Multidimensional-unified topological relations computation: a hierarchical geometric algebra-based approach
Multidimensional-unified topological relations computation: a hierarchical geometric algebra-based approach
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多维统一拓扑关系计算：基于层次几何代数的方法
DOI：
10.1080/13658816.2014.929136
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发表时间：
2014-12
影响因子：
5.7
通讯作者：
Lv Guonian
中科院分区：
文献类型：
--
作者：
Yuan Linwang;Yu Zhaoyuan;Luo Wen;Yi Lin;Lv Guonian
本文提出了一种基于几何代数的拓扑关系计算模型。该计算模型由三个主要部分组成：保留分层多向量树表示（MVTree）的Grassmann结构、计算相交关系的多维统一算子和将相交组合成拓扑关系的判断规则。在该模型中，使用Tree Meet算子计算不同维度对象（不同层次的节点）之间的相交关系。任意两个对象之间的相遇运算通过将计算转化为每对MVTree节点之间的相遇积来完成，从而产生一系列MVTree形式的相交关系。然后通过一组判断规则对相交树进行处理，确定层次结构中两个对象之间的拓扑关系。以三维空间中两个三角形之间的拓扑关系为例说明了该模型。结果表明，该模型可以在不涉及维数的情况下简单地计算拓扑关系。考虑到数字时代地理信息维数的增加，这种从地理数据中计算拓扑关系的无量纲方法具有重要意义。
This article presents a geometric algebra-based model for topological relation computation. This computational model is composed of three major components: the Grassmann structure preserving hierarchical multivector-tree representation (MVTree), multidimensional unified operators for intersection relation computation, and the judgement rules for assembling the intersections into topological relations. With this model, the intersection relations between the different dimensional objects (nodes at different levels) are computed using the Tree Meet operator. The meet operation between two arbitrary objects is accomplished by transforming the computation into the meet product between each pair of MVTree nodes, which produces a series of intersection relations in the form of MVTree. This intersection tree is then processed through a set of judgement rules to determine the topological relations between two objects in the hierarchy. Case studies of topological relations between two triangles in 3D space are employed to illustrate the model. The results show that with the new model, the topological relations can be computed in a simple way without referring to dimension. This dimensionless way of computing topological relations from geographic data is significant given the increased dimensionality of geographic information in the digital era.
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影响因子：
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