Constrained Generation of Voronoi Meshes using Inscribed Sphere Distance
Master thesis
Permanent lenke
https://hdl.handle.net/11250/3094276Utgivelsesdato
2023Metadata
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Sammendrag
Voronoi meshes, also known as PEBI (Perpendicular Bisector) grids, have garnered considerableattention 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 theyare able to incorporate geometric features within the resulting mesh. However, the presence of sharpintersections and narrow spaces poses challenges to constructing such meshes, often necessitatingcompromises to the mesh integrity.This thesis aims to address these challenges by introducing new methods for creating constrainedVoronoi meshes in three dimensions. We propose a novel distance function, the Inscribed SphereDistance, and employ this to enhance the stability of the mesh generation. Throughout thisresearch, we will explore and evaluate the advantages and disadvantages of Voronoi meshing as awhole, shedding light on its potential benefits and limitations.By employing the newly developed methods and leveraging the Gmsh mesh generator, we havesuccessfully implemented a Voronoi mesh generator that excels in capturing narrow spaces andsharp intersections. This enhanced capability allows for the creation of meshes that accuratelyrepresent complex geometries with intricate details, resulting in improved simulation accuracy andfidelity. Voronoi meshes, also known as PEBI (Perpendicular Bisector) grids, have garnered considerableattention 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 theyare able to incorporate geometric features within the resulting mesh. However, the presence of sharpintersections and narrow spaces poses challenges to constructing such meshes, often necessitatingcompromises to the mesh integrity.This thesis aims to address these challenges by introducing new methods for creating constrainedVoronoi meshes in three dimensions. We propose a novel distance function, the Inscribed SphereDistance, and employ this to enhance the stability of the mesh generation. Throughout thisresearch, we will explore and evaluate the advantages and disadvantages of Voronoi meshing as awhole, shedding light on its potential benefits and limitations.By employing the newly developed methods and leveraging the Gmsh mesh generator, we havesuccessfully implemented a Voronoi mesh generator that excels in capturing narrow spaces andsharp intersections. This enhanced capability allows for the creation of meshes that accuratelyrepresent complex geometries with intricate details, resulting in improved simulation accuracy andfidelity.