局部保形映射到整体能量优化的曲面展平

彭威; 吉卫喜

doi:10.13433/j.cnki.1003-8728.20190108

局部保形映射到整体能量优化的曲面展平

doi: 10.13433/j.cnki.1003-8728.20190108

彭威^1,2,,
吉卫喜^1,2

1.
江南大学机械工程学院, 江苏无锡 214122
2.
江苏省食品先进制造装备技术重点实验室, 江苏无锡 214122

基金项目:

国家自然科学基金项目 11402264

中央高校基本科研业务费专项资金项目 JUSRP116026

详细信息

作者简介:
彭威(1984-), 讲师, 博士, 研究方向为数字化设计制造及有限元技术, weipeng@jiangnan.edu.cn

中图分类号: TP391
计量
- 文章访问数: 500
- HTML全文浏览量: 223
- PDF下载量: 31
- 被引次数: 0
出版历程
- 收稿日期: 2019-01-05
- 刊出日期: 2019-08-05

Surface Flattening Algorithm from Local Conformal Mapping to Global Energy Optimization

Peng Wei^{1,2
,},
Ji Weixi^1,2

1.
School of Mechanical Engineering, Jiangnan University, Jiangsu Wuxi, 214122, China
2.
Jiangsu Key laboratory of Advanced Food Manufacturing Equipment and Technology, Jiangsu Wuxi 214122, China

摘要

摘要: 针对复杂网格曲面提出了一种局部保形映射到整体弹性能量优化的曲面展平算法。该方法基于局部到整体的思路，通过分析作用在局部三角形上的仿射变换雅可比矩阵的奇异值，得到三角形到平面参数域的保形映射。在此基础上，通过迭代优化由网格线弹性应变能组成的能量函数，使得整体网格的节点内力达到平衡状态，对局部保形映射后的网格进行整体拼接和优化。应用实例表明，该方法稳定可靠，能得到较好的网格曲面展平结果。
- 曲面网格 /
- 曲面展平 /
- 保形映射 /
- 应变能 /
Abstract: A surface flattening algorithm based on local conformal mapping and global elastic energy optimization is proposed for complex surface mesh. Based on the local-to-global methodology, the local conformal mapping can be obtained by analyzing the singular values of the Jacobian matrix of affine transform on each local triangle. On the basis of local operations, these transformed meshes can be further stitched and optimized by iteratively minimizing a quadric energy function composed of linear elastic strain energy, which makes the internal force of the nodes reach the equilibrium state. Applications show that the proposed algorithm is stable and reliable, and can get good surface mesh flattening results.
- surface mesh /
- surface flattening /
- conformal mapping /
- strain energy /
- algorithm

HTML全文

图 1 三角形保形映射

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图 2 曲面网格展平过程

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图 3 钣金件模型曲面网格展平对比

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图 4 覆盖件模型曲面网格展平

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图 5 摇臂模型曲面网格展平

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图 6 翼子板模型曲面网格展平

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表 1 曲面展平结果统计

参数名		模型
参数名		图 2	图 3	图 4	图 5	图 6
	单元数	280	18 444	24 584	9 312	12 247
	节点数	518	9 407	12 488	4 952	11 177
ABF++	角度扭曲	2.02	2.03	2.01	2.05	2.00
	面积扭曲	2.35	2.64	2.19	4.37	2.09
	计算时间/s	0.89	19.53	25.12	7.01	30.68
本文方法	角度扭曲	2.06	2.02	2.01	2.09	2.00
	面积扭曲	2.01	2.00	2.00	2.04	2.00
	计算时间/s	0.04	10.34	13.84	3.55	21.59

下载: 导出CSV

参考文献(17)

[1]	郭凤华, 张彩明, 焦文江.网格参数化研究进展[J].软件学报, 2016, 27(1):112-135 http://d.old.wanfangdata.com.cn/Periodical/rjxb201601006 Guo F H, Zhang C M, Jiao W J. Research progress on mesh parameterization[J]. Journal of Software, 2016, 27(1):112-135(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/rjxb201601006
[2]	许晨旸, 李静蓉, 王清辉, 等.利用ABF++保角参数化的网格曲面刀轨规划[J].计算机辅助设计与图形学学报, 2017, 29(4):728-733 doi: 10.3969/j.issn.1003-9775.2017.04.018 Xu C Y, Li J R, Wang Q H, et al. Tool path planning using angle-based flattening for mesh surfaces machining[J]. Journal of Computer-Aided Design & Computer Graphics, 2017, 29(4):728-733(in Chinese) doi: 10.3969/j.issn.1003-9775.2017.04.018
[3]	Floater M S. Mean value coordinates[J]. Computer Aided Geometric Design, 2003, 20(1):19-27 doi: 10.1016/S0167-8396(03)00002-5
[4]	张磊, 刘利刚, 王国瑾.保相似的网格参数化[J].中国图象图形学报, 2008, 13(12):2383-2387 doi: 10.11834/jig.20081221 Zhang L, Liu L G, Wang G J. As-similar-as-possible planar parameterization[J]. Journal of Image and Graphics, 2008, 13(12):2383-2387(in Chinese) doi: 10.11834/jig.20081221
[5]	Sheffer A, Lévy B, Mogilnitsky M, et al. ABF++:fast and robust angle based flattening[J]. ACM Transactions on Graphics, 2005, 24(2):311-330 doi: 10.1145/1061347.1061354
[6]	Liu Q S, Xi J T, Wu Z Q. An energy-based surface flattening method for flat pattern development of sheet metal components[J]. The International Journal of Advanced Manufacturing Technology, 2013, 68(5-8):1155-1166 doi: 10.1007/s00170-013-4908-y
[7]	Liu X H, Li S P, Zheng X H, et al. Development of a flattening system for sheet metal with free-form surface[J]. Advances in Mechanical Engineering, 2016, 8(2):1-12, doi: 10.1177/1687814016630517
[8]	Yi B, Yang Y, Zheng R, et al. Triangulated surface flattening based on the physical shell model[J]. Journal of Mechanical Science and Technology, 2018, 32(5):2163-2171 doi: 10.1007/s12206-018-0425-0
[9]	Zhu X F, Hu P, Ma Z D, et al. A new surface parameterization method based on one-step inverse forming for isogeometric analysis-suited geometry[J]. The International Journal of Advanced Manufacturing Technology, 2013, 65(9-12):1215-1227 doi: 10.1007/s00170-012-4251-8
[10]	Zhuang M L, Zhang X F. A novel apparel surface flattening algorithm[J]. International Journal of Clothing Science and Technology, 2013, 25(4):300-316 doi: 10.1108/09556221311326329
[11]	Wang Z, Luo Z X, Zhang J L, et al. ARAP++:an extension of the local/global approach to mesh parameterization[J]. Frontiers of Information Technology & Electronic Engineering, 2016, 17(6):501-515 http://d.old.wanfangdata.com.cn/OAPaper/oai_doaj-articles_d2d7e49db156d57f1bce47010af8c75b
[12]	Zhang Y B, Wang C C L, Ramani K. Optimal fitting of strain-controlled flattenable mesh surfaces[J]. The International Journal of Advanced Manufacturing Technology, 2016, 87(9-12):2873-2887 doi: 10.1007/s00170-016-8669-2
[13]	Su K H, Cui L, Qian K, et al. Area-preserving mesh parameterization for poly-annulus surfaces based on optimal mass transportation[J]. Computer Aided Geometric Design, 2016, 46:76-91 doi: 10.1016/j.cagd.2016.05.005
[14]	Zhao H, Li X, Ge H B, et al. Conformal mesh parameterization using discrete Calabi flow[J]. Computer Aided Geometric Design, 2018, 63:96-108 doi: 10.1016/j.cagd.2018.03.001
[15]	Xue J X, Li Q B, Liu C M, et al. Parameterization of triangulated surface meshes based on constraints of distortion energy optimization[J]. Journal of Visual Languages & Computing, 2018, 46:53-62 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=4ea83d96d427d270e688fddc3f94c9df
[16]	Chandrupatla T R, Belegundu A D.工程中的有限元方法[M].曾攀, 雷丽萍, 译.北京: 机械工业出版社, 2015 Chandrupatla T R, Belegundu A D. Introduction to finite elements in engineering[M]. Zeng P, Lei L P, trans. Beijing: China Machine Press, 2015(in Chinese)
[17]	Degener P, Meseth J, Klein R. An adaptable surface parametrization method[C]//Proceedings of the 12th International Meshing Roundtable. Santa Fe, New Mexico, USA: IMR, 2003: 201-213