Quad Meshing

Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi-regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this State of the Art Report, we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrization, and remeshing

A Multi-Resolution Interactive Previewer for Volumetric Data on Arbitary Meshes

In this paper we describe a rendering method suitable for interactive previewing of large-scale arbitary-mesh volume data sets. A data set to be visualized is represented by a ''point cloud,'' i. e., a set of points and associated data values without known connectivity between the points. The method uses a multi-resolution approach to achieve interactive rendering rates of several frames per second for arbitrarily large data sets. Lower-resolution approximations of an original data set are created by iteratively applying a point- decimation operation to higher-resolution levels. The goal of this method is to provide the user with an interactive navigation and exploration tool to determine good viewpoints and transfer functions to pass on to a high-quality volume renderer that uses a standard algorithm

Optimal Dual Schemes for Adaptive Grid Based Hexmeshing

Hexahedral meshes are an ubiquitous domain for the numerical resolution of partial differential equations. Computing a pure hexahedral mesh from an adaptively refined grid is a prominent approach to automatic hexmeshing, and requires the ability to restore the all hex property around the hanging nodes that arise at the interface between cells having different size. The most advanced tools to accomplish this task are based on mesh dualization. These approaches use topological schemes to regularize the valence of inner vertices and edges, such that dualizing the grid yields a pure hexahedral mesh. In this paper we study in detail the dual approach, and propose four main contributions to it: (i) we enumerate all the possible transitions that dual methods must be able to handle, showing that prior schemes do not natively cover all of them; (ii) we show that schemes are internally asymmetric, therefore not only their implementation is ambiguous, but different implementation choices lead to hexahedral meshes with different singular structure; (iii) we explore the combinatorial space of dual schemes, selecting the minimum set that covers all the possible configurations and also yields the simplest singular structure in the output hexmesh; (iv) we enlarge the class of adaptive grids that can be transformed into pure hexahedral meshes, relaxing one of the tight requirements imposed by previous approaches, and ultimately permitting to obtain much coarser meshes for same geometric accuracy. Last but not least, for the first time we make grid-based hexmeshing truly reproducible, releasing our code and also revealing a conspicuous amount of technical details that were always overlooked in previous literature, creating an entry barrier that was hard to overcome for practitioners in the field

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

Connection between electrical conductivity and diffusion coefficient of a conductive porous material filled with electrolyte

The paper focuses on the cross-property connection between the effective electrical conductivity and the overall mass transfer coefficient of a two phase material. The two properties are expressed in terms of the tortuosity parameter which generalized to the case of a material with two conductive phases. Elimination of this parameter yields the cross-property connection. The theoretical derivation is verified by comparison with computer simulation

HexaLab.net: An online viewer for hexahedral meshes

© 2018 Elsevier Ltd We introduce HexaLab: a WebGL application for real time visualization, exploration and assessment of hexahedral meshes. HexaLab can be used by simply opening www.hexalab.net. Our visualization tool targets both users and scholars. Practitioners who employ hexmeshes for Finite Element Analysis, can readily check mesh quality and assess its usability for simulation. Researchers involved in mesh generation may use HexaLab to perform a detailed analysis of the mesh structure, isolating weak points and testing new solutions to improve on the state of the art and generate high quality images. To this end, we support a wide variety of visualization and volume inspection tools. Our system offers also immediate access to a repository containing all the publicly available meshes produced with the most recent techniques for hexmesh generation. We believe HexaLab, providing a common tool for visualizing, assessing and distributing results, will push forward the recent strive for replicability in our scientific community

At-Most-Hexa Meshes

AbstractVolumetric polyhedral meshes are required in many applications, especially for solving partial differential equations on finite element simulations. Still, their construction bears several additional challenges compared to boundary‐based representations. Tetrahedral meshes and (pure) hex‐meshes are two popular formats in scenarios like CAD applications, offering opposite advantages and disadvantages. Hex‐meshes are more intricate to construct due to the global structure of the meshing, but feature much better regularity, alignment, are more expressive, and offer the same simulation accuracy with fewer elements. Hex‐dominant meshes, where most but not all cell elements have a hexahedral structure, constitute an attractive compromise, potentially unlocking benefits from both structures, but their generality makes their employment in downstream applications difficult. In this work, we introduce a strict subset of general hex‐dominant meshes, which we term 'at‐most‐hexa meshes', in which most cells are still hexahedral, but no cell has more than six boundary faces, and no face has more than four sides. We exemplify the ease of construction of at‐most‐hexa meshes by proposing a frugal and straightforward method to generate high‐quality meshes of this kind, starting directly from hulls or point clouds, for example, from a 3D scan. In contrast to existing methods for (pure) hexahedral meshing, ours does not require an intermediate parameterization of other costly pre‐computations and can start directly from surfaces or samples. We leverage a Lloyd relaxation process to exploit the synergistic effects of aligning an orientation field in a modified 3D Voronoi diagram using the norm for cubical cells. The extracted geometry incorporates regularity as well as feature alignment, following sharp edges and curved boundary surfaces. We introduce specialized operations on the three‐dimensional graph structure to enforce consistency during the relaxation. The resulting algorithm allows for an efficient evaluation with parallel algorithms on GPU hardware and completes even large reconstructions within minutes