基于几何代数的时空宗地meet计算研究

doi:10.3785/j.issn.1008-9497.2017.01.012

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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.

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	王巧燕
	蒋晓敏
	张丰
	杜震洪
	刘仁义

关键词 ：几何代数, 时空拓扑关系计算, meet算子, 时空宗地求交

Abstract：Geometric algebra has advantages in solving problems of geometric object modeling and multidimensional data analysis. This paper conducts studies on the meaning, construction and application of its two operators:meet and join. By exploiting their merits of multidimensional consistency and high dimension adaptivity, we propose a spatio-temporal parcel meet algorithm. We also give definitions and representations of 3D and 4D spatio-temporal parcel within the domain of conformal geometric algebra and spatio-temporal algebra. The algorithm is successfully applied to conduct the topology computation of three dimension spatio-temporal parcels and achieves satisfactory results.. Experiment show that our approach provides a novel and effective way for the representation and topology computation of three dimensional spatio-temporal parcel and hopefully a new resolution for four dimensional spatio-temporal parcels.

Key words： geometric algebra spatio-temporal topology relation computation meet operator spatio-temporal parcel meet

收稿日期: 2016-01-05

ZTFLH:

P208

基金资助: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）

通讯作者: 张丰,ORCID:http://orcid:org/0000-0003-1475-8480,E-mail:zfcarnation@zju.edu.cn E-mail: zfcarnation@zju.edu.cn

作者简介: 王巧燕(1991-),ORCID:http://orcid.org/0000-0002-5636-8184,女,硕士研究生,主要从事时空数据建模研究,E-mail:qywangZJUGIS@163.com.

引用本文:

王巧燕, 蒋晓敏, 张丰, 杜震洪, 刘仁义. 基于几何代数的时空宗地meet计算研究[J]. 浙江大学学报（理学版）, 2017, 44(1): 76-83.
WANG Qiaoyan, JIANG Xiaomin, ZHANG Feng, DU Zhenhong, LIU Renyi. A study on meet computation of spatio-temporal parcel based on conformal geometric algebra. Journal of ZheJIang University(Science Edition), 2017, 44(1): 76-83.

链接本文:

http://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.01.012 或 http://www.zjujournals.com/sci/CN/Y2017/V44/I1/76

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