Generation and Optimization of Quadrilateral and Hexahedral Meshes

dc.contributor.advisorChen, Guoning
dc.contributor.committeeMemberDeng, Zhigang
dc.contributor.committeeMemberHaynes, Alan
dc.contributor.committeeMemberWu, Panruo
dc.creatorAkram, Muhammad Naeem
dc.creator.orcid0000-0002-1813-2998 2023
dc.description.abstractStructured quadrilateral (quad) meshes are preferred in many engineering and medical applications due to their desired numerical properties. Despite the extensive research, automatic generation of quad- and hex- meshes with optimal structure remains a challenge. In-lieu-of generating a quad-mesh directly from an arbitrary input, structure simplification can be performed on quad-meshes obtained from triangular meshes. Several techniques utilizing local and global operations for structure simplification have been proposed in this regard. Despite promising results, robustness, scalability, feature preservation and limitations of both local and global simplifications call for a novel and comprehensive framework that addresses the aforementioned limiting factors. In this work, we introduce a few semi-global simplification operations and devise a new framework that utilizes separatrix based operations along with local and global operations for structure simplification of planar and surface quadrilateral meshes. We also employ an automated singularity movement technique to further simplify the mesh structure. In addition, we propose an angle-based mesh optimization algorithm to enhance the quality of simplified meshes. We provide a comprehensive comparison of the results obtained through our simplification framework with existing techniques on a variety of models and demonstrate that our framework is robust and can effectively reduce the mesh singularities to a large extent while preserving the features of quad meshes with complex structures. We also attempt to extend the framework to address the structure simplification of unstructured hexahedral (hex-) meshes that contain more complex scenarios due to the additional dimension. Even though the initial simplification results on some simple hex-meshes are promising, more works need to be done to extend the operations used in quad-meshes simplification for hex-meshes.
dc.description.departmentComputer Science, Department of
dc.format.digitalOriginborn digital
dc.identifier.citationPortions of this document appear in: Xu, K., Akram, M. N., & Chen, G. (2020). Semi-global Quad Mesh Structure Simplification via Separatrix Operations. SA'20: SIGGRAPH Asia 2020 Technical Communications; and in: Akram, M. N., Si, L., & Chen, G. (2021). An Embedded Polygon Strategy for Quality Improvement of 2D Quadrilateral Meshes with Boundaries. In VISIGRAPP (1: GRAPP) (pp. 177-184); and in: Akram, M. N., Xu, K., & Chen, G. (2022). Structure simplification of planar quadrilateral meshes. Computers & Graphics, 109, 1-14.
dc.rightsThe 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).
dc.subjectGeometry Processing, Computational Geometry, Mesh Optimization, Mesh Generation
dc.titleGeneration and Optimization of Quadrilateral and Hexahedral Meshes
dcterms.accessRightsThe full text of this item is not available at this time because the student has placed this item under an embargo for a period of time. The Libraries are not authorized to provide a copy of this work during the embargo period.
local.embargo.terms2025-12-01 of Natural Sciences and Mathematics Science, Department of Science of Houston of Philosophy


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