基于空间信息的保对称性共形参数化算法  

Symmetry preserving conformal parameterization algorithm based on spatial information

作　　者：王鹏 李海生[1] WANG Peng;LI Haisheng(School of Computer Science and Engineering,Beijing Technology and Business University,Beijing 100048,China)

机构地区：[1]北京工商大学计算机学院,北京100048

出　　处：《中国科技论文》2022年第11期1276-1280,1288,共6页China Sciencepaper

基　　金：国家自然科学基金资助项目(61877002);北京市自然科学基金-交控科技资助项目(L191009)。

摘　　要：针对传统自由边界平面域共形参数化在模型表面曲面从三维空间共形映射到二维参数域空间时无法保证原有模型对称性的问题,提出了一种基于空间几何信息的保对称性共形参数化(symmetry preserving conformal parameterization,SPCP)算法。使用基于边界的平面反射对称变换求解输入模型的主对称面,并利用主对称面和边界顶点信息计算对称约束因子,最后通过对称约束因子确定自由边界共形参数化边界固定点,以得到能够保持对称性的共形参数化结果。结果表明,所提方法能够有效保证共形参数化的保对称性特性,并降低共形参数化映射结果的面积畸变和角度畸变,可在飞行器表面结构网格生成中有效提高结构网格生成的对称性和质量。In view of the problem that the traditional free boundary plane domain conformal parameterization can not guarantee the symmetry of the original model when the conformal parameterization method maps the surface of the model from 3D space to 2D parameter domain space,a symmetry preserving conformal parameterization(SPCP)algorithm based on spatial geometric information was proposed.The boundary-based plane reflection symmetry transformation was used to solve the main symmetry plane of the input model.The symmetry constraint factor was calculated by using the information of the principal symmetry plane and boundary vertices.Finally,the fixed points of the boundary of free boundary conformal parameterization were determined by symmetry constraint factors to obtain the result that can maintain symmetry.The experimental results show that this method can effectively ensure the symmetry preserving characteristics of conformal parameterization,reduce the area distortion and angle distortion of conformal parameterization mapping results,and effectively improve the symmetry and quality of structural mesh generation in aircraft surface structural mesh generation.

关 键 词：共形参数化 对称约束因子 空间信息约束 保对称性 

分 类 号：TP314[自动化与计算机技术—计算机软件与理论]