“FlowRep: descriptive curve networks for free-form design shapes” by Gori, Sheffer, Carr, Ju, Vining, et al. …

  • ©Giorgio Gori, Alla Sheffer, Nathan Carr, Tao Ju, Nicholas Vining, and Enrique Rosales




    FlowRep: descriptive curve networks for free-form design shapes

Session/Category Title: Being Discrete About Geometry Processing




    We present FlowRep, an algorithm for extracting descriptive compact 3D curve networks from meshes of free-form man-made shapes. We infer the desired compact curve network from complex 3D geometries by using a series of insights derived from perception, computer graphics, and design literature. These sources suggest that visually descriptive networks are cycle-descriptive, i.e their cycles unambiguously describe the geometry of the surface patches they surround. They also indicate that such networks are designed to be projectable, or easy to envision when observed from a static general viewpoint; in other words, 2D projections of the network should be strongly indicative of its 3D geometry. Research suggests that both properties are best achieved by using networks dominated by flowlines, surface curves aligned with principal curvature directions across anisotropic regions and strategically extended across sharp-features and isotropic areas. Our algorithm leverages these observation in the construction of a compact descriptive curve network. Starting with a curvature aligned quad dominant mesh we first extract sequences of mesh edges that form long, well-shaped and reliable flowlines by leveraging directional similarity between nearby meaningful flowline directions We then use a compact subset of the extracted flowlines and the model’s sharp-feature, or trim, curves to form a sparse, projectable network which describes the underlying surface. We validate our method by demonstrating a range of networks computed from diverse inputs, using them for surface reconstruction, and showing extensive comparisons with prior work and artist generated networks.


    1. Pierre Alliez, David Cohen-Steiner, Olivier Devillers, Bruno Lévy, and Mathieu Desbrun. 2003. Anisotropic Polygonal Remeshing. ACM Trans. Graph. 22, 3 (2003), 485–493. Google ScholarDigital Library
    2. Nikhil Bansal, Avrim Blum, and Shuchi Chawla. 2004. Correlation Clustering. Mach. Learn. 56, 1–3 (2004), 89–113.Google ScholarDigital Library
    3. Mikhail Bessmeltsev, Caoyu Wang, Alla Sheffer, and Karan Singh. 2012. Design-driven Quadrangulation of Closed 3D Curves. ACM Trans. Graph. 31, 6, Article 178 (2012), 178:1–178:11 pages.Google ScholarDigital Library
    4. Roseline Bnire, Grard Subsol, Gilles Gesquire, Franois Le Breton, and William Puech. 2013. A comprehensive process of reverse engineering from 3D meshes to CAD models. Computer-Aided Design 45, 11 (2013), 1382 — 1393. Google ScholarDigital Library
    5. David Bommes, Marcel Campen, Hans-Christian Ebke, Pierre Alliez, and Leif Kobbelt. 2013. Integer-grid Maps for Reliable Quad Meshing. ACM Trans. Graph. 32, 4, Article 98 (2013), 98:1–98:12 pages.Google ScholarDigital Library
    6. David Bommes, Timm Lempfer, and Leif Kobbelt. 2011. Global Structure Optimization of Quadrilateral Meshes. Computer Graphics Forum 30, 2 (2011), 375–384. Google ScholarCross Ref
    7. David Bommes, Tobias Vossemer, and Leif Kobbelt. 2008. Quadrangular Parameterization for Reverse Engineering. (Lecture Notes in Computer Science), Vol. 5862. Springer, 55–69.Google Scholar
    8. Monica Bordegoni and Caterina Rizzi. 2011. Innovation in product design. Springer. Google ScholarCross Ref
    9. Marcel Campen, David Bommes, and Leif Kobbelt. 2012. Dual Loops Meshing: Quality Quad Layouts on Manifolds. ACM Trans. Graph. 31, 4, Article 110 (2012), 110:1–110:11 pages.Google ScholarDigital Library
    10. Marcel Campen, Moritz Ibing, Hans-Christian Ebke, Denis Zorin, and Leif Kobbelt. 2016. Scale-Invariant Directional Alignment of Surface Parametrizations. Computer Graphics Forum (2016).Google Scholar
    11. Marcel Campen and Leif Kobbelt. 2014. Dual Strip Weaving: Interactive Design of Quad Layouts Using Elastica Strips. ACM Trans. Graph. 33, 6 (2014). Google ScholarDigital Library
    12. Paolo Cignoni, Nico Pietroni, Luigi Malomo, and Roberto Scopigno. 2014. Field-aligned Mesh Joinery. ACM Trans. Graph. 33, 1, Article 11 (2014), 11:1–11:12 pages.Google ScholarDigital Library
    13. P. Cignoni, C. Rocchini, and R. Scopigno. 1998. Metro: Measuring Error on Simplified Surfaces. Computer Graphics Forum (1998).Google Scholar
    14. David Cohen-Steiner, Pierre Alliez, and Mathieu Desbrun. 2004. Variational Shape Approximation. ACM Trans. Graph. 23, 3 (2004), 905–914. Google ScholarDigital Library
    15. Forrester Cole, Aleksey Golovinskiy, Alex Limpaecher, Heather Stoddart Barros, Adam Finkelstein, Thomas Funkhouser, and Szymon Rusinkiewicz. 2008. Where Do People Draw Lines? ACM Trans. Graph. 27, 3 (2008). Google ScholarDigital Library
    16. Fernando De Goes, Siome Goldenstein, Mathieu Desbrun, and Luiz Velho. 2011. Exo-skeleton: Curve Network Abstraction for 3D Shapes. Comput. Graph. 35, 1 (2011), 112–121. Google ScholarDigital Library
    17. Doug DeCarlo, Adam Finkelstein, Szymon Rusinkiewicz, and Anthony Santella. 2003. Suggestive Contours for Conveying Shape. ACM Trans. Graph. 22, 3 (2003), 848–855. Google ScholarDigital Library
    18. Koos Eissen and Roselien Steur. 2008. Sketching: Drawing Techniques for Product Designers. Bis Publishers.Google Scholar
    19. Koos Eissen and Roselien Steur. 2011. Sketching: The Basics. Bis Publishers.Google Scholar
    20. David Eppstein, Michael T. Goodrich, Ethan Kim, and Rasmus Tamstorf. 2008. Motorcycle Graphs: Canonical Quad Mesh Partitioning. In Proceedings of the Symposium on Geometry Processing. 1477–1486. Google ScholarCross Ref
    21. Ran Gal, Olga Sorkine, Niloy J. Mitra, and Daniel Cohen-Or. 2009. iWIRES: An Analyze-and-Edit Approach to Shape Manipulation. ACM Trans. Graph. 28, 3 (2009), #33, 1–10.Google ScholarDigital Library
    22. Anne Gehre, Isaak Lim, and Leif Kobbelt. 2016. Adapting Feature Curve Networks to a Prescribed Scale. Computer Graphics Forum (2016).Google Scholar
    23. Erkan Gunpinar, Masaki Moriguchi, Hiromasa Suzuki, and Yutaka Ohtake. 2014a. Feature-aware Partitions from the Motorcycle Graph. Comput. Aided Des. 47 (2014), 85–95. Google ScholarDigital Library
    24. Erkan Gunpinar, Masaki Moriguchi, Hiromasa Suzuki, and Yutaka Ohtake. 2014b. Motorcycle Graph Enumeration from Quadrilateral Meshes for Reverse Engineering. Comput. Aided Des. 55 (2014), 64–80. Google ScholarDigital Library
    25. Klaus Hildebrandt, Konrad Polthier, and Max Wardetzky. 2005. Smooth Feature Lines on Surface Meshes. In Proc. SGP 2005 (SGP ’05). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, Article 85.Google Scholar
    26. Emmanuel Iarussi, David Bommes, and Adrien Bousseau. 2015. BendFields: Regularized Curvature Fields from Rough Concept Sketches. ACM Trans. Graph. (2015).Google Scholar
    27. Wenzel Jakob, Marco Tarini, Daniele Panozzo, and Olga Sorkine-Hornung. 2015. Instant Field-Aligned Meshes. ACM Trans. Graph 34, 6 (2015). Google ScholarDigital Library
    28. Dan Julius, Vladislav Kraevoy, and Alla Sheffer. 2005. D-Charts: Quasi-Developable Mesh Segmentation. Computer Graphics Forum (2005).Google Scholar
    29. Margret Keuper, Evgeny Levinkov, Nicolas Bonneel, Guillaume Lavoué, Thomas Brox, and Bjoern Andres. 2015. Efficient Decomposition of Image and Mesh Graphs by Lifted Multicuts. In Proc. ICCV. Google ScholarDigital Library
    30. Yu-Kun Lai, Qian-Yi Zhou, Shi-Min Hu, Johannes Wallner, and Helmut Pottmann. 2007. Robust Feature Classification and Editing. IEEE Trans. Vis. Comp. Graphics 13, 1 (2007), 34–45. Google ScholarDigital Library
    31. James McCrae, Karan Singh, and Niloy J. Mitra. 2011. Slices: A Shape-proxy Based on Planar Sections. ACM Trans. Graph. 30, 6 (2011). Google ScholarDigital Library
    32. Ravish Mehra, Qingnan Zhou, Jeremy Long, Alla Sheffer, Amy Gooch, and Niloy J. Mitra. 2009. Abstraction of Man-Made Shapes. ACM Trans. Graph. 28, 5 (2009). Google ScholarDigital Library
    33. Ashish Myles, Nico Pietroni, and Denis Zorin. 2014. Robust Field-aligned Global Parametrization. ACM Trans. Graph. 33, 4, Article 135 (2014), 135:1–135:14 pages.Google ScholarDigital Library
    34. Mathias Nieser, Christian Schulz, and Konrad Polthier. 2010. Patch Layout from Feature Graphs. Comput. Aided Design 42, 3 (2010). Google ScholarDigital Library
    35. Hao Pan, Yang Liu, Alla Sheffer, Nicholas Vining, Changjian Li, and Wenping Wang. 2015. Flow Aligned Surfacing of Curve Networks. ACM Trans. Graph. 34, 4 (2015). Google ScholarDigital Library
    36. Nicolas Ray and Dmitry Sokolov. 2014. Robust Polylines Tracing for N-Symmetry Direction Field on Triangulated Surfaces. ACM Trans. Graph. 33, 3, Article 30 (2014), 30:1–30:11 pages.Google ScholarDigital Library
    37. Faniry H. Razaflndrazaka, Ulrich Reitebuch, and Konrad Polthier. 2015. Perfect Matching Quad Layouts for Manifold Meshes. In Proceedings of the Eurographics Symposium on Geometry Processing. 219–228.Google Scholar
    38. Cloud Shao, Adrien Bousseau, Alla Sheffer, and Karan Singh. 2012. CrossShade: shading concept sketches using cross-section curves. ACM Trans. Graph. 31, 4 (2012). Google ScholarDigital Library
    39. Kent A. Stevens. 1981. The visual interpretation of surface contours. Artificial Intelligence 17 (1981). Issue 1–3.Google Scholar
    40. Vitaly Surazhsky and Craig Gotsman. 2004. High quality compatible triangulations. Eng. Comput. (Lond.) 20, 2 (2004), 147–156.Google ScholarDigital Library
    41. Marco Tarini, Enrico Puppo, Daniele Panozzo, Nico Pietroni, and Paolo Cignoni. 2011. Simple Quad Domains for Field Aligned Mesh Parametrization. ACM Trans. Graph. 30, 6, Article 142 (2011), 12 pages.Google ScholarDigital Library
    42. J Todd and F. Reeichel. 1990. Visual perception of smoothly curved surfaces from double-projected contour patterns. J. of Exp. Psych.: Human Percep. and Performance 16 (1990), 665–674. Google ScholarCross Ref
    43. Jianhua Wu and Leif Kobbelt. 2005. Structure Recovery via Hybrid Variational Surface Approximation. Computer Graphics Forum 24, 3 (2005), 277–284. Google ScholarCross Ref
    44. Baoxuan Xu, William Chang, Alla Sheffer, Adrien Bousseau, James Mccrae, and Karan Singh. 2014. True2Form: 3D Curve Networks from 2D Sketches via Selective Regularization. ACM Trans. Graph. 33, 4 (2014). Google ScholarDigital Library
    45. Shin Yoshizawa, Alexander Belyaev, and Hans-Peter Seidel. 2005. Fast and Robust Detection of Crest Lines on Meshes. In Proc. Symp. on Solid and Physical Modeling (SPM ’05). 227–232. Google ScholarDigital Library
    46. Yixin Zhuang, Ming Zou, Nathan Carr, and Tao Ju. 2014. Anisotropic Geodesics for Live-wire Mesh Segmentation. Computer Graphics Forum (2014).Google Scholar

ACM Digital Library Publication:

Overview Page: