7th International Meshing Roundtable '98

The goal of the 7th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the past, the Roundtable has enjoyed significant participation from each of these groups from a wide variety of countries

Finding Hexahedrizations for Small Quadrangulations of the Sphere

This paper tackles the challenging problem of constrained hexahedral meshing. An algorithm is introduced to build combinatorial hexahedral meshes whose boundary facets exactly match a given quadrangulation of the topological sphere. This algorithm is the first practical solution to the problem. It is able to compute small hexahedral meshes of quadrangulations for which the previously known best solutions could only be built by hand or contained thousands of hexahedra. These challenging quadrangulations include the boundaries of transition templates that are critical for the success of general hexahedral meshing algorithms. The algorithm proposed in this paper is dedicated to building combinatorial hexahedral meshes of small quadrangulations and ignores the geometrical problem. The key idea of the method is to exploit the equivalence between quad flips in the boundary and the insertion of hexahedra glued to this boundary. The tree of all sequences of flipping operations is explored, searching for a path that transforms the input quadrangulation Q into a new quadrangulation for which a hexahedral mesh is known. When a small hexahedral mesh exists, a sequence transforming Q into the boundary of a cube is found; otherwise, a set of pre-computed hexahedral meshes is used. A novel approach to deal with the large number of problem symmetries is proposed. Combined with an efficient backtracking search, it allows small shellable hexahedral meshes to be found for all even quadrangulations with up to 20 quadrangles. All 54,943 such quadrangulations were meshed using no more than 72 hexahedra. This algorithm is also used to find a construction to fill arbitrary domains, thereby proving that any ball-shaped domain bounded by n quadrangles can be meshed with no more than 78 n hexahedra. This very significantly lowers the previous upper bound of 5396 n.Comment: Accepted for SIGGRAPH 201

HexBox: Interactive Box Modeling of Hexahedral Meshes

We introduce HexBox, an intuitive modeling method and interactive tool for creating and editing hexahedral meshes. Hexbox brings the major and widely validated surface modeling paradigm of surface box modeling into the world of hex meshing. The main idea is to allow the user to box-model a volumetric mesh by primarily modifying its surface through a set of topological and geometric operations. We support, in particular, local and global subdivision, various instantiations of extrusion, removal, and cloning of elements, the creation of non-conformal or conformal grids, as well as shape modifications through vertex positioning, including manual editing, automatic smoothing, or, eventually, projection on an externally-provided target surface. At the core of the efficient implementation of the method is the coherent maintenance, at all steps, of two parallel data structures: a hexahedral mesh representing the topology and geometry of the currently modeled shape, and a directed acyclic graph that connects operation nodes to the affected mesh hexahedra. Operations are realized by exploiting recent advancements in grid- based meshing, such as mixing of 3-refinement, 2-refinement, and face-refinement, and using templated topological bridges to enforce on-the-fly mesh conformity across pairs of adjacent elements. A direct manipulation user interface lets users control all operations. The effectiveness of our tool, released as open source to the community, is demonstrated by modeling several complex shapes hard to realize with competing tools and techniques

The All-Hex Geode-Template for Conforming a Diced Tetrahedral Mesh to any Diced Hexahedral Mesh

Take a hexahedral mesh and an adjoining tetrahedral mesh that splits each boundary quadrilateral into two triangles. Separate the meshes with a buffer layer of hexes. Dice the original hexes into eight, and the tetrahedra into four hexahedra. Then I show that the buffer layer hexes can be filled with the geode-template, creating a conforming all-hex mesh of the entire model. The geode-template is composed of 26 hexahedra. The hexahedra have acceptable quality, depending on the geometry of the buffer layer. The method used to generate the geode-template is general, based on interleaving completed dual surfaces, and might be extended to other transition problems

Physically Based Forehead Modelling and Animation including Wrinkles

There has been a vast amount of research on the production of realistic facial models and animations, which is one of the most challenging areas of computer graphics. Recently, there has been an increased interest in the use of physically based approaches for facial animation, whereby the effects of muscle contractions are propagated through facial soft-tissue models to automatically deform them in a more realistic and anatomically accurate manner. Presented in this thesis is a fully physically based approach for efficiently producing realistic-looking animations of facial movement, including animation of expressive wrinkles, focussing on the forehead. This is done by modelling more physics-based behaviour than current computer graphics approaches. The presented research has two major components. The first is a novel model creation process to automatically create animatable non-conforming hexahedral finite element (FE) simulation models of facial soft tissue from any surface mesh that contains hole-free volumes. The generated multi-layered voxel-based models are immediately ready for simulation, with skin layers and element material properties, muscle properties, and boundary conditions being automatically computed. The second major component is an advanced optimised GPU-based process to simulate and visualise these models over time using the total Lagrangian explicit dynamic (TLED) formulation of the FE method. An anatomical muscle contraction model computes active and transversely isotropic passive muscle stresses, while advanced boundary conditions enable the sliding effect between the superficial and deep soft-tissue layers to be simulated. Soft-tissue models and animations with varying complexity are presented, from a simple soft-tissue-block model with uniform layers of skin and muscle, to a complex forehead model. These demonstrate the flexibility of the animation approach to produce detailed animations of realistic gross- and fine-scale soft-tissue movement, including wrinkles, with different muscle structures and material parameters, for example, to animate different-aged skin. Owing to the detail and accuracy of the models and simulations, the animation approach could also be used for applications outside of computer graphics, such as surgical applications. Furthermore, the animation approach can be used to animate any multi-layered soft body (not just soft tissue)

Meshing methods and adaptive algorithms in two and three dimensions for solving closed electromagnetic problems by means of the finite element method

[SPA] La primera parte de esta tesis, desarrollada en los capítulos 1, 2, 3 y 4, está dedicada al diseño de nuevos métodos de mallado bidimensional, superficial y volumétrico que sigan estas premisas. Aunque esos métodos han sido desarrollados en el contexto del análisis de guiado de ondas y el diseño de cavidades resonantes de microondas, su aplicación puede abarcar cualquier campo de la física, pues la fase de discretización del MEF presenta una clara independencia del problema tratado. La segunda parte de esta tesis, presentada en el capítulo 5, está dedicada al estudio de este tipo de métodos. En ella se describen los distintos indicadores de error y estrategias de refinamiento h desarrolladas, y se presentan y analizan los resultados obtenidos con ellos en distintas estructuras de guiado de ondas.[ENG] In its first part, the dissertation develops a multiblock methodology of surface and volumetric mesh generation from the discretization of the problem boundary, in order to apply the finite element method. Different structured and unstructured meshing techniques in 2D (interpolation and generalized fast advancing front), 3D surface and volumetric (advancing front) domains are presented. Moreover, some a posteriori techniques for improvement of quality mesh are described. The second part of this dissertation deals with adaptive meshing within an adaptive finite element method. This technique is an iterative variant of the finite element method where, in a first step, an initial mesh with few and low order elements is generated, the corresponding algebraic problem is solved and the error in the solution is estimated in order to add degrees of freedom in those regions of the domain with the biggest error estimation. This process is repeated until an ending condition is reached. The two basic stages in this method are the error indication and the mesh enrichment. In this dissertation, within the analysis of waveguiding structures, three kinds of error indicator have been developed: (1) Error indicators based on the residual of the vector wave equation and the boundary conditions at the edges of each element. (2) Error indicators based on the comparison of the solution curl with a smoothed or recovered curl, obtained from the solution curl. (3) Error indicators based on the flux (electric or magnetic) continuity through the inner edges in the mesh. In addition, an overview on refinement techniques is presented, and the h-refinement employed in this work is in depth described. Results obtained with the different error indicators and refinement strategies are discussed and compared with the classical, non-adaptive finite element method.Universidad Politécnica de ValenciaPrograma de doctorado de Telecomunicació