Simple Skeleton Generation Algorithm for Free-form Surface with Main Normal Direction Monotonous
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摘要: 利用骨架图进行三维模型的相似性比较研究在工程中有着重要的应用，可以有效地解决检索与重用等问题。本文给出了一种用简易骨架图描述主法向方向单调自由曲面（沿曲面的主法向方向的任一直线与该曲面最多只有一个交点）的方法。首先，求自由曲面的总法向量，按照总法向量的反方向将自由曲面投影到二维平面上，得到投影曲面；然后，求取投影曲面的骨架点和骨架线；最后，将投影曲面的骨架线按照自由曲面的总法向量方向进行柱面拉伸与自由曲面产生交线，该交线就是自由曲面的简易骨架图。并将本文算法与MATLAB中求骨架算法进行比较，实验表明，本文所得的简易骨架图可以更好地描述主法向方向单调自由曲面的几何与拓扑特征，为比较自由曲面的相似性提供了理论技术基础。Abstract: The similarity study of three-dimensional models using skeleton diagrams has important applications in engineering, which can effectively solve problems such as retrieval and reuse. In this study, a simple skeleton diagram is used to describe the main normal direction monotonous free-form surface (any line along the main normal direction of the surface has at most one intersection with the surface). First, the total normal vector of the free surface is obtained. The free surface is projected onto the two-dimensional plane in the opposite direction of the total normal vector to obtain the projected surface. Then, the skeleton point and skeleton line of the projected surface is obtained. Finally, the skeleton line of the projected surface is stretched cylindrically in the direction of the total normal vector of the free surface and intersected with the free surface. The intersection line is a simple skeleton diagram of the free surface. The algorithm is compared with MATLAB's skeletal algorithm. Experiments show that the simple skeleton diagram obtained in this paper can better describe the geometric and topological features of the mononormal free-form surface in the main normal direction, which provides a theoretical and technical basis for the similarity of free-form surfaces.
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表 1 等间距取点对总法向量的影响
等参数间隔 总取点个数 总法向量 0.03 1 156 (0.01, 0.01, 1.00) 0.01 10 000 (0.01, 0.00, 1.00) 0.009 12 544 (0.00, 0.00, 1.00) 0.008 15 625 (0.00, 0.00, 1.00) 0.006 27 889 (0.00, 0.00, 1.00) 
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表 2 三个自由曲面主方向
曲面 e1 e2 e3 S1 (-1.000 0, 0.000 0, 0.000 0) (0.000, 0.999 8, 0.021 8) (0.000 0, 0.021 8, 0.999 8) S2 (-0.971 5, -0.236 9, 0.000 0) (-0.236 9, 0.971 5, 0.000 0) (0.000 0, 0.000 0, 1.000 0) S3 (0.000 0, 1.000 0, 0.000 0) (1.000 0, 0.000 0, 0.000 0) (0.000 0, 0.000 0, 1.000 0)
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表 3 三个自由曲面以e1, e2为法向量所做平面, 交线, 交点, B样条拟合骨架线和自由曲面的骨架线
表 4 不同算法得到骨架图
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[1] Blum H. A transformation for extracting new descriptors of shape[J]. Models for the Perception of Speech and Visual Form, 1967, 19(5):362-380 [2] Blum H. Biological shape and visual science (part Ⅰ)[J]. Journal of Theoretical Biology, 1973, 38(2):205-287 [3] 万雅娟, 李海生, 刘璇, 等.基于距离变换的三维连通骨架提取算法[J].计算机仿真, 2014, 31(6):256-260 doi: 10.3969/j.issn.1006-9348.2014.06.057Wan Y J, Li H S, Liu X, et al. Three-dimension connectivity skeleton extraction algorithm based on distance transform[J]. Computer Simulation, 2014, 31(6):256-260(in Chinese) doi: 10.3969/j.issn.1006-9348.2014.06.057 [4] 朱文博, 耿国庆, 刘阳阳, 等.基于骨架树的机械零件三维模型检索方法[J].机械工程学报, 2016, 52(13):204-212. http://d.old.wanfangdata.com.cn/Periodical/jxgcxb201613025Zhu W B, Geng G Q, Liu Y Y, et al. 3D Model retrieval method of mechanical parts based on skeleton tree[J] Journal of Mechanical Engineering, 2016, 52(13):204-212(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/jxgcxb201613025 [5] 赵劲超.肺部气道树骨架的自动提取、标记和结构分析[D].沈阳: 东北大学, 2015 http://cdmd.cnki.com.cn/Article/CDMD-10145-1017041794.htmZhao J C. Automatic extraction, labeling and structural analysis of lung airway tree[D]. Shenyang: Northeastern University, 2015(in Chinese) http://cdmd.cnki.com.cn/Article/CDMD-10145-1017041794.htm [6] Herda L, Fua P, Plankers R, et al. Skeleton-based motion capture for robust reconstruction of human motion[C]//Proceedings of 2000 Computer Animation. Philadelphia, PA, USA: IEEE, 2000: 77 [7] Hilaga M, Shinagawa Y, Kohmura T, et al. Topology matching for fully automatic similarity estimation of 3D shapes[C]//Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques. New York: ACM, 2001: 203-212 [8] Dey T K, Zhao W. Approximating the medial axis from the Voronoi diagram with a convergence guarantee[J]. Algorithmica, 2004, 38(1):179-200 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=5d13893370cdb06a5087344586c8a542 [9] Liu W P, Jiang H B, Bai X, et al. Distance transform-based skeleton extraction and its applications in sensor networks[J]. IEEE Transactions on Parallel and Distributed Systems, 2013, 24(9):1763-1772 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=63f95081c803d2612d5e5da70620c461 [10] Kobbelt L, Schrder P, Wu F C, et al. Skeleton extraction of 3D objects with visible repulsive force[DB/OL]. http://graphics.im.ntu.edu.tw/~joyce/publish/cgw2003.pdf, 2018.09.1 [11] Gong W, Bertrand G. A simple parallel 3D thinning algorithm[C]//Proceedings of the10th International Conference on Pattern Recognition. Atlantic City, NJ, USA: IEEE, 1990: 188-190 [12] 李振, 李伟光, 赵学智, 等.基于主成分分析的特征频率提取算法及应用[J].振动、测试与诊断, 2018, 38(4):834-842 http://d.old.wanfangdata.com.cn/Periodical/zdcsyzd201804027Li Z, Li W G, Zhao X Z, et al. Feature frequency extraction algorithm based on principal component anaiysis and its application[J]. Journal of Vibration, Measurement & Diagnosis, 2018, 38(4):834-842(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/zdcsyzd201804027 -
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