基于胞腔复形的地下空间表达数据模型

A Data Model of Subsurface Spatial Representation Based on Cell Complex

针对地层和地下水的空间表达,提出了一种地下空间表达模型。该模型将地下空间对象表达方法从单纯同调理论扩展到胞腔同调,使用胞腔同调理论表达地下空间对象。模型分为四个层次:实体层将地下空间对象用拓扑抽象的点、线、面、体要素描述,将其拓扑模型表示为由拓扑空间中K维胞腔组成的胞腔复形。几何层采用k-embedding表示,k-embedding与拓扑信息k维胞腔相关联,维护地下对象几何连续性和拓扑一致性。在可视化时,将胞腔或胞腔复形剖分为单纯复形,采用TIN表达地层面,TEN表达地质体,形成表达层。该模型可用于地下水的建模和表达,通过将水文长观孔地质高程值对地层面进行插值计算,生成TIN;以每一个地层的上下TIN为约束,生成TEN。实验结果表明,该模型可以有效的建模和表达地层对象。

Aiming at the spatial representation of stratum and groundwater, an underground spatial data model is proposed. This model extends the method of expressing objects in underground space from simple homology theory to cellular homology, and uses the theory of cellular homology to represent underground space objects. The model is divided into four layers: The entity layer describes the underground space objects with topologically abstract points, lines, planes, and volume elements, and represents its topological model as a cell complex composed of K-dimensional cells in the topological space. The geometry layer is represented by k-embedding, and k-embedding is associated with k-dimensional cells of topological information to maintain the geometric continuity and topological consistency of underground objects. When visualizing, the cell or cell complex is divided into simple complexes, and TIN is used to represent the formation layer, and TEN is used to represent the geological body to form the representation layer. The model can be used for modeling and representation of groundwater, and generates TIN by interpolating the geological elevation value of the hydrological long observation hole with the stratum;generating TEN with the upper and lower TINs of each stratum as constraints. The experimental results show that the model can effectively model and represent stratigraphic objects.