“Designing patterns using triangle-quad hybrid meshes” by Peng, Pottmann and Wonka

  • ©Chi-Han Peng, Helmut Pottmann, and Peter Wonka

Conference:


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Entry Number: 107

Title:

    Designing patterns using triangle-quad hybrid meshes

Session/Category Title:   Flattening, Unflattening and Sampling

Presenter(s)/Author(s):


Moderator(s):


Abstract:


    We present a framework to generate mesh patterns that consist of a hybrid of both triangles and quads. Given a 3D surface, the generated patterns fit the surface boundaries and curvatures. Such regular and near regular triangle-quad hybrid meshes provide two key advantages: first, novel-looking polygonal patterns achieved by mixing different arrangements of triangles and quads together; second, a finer discretization of angle deficits than utilizing triangles or quads alone. Users have controls over the generated patterns in global and local levels. We demonstrate applications of our approach in architectural geometry and pattern design on surfaces.

References:


    1. Sameer Agarwal, Keir Mierle, and Others. 2016. Ceres Solver, http://ceres-solver.org. (2016).Google Scholar
    2. Abdalla G. M. Ahmed, Helene Perrier, David Coeurjolly, Victor Ostromoukhov, Jianwei Guo, Dong-Ming Yan, Hui Huang, and Oliver Deussen. 2016. Low-discrepancy Blue Noise Sampling. ACM Trans. Graph. 35, 6, Article 247 (Nov. 2016), 13 pages. Google ScholarDigital Library
    3. Pierre Alliez, Éric Colin de Verdière, Olivier Devillers, and Martin Isenburg. 2005. Centroidal Voronoi Diagrams for Isotropic Surface Remeshing. Graph. Models 67, 3 (May 2005), 204–231. Google ScholarDigital Library
    4. David Bommes, Bruno Lévy, Nico Pietroni, Enrico Puppo, Claudio Silva, Marco Tarini, and Denis Zorin. 2013. Quad-Mesh Generation and Processing: A Survey. Comput. Graph. Forum 32, 6 (Sept. 2013), 51–76. Google ScholarDigital Library
    5. Mario Botsch, Leif Kobbelt, Mark Pauly, Pierre Alliez, and Bruno Levy. 2010. Polygon Mesh Processing. A K Peters/CRC Press.Google Scholar
    6. Weikai Chen, Yuexin Ma, Sylvain Lefebvre, Shiqing Xin, Jonas Martínez, and Wenping Wang. 2017. Fabricable Tile Decors. ACM Trans. Graph. 36, 6, Article 175 (Nov. 2017), 15 pages. Google ScholarDigital Library
    7. Michael F. Cohen, Jonathan Shade, Stefan Hiller, and Oliver Deussen. 2003. Wang Tiles for Image and Texture Generation. ACM Trans. Graph. 22, 3 (July 2003), 287–294. Google ScholarDigital Library
    8. David Cohen-Steiner, Pierre Alliez, and Mathieu Desbrun. 2004. Variational Shape Approximation. ACM Trans. Graph. 23, 3 (Aug. 2004), 905–914. Google ScholarDigital Library
    9. Branko Grunbaum and Geoffrey Colin Shephard. 2016. Tilings and Patterns: Second Edition. Dover Publications.Google Scholar
    10. Gurobi. 2016. Gurobi Optimizer Reference Manual. (2016). http://www.gurobi.comGoogle Scholar
    11. Alejo Hausner. 2001. Simulating Decorative Mosaics. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’01). 573–580. Google ScholarDigital Library
    12. Joachim Hermisson, Christoph Richard, and Michael Baake. 2002. A Guide to the Symmetry Structure of Quasiperiodic Tiling Classes. 7 (05 2002).Google Scholar
    13. Wenchao Hu, Zhonggui Chen, Hao Pan, Yizhou Yu, Eitan Grinspun, and Wenping Wang. 2016. Surface Mosaic Synthesis with Irregular Tiles. IEEE Transactions on Visualization and Computer Graphics 22, 3 (March 2016), 1302–1313. Google ScholarDigital Library
    14. Alec Jacobson, Daniele Panozzo, et al. 2016. libigl: A simple C++ geometry processing library. (2016). http://libigl.github.io/libigl/.Google Scholar
    15. Caigui Jiang, Chengcheng Tang, Amir Vaxman, Peter Wonka, and Helmut Pottmann. 2015. Polyhedral Patterns. ACM Trans. Graph. 34, 6, Article 172 (Oct. 2015), 12 pages. Google ScholarDigital Library
    16. Craig S. Kaplan and David H. Salesin. 2000. Escherization. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’00). 499–510. Google ScholarDigital Library
    17. Craig S. Kaplan and David H. Salesin. 2004. Dihedral Escherization. In Proceedings of Graphics Interface 2004 (GI ’04). 255–262. Google ScholarDigital Library
    18. Junhwan Kim and Fabio Pellacini. 2002. Jigsaw Image Mosaics. ACM Trans. Graph. 21, 3 (July 2002), 657–664. Google ScholarDigital Library
    19. Johannes Kopf, Daniel Cohen-Or, Oliver Deussen, and Dani Lischinski. 2006. Recursive Wang Tiles for Real-time Blue Noise. ACM Trans. Graph. 25, 3 (July 2006), 509–518. Google ScholarDigital Library
    20. Bruno Lévy, Sylvain Petitjean, Nicolas Ray, and Jérome Maillot. 2002. Least Squares Conformal Maps for Automatic Texture Atlas Generation. ACM Trans. Graph. 21, 3 (July 2002), 362–371. Google ScholarDigital Library
    21. Yufei Li, Yang Liu, and Wenping Wang. 2015. Planar Hexagonal Meshing for Architecture. 21 (09 2015), 95–106.Google Scholar
    22. Alain Lobel. 2004. Lobel Frames: Forms and structures generated by identical elements. (2004). http://www.equilatere.netGoogle Scholar
    23. Giorgio Marcias, Kenshi Takayama, Nico Pietroni, Daniele Panozzo, Olga Sorkine-Hornung, Enrico Puppo, and Paolo Cignoni. 2015. Data-driven Interactive Quadrangulation. ACM Trans. Graph. 34, 4, Article 65 (July 2015), 10 pages. Google ScholarDigital Library
    24. Chi-Han Peng, Yong-Liang Yang, and Peter Wonka. 2014. Computing Layouts with Deformable Templates. ACM Trans. Graph. 33, 4, Article 99 (July 2014), 11 pages. Google ScholarDigital Library
    25. Helmut Pottmann, Michael Eigensatz, Amir Vaxman, and Johannes Wallner. 2015. Architectural Geometry. Computers and Graphics 47 (2015), 145–164. Google ScholarDigital Library
    26. Bernhard Reinert, Tobias Ritschel, and Hans-Peter Seidel. 2013. Interactive By-example Design of Artistic Packing Layouts. ACM Trans. Graph. 32, 6, Article 218 (Nov. 2013), 7 pages. Google ScholarDigital Library
    27. Pedro V. Sander, John Snyder, Steven J. Gortler, and Hugues Hoppe. 2001. Texture Mapping Progressive Meshes. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’01). 409–416. Google ScholarDigital Library
    28. Scott Schaefer and Joe Warren. 2005. On C2 Triangle/Quad Subdivision. ACM Trans. Graph. 24, 1 (Jan. 2005), 28–36. Google ScholarDigital Library
    29. Christian Schumacher, Bernhard Thomaszewski, and Markus Gross. 2016. Stenciling: Designing Structurally-Sound Surfaces with Decorative Patterns. Comput. Graph. Forum 35, 5 (Aug. 2016), 101–110.Google ScholarDigital Library
    30. Jos Stam and Charles Loop. 2003. Quad/Triangle Subdivision. Computer Graphics Forum 22, 1 (2003), 79–85.Google ScholarCross Ref
    31. Jens-Boie Suck, Michael Schreiber, and Peter Häussier. 2002. Quasicrystals. An Introduction to Structure, Physical Properties and Applications. Springer-Verlag.Google Scholar
    32. Kenshi Takayama, Daniele Panozzo, and Olga Sorkine-Hornung. 2014. Pattern-Based Quadrangulation for N-Sided Patches. Comput. Graph. Forum 33, 5 (Aug. 2014), 177–184. Google ScholarDigital Library
    33. Amir Vaxman, Christian Müller, and Ofir Weber. 2017. Regular Meshes from Polygonal Patterns. ACM Trans. Graph. 36, 4, Article 113 (July 2017), 15 pages. Google ScholarDigital Library
    34. Shi-Qing Xin, Bruno Lévy, Zhonggui Chen, Lei Chu, Yaohui Yu, Changhe Tu, and Wenping Wang. 2016. Centroidal Power Diagrams with Capacity Constraints: Computation, Applications, and Extension. ACM Trans. Graph. 35, 6, Article 244 (Nov. 2016), 12 pages. Google ScholarDigital Library
    35. Yong-Liang Yang, Jun Wang, Etienne Vouga, and Peter Wonka. 2013. Urban Pattern: Layout Design by Hierarchical Domain Splitting. ACM Trans. Graph. 32, 6, Article 181 (Nov. 2013), 12 pages. Google ScholarDigital Library

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