{"id":{"repo_id":"houston","oai_identifier":"oai:uh-ir.tdl.org:10657/16194"},"canonical_url":"https://search.dev.ndltd.org/etd/houston/oai:uh-ir.tdl.org:10657/16194","repository":{"repo_id":"houston","name":"University of Houston","base_url":"https://uh-ir.tdl.org/server/oai/request"},"display":{"title":"Generation and Optimization of Quadrilateral and Hexahedral Meshes","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Akram, Muhammad Naeem"],"institution":"University of Houston","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":[],"advisors":["Chen, Guoning"],"committee_chairs":[],"committee_members":["Deng, Zhigang","Haynes, Alan","Wu, Panruo"],"year":2023,"date_issued":"2023-12","date_published":"2023-12","updated_at":"2026-07-24T02:32:58Z","subjects":["Geometry Processing, Computational Geometry, Mesh Optimization, Mesh Generation"],"languages":["eng"],"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)."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10657/16194","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Chen, Guoning"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Deng, Zhigang","Haynes, Alan","Wu, Panruo"]},{"key":"dc:creator","label":"Author","values":["Akram, Muhammad Naeem"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-01-26T19:40:58Z"]},{"key":"dc:date.issued","label":"Date","values":["2023-12"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Houston"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Geometry Processing, Computational Geometry, Mesh Optimization, Mesh Generation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["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)."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10657/16194"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Generation and Optimization of Quadrilateral and Hexahedral Meshes"]}]}],"canonical_facts":{"dc:contributor.advisor":["Chen, Guoning"],"dc:contributor.committeemember":["Deng, Zhigang","Haynes, Alan","Wu, Panruo"],"dc:creator":["Akram, Muhammad Naeem"],"dc:date.accessioned":["2024-01-26T19:40:58Z"],"dc:date.issued":["2023-12"],"dc:description.abstract":["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."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/10657/16194"],"dc:language.iso":["eng"],"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)."],"dc:subject":["Geometry Processing, Computational Geometry, Mesh Optimization, Mesh Generation"],"dc:title":["Generation and Optimization of Quadrilateral and Hexahedral Meshes"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["University of Houston"]},"updated_at":"2026-07-24T02:32:58Z"}