基于共形几何代数的三维地籍空间数据建模探讨  

Study on Construction for the Three-Dimensional Cadastral Data Model Based on Conformal Geometric Algebra

作　　者：张季一[1] 尹鹏程[2] 李钢[3] 史志凤[1] 刘友志 于金羽[1] ZHANG Ji-yi;YIN Peng-cheng;LI Gang;SHI Zhi-feng;LIU You-zhi;YU Jin-yu(Bureau of Land and Resources of Xinyi,Xuzhou 221400;Bureau of Land and Resources of Xuzhou,Xuzhou 221006;China University of Mining and Technology,Xuzhou 221008,China)

机构地区：[1]新沂市国土资源局,江苏徐州221400 [2]徐州市国土资源局,江苏徐州221006 [3]中国矿业大学,江苏徐州221008

出　　处：《地理与地理信息科学》2018年第4期7-12,共6页Geography and Geo-Information Science

基　　金：江苏省测绘地理信息科研项目(JSCHKY201711;JSCHKY201509);国家自然科学基金项目(41401610)

摘　　要：为解决欧氏空间中基于边界表达模型构建的三维地籍数据模型无法进行三维空间分析计算的问题,该文引入基于共形几何代数(Conformal Geometric Algebra,CGA)的三维数据模型,利用边界表达模型对地籍权属边界进行准确表达的同时,基于表达地籍对象几何信息的共形表达式实现了三维地籍空间关系分析计算,最后通过案例对提出的模型进行了验证。该文为三维地籍数据模型构建提供了新的研究方向,而几何代数在几何关系运算及多维融合表达等方面的优势将有助于三维地籍空间分析的实现。A 3D data model based on conformal geometric algebra(CGA)is introduced into the field of 3D cadastre data modeling to solve the problem that the geometric and topological information of 3D cadastral objects cannot be represented in a unified form with boundary representation models in Euclidean space in this paper.The cadastral objects′boundaries are described by boundary representation model and their geometric information is expressed in conformal expressions.Those conformal expressions can be used to relative spatial computations in 3D cadastral space.The 3D cadastral data model based on CGA was verified by a case study.It shows that the paper provides a new research direction for 3D cadastral data modeling.The geometric algebra′s advantages in geometric relations computation and multi-dimensional expression are helpful for the research and realization of 3D cadastral spatial analysis.

关 键 词：三维地籍 数据模型 边界表达 共形几何代数 

分 类 号：P208[天文地球—地图制图学与地理信息工程]