Generation and Optimization of Quadrilateral and Hexahedral Meshes

Structured 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.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Houston

Year dc:date.issued

2023

Author dc:creator

• Akram, Muhammad Naeem

Advisor dc:contributor.advisor

• Chen, Guoning

Committee members dc:contributor.committeemember

• Deng, Zhigang
• Haynes, Alan
• Wu, Panruo

• Geometry Processing, Computational Geometry, Mesh Optimization, Mesh Generation

Statement dc:rights

• The 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).

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/10657/16194

OAI identifier oai:identifier

oai:uh-ir.tdl.org:10657/16194