Chen, GuoningDeng, Zhigang2021-07-152021-07-15May 20162016-05May 2016Portions of this document appear in: Gao, Xifeng, Zhigang Deng, and Guoning Chen. "Hexahedral mesh re-parameterization from aligned base-complex." ACM Transactions on Graphics (TOG) 34, no. 4 (2015): 1-10. And in: Gao, Xifeng, Jin Huang, Siwang Li, Zhigang Deng, and Guoning Chen. "An evaluation of the quality of hexahedral meshes via modal analysis." In 1st Workshop on Structured Meshing: Theory, Applications, and Evaluation. 2014. And in: Gao, Xifeng, Jin Huang, Kaoji Xu, Zherong Pan, Zhigang Deng, and Guoning Chen. "Evaluating Hex‐mesh Quality Metrics via Correlation Analysis." In Computer Graphics Forum, vol. 36, no. 5, pp. 105-116. 2017. And in: Gao, Xifeng, Tobias Martin, Sai Deng, Elaine Cohen, Zhigang Deng, and Guoning Chen. "Structured volume decomposition via generalized sweeping." IEEE transactions on visualization and computer graphics 22, no. 7 (2015): 1899-1911. And in: Gao, Xifeng, Daniele Panozzo, Wenping Wang, Zhigang Deng, and Guoning Chen. "Robust structure simplification for hex re-meshing." ACM Transactions on Graphics (TOG) 36, no. 6 (2017): 1-13.https://hdl.handle.net/10657/7899Hexahedral meshes are a preferred volumetric representation in a wide range of scientific and engineering applications that require solving partial differential equations (PDEs) and fitting tensor product/trivariate splines, such as mechanical analysis, kinematic and dynamic analysis of mechanisms, bio-mechanical engineering, computational fluid dynamics, and physically-based simulations. Recently, the generation of a high quality all-hex mesh of a given volume has gained much attention, where a hex-mesh should have high surface conformity, regular element shapes, and simple global structure. This dissertation investigates the problem of obtaining a high quality hex-mesh with respect to the above quality requirements and makes the following contributions: Firstly, I introduce a volumetric partitioning strategy based on a generalized sweeping framework to seamlessly partition the volume enclosed by an input triangle mesh into a small number of deformed cube-like components. This is achieved by a user-designed volumetric harmonic function that guides the decomposition of the input volume into a skeletal structure aligning with features of the input object. This pipeline has been applied to a variety of 3D objects to demonstrate its utility. Secondly, I present a first and complete pipeline to reduce the complexity of the global structure of an input hex-mesh by aligning mis-matched singularities. Specifically, I first remove redundant cube-like components to reduce the complexity of the structure while maintaining singularities unchanged, and then perform a structure-aware optimization to improve the geometric fidelity of the resulting hex-mesh. Thirdly, I propose the first practical framework to simplify the global structure of any valid all-hex meshes. My simplification was achieved by procedurally removing base complex sheets and base complex chords that constitute the base complex of a hex-mesh. To maintain the surface geometric features, I introduced a parameterization based collapsing strategy for the removal operations. Given a user-specified level of simplicity, I identified the inversion-free hex-mesh with the optimal simplified structure using a binary search strategy from the obtained all-hex structure hierarchy. Finally, given that there currently does not exist a widely accepted guideline for the selection of proper element quality metrics for hex-meshes, I performed the first comprehensive study on the correlation among available quality metrics for hex-meshes. My analysis first computed the linear correlation coefficients between pairs of metrics. Then, the most relevant metrics were identified for three selected applications -- the linear elasticity, Poisson, and Stoke problems, respectively. To address the need of a large set of sampled meshes well-distributed in the metric space, I proposed a two-level noise insertion strategy. Results of this work can be used as preliminary yet practical guidelines for the development of effective hex-mesh generation and optimization techniques.application/pdfengThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. UH Libraries has secured permission to reproduce any and all previously published materials contained in the work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).Hexahedral Mesh, Base Complex, Global Structure, Simplification, Evaluation2021-07-15Thesisborn digital