E-WID三维拓扑关系计算方法与实现  

Calculation method and implementation of E-WID(3D)topological relationship

作　　者：杨国红 周晓光[1,2] 贺鸿愿 侯东阳 李存志 YANG Guohong;ZHOU Xiaoguang;HE Hongyuan;HOU Dongyang;LI Cunzhi(School of Geosciences and Info-Physics,Central South University,Changsha 410083,China;Key Laboratory of Spatio-temporal Information and Intelligent Services,Ministry of Natural Resources of the People’s Republic of China,Changsha 410083,China)

机构地区：[1]中南大学地球科学与信息物理学院,长沙410083 [2]自然资源部时空信息与智能服务重点实验室,长沙410083

出　　处：《时空信息学报》2023年第4期536-542,共7页JOURNAL OF SPATIO-TEMPORAL INFORMATION

基　　金：国家自然科学基金项目(41971360)。

摘　　要：E-WID(Euler-number-based whole-object intersection and difference)三维拓扑关系模型能够表达三维空间简单、复杂目标间的拓扑关系,具有区分能力强、无理论缺陷等优势,但目前尚缺乏E-WID三维模型自动计算的相关研究。因此,利用Nef多面体三维数据模型能够表达带通道或空穴等复杂目标的特点,本文研究了一种基于Nef多面体的E-WID三维基本拓扑关系计算方法,其中包括三维基本空间数据间布尔运算结果的组件构建和欧拉数计算方法;并与已有方法进行对比。结果表明,本文方法实现了三维空间数据间的E-WID三维基本拓扑关系自动计算,并能够准确区分。The calculation of three-dimensional topological relationship is one of the main issues with the quality control of three-dimensional spatial data.E-WID(Euler-number-based whole-object intersection and difference)(3D)topological model can distinguish the topological relationship between simple and complex 3D objects,and it has the advantages of strong distinguishing ability without theoretical flaws and more.Currently,however,the automatic calculation of E-WID(3D)has not been fully realized.Nevertheless,at present,the effective calculation of the topological relationship of the three-dimensional E-WID model has not been realized.In order to solve this problem,the authors design an E-WID(3D)topological relationship calculation method based on Nef polyhedron.In this method,the intersection/difference operations result set of the two Nef polyhedral objects are gotten at first.The result sets include point,edge,polygon and body sets.The edge,polygon,and body sets may contain non-manifold surfaces.Then seven non-manifold to manifold reconstruction rules are designed,and the above sets are reconstructed to point,line,surface and volume manifold component sets using the corresponding rules.Then,the calculation methods of dimensionality and Euler number(i.e.f_(D)(A∩B),f_(D)(A\B),f_(D)(B\A),f_(E)(A∩B),f_(E)(A\B),f_(E)(B\A))of each component are designed.With a specific focus on the Euler number calculation problem of complex objects with channel volume or holes,a method for calculating Euler numbers based on complex objects triangulation is designed.Finally,according to the calculated dimension and Euler value,an E-WID(3D)topological relationship matrix is established to distinguish the three-dimensional topological relationship.At last,the E-WID(3D)basic topological relationship calculation between two 3D objects was achieved using C++language and CGAL computational geometry library.The effectiveness of the method proposed in this paper is verified using analog data.

关 键 词：3D E-WID 拓扑关系计算 拓扑构建 欧拉数 

分 类 号：P208[天文地球—地图制图学与地理信息工程]