Higher-order Voronoi diagrams and Delaunay mosaics in polygonal metrics have only recently been studied, yet no tools exist for visualizing them. We introduce a tool that fills this gap, providing dynamic interactive software for visualizing higher-order Voronoi diagrams and Delaunay mosaics along with clustering and tools for exploring overlap and outer regions in the Hilbert polygonal metric. We prove that $k^{th}$ order Voronoi cells are not always star-shaped and establish complexity bounds for our algorithm, which generates all order Voronoi diagrams at once. Our software unifies and extends previous tools for visualizing the Hilbert, Funk, and Thompson geometries.

翻译：多边形度量中的高阶Voronoi图与Delaunay镶嵌近期才被研究，但目前尚无用于可视化的工具。我们引入了一种填补这一空白的工具，提供动态交互式软件，用于可视化高阶Voronoi图、Delaunay镶嵌及其聚类，并探索希尔伯特多边形度量中的重叠区域与外围区域。我们证明了k阶Voronoi胞腔并非总是星形，并建立了算法的复杂度上界——该算法可同时生成所有阶次的Voronoi图。该软件统一并扩展了此前用于可视化希尔伯特、Funk与Thompson几何的工具。