Page 290 - 《软件学报》2020年第10期

软件学报 ISSN 1000-9825, CODEN RUXUEW E-mail: jos@iscas.ac.cn
Journal of Software,2020,31(10):3266−3279 [doi: 10.13328/j.cnki.jos.005804] http://www.jos.org.cn
©中国科学院软件研究所版权所有. Tel: +86-10-62562563

∗
距离约束的网格曲面曲线设计方法

1
1
2
1
1
金 耀 , 宋 丹 , 俞成海 , 马文娟 , 宋 滢 , 何利力 1
1
(浙江理工大学 信息学院,浙江 杭州 310018)
2 (天津大学 电气自动化与信息工程学院,天津 300072)
通讯作者: 宋滢, E-mail: ysong@zstu.edu.cn

摘 要: 针对现有网格曲面曲线设计方法鲁棒性差、收敛慢、适用范围窄等不足,提出一种基于距离约束的新方
法.该方法将复杂的流形约束转化为距离约束,并与光滑、插值(逼近)约束共同描述成优化问题.求解时,用切平面逼
近局部曲面,并将距离约束松弛成用点到切平面的距离.由于计算距离所用的曲线上的点与其对应的切点相互依赖,
采用“整体-局部”交替迭代的策略,并运用 Gauss-Newton 法的思想控制其收敛行为:整体阶段,通过距离近似将其松
弛成凸优化问题求解迭代步长;局部阶段,采用鲁棒高效的投影法将优化后的曲线映射到曲面以更新切平面;最后,
利用切割平面法将所有处于松弛状态的折线映射到网格曲面.实验结果表明:该方法与现有方法相比,在效率、鲁棒
性、可控性、应用范围等方面均表现出优势.
关键词: 网格曲面;曲线设计;距离约束;交替迭代
中图法分类号: TP391

中文引用格式: 金耀,宋丹,俞成海,马文娟,宋滢,何利力.距离约束的网格曲面曲线设计方法.软件学报,2020,31(10):
3266−3279. http://www.jos.org.cn/1000-9825/5804.htm
英文引用格式: Jin Y, Song D, Yu CH, Ma WJ, Song Y, He LL. Curve design method on mesh surface based on distance
constraints. Ruan Jian Xue Bao/Journal of Software, 2020,31(10):3266−3279 (in Chinese). http://www.jos.org.cn/1000-9825/5804.
htm

Curve Design Method on Mesh Surface Based on Distance Constraints

1
2
1
1
1
JIN Yao , SONG Dan , YU Cheng-Hai , MA Wen-Juan , SONG Ying , HE Li-Li 1
1 (School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China)
2 (School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China)
Abstract: Existing work of designing curves on mesh surface suffers from issues such as weak robustness, slow convergence, and
narrow application ranges. To address these issues, a distance constrained approach is proposed, which converts the complicated manifold
constraint into distance constraint, and formulates the problem as a constrained optimization combining with smoothness and interpolation
(approximation) constraints. To solve the optimization, the curve is discretized into a poly-line, and the distance constraint is relaxed to
point-to-plane distance by approximating the local surface patch with tangent plane. Since the curve points and the corresponding tangent
points involved in the distance calculation are interdependence, a “local/global” alternating iteration scheme is adopted and the idea of
Gauss-Newton method is used to control the convergence behavior. In the global stage, the iterative step is solved by relaxingthe problem

∗ 基金项目: 国家自然科学基金(61702458, 61602416); 浙江省自然科学基金(LY17F020031, LQ12F03012); 浙江省公益技术研
究工业项目(2016C31072, 2017C31032); 浙江省重大科技专项重点社会发展项目(2015C03001), 浙江省服装个性化定制协同创新中
心项目(浙教高科[2016] 63 号); 浙江理工大学科研启动基金(15032165-Y, 15032166-Y)
Foundation item: National Natural Science Foundation of China (61702458, 61602416); Natural Science Foundation of Zhejiang
Province of China (LY17F020031, LQ12F03012); Public-interest Technology Research for Industrial Project of Zhejiang Province
(2016C31072, 2017C31032); Science & Technology Program of Zhejiang Province (2015C03001); 2011 Collaborative Innovation Center
for Garment Personalized Customization of Zhejiang Province (No.63, 2016); Startup Foundation of ZSTU (15032165-Y, 15032166-Y)
收稿时间: 2018-07-16; 修改时间: 2018-09-26, 2018-12-03; 采用时间: 2018-12-28