基于几何代数的时空宗地meet计算研究

A study on meet computation of spatio-temporal parcel based on conformal geometric algebra

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.

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 re- suits.. 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.