The lack of efficient access and query method remains a barrier for three-dimensional (3D) geological tetrahedral models (GTMs) to support high-performance 3D spatial analysis and calculation. To organize and manage GTMs efficiently, this paper proposes a GTM-oriented hybrid spatial indexing structure, named 3DOR*-tree, which can fully exploit the advantages of the fast spatial partition of Octree and the efficient spatial query of 3D R*-tree. GTM-oriented data structures are designed on the basis of 3DOR*-tree by setting appropriate thresholds for construction. Geological spatial data query based on 3DOR*-tree can then be implemented. Through test verification and comparative analysis, the accuracy and efficiency of the proposed spatial indexing structure are verified. The node-splitting thresholds of the 3DOR*-tree indexing structure are discussed and analyzed. The 3DOR*-tree can implement efficient construction and query simultaneously. Results corroborate that the node-splitting threshold of Octree is recommend to be set as 500 tetrahedrons, and that the node-splitting thresholds of 3D R*-tree are recommended to be set as 128 and 256 individuals (minimum and maximum tetrahedrons, respectively). This study not only provides technical support for the storage, management, and analysis of GTMs but also provides reference for the theoretical research of a hybrid spatial indexing method.

中文翻译：

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基于Octree和3D R * -tree的面向地质四面体模型的混合空间索引结构

缺乏有效的访问和查询方法仍然是三维（3D）地质四面体模型（GTM）支持高性能3D空间分析和计算的障碍。为了有效地组织和管理GTM，本文提出了一种面向GTM的混合空间索引结构，称为3DOR * -tree，它可以充分利用Octree快速空间划分和3D R * -tree高效空间查询的优势。面向GTM的数据结构是在3DOR *树的基础上设计的，方法是设置适当的构造阈值。然后可以实现基于3DOR *-树的地质空间数据查询。通过测试验证和比较分析，验证了所提出的空间索引结构的准确性和效率。讨论并分析了3DOR *-树索引结构的节点拆分阈值。3DOR *树可以同时实现高效的构造和查询。结果证实了建议将Octree的节点拆分阈值设置为500个四面体，并建议将3D R * -tree的节点拆分阈值设置为128个和256个个体（分别为最小和最大四面体） 。该研究不仅为GTM的存储，管理和分析提供了技术支持，而且为混合空间索引方法的理论研究提供了参考。建议将3D R *-树的节点分割阈值设置为128和256个人（分别为最小和最大四面体）。该研究不仅为GTM的存储，管理和分析提供了技术支持，而且为混合空间索引方法的理论研究提供了参考。建议将3D R *-树的节点分割阈值设置为128和256个人（分别为最小和最大四面体）。该研究不仅为GTM的存储，管理和分析提供了技术支持，而且为混合空间索引方法的理论研究提供了参考。