Tracing Field-Coherent Quad Layouts

Given a cross field over a triangulated surface we present a practical and robust method to compute a field aligned coarse quad layout over the surface. The method works directly on a triangle mesh without requiring any parametrization and it is based on a new technique for tracing field‐coherent ge...

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Published inComputer graphics forum Vol. 35; no. 7; pp. 485 - 496
Main Authors Pietroni, Nico, Puppo, Enrico, Marcias, Giorgio, Roberto, Roberto, Cignoni, Paolo
Format Journal Article
LanguageEnglish
Published Oxford Blackwell Publishing Ltd 01.10.2016
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ISSN0167-7055
1467-8659
DOI10.1111/cgf.13045

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Abstract Given a cross field over a triangulated surface we present a practical and robust method to compute a field aligned coarse quad layout over the surface. The method works directly on a triangle mesh without requiring any parametrization and it is based on a new technique for tracing field‐coherent geodesic paths directly on a triangle mesh, and on a new relaxed formulation of a binary LP problem, which allows us to extract both conforming quad layouts and coarser layouts containing t‐junctions. Our method is easy to implement, very robust, and, being directly based on the input cross field, it is able to generate better aligned layouts, even with complicated fields containing many singularities. We show results on a number of datasets and comparisons with state‐of‐the‐art methods.
AbstractList Given a cross field over a triangulated surface we present a practical and robust method to compute a field aligned coarse quad layout over the surface. The method works directly on a triangle mesh without requiring any parametrization and it is based on a new technique for tracing field-coherent geodesic paths directly on a triangle mesh, and on a new relaxed formulation of a binary LP problem, which allows us to extract both conforming quad layouts and coarser layouts containing t-junctions. Our method is easy to implement, very robust, and, being directly based on the input cross field, it is able to generate better aligned layouts, even with complicated fields containing many singularities. We show results on a number of datasets and comparisons with state-of-the-art methods.
Author Marcias, Giorgio
Puppo, Enrico
Pietroni, Nico
Roberto, Roberto
Cignoni, Paolo
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  givenname: Paolo
  surname: Cignoni
  fullname: Cignoni, Paolo
  organization: ISTI, CNR, Italy
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Pietroni N., Tonelli D., Puppo E., Froli M., Scopigno R., Cignoni P.: Statics aware grid shells. Comput. Graph. Forum 34, 2 (2015), 627-641. 7, 9
Bommes D., Campen M., Ebke H.-C., Alliez P., Kobbelt L., et al.: Integer-grid maps for reliable quad meshing. ACM Trans. Graph. 32, 4 (2013). 2, 3, 8, 9
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Bommes D., Lempfer T., Kobbelt L.: Global structure optimization of quadrilateral meshes. Comput. Graph. Forum 30, 2 (2011), 375-384. 2
Pietroni N., Tarini M., Sorkine O., Zorin D.: Global parametrization of range image sets. ACM Trans. Graph. (SIGGRAPH Asia 20119 30, 6(2011). 2
Ji Z., Liu L., Wang Y.: B-mesh: A modeling system for base meshes of 3d articulated shapes. Computer Graphics Forum (Proceedings of Pacific Graphics) 29, 7 (2010), 2169-2178. 3
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Surazhsky V., Surazhsky T., Kirsanov D., Gortler S.J., Hoppe H.: Fast exact and approximate geodesics on meshes. ACM Trans. Graph. 24, 3 (2005), 553-560. 2
Zhang S., Zhang H., Yong J.-H.: Automatic quad patch layout extraction for quadrilateral meshes. Computer-Aided Design and Applications 13, 3 (2016), 409-416. 3
Campen M., Heistermann M., Kobbelt L.: Practical anisotropic geodesy. Comput. Graph. Forum 32, 5 (2013), 63-71. 2
Crane K., Weischedel C., Wardetzky M.: Geodesics in heat: A new approach to computing distance based on heat flow. ACM Trans. Graph. 32, 5 (Oct. 2013), 152:1-152:11. 2
Achterberg T.: SCIP: Solving constraint integer programs. Mathematical Programming Computation 1, 1 (2009), 1-41. 6, 7
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Campen M., Kobbelt L.: Dual strip weaving: Interactive design of quad layouts using elastica strips. ACM Trans. Graph. 33, 6 (2014), 183:1-183:10. 3
Bommes D., Zimmer H., Kobbelt L.: Mixed-integer quadrangulation. ACM Trans. Graph. 28, 3 (2009), 77. 2, 9, 12
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References_xml – reference: Daniels II J., Silva C. T., Cohen E.: Semi-regular quadrilateral-only remeshing from simplified base domains. Comput. Graph. Forum 28, 5 (July 2009), 1427-1435. 2
– reference: Bommes D., Lempfer T., Kobbelt L.: Global structure optimization of quadrilateral meshes. Comput. Graph. Forum 30, 2 (2011), 375-384. 2
– reference: Kälberer F., Nieser M., Polthier K.: QuadCover: Surface Parameterization using Branched Coverings. Comput. Graph. Forum 26, 3 (2007), 375-384. 2
– reference: Achterberg T.: SCIP: Solving constraint integer programs. Mathematical Programming Computation 1, 1 (2009), 1-41. 6, 7
– reference: Campen M., Bommes D., Kobbelt L.: Dual loops meshing: quality quad layouts on manifolds. ACM Trans. Graph. 31, 4 (2012), 110. 2, 5
– reference: Myles A., Pietroni N., Zorin D.: Robust field-aligned global parametrization. ACM Trans. Graph. 33, 4 (July 2014), 135:1-135:14. 2, 3, 7, 9, 11
– reference: Zhang S., Zhang H., Yong J.-H.: Automatic quad patch layout extraction for quadrilateral meshes. Computer-Aided Design and Applications 13, 3 (2016), 409-416. 3
– reference: Campen M., Kobbelt L.: Dual strip weaving: Interactive design of quad layouts using elastica strips. ACM Trans. Graph. 33, 6 (2014), 183:1-183:10. 3
– reference: Crane K., Weischedel C., Wardetzky M.: Geodesics in heat: A new approach to computing distance based on heat flow. ACM Trans. Graph. 32, 5 (Oct. 2013), 152:1-152:11. 2
– reference: Ray N., Vallet B., Li W., Lévy B.: N-Symmetry direction field design. ACM Trans. Graph. 27 (2008), 2. 2
– reference: Bommes D., Zimmer H., Kobbelt L.: Mixed-integer quadrangulation. ACM Trans. Graph. 28, 3 (2009), 77. 2, 9, 12
– reference: Takayama K., Panozzo D., Sorkine-Hornung A., Sorkine-Hornung O.: Sketch-based generation and editing of quad meshes. ACM Trans. Graph. 32, 4 (2013), 97:1-97:8. 3
– reference: Pietroni N., Tonelli D., Puppo E., Froli M., Scopigno R., Cignoni P.: Statics aware grid shells. Comput. Graph. Forum 34, 2 (2015), 627-641. 7, 9
– reference: Pietroni N., Tarini M., Sorkine O., Zorin D.: Global parametrization of range image sets. ACM Trans. Graph. (SIGGRAPH Asia 20119 30, 6(2011). 2
– reference: Tarini M., Puppo E., Panozzo D., Pietroni N., Cignoni P.: Simple quad domains for field aligned mesh parametrization. In ACM Trans. Graph. (2011), vol. 30, pp. 142:1-142:12. 1, 2
– reference: Campen M., Heistermann M., Kobbelt L.: Practical anisotropic geodesy. Comput. Graph. Forum 32, 5 (2013), 63-71. 2
– reference: Ji Z., Liu L., Wang Y.: B-mesh: A modeling system for base meshes of 3d articulated shapes. Computer Graphics Forum (Proceedings of Pacific Graphics) 29, 7 (2010), 2169-2178. 3
– reference: Marcias G., Takayama K., Pietroni N., Panozzo D., Sorkine O., Puppo E., Cignoni P.: Data-driven interactive quadrangulation. ACM Trans. Graph. (Siggraph 2015) 34, 65 (2015). 3
– reference: Surazhsky V., Surazhsky T., Kirsanov D., Gortler S.J., Hoppe H.: Fast exact and approximate geodesics on meshes. ACM Trans. Graph. 24, 3 (2005), 553-560. 2
– reference: Myles A., Pietroni N., Kovacs D., Zorin D.: Feature-aligned t-meshes. ACM Trans. Graph. 29, 4 (2010), 117:1-117:11. 2
– reference: Diamanti O., Vaxman A., Panozzo D., Sorkine-Hornung O.: Integrable PolyVector fields. ACM Trans. Graph. 34, 4 (2015). 3
– reference: Lipman Y.: Bounded distortion mapping spaces for triangular meshes. ACM Trans. Graph. 31, 4 (2012), 108. 3
– reference: Campen M., Kobbelt L.: Quad layout embedding via aligned parameterization. Comput. Graph. Forum 33, 8 (Dec. 2014), 69-81. 7
– reference: Mitchell J. S. B., Mount D.M., Papadimitriou C.H.: The discrete geodesic problem. SIAM J. Comput. 16, 4 (Aug. 1987), 647-668. 2
– reference: Campen M., Bommes D., Kobbelt L.: Quantized global parametrization. ACM Trans. Graph. 34, 6 (2015), 192:1-192:12. 2
– reference: Bommes D., Campen M., Ebke H.-C., Alliez P., Kobbelt L., et al.: Integer-grid maps for reliable quad meshing. ACM Trans. Graph. 32, 4 (2013). 2, 3, 8, 9
– reference: Ray N., Sokolov D.: Robust polylines tracing for n-symmetry direction field on triangulated surfaces. ACM Trans. Graph. 33, 3 (June 2014), 30:1-30:11. 2
– volume: 26
  start-page: 375
  issue: 3
  year: 2007
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  article-title: QuadCover: Surface Parameterization using Branched Coverings
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  end-page: 190
– volume: 30
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  article-title: Global structure optimization of quadrilateral meshes
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  article-title: Quantized global parametrization
  publication-title: ACM Trans. Graph.
– start-page: 517
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– volume: 13
  start-page: 409
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  article-title: Automatic quad patch layout extraction for quadrilateral meshes
  publication-title: Computer‐Aided Design and Applications
– volume: 29
  start-page: 2169
  issue: 7
  year: 2010
  end-page: 2178
  article-title: B‐mesh: A modeling system for base meshes of 3d articulated shapes
  publication-title: Computer Graphics Forum (Proceedings of Pacific Graphics)
– volume: 34
  issue: 4
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Snippet Given a cross field over a triangulated surface we present a practical and robust method to compute a field aligned coarse quad layout over the surface. The...
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StartPage 485
SubjectTerms Alignment
Analysis
Categories and Subject Descriptors (according to ACM CCS)
Formulations
Geodesy
I.3.3 [Computer Graphics]: Picture/Image Generation-Line and curve generation
Image processing systems
Layouts
Parametrization
Singularities
State of the art
Studies
Topological manifolds
Triangles
Title Tracing Field-Coherent Quad Layouts
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https://www.proquest.com/docview/1855386452
Volume 35
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