大范围网格曲面曲线设计方法及应用  

Curve Design Method and Application of Large-scale Mesh Surface

作　　者：姜晓通 戴宁[2] 武智磊 杨思远 JIANG Xiao-tong;DAI Ning;WU Zhi-lei;YANG Si-yuan(School of Mechanical Engineering,Changshu Institute of Technology,Suzhou 215500,China;School of Mechanical and Electrical Engineering,Nanjing University of Aeronautics&Astronautics,Nanjing 210016,China)

机构地区：[1]常熟理工学院机械工程学院,江苏苏州215500 [2]南京航空航天大学机电学院,江苏南京210016

出　　处：《计算机技术与发展》2023年第8期74-80,共7页Computer Technology and Development

基　　金：国家自然科学基金(62002033)。

摘　　要：为了满足齿科在离散网格曲面建模中对曲线设计高效性、鲁棒性及基于网格曲线个性化建模等方面的要求,提出了一种基于局部参数化的离散网格曲面样条曲线设计方法。该方法放松了对样条曲线全局连续性的约束,将平面参数域内的全局样条线设计转化成在局部区域内的分段样条曲线设计,提高了参数化网格曲线设计方法的效率及鲁棒性,使其能够不受编辑范围、网格模型复杂度及网格亏格的影响,满足大范围的网格曲线实时编辑的要求,以及齿科个性化建模软件中基于曲线建模的需求;引入两型值点间的最短路径,解决在样条线设计过程中,因相邻两型值点距离过大而导致算法存在的鲁棒性问题;引入局部光顺算法,在型值点附近进行流行约束下的光顺,提高样条曲线的光滑度。实验表明,基于平面参数化域的局部分段样条曲线设计方法在效率、鲁棒性及实用性方面具有一定的优势,综合性能较好,能够满足齿科建模软件的实际应用需求。In order to meet the requirements of high efficiency and robustness of curve design in discrete mesh surface modeling of dentistry,we propose a spline curve design method for discrete mesh surface based on local parameterization.This method relaxes the constraint on the global continuity of spline curves,transforms the global spline design in the plane parameter domain into the piecewise spline design in the local area,and improves the efficiency and robustness of the parametric mesh curve design method,which makes it not affected by the editing range,grid model complexity and grid defect,and meets the requirements of real-time editing of a wide range of grid curves,as well as the requirements of curv-based modeling in personalized dental modeling software.The shortest path between two types of value points is introduced to solve the robustness problem caused by the large distance between adjacent two types of value points in the process of spline design.Local fairing algorithm is introduced to fair points near the data points under manifold constraints to improve the smoothness of spline curves.The experiment shows that the piecewise spline curve design method based on local parametric area has certain advantages in efficiency,robustness and practicality with excellent comprehensive performance,which can meet the practical application needs of engineering software such as dentistry.

关 键 词：大范围网格曲面 分段样条曲线 局部参数化 最短路径优化 曲线建模 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]