基于凸凹理论的三维地质体空间关系模型研究

Study on 3D Geological Body Spatial Relation Model Based on Concave Convex Theory

目前的三维地质体空间关系模型表达能力较弱,限制了其在空间分析、查询等方面的应用。三维模型的应用与发展迫切需要一种新的底层分解与理论建模解决此类问题。该文基于凸凹理论重新对地质体进行结构定义与空间关系建模,提出了内凸体、外凸体、内缘体、外缘体等构造,并在此基础上建立了三维地质体R7×7空间关系模型,将地质体间空间关系表达能力理论上扩充至249种,实际能够表达40余种空间关系;给出了包容、镶嵌、部分镶嵌等关系的定义并对其进行了模型表达;针对不同应用,给出了R7×7模型的变换模型R(5×5 3×3)等。为能够表达地质体交集的边界长度、交面面积、地质体体积、外缘体体积、镶嵌体积等地质空间重要关系,基于凸凹理论建立了地质体度量关系模型,是矿区地质体拓扑关系查询、空间分析推理等应用的基础模型。给出了模型与地质体模糊理论的相契性分析,二者模型能够相辅相成,相互借鉴使用。

Because of the weak expressive ability of spatial relational models,the application of 3D geological bodies in spatial analysis and query is restricted.The application and development of 3D models urgently need a new underlying decomposition and theoretical modeling to solve such problems.Based on convex concave theory,the structural definition and spatial relationship model of geological bodies is reestablished.In this paper,the structures of inner convex body,outer convex body,inner edge,body edge are put forward,and a three-dimensional geological body spatial relationship model R7×7 is established based on convex body theory.The model extends the spatial relationship expression ability between geological bodies to 2^49 kinds in theory.R7×7 can express more than 40 kinds of spatial relations in application.This paper gives the definition of the relationship between inclusion,mosaic,partial mosaic and so on.For different applications,the transformation model of the R7×7,such as R(5×5,3×3),is given.The transformation model ignores external relations and is suitable for fast modeling and expression of geological bodies.In order to express the important relation of geological space,such as boundary length,surface area,volume of geological body,volume of outer edge body and mosaic volume,the relationship model of geological body measurement is built on the basis of convex and concave theory.The model in this paper is a basic model for the application of topological relations,geological analysis,reasoning and so on.Finally,the corresponding analysis of the model and the geological body fuzzy theory is given.The model proposed in this paper can be applied to the fuzzy geological body better.