，節省實際在模型上操作及排牙的時間。由於正顎手術患者常因不當咬合所導致牙齒偏離正常的型態，相較於一般齒列矯正，正顎手術術前齒列排牙更需要消除代償現象，本研究目的在消除正顎手術術中的咬合干擾並去除代償，使上下顎骨可以根據正顎計畫到位固定，術後再以一般齒列矯正方法獲得穩定的對咬結果。
取得準備接受正顎手術之患者牙模，掃描得數位牙模，建立術前專家排牙咬合面理想目標，以質量彈簧系統的模擬排牙過程，每一顆牙齒模型皆視為質量塊，牙冠特徵點、牙弓曲線與牙齒主軸之間的互相拘束關係視為彈簧，自動步進模擬變化過程，找出齒列拘束關係最佳解。根據排牙模擬結果，獲得排牙前後各顆牙齒的舌頰向移動量、近遠心向移動量、高度移動量、舌頰軸向旋轉量、近遠心軸向旋轉量與牙齒主軸旋轉量，產生數位排牙前後的碰撞偵測，提供矯正科醫師術前矯正規劃的參考。

The aim of this research is to develop a digital planning software for dentition alignment before orthognathic surgery. We have developed a dedicated software to simulate the goal of orthodontics treatment before orthognathic surgery and provide orthodontists orthodontic planning in order to save time during traditional practice on the dental cast. Improper occlusions usually occur in those patients who are planning to undergo orthognathic surgery. This kind of orthodontic planning is different from general orthodontics treatment which needs dentition decompensation. In this research, we focus on eliminating occlusal interference and decompensation during the orthognathic surgery, so that the proper occlusion can be obtained. We simulate the interactive processes of tooth rearrangement step by step according to the theory of mass-spring system. Each tooth are regarded as a node, and the relationship of each node features, arch, and tooth axis are regarded as single spring. Finally, the alignment process is simulated stepwise to reveal the optimal occlusion as final occlusion. The deviations outcomes before and after simulation is listed. They are displacement along buccal-lingual sides, displacement along mesial-distal directions, displacement of the of principle axes of tooth, rotation angles along buccal-lingual axes, rotation angle along mesial-distal axes, and rotation angle of tooth axes, and finally collision detection between pre-op and alignment planning is applied. All above functions provide reference of treatment planning for orthodontists.

[1] Andrews, L. F., "The six keys of normal occlusion," American Journal of Orthodontics and Orthopedics, Vol.62, pp.296-309, 1972.
[2] 正顎手術"，https://zh.wikipedia.org/wiki/正顎手術，accessed on May 10th 2016.
[3] 林子源，"實體模型與電腦輔助技術於口腔顎面術前計劃之應用"，國立成功大學機械工程研究所碩士論文，2000.
[4] 李俊毅，"顎面手術輔助空間導引系統之設計與實作"，國立成功大學機械工程研究所碩士論文，2001.
[5] 郭泰宏，"醫療影像軟體開發－基礎介面與三維實體模型重建"，國立成功大學機械工程研究所碩士論文，2001.
[6] 吳東錦，"口腔顎面多面向手術計畫基礎建構與臨床應用"，國立成功大學機械工程研究所碩士論文，2006.
[7] 方晶晶，王東堯，吳東錦, 可量化之對稱性判準方法, 中華民國發民專利 I288894, 2007/10/21~2025/10/16.
[8] 蔡佳彰，"新型咬合器雛形系統之開發"，國立成功大學機械工程研究所碩士論文，2010.
[9] 郭泰宏，"發展運動追蹤式咬合分析與正顎手術計畫"，國立成功大學機械工程研究所博士論文，2009.
[10] Casko, J. S., Vaden, J. L., Kokich, V. G., Damone, J., James, R. D., Cangialosi, T. J., Riolo, M. L., Owens, S. E., Jr., and Bills, E. D., "Objective grading system for dental casts and panoramic radiographs," American Journal of Orthodontics and Dentofacial Orthopedics, Vol.114, No.5, pp.589-599, 2012.
[11] Felton, J. M., Sinclair, P. M., Jones, D. L., and Alexander, R. G., "A computerized analysis of the shape and stability of mandibular arch form," American Journal of Orthodontics and Dentofacial Orthopedics, Vol.92, No.6, pp.478-483, 1987.
[12] Braun, S., Hnat, W. P., Fender, D. E., and Legan, H. L., "The form of the human dental arch," The Angle Orthodontist, Vol.68, No.1, pp.29-36, 1998.
[13] Noroozi, H., Hosseinzadeh Nik, T., and Saeeda, R., "The dental arch form revisited," The Angle Orthodontist, Vol.71, No.5, pp.386-389, 2001.
[14] Noroozi, H., Djavid, G. E., Moeinzad, H., and Teimouri, A. P., "Prediction of arch perimeter changes due to orthodontic treatment," American Journal of Orthodontics and Dentofacial Orthopedics, Vol.122, No.6, pp.601-607, 2002.
[15] Attene, M., Katz, S., Mortara, M., Patane, G., Spagnuolo, M., and Tal, A., "Mesh Segmentation - A Comparative Study," Proceedings of the 2006 IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06), pp.7-7,2006.
[16] Shamir, A., "A survey on Mesh Segmentation Techniques," Computer Graphics Forum, Vol.27, No.6, pp.1539-1556, 2008.
[17] Mangan, A. P. and Whitaker, R. T., "Partitioning 3D surface meshes using watershed segmentation," IEEE Transactions on Visualization and Computer Graphics, Vol.5, No.4, pp.308-321, 1999.
[18] Shlafman, S., Tal, A., and Katz, S., "Metamorphosis of polyhedral surfaces using decomposition," Proceedings of Computer Graphics Forum, pp.219-228,2002.
[19] Katz, S. and Tal, A., Hierarchical mesh decomposition using fuzzy clustering and cuts, ACM, 2003.
[20] Koschan, A., "Perception-based 3D triangle mesh segmentation using fast marching watersheds," Proceedings of the 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.II-27-II-32 vol. 2,2003.
[21] Lavoué, G., Dupont, F., and Baskurt, A., "A new CAD mesh segmentation method, based on curvature tensor analysis," Computer-Aided Design, Vol.37, No.10, pp.975-987, 2005.
[22] Attene, M., Falcidieno, B., and Spagnuolo, M., "Hierarchical mesh segmentation based on fitting primitives," The Visual Computer, Vol.22, No.3, pp.181-193, 2006.
[23] Lai, Y.-K., Hu, S.-M., Martin, R. R., and Rosin, P. L., "Fast mesh segmentation using random walks," Proceedings of the 2008 ACM symposium on Solid and physical modeling, pp.183-191,2008.
[24] Lee, Y., Lee, S., Shamir, A., Cohen-Or, D., and Seidel, H.-P., "Intelligent mesh scissoring using 3d snakes," Proceedings of the 12th Pacific Conference on Computer Graphics and Applications, pp.279-287,2004.
[25] Katz, S., Leifman, G., and Tal, A., "Mesh segmentation using feature point and core extraction," The Visual Computer, Vol.21, No.8-10, pp.649-658, 2005.
[26] Lee, Y., Lee, S., Shamir, A., Cohen-Or, D., and Seidel, H.-P., "Mesh scissoring with minima rule and part salience," Computer Aided Geometric Design, Vol.22, No.5, pp.444-465, 2005.
[27] Podolak, J., Shilane, P., Golovinskiy, A., Rusinkiewicz, S., and Funkhouser, T., "A planar-reflective symmetry transform for 3D shapes," Proceedings of ACM transactions on graphics (TOG), pp.549-559,2006.
[28] Golovinskiy, A. and Funkhouser, T., "Randomized cuts for 3D mesh analysis," ACM transactions on graphics (TOG), Vol.27, No.5, p.145, 2008.
[29] Shapira, L., Shamir, A., and Cohen-Or, D., "Consistent mesh partitioning and skeletonisation using the shape diameter function," The Visual Computer, Vol.24, No.4, pp.249-259, 2008.
[30] Kronfeld, T., Brunner, D., and Brunnett, G., "Snake-based segmentation of teeth from virtual dental casts," Computer-Aided Design and Applications, Vol.7, No.2, pp.221-233, 2010.
[31] Kondo, T., Ong, S., and Foong, K. W., "Tooth segmentation of dental study models using range images," Medical Imaging, IEEE Transactions on, Vol.23, No.3, pp.350-362, 2004.
[32] Grzegorzek, M., Trierscheid, M., Papoutsis, D., and Paulus, D., A multi-stage approach for 3D teeth segmentation from dentition surfaces, in Image and Signal Processing. 2010, Springer. p. 521-530.
[33] Zhao, M., Ma, L., Tan, W., and Nie, D., "Interactive tooth segmentation of dental models," Proceedings of the 27th Annual International Conference on Engineering in Medicine and Biology Society, pp.654-657,2006.
[34] Tian-ran, Y., Ning, D., Guo-dong, H., Xiao-Sheng, C., Hai-hua, C., Wen-he, L., Qing, Y., and Peijun, L., "Bio-information based segmentation of 3D dental models," Proceedings of the 2nd International Conference on Bioinformatics and Biomedical Engineering, pp.624-627,2008.
[35] Li, Z., Ning, X., and Wang, Z., "A fast segmentation method for STL teeth model," Proceedings of the 2007 IEEE/ICME International Conference on Complex Medical Engineering, pp.163-166,2007.
[36] "DigiModel," http://www.orthoproofusa.com/, accessed on May 3rd 2016.
[37] "SureSmile," www.suresmile.com, accessed on May 3rd 2016.
[38] "OrthoCAD," http://www.itero.com/en/products/orthodontic_ecosystem, accessed on May 3rd 2016.
[39] "emodel," http://www.dentalemodels.com/emodel_services/emodel_by_geodigm.html, accessed on May 3rd 2016.
[40] "Orapix," http://www.orapix.com/, accessed on May 3rd 2016.
[41] Lin, A. C., "Integration of 3D CAD, reverse engineering and rapid prototyping in fabrication of invisible tooth aligner," Proceedings of 2005 IEEE International Conference on Systems, Man and Cybernetics, pp.2431-2436 Vol. 3,2005.
[42] Chengjun, L., Guoping, W., Tianmin, X., and Yan, L., "Orthodontic Simulation and Diagnosis: An Enhanced Tool for Dentists," Proceedings of the 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference, pp.4345-4348,2005.
[43] Yau, H.-T., Yang, T.-J., Hsu, C.-Y., and Tseng, H.-S., "Development of a Virtual Orthodontic Alignment System using a Haptic Device," Computer-Aided Design and Applications, Vol.7, No.6, pp.889-898, 2010.
[44] Kumar, Y., Janardan, R., and Larson, B., "Automatic Feature Identification in Dental Meshes," Computer-Aided Design and Applications, Vol.9, No.6, pp.747-769, 2012.
[45] Kumar, Y., Janardan, R., and Larson, B., "Automatic Virtual Alignment of Dental Arches in Orthodontics," Computer-Aided Design and Applications, Vol.10, No.3, pp.371-398, 2013.