距离约束的网格曲面曲线设计方法  

Curve Design Method on Mesh Surface Based on Distance Constraints

作　　者：金耀 宋丹 俞成海 马文娟 宋滢 何利力 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)

机构地区：[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

出　　处：《软件学报》2020年第10期3266-3279,共14页Journal of Software

基　　金：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)。

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.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.

关 键 词：网格曲面 曲线设计 距离约束 交替迭代 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]