All-Hex Meshing of Multiple-Region Domains without Cleanup

AbstractIn this paper, we present a new algorithm for all-hex meshing of domains with multiple regions without post-processing cleanup. Our method starts with a strongly balanced octree. In contrast to snapping the grid points onto the geometric boundaries, we move points a slight distance away from the common boundaries. Then we intersect the moved grid with the geometry. This allows us to avoid creating any flat angles, and we are able to handle two-sided regions and more complex topologies than prior methods. The algorithm is robust and cleanup-free; without the use of any pillowing, swapping, or smoothing. Thus, our simple algorithm is also more predictable than prior art

Learning topological operations on meshes with application to block decomposition of polygons

We present a learning based framework for mesh quality improvement on unstructured triangular and quadrilateral meshes. Our model learns to improve mesh quality according to a prescribed objective function purely via self-play reinforcement learning with no prior heuristics. The actions performed on the mesh are standard local and global element operations. The goal is to minimize the deviation of the node degrees from their ideal values, which in the case of interior vertices leads to a minimization of irregular nodes.Comment: Submitted to Computer-Aided Design Journal. Presented at 17th US National Conference on Computational Mechanics, Albuquerque, N

ℓ_1-Based Construction of Polycube Maps from Complex Shapes

Polycube maps of triangle meshes have proved useful in a wide range of applications, including texture mapping and hexahedral mesh generation. However, constructing either fully automatically or with limited user control a low-distortion polycube from a detailed surface remains challenging in practice. We propose a variational method for deforming an input triangle mesh into a polycube shape through minimization of the ℓ_1-norm of the mesh normals, regularized via an as-rigid-as-possible volumetric distortion energy. Unlike previous work, our approach makes no assumption on the orientation, or on the presence of features in the input model. User-guided control over the resulting polycube map is also offered to increase design flexibility. We demonstrate the robustness, efficiency, and controllability of our method on a variety of examples, and explore applications in hexahedral remeshing and quadrangulation

Q-Morph - Implementing a Quadrilateral Meshing Algorithm

This thesis treats the implementational and some theoretical aspects of the Q-Morph algorithm for 2D domains. The main application areas are within FE methods. Q-Morph uses an advancing front method for generating unstructured, almost all-quadrilateral meshes containing at most one triangle, and few irregular nodes. The main algorithm is described in (1), while the post-processing methods are covered in (2,3). In addition to an introduction to the Q-Morph algorithm, the thesis also consists of some general background material for FEM meshing, discussions of many issues concerning the implementation, a presentation of important results, and a discussion of possible improvements. To ensure that the implementation conforms to the specifications of the algorithm, it has been tested on a number of different cases. 1) S.J. Owen, M.L. Staten, S.A. Canann, S.Saigal: Advancing Front Quadrilateral Meshing Using Triangle Transformations, 1998 2) P. Kinney: CleanUp: Improving Quadrilateral Finite Element Meshes, 1997 3) S.A. Canann, J.R. Tristano, M.L. Staten: An Approach to Combined Laplacian and Optimization-Based Smoothing for Triangular Quadrilateral and Quad-Dominant Meshes, 199

Rule-based Machine Learning Algorithms for Smart Automatic Quadrilateral Mesh Generation System

Mesh generation, as one of six basic research directions identified in NASA Vision 2030, is an important area in computational geometry and plays a fundamental role in numerical simulations in the area of finite element analysis (FEA) and computational fluid dynamics (CFD). With the rapid progress of high-performance computing hardware, mesh generation methods are required to handle geometric domains with more complex shapes and higher resolution in reliable and fast fashions. Yet, existing mesh generation methods suffer from high computational complexity, low mesh quality in complex geometries, and speed limitations, and have continued to be the bottleneck in those simulation tasks. This thesis addresses the quadrilateral mesh generation problem from three aspects, element extraction, sequential decision making, and data generation, and their combinations. First, a self-learning system, FreeMesh-S, for finite element extraction system is investigated. Element extraction is a major mesh generation method for its capabilities to generate high-quality meshes around the domain boundary and can be formulated into a sequential decision making process. Three kinds of primitive element extraction rules are conceptually identified. FreeMesh-S, then learns the rules by 1) sampling the element generation rules by a reinforcement learning (RL) algorithm, 2) extracting high quality samples, and 3) training the final rules by a feedforward neural network (FNN). The comprehensive experiments demonstrate the effectiveness of the self-learned meshing rules by FreeMesh-S. Second, an RL-based computational framework for automatic mesh generation is proposed to improve algorithm automation further. A state-of-the-art RL algorithm, soft actor-critic (SAC), is used to learn the mesh generator's policy from trials. It achieves a fully automatic mesh generation without human intervention and any extra clean-up operations, which are typically needed in current commercial software. The reward function is carefully designed to balance the contradiction between the instant element quality and the remaining boundary quality, in order to achieve an overall high quality mesh. The experiments have shown the competitive performance with two representative meshing methods with respect to generalizability, robustness, and effectiveness. The potentials of mesh generation as a benchmark problem for RL are also identified. Last, a quality function-based data generation method for the meshing algorithm is devised to increase learning efficiency and algorithm performance. For any data-driven algorithms, high quality and balanced data are essential and deterministic to the performance. This method samples the input-output of the three rules according to their feature spaces; selects high quality samples by a quality function that evaluates if the output is an appropriate solution to the input; and trains an FNN model to simulate the mapping relation via the obtained data. The experiments show that the learning time is greatly reduced while the model has competitive performance comparing with other meshing methods. To conclude, this thesis combines artificial intelligence techniques, rule-based system, neural networks, and RL, to automate the quadrilateral mesh generation while significantly reducing the time and expertise needed during the creation of high quality mesh generation algorithm. All the techniques can be directly generalized to 3D mesh generation

Practical quad mesh simplification

In this paper we present an innovative approach to incremental quad mesh simplification, i.e. the task of producing a low complexity quad mesh starting from a high complexity one. The process is based on a novel set of strictly local operations which preserve quad structure. We show how good tessellation quality (e.g. in terms of vertex valencies) can be achieved by pursuing uniform length and canonical proportions of edges and diagonals. The decimation process is interleaved with smoothing in tangent space. The latter strongly contributes to identify a suitable sequence of local modification operations. The method is naturally extended to manage preservation of feature lines (e.g. creases) and varying (e.g. adaptive) tessellation densities. We also present an original Triangle-to-Quad conversion algorithm that behaves well in terms of geometrical complexity and tessellation quality, which we use to obtain the initial quad mesh from a given triangle mesh

Practical quad mesh simplification

In this paper we present an innovative approach to incremental quad mesh simplification, i.e. the task of producing a low complexity quad mesh starting from a high complexity one. The process is based on a novel set of strictly local operations which preserve quad structure. We show how good tessellation quality (e.g. in terms of vertex valencies) can be achieved by pursuing uniform length and canonical proportions of edges and diagonals. The decimation process is interleaved with smoothing in tangent space. The latter strongly contributes to identify a suitable sequence of local modification operations. The method is naturally extended to manage preservation of feature lines (e.g. creases) and varying (e.g. adaptive) tessellation densities. We also present an original Triangle-to-Quad conversion algorithm that behaves well in terms of geometrical complexity and tessellation quality, which we use to obtain the initial quad mesh from a given triangle mesh

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