VoroCrust: Voronoi Meshing Without Clipping

Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting arbitrarily curved boundaries and sharp features. In addition, the power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous formulations. The VoroCrust algorithm is the first provably-correct algorithm for conforming polyhedral Voronoi meshing for non-convex and non-manifold domains with guarantees on the quality of both surface and volume elements. A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface circumventing the need for clipping and avoiding its many drawbacks. The algorithm has the flexibility of filling the interior by either structured or random samples, while preserving all sharp features in the output mesh. We demonstrate the capabilities of the algorithm on a variety of models and compare against state-of-the-art polyhedral meshing methods based on clipped Voronoi cells establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf. Supplemental materials available on https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd

Doctor of Philosophy

dissertationOne of the fundamental building blocks of many computational sciences is the construction and use of a discretized, geometric representation of a problem domain, often referred to as a mesh. Such a discretization enables an otherwise complex domain to be represented simply, and computation to be performed over that domain with a finite number of basis elements. As mesh generation techniques have become more sophisticated over the years, focus has largely shifted to quality mesh generation techniques that guarantee or empirically generate numerically well-behaved elements. In this dissertation, the two complementary meshing subproblems of vertex placement and element creation are analyzed, both separately and together. First, a dynamic particle system achieves adaptivity over domains by inferring feature size through a new information passing algorithm. Second, a new tetrahedral algorithm is constructed that carefully combines lattice-based stenciling and mesh warping to produce guaranteed quality meshes on multimaterial volumetric domains. Finally, the ideas of lattice cleaving and dynamic particle systems are merged into a unified framework for producing guaranteed quality, unstructured and adaptive meshing of multimaterial volumetric domains

Out-of-core representation of triangle meshes for rendering of large data volumes

Orientador: Hélio PedriniDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Malhas triangulares são representações de dados espaciais comumente utilizadas na manipulação e visualização de superfícies complexas. Este trabalho apresenta e avalia uma proposta de representação out-of-core estática de malhas de triângulos tridimensionais, a qual permite a consulta de vértices e triângulos adjacentes em tempo constante e o acesso aleatório aos vértices e triângulos da malha, requerendo pouco espaço em memória principal. A característica out-of-core da representação consiste no fato de que apenas as informações necessárias para a aplicação são carregadas em memória primária, ficando o restante armazenado em memória secundária. A representação é estática no sentido de que, ao ocorrer qualquer alteração topológica, ela deverá ser reconstruída novamente. Experimentos são realizados em vários modelos de malhas de triângulos para demonstrar a eficácia da metodologia propostaAbstract: Triangular meshes are spatial data representations commonly used in the manipulation and visualization of complex surfaces. This work proposes and evaluates a static out-of-core representation of three-dimensional triangle meshes, which allows the query of adjacent vertices and triangles in constant time and the random access to the vertices and triangles of the mesh, requiring little space in main memory. The out-of-core feature of the representation consists in the fact that only the necessary information for the application is loaded into primary memory, such that the remainder is stored in secondary memory. The representation is static in the sense that when any topological change occurs, it must be rebuilt again. Experiments are conducted on several triangle mesh models to demonstrate the efficacy of the proposed methodologyMestradoCiência da ComputaçãoMestre em Ciência da Computaçã