All-quad meshing without cleanup

Rushdi, Ahmad A.; Mitchell, Scott A.; Mahmoud, Ahmed H.; Bajaj, Chandrajit C.; Ebeida, Mohamed S.

doi:10.1016/j.cad.2016.07.009

Title: All-quad meshing without cleanup

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Abstract

Here, we present an all-quad meshing algorithm for general domains. We start with a strongly balanced quadtree. In contrast to snapping the quadtree corners onto the geometric domain boundaries, we move them away from the geometry. Then we intersect the moved grid with the geometry. The resulting polygons are converted into quads with midpoint subdivision. Moving away avoids creating any flat angles, either at a quadtree corner or at a geometry–quadtree intersection. We are able to handle two-sided domains, and more complex topologies than prior methods. The algorithm is provably correct and robust in practice. It is cleanup-free, meaning we have angle and edge length bounds without the use of any pillowing, swapping, or smoothing. Thus, our simple algorithm is fast and predictable. This paper has better quality bounds, and the algorithm is demonstrated over more complex domains, than our prior version.

Authors:

^[1]; Mitchell, Scott A. ^[2]; Mahmoud, Ahmed H. ^[3]; Bajaj, Chandrajit C. ^[4]; Ebeida, Mohamed S. ^[2]

Univ. of Texas, Austin, TX (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Univ. of California, Davis, CA (United States)
Univ. of Texas, Austin, TX (United States)

Publication Date:: Mon Aug 22 00:00:00 EDT 2016

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1328744

Alternate Identifier(s):: OSTI ID: 1411843

Report Number(s):: SAND-2016-9891J
Journal ID: ISSN 0010-4485; PII: S001044851630080X; TRN: US1700163

Grant/Contract Number:: AC04-94AL85000

Resource Type:: Accepted Manuscript

Journal Name:: Computer Aided Design

Additional Journal Information:: Journal Name: Computer Aided Design; Journal ID: ISSN 0010-4485

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; all-quadrilateral meshing; guaranteed quality; sharp features

Citation Formats


                    Rushdi, Ahmad A., Mitchell, Scott A., Mahmoud, Ahmed H., Bajaj, Chandrajit C., and Ebeida, Mohamed S. All-quad meshing without cleanup.  United States: N. p., 2016. 
Web.  doi:10.1016/j.cad.2016.07.009.

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                    Rushdi, Ahmad A., Mitchell, Scott A., Mahmoud, Ahmed H., Bajaj, Chandrajit C., & Ebeida, Mohamed S. All-quad meshing without cleanup.  United States.  https://doi.org/10.1016/j.cad.2016.07.009

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                    Rushdi, Ahmad A., Mitchell, Scott A., Mahmoud, Ahmed H., Bajaj, Chandrajit C., and Ebeida, Mohamed S. Mon .  
"All-quad meshing without cleanup".  United States.  https://doi.org/10.1016/j.cad.2016.07.009.  https://www.osti.gov/servlets/purl/1328744.

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@article{osti_1328744,

  title        = {All-quad meshing without cleanup},

  author       = {Rushdi, Ahmad A. and Mitchell, Scott A. and Mahmoud, Ahmed H. and Bajaj, Chandrajit C. and Ebeida, Mohamed S.},

  abstractNote = {Here, we present an all-quad meshing algorithm for general domains. We start with a strongly balanced quadtree. In contrast to snapping the quadtree corners onto the geometric domain boundaries, we move them away from the geometry. Then we intersect the moved grid with the geometry. The resulting polygons are converted into quads with midpoint subdivision. Moving away avoids creating any flat angles, either at a quadtree corner or at a geometry–quadtree intersection. We are able to handle two-sided domains, and more complex topologies than prior methods. The algorithm is provably correct and robust in practice. It is cleanup-free, meaning we have angle and edge length bounds without the use of any pillowing, swapping, or smoothing. Thus, our simple algorithm is fast and predictable. This paper has better quality bounds, and the algorithm is demonstrated over more complex domains, than our prior version.},

  doi          = {10.1016/j.cad.2016.07.009},

  journal      = {Computer Aided Design},

  number       = ,

  volume       = ,

  place        = {United States},

  year         = {Mon Aug 22 00:00:00 EDT 2016},

  month        = {Mon Aug 22 00:00:00 EDT 2016}

}

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