Although a Discrete Global Grid (DGG) is uniform in its initial subdivision, its geometric deformation increases with the level of subdivisions. The Goodchild Criteria are often used to evaluate the quality of DGGs. However, some indicators in these criteria are mutually incompatible and overlap. If the criteria are used directly, the evaluation of the DGGs is inaccurate or unreliable. In this paper, we calculated and analyzed the correlation between the evaluation indicators of the DGG and reconstructed a quality evaluation system of DGGs with independent indicators. Firstly, we classified the Goodchild Criteria into quantitative and qualitative indicators. Then, we calculated the correlation among the quantitative indicators and extracted the independent evaluation factors and related weights of the observed values by factor analysis. After eliminating or merging the incompatible and overlapping quantitative indicators and performing a logical reasoning of the qualitative indicators, we reconstructed a comprehensive evaluation system with independent indicators. Finally, taking the Quaternary Triangular Mesh (QTM) model as an example, we verified the independence of the indicators and the feasibility of the evaluation system. The new indicator system ensures the reliability of the evaluation of DGGs in many fields.

DGGS (Discrete Global Grid System) has many subdivision models and coding methods. Due to the lack of underlying consistency of different DGGS codes, most of them are converted through longitude–latitude, which greatly reduces the interoperability efficiency of different DGGS data and has become one of the bottlenecks in efficient integration of multi-source DGGS data. Therefore, a direct mapping method from one grid code to another (Grid to Grid, GtoG) for multi-type DGGSs is proposed based on three classical DGGSs (triangular, diamond and hexagonal grids) and two commonly used filling curves (Hilbert curve and Z-curve). The mutual conversion rules of different grids expressing spatial point, line and surface data are constructed. Then, the above method is extended to the spherical icosahedral grid framework, and three different region coding mapping rule tables of the basic inside cells, boundary cells and vertex cells are designed. Finally, the experimental results show that, compared with the longitude–latitude conversion method, the average conversion efficiency of spatial point, line and surface data is increased by 2–4 orders of magnitude. This new method greatly improves the interoperability efficiency and provides a feasible solution for the efficient integration of multi-source DGGS data.

The Voronoi diagram on the Earth’s surface is a significant data model, characterized by natural proximity and dynamic stability, which has emerged as one of the most promising solutions for global spatial dynamic management and analysis. However, traditional algorithms for generating spherical raster Voronoi diagrams find it challenging to dynamically adjust the Voronoi diagram while maintaining precision and efficiency. The efficient and accurate construction of the spherical Voronoi diagram has become one of the bottleneck issues limiting its further large-scale application. To this end, this paper proposes a dynamic construction scheme for the spherical Voronoi diagram based on the QTM (Quaternary Triangular Mesh) system, with the aim of enabling efficient generation, local updates, and multi-scale visualization of the spherical Voronoi diagrams. In this paper, canonical ordering is introduced. Tailored for the properties of the spherical triangular grid, it constructs a unified and standardized sorting strategy for the dilation of the spherical grids. The construction and updating of the spherical Voronoi diagram are achieved through the ordered dilation of sites. Furthermore, the multi-scale visualization of the spherical Voronoi diagram is realized through the hierarchical structure of the QTM. The paper presents our algorithm intuitively through pseudocode, conducts comparative experiments on the feasibility and efficiency, and designs an experiment for the dynamic navigation and management of ocean-going vessels based on the global multi-resolution Voronoi diagram. The experimental results demonstrate that our algorithm effectively controls the error of the generation of the raster Voronoi diagram and has a significant efficiency advantage when processing dynamic environments.

The improvement of overall uniformity and smoothness of spherical icosahedral grids, the basic framework of atmospheric models, is a key to reducing simulation errors. However, most of the existing grid optimization methods have optimized grid from different aspects and not improved overall uniformity and smoothness of grid at the same time, directly affecting the accuracy and stability of numerical simulation. Although a well-defined grid with more than 12 points cannot be constructed on a sphere, the area uniformity and the interval uniformity of the spherical grid can be traded off to enhance extremely the overall grid uniformity and smoothness. To solve this problem, an overall uniformity and smoothness optimization method of the spherical icosahedral grid is proposed based on the optimal transformation theory. The spherical cell decomposition method has been introduced to iteratively update the grid to minimize the spherical transportation cost, achieving an overall optimization of the spherical icosahedral grid. Experiments on the four optimized grids (the spring dynamics optimized grid, the Heikes and Randall optimized grid, the spherical centroidal Voronoi tessellations optimized grid and XU optimized grid) demonstrate that the grid area uniformity of our method has been raised by 22.60% of SPRG grid, −1.30% of HR grid, 38.30% of SCVT grid and 38.20% of XU grid, and the grid interval uniformity has been improved by 2.50% of SPRG grid, 2.80% of HR grid, 11.10% of SCVT grid and 11.00% of XU grid. Although the grid uniformity of the proposed method is similar with the HR grid, the smoothness of grid deformation has been enhanced by 79.32% of grid area and 24.07% of grid length. To some extent, the proposed method may be viewed as a novel optimization approach of the spherical icosahedral grid which can improve grid overall uniformity and smoothness of grid deformation.