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.

With the rapid development of computer technology, emerging programming languages and compilers are constantly being introduced.However, these new compilers often have defects due to their short development time, insufficient testing, and the challenges they face, which affect their reliability and adoption.Traditional testing methods are limited in addressing the challenges of testing these new compilers.This paper proposes a new method for testing emerging compilers based on test case reuse, utilizing large language models to convert test cases from one programming language to another.Using C++ and Carbon language as examples, historical test cases from C++ are converted to Carbon language versions to expand the test case library for the Carbon compiler.This method involves fine-tuning a large language model to transform C++ historical bugs codes into codes suitable for the Carbon compiler, followed by verification to ensure their effectiveness.By converting and reusing test cases and implementing feature conversions to generate mutations, we improve 6.63% test coverage for Carbon compiler and discover 8 bugs.