HEXHOOP: Modular Templates for Converting a Hex-Dominant Mesh to an ALL-Hex Mesh

Abstract

This paper presents a new mesh conversion template, called HEXHOOP, that fully automates a conversion from a hex-dominant mesh to an all-hex mesh. A HEXHOOP template subdivides a hex/prism/pyramid element to a set of smaller hex elements while maintaining the topological conformity with neighboring elements. A HEXHOOP template is constructed by assembling subtemplates, cores and caps. A dicing template for a hex and a prism is constructed by choosing the appropriate combination of a core and caps. A template that dices a pyramid without losing conformity to the adjacent element is derived from a HEXHOOP template. Some experimental results show that the HEXHOOP templates successfully convert a hex-dominant mesh to an all-hex mesh.

Prognostic significance of the number of lymph nodes examined in patients with lymph node-negative breast carcinoma

“…The solution should fill the pyramid with as few elements as possible, and as good‐quality elements as possible. The only known solution to the problem consists of 118 elements 2. This paper presents a new solution to the problem that consists of 88 elements.…”

“…For such an analysis, a grid‐based method may create an acceptable‐quality all‐hex mesh 5–9. However, despite numerous research attempts, none of the known methods can create an all‐hex mesh of adequate quality for an arbitrary geometric domain 2, 10–16.…”

Fully‐automated hex‐dominant mesh generation with directionality control via packing rectangular solid cells

“…Section 10 also shows some results of ÿnite element analyses, which indicate that a hex-dominant mesh outperforms a tetrahedral mesh. A method that converts a hex-dominant mesh to an all-hex mesh is also available [6], and the conversion method requires a high quality hex-dominant mesh to create a high quality all-hex mesh. Therefore, it is important to develop a high quality hex-dominant meshing technique.…”

Construction Techniques for Cubical Complexes, Odd Cubical 4-Polytopes, and Prescribed Dual Manifolds

“…In the polytopal category there is a construction in dimension 3 called the Hexhoop template due to Yamakawa & Shimada [35], which is depicted in following figure.…”

“…We are indebted to Arnold Waßmer for proposing the lifted prism construction, Kolya Mnëv for help on PL-topology questions, and Matthias Müller-Hannemann for bringing the Hexhoop template [35] to our attention. We thank Mark de Longueville for careful reading earlier versions of the paper and for stimulating discussions.…”