Coarse Quad Layouts Through Robust Simplification of Cross Field Separatrix Partitions Article Swipe
Ryan Viertel
,
Braxton Osting
,
Matthew L. Staten
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1905.09097
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1905.09097
Streamline-based quad meshing algorithms use smooth cross fields to partition surfaces into quadrilateral regions by tracing cross field separatrices. In practice, re-entrant corners and misalignment of singularities lead to small regions and limit cycles, negating some of the benefits a quad layout can provide in quad meshing. We introduce three novel methods to improve on a pipeline for coarse quad partitioning. First, we formulate an efficient method to compute high-quality cross fields on curved surfaces by extending the diffusion generated method from Viertel and Osting (SISC, 2019). Next, we introduce a method for accurately computing the trajectory of streamlines through singular triangles that prevents tangential crossings. Finally, we introduce a robust method to produce coarse quad layouts by simplifying the partitions obtained via naive separatrix tracing. Our methods are tested on a database of 100 objects and the results are analyzed. The algorithm performs well both in terms of efficiency and visual results on the database when compared to state-of-the-art methods.
Related Topics
Concepts
Separatrix
Quadrilateral
Streamlines, streaklines, and pathlines
Computer science
Partition (number theory)
Algorithm
Tracing
Limit (mathematics)
Gravitational singularity
Computational science
Field (mathematics)
Geometry
Mathematics
Mathematical analysis
Engineering
Physics
Mechanics
Combinatorics
Structural engineering
Plasma
Quantum mechanics
Pure mathematics
Operating system
Finite element method
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://arxiv.org/pdf/1905.09097.pdf
- OA Status
- green
- Cited By
- 4
- References
- 35
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2945739108
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W2945739108Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.1905.09097Digital Object Identifier
- Title
-
Coarse Quad Layouts Through Robust Simplification of Cross Field Separatrix PartitionsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2019Year of publication
- Publication date
-
2019-05-22Full publication date if available
- Authors
-
Ryan Viertel, Braxton Osting, Matthew L. StatenList of authors in order
- Landing page
-
https://arxiv.org/pdf/1905.09097.pdfPublisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/1905.09097.pdfDirect OA link when available
- Concepts
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Separatrix, Quadrilateral, Streamlines, streaklines, and pathlines, Computer science, Partition (number theory), Algorithm, Tracing, Limit (mathematics), Gravitational singularity, Computational science, Field (mathematics), Geometry, Mathematics, Mathematical analysis, Engineering, Physics, Mechanics, Combinatorics, Structural engineering, Plasma, Quantum mechanics, Pure mathematics, Operating system, Finite element methodTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
4Total citation count in OpenAlex
- Citations by year (recent)
-
2023: 1, 2022: 1, 2021: 2Per-year citation counts (last 5 years)
- References (count)
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35Number of works referenced by this work
- Related works (count)
-
20Other works algorithmically related by OpenAlex
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