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 in | Computer graphics forum Vol. 35; no. 7; pp. 485 - 496 |
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Main Authors | , , , , |
Format | Journal Article |
Language | English |
Published |
Oxford
Blackwell Publishing Ltd
01.10.2016
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Subjects | |
Online Access | Get full text |
ISSN | 0167-7055 1467-8659 |
DOI | 10.1111/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. |
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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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Copyright | 2016 The Author(s) Computer Graphics Forum © 2016 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. 2016 The Eurographics Association and John Wiley & Sons Ltd. |
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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. 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Graph. – volume: 29 start-page: 117:1 issue: 4 year: 2010 end-page: 117:11 article-title: Feature‐aligned t‐meshes publication-title: ACM Trans. Graph. – volume: 32 start-page: 63 issue: 5 year: 2013 end-page: 71 article-title: Practical anisotropic geodesy publication-title: Comput. Graph. Forum – volume: 24 start-page: 553 issue: 3 year: 2005 end-page: 560 article-title: Fast exact and approximate geodesics on meshes publication-title: ACM Trans. Graph. – volume: 32 start-page: 97:1 issue: 4 year: 2013 end-page: 97:8 article-title: Sketch‐based generation and editing of quad meshes publication-title: ACM Trans. Graph. – volume: 30 issue: 6 year: 2011 article-title: Global parametrization of range image sets publication-title: ACM Trans. Graph. (SIGGRAPH Asia – volume: 33 start-page: 69 issue: 8 year: 2014 end-page: 81 article-title: Quad layout embedding via aligned parameterization publication-title: Comput. Graph. Forum – year: 2014 – volume: 1 start-page: 1 issue: 1 year: 2009 end-page: 41 article-title: SCIP: Solving constraint integer programs publication-title: Mathematical Programming Computation – start-page: 8431 year: 1998 end-page: 8435 – volume: 27 start-page: 2 year: 2008 article-title: N‐Symmetry direction field design publication-title: ACM Trans. Graph. – volume: 28 start-page: 1427 issue: 5 year: 2009 end-page: 1435 article-title: Semi‐regular quadrilateral‐only remeshing from simplified base domains publication-title: Comput. Graph. Forum – volume: 33 start-page: 30:1 issue: 3 year: 2014 end-page: 30:11 article-title: Robust polylines tracing for n‐symmetry direction field on triangulated surfaces publication-title: ACM Trans. Graph. – volume: 32 issue: 4 year: 2013 article-title: Integer‐grid maps for reliable quad meshing publication-title: ACM Trans. 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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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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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