Constrained Generation of Voronoi Meshes using Inscribed Sphere Distance

Abstract

Voronoi meshes, also known as PEBI (Perpendicular Bisector) grids, have garnered considerable attention due to their ability to simplify the generation of general polygonal/polyhedral meshes. Constrained Voronoi meshes, in particular, have emerged as a significant area of research, as they are able to incorporate geometric features within the resulting mesh. However, the presence of sharp intersections and narrow spaces poses challenges to constructing such meshes, often necessitating compromises to the mesh integrity. This thesis aims to address these challenges by introducing new methods for creating constrained Voronoi meshes in three dimensions. We propose a novel distance function, the Inscribed Sphere Distance, and employ this to enhance the stability of the mesh generation. Throughout this research, we will explore and evaluate the advantages and disadvantages of Voronoi meshing as a whole, shedding light on its potential benefits and limitations. By employing the newly developed methods and leveraging the Gmsh mesh generator, we have successfully implemented a Voronoi mesh generator that excels in capturing narrow spaces and sharp intersections. This enhanced capability allows for the creation of meshes that accurately represent complex geometries with intricate details, resulting in improved simulation accuracy and fidelity.

Voronoi meshes, also known as PEBI (Perpendicular Bisector) grids, have garnered considerable attention due to their ability to simplify the generation of general polygonal/polyhedral meshes. Constrained Voronoi meshes, in particular, have emerged as a significant area of research, as they are able to incorporate geometric features within the resulting mesh. However, the presence of sharp intersections and narrow spaces poses challenges to constructing such meshes, often necessitating compromises to the mesh integrity. This thesis aims to address these challenges by introducing new methods for creating constrained Voronoi meshes in three dimensions. We propose a novel distance function, the Inscribed Sphere Distance, and employ this to enhance the stability of the mesh generation. Throughout this research, we will explore and evaluate the advantages and disadvantages of Voronoi meshing as a whole, shedding light on its potential benefits and limitations. By employing the newly developed methods and leveraging the Gmsh mesh generator, we have successfully implemented a Voronoi mesh generator that excels in capturing narrow spaces and sharp intersections. This enhanced capability allows for the creation of meshes that accurately represent complex geometries with intricate details, resulting in improved simulation accuracy and fidelity.