Flipping Cubical Meshes: A Study on Quadrilateral and Hexagonal Mesh Generation and Improvement

Title: Flipping Cubical Meshes: A Study on Quadrilateral and Hexagonal Mesh Generation and Improvement

Abstract: This research explores the concept of flipping transformations for cubical meshes, such as quadrilateral and hexahedral meshes. These transformations are precise analogues of the well-known flipping transformations for simplicial meshes. The study aims to understand the applicability of these transformations in mesh generation, improvement, and refinement/derefinement. Additionally, the research examines the existence of hexahedral meshes using flipping operations.

Main Research Question: Can flipping operations be used to generate and improve cubical meshes, specifically quadrilateral and hexahedral meshes?

Methodology: The study uses mathematical and computational techniques to analyze the properties of cubical meshes. It proposes flipping transformations for quad and hex meshes and studies their implications on mesh generation and improvement. The research also uses flipping operations to study the existence of hexahedral meshes.

Results: The study finds that flipping transformations can be used to generate and improve cubical meshes. It also identifies certain conditions under which these transformations can be applied. Furthermore, the research provides insights into the existence of hexahedral meshes using flipping operations.

Implications: The findings of this research have significant implications for the field of mesh generation and improvement. The use of flipping transformations can lead to more efficient and accurate mesh generation processes. Additionally, the study provides a better understanding of the existence of hexahedral meshes, which can be useful in various applications, such as finite element analysis and computer graphics.

Link to Article: https://arxiv.org/abs/0108020v3 Authors: arXiv ID: 0108020v3