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Journal of Software:2020.31(10):3266-3279

距离约束的网格曲面曲线设计方法
金耀,宋丹,俞成海,马文娟,宋滢,何利力
(浙江理工大学 信息学院, 浙江 杭州 310018;天津大学 电气自动化与信息工程学院, 天津 300072)
Curve Design Method on Mesh Surface Based on Distance Constraints
JIN Yao,SONG Dan,YU Cheng-Hai,MA Wen-Juan,SONG Ying,HE Li-Li
(School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China;School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China)
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Received:July 16, 2018    Revised:December 03, 2018
> 中文摘要: 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.
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 into a convex optimization via distance approximation. In the local stage, a robust and efficient projection method is applied to update tangent planes. Finally, each segment of the poly-line is projected onto the surface by cutting planes. Experiments exhibit that the proposed method outperforms existing work on various aspects, including effectiveness, robustness, controllability, and practicability.
文章编号:     中图分类号:TP391    文献标志码:
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) 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 items: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)
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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

JIN Yao,SONG Dan,YU Cheng-Hai,MA Wen-Juan,SONG Ying,HE Li-Li.Curve Design Method on Mesh Surface Based on Distance Constraints.Journal of Software,2020,31(10):3266-3279