使用最简几何基元构建3维空间数据模型

在对现实世界进行高度抽象化的表达过程中,许多学者和机构提出了多种空间数据模型(或称之为空间数据结构)。文章首先总结了现有模型所使用的基本几何要素,并对其利弊进行了讨论;然后总结了使用这些几何要素进行组合、扩展以构建更为复杂的空间实体的理论即空间数据建模理论,同时也对不同理论的适用性和局限性进行了讨论。笔者随后以4维空间为基础,从空间内嵌的角度去思考不同维度下的空间构成,得出了3维空间的最简基本要素,并通过对比相关文献对geometric primitives的中文翻译将其命名为"几何基元"。在此基础上笔者探讨了3维几何基元构成空间实体的数学表达本质,论述了依此几何基元构成的空间实体之间基本拓扑关系的表达方法。最后笔者设计了一套数据结构以系统构建空间数据模型,该模型有利于实现3维空间数据库,可为形成3维数据资产提供基础。本文的结论认为,该3维空间数据模型可以有效地解决体3维和表面3维的模型一致性问题,提供了结合"地学3维"和"3维数字城市"等不同应用系统的途径;同时可将当前的2维地理信息系统自然地扩展到3维;另外还可以为3维空间分析和专门的3维渲染引擎提供理论支持。

Three-dimensional Spatial Data Modeling with Simplest Geometric Primitives

For abstracting the objects to express the real world,scholars and institutions have put forward some useful spatial data models(or so-called spatial data structure).Firstly,this article summarized the basic geometric elements of the existing models,and discussed their pros and cons;then summed up the modeling theories-spatial data modeling theory-that use geometric elements to build more complex spatial entities by combination and extension,also the applicability and limitation of the different theories are discussed.In addition,with thinking space structure in different dimensions from the perspective of space embedding based on four-dimensional space,the author obtained three-dimensional simplest elements,so-called geometric primitives.Even,the author discussed the mathematical expression for three-dimensional simplest geometric primitives and constitution of the more complex spatial entities;the basic topological relations between entities and simplified algorisms for computing these relationships were introduced.Finally,the author systematically designed a set of data structures to architect a spatial data models that is facility to the realization of three-dimensional spatial database and even beneficial to generate the 3D data assets.The paper concludes that this geometric primitives based three-dimensional data model can effectively solve the consistency problem of the body and surface models,and provide a way to combine the different applications for instance "geological 3D applications" and "3D digital city".Further more,this model would help the current two-dimensional geographic information system smoothly extend to 3D,and also been expected to promote the spatial analysis and specialized 3D rendering engine of three-dimension.