基于几何代数的时空宗地meet计算研究

发布时间：2018-05-08 10:29

  本文选题：几何代数 + 时空拓扑关系计算　； 参考：《浙江大学学报(理学版)》2017年01期

【摘要】：根据几何代数在地理空间对象建模和多维数据分析应用的特点,研究了共形几何代数交/并(meet/join)算子的含义、构建和应用.利用几何代数多维统一、高维计算适应的优势,设计了基于几何代数meet算子和有向半空间划分理论的时空宗地meet算法.从三维地籍和时空数据建模出发,在共形几何代数和时空代数范畴中,给出了三维、四维时空宗地的定义和表达.同时,以宗地数据的拓扑计算为例,将该算法运用于三维时空宗地拓扑计算场景——历史回溯中,取得了良好的效果.该算法的理念同样适用于四维时空宗地的历史回溯meet求解.
[Abstract]:According to the characteristics of geometric algebra in geo-spatial object modeling and multidimensional data analysis, the meaning, construction and application of conformal geometric algebra intersection / parallel meet-join operator are studied. Based on the advantages of multi-dimensional unification of geometric algebra and adaptability of high-dimensional computation, a spatio-temporal meet algorithm based on geometric algebra meet operator and directed midspace partition theory is designed. Based on the modeling of three-dimensional cadastral and space-time data, the definition and expression of three-dimensional and four-dimensional space-time land are given in the category of conformal geometric algebra and space-time algebra. At the same time, taking the topological calculation of the land data as an example, the algorithm is applied to the scene of 3D temporal and spatial land topology calculation-historical backtracking, and good results are obtained. The idea of this algorithm is also applicable to the historical backtracking meet solution of four dimensional temporal and spatial land.
【作者单位】： 浙江大学浙江省资源与环境信息系统重点实验室;浙江大学地球科学学院;
【基金】：国家自然科学基金资助项目(41471313,41101356,41101371,41171321) 国家科技基础性工作专项(2012FY112300) 海洋公益性行业科研专项经费资助(2015418003,201305012) 浙江省攻关项目(2014C33G20,2013C33051)
【分类号】：P208
，

本文编号：1861040