Singularities in structured meshes and cross-fields

Harold J. Fogg; Liang Sun; Jonathan E. Makem; Cecil G. Armstrong; Trevor T. Robinson

doi:10.1016/j.cad.2018.06.002

Singularities in structured meshes and cross-fields

Harold J. Fogg
, Liang Sun
, Jonathan E. Makem
, Cecil G. Armstrong
, Trevor T. Robinson

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

228 Downloads (Pure)

Abstract

Singularities in structured meshes are vertices that have an irregular valency.The integer irregularity in valency is called the singularity index of the vertex of the mesh. Singularities in cross-fields are closely related which are isolated points where the cross-field vectors are defined in its limit neighbourhood but not at the point itself. For a closed surface the genus determines the minimum number of singularities that are required in a structured mesh or in a cross-field on the surface. Adding boundaries and forcing conformity of the mesh or alignment of the cross-field to them also affects the minimum number of singularities required. In this paper a simple formula is derived from Bunin's Continuum Theory for Unstructured Mesh Generation (Bunin, 2008) that specifies the net sum of singularity indices that must occur in a cross-field with even numbers of vectors on a face or surface region with alignment conditions. The formula also applies to mesh singularities in quadrilateral and triangle meshes and the correspondence to 3-D hexahedral meshes is related. Some potential applications are discussed.

Original language	English
Pages (from-to)	11-25
Number of pages	15
Journal	CAD Computer Aided Design
Volume	105
Early online date	5 Jul 2018
DOIs	https://doi.org/10.1016/j.cad.2018.06.002
Publication status	Published (in print/issue) - 1 Dec 2018

Funding

The authors from the Meshing and Abstraction Group, Simcenter, Siemens PLM would like to thank their manager Mary Otte for her support and encouragement in doing this work. The authors from Queen’s University Belfast would like to acknowledge the financial support provided by Innovate UK , a UK Centre for Aerodynamics project, via GHandI project ( TSB 101372 ). The QUB authors also acknowledge Rolls-Royce for granting permission to publish this paper.

Keywords

Cross-field
Singularities
Structured mesh

Access to Document

10.1016/j.cad.2018.06.002

L Sun Computer-Aided DesignAuthor Accepted Manuscript, 12.2 MB

Cite this

@article{b045154b56834c8098c860dc84f4d9b3,

title = "Singularities in structured meshes and cross-fields",

abstract = "Singularities in structured meshes are vertices that have an irregular valency.The integer irregularity in valency is called the singularity index of the vertex of the mesh. Singularities in cross-fields are closely related which are isolated points where the cross-field vectors are defined in its limit neighbourhood but not at the point itself. For a closed surface the genus determines the minimum number of singularities that are required in a structured mesh or in a cross-field on the surface. Adding boundaries and forcing conformity of the mesh or alignment of the cross-field to them also affects the minimum number of singularities required. In this paper a simple formula is derived from Bunin's Continuum Theory for Unstructured Mesh Generation (Bunin, 2008) that specifies the net sum of singularity indices that must occur in a cross-field with even numbers of vectors on a face or surface region with alignment conditions. The formula also applies to mesh singularities in quadrilateral and triangle meshes and the correspondence to 3-D hexahedral meshes is related. Some potential applications are discussed.",

keywords = "Cross-field, Singularities, Structured mesh",

author = "Fogg, \{Harold J.\} and Liang Sun and Makem, \{Jonathan E.\} and Armstrong, \{Cecil G.\} and Robinson, \{Trevor T.\}",

year = "2018",

month = dec,

day = "1",

doi = "10.1016/j.cad.2018.06.002",

language = "English",

volume = "105",

pages = "11--25",

journal = "CAD Computer Aided Design",

issn = "0010-4485",

publisher = "Elsevier Ltd",

}

TY - JOUR

T1 - Singularities in structured meshes and cross-fields

AU - Fogg, Harold J.

AU - Sun, Liang

AU - Makem, Jonathan E.

AU - Armstrong, Cecil G.

AU - Robinson, Trevor T.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - Singularities in structured meshes are vertices that have an irregular valency.The integer irregularity in valency is called the singularity index of the vertex of the mesh. Singularities in cross-fields are closely related which are isolated points where the cross-field vectors are defined in its limit neighbourhood but not at the point itself. For a closed surface the genus determines the minimum number of singularities that are required in a structured mesh or in a cross-field on the surface. Adding boundaries and forcing conformity of the mesh or alignment of the cross-field to them also affects the minimum number of singularities required. In this paper a simple formula is derived from Bunin's Continuum Theory for Unstructured Mesh Generation (Bunin, 2008) that specifies the net sum of singularity indices that must occur in a cross-field with even numbers of vectors on a face or surface region with alignment conditions. The formula also applies to mesh singularities in quadrilateral and triangle meshes and the correspondence to 3-D hexahedral meshes is related. Some potential applications are discussed.

AB - Singularities in structured meshes are vertices that have an irregular valency.The integer irregularity in valency is called the singularity index of the vertex of the mesh. Singularities in cross-fields are closely related which are isolated points where the cross-field vectors are defined in its limit neighbourhood but not at the point itself. For a closed surface the genus determines the minimum number of singularities that are required in a structured mesh or in a cross-field on the surface. Adding boundaries and forcing conformity of the mesh or alignment of the cross-field to them also affects the minimum number of singularities required. In this paper a simple formula is derived from Bunin's Continuum Theory for Unstructured Mesh Generation (Bunin, 2008) that specifies the net sum of singularity indices that must occur in a cross-field with even numbers of vectors on a face or surface region with alignment conditions. The formula also applies to mesh singularities in quadrilateral and triangle meshes and the correspondence to 3-D hexahedral meshes is related. Some potential applications are discussed.

KW - Cross-field

KW - Singularities

KW - Structured mesh

UR - http://www.scopus.com/inward/record.url?scp=85049790936&partnerID=8YFLogxK

UR - https://pure.ulster.ac.uk/en/publications/singularities-in-structured-meshes-and-cross-fields

U2 - 10.1016/j.cad.2018.06.002

DO - 10.1016/j.cad.2018.06.002

M3 - Article

AN - SCOPUS:85049790936

SN - 0010-4485

VL - 105

SP - 11

EP - 25

JO - CAD Computer Aided Design

JF - CAD Computer Aided Design

ER -

Singularities in structured meshes and cross-fields

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this