The Community for Technology Leaders
RSS Icon
Issue No.10 - Oct. (2012 vol.18)
pp: 1650-1663
Julien Tierny , CNRS at Telecom ParisTech, Paris
Joel Daniels II , NYU-Poly, New York City
Luis Gustavo Nonato , ICMC, Universidade de São Paulo, São Carlos
Valerio Pascucci , University of Utah, Salt Lake City
Cláudio T. Silva , NYU-Poly, New York City
Creating high-quality quad meshes from triangulated surfaces is a highly nontrivial task that necessitates consideration of various application specific metrics of quality. In our work, we follow the premise that automatic reconstruction techniques may not generate outputs meeting all the subjective quality expectations of the user. Instead, we put the user at the center of the process by providing a flexible, interactive approach to quadrangulation design. By combining scalar field topology and combinatorial connectivity techniques, we present a new framework, following a coarse to fine design philosophy, which allows for explicit control of the subjective quality criteria on the output quad mesh, at interactive rates. Our quadrangulation framework uses the new notion of Reeb atlas editing, to define with a small amount of interactions a coarse quadrangulation of the model, capturing the main features of the shape, with user prescribed extraordinary vertices and alignment. Fine grain tuning is easily achieved with the notion of connectivity texturing, which allows for additional extraordinary vertices specification and explicit feature alignment, to capture the high-frequency geometries. Experiments demonstrate the interactivity and flexibility of our approach, as well as its ability to generate quad meshes of arbitrary resolution with high-quality statistics, while meeting the user's own subjective requirements.
Topology, Mesh generation, Harmonic analysis, Level set, Linear systems, Electronic mail, connectivity operators., Quadrangulation, Reeb graph
Julien Tierny, Joel Daniels II, Luis Gustavo Nonato, Valerio Pascucci, Cláudio T. Silva, "Interactive Quadrangulation with Reeb Atlases and Connectivity Textures", IEEE Transactions on Visualization & Computer Graphics, vol.18, no. 10, pp. 1650-1663, Oct. 2012, doi:10.1109/TVCG.2011.270
[1] P. Alliez, D. Cohen-Steiner, O. Devillers, B. Lévy, and M. Desbrun, "Anisotropic Polygonal Remeshing," ACM Trans. Graphics, vol. 22, no. 3, pp. 485-493, 2003.
[2] P. Alliez, G. Ucelli, C. Gotsman, and M. Attene, "Recent Advances in Remeshing of Surfaces," Shape Analysis and Structuring, L.D. Floriani and M. Spagnuolo, eds., Mathematics and Visualization, Springer, 2008.
[3] M. Ben-chen, C. Gotsman, and G. Bunin, "Conformal Flattening by Curvature Prescription and Metric Scaling," Computer Graphics Forum, vol. 27, no. 2, pp. 449-458, 2008.
[4] S. Biasotti, D. Giorgi, M. Spagnuolo, and B. Falcidieno, "Reeb Graphs for Shape Analysis and Applications," Theoretical Computer Science, vol. 392, pp. 5-22, 2008.
[5] I. Boier-Martin, H. Rushmeier, and J. Jin, "Parameterization of Triangle Meshes over Quadrilateral Domains," Proc. ACM SIGGRAPH Symp. Geometry Processing, pp. 193-203, 2004.
[6] D. Bommes, H. Zimmer, and L. Kobbelt, "Mixed-Integer Quadrangulation," ACM Trans. Graphics, vol. 28, no. 3, pp. 1-10, 2009.
[7] P. Bremer, S. Porumbescu, B. Hamann, and K. Joy, "Automatic Semi-Regular Mesh Construction from Adaptive Distance Fields," Proc. Int'l Conf. Curve and Surface Fitting, 2002.
[8] N. Carr, J. Hoberock, K. Crane, and J. Hart, "Rectangular Multi-Chart Geometry Images," Proc. Fourth Eurographics Symp. Geometry Processing, pp. 181-190, 2006.
[9] K. Cole-McLaughlin, H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci, "Loops in Reeb Graphs of 2-Manifolds," Proc. ACM Symp. Computational Geometry, pp. 344-350, 2003.
[10] J. Daniels, C. Silva, and E. Cohen, "Semi-Regular Quadrilateral-Only Mesh Generation from Simplified Base Domains," Computer Graphics Forum, vol. 28, no. 5, pp. 1427-1435, 2009.
[11] J. Daniels, C.T. Silva, J. Shepherd, and E. Cohen, "Quadrilateral Mesh Simplification," ACM Trans. Graphics, vol. 27, no. 5, pp. 1-9, 2008.
[12] T. Davis and W. Hager, "Dynamic Supernodes in Sparse Cholesky Update/Downdate and Triangular Solves," ACM Trans. Math. Software, vol. 35, no. 4, pp. 1-23, 2009.
[13] S. Dong, P.-T. Bremer, M. Garland, V. Pascucci, and J. Hart, "Spectral Surface Quadrangulation," ACM Trans. Graphics, vol. 25, no. 3, pp. 1057-1066, 2006.
[14] S. Dong, S. Kircher, and M. Garland, "Harmonic Functions for Quadrilateral Remeshing of Arbitrary Manifolds," Computer-Aided Design, vol. 22, pp. 392-423, 2005.
[15] H. Edelsbrunner, D. Letscher, and A. Zomorodian, "Topological Persistence and Simplification," Discrete and Computational Geometry, vol. 28, pp. 511-533, 2002.
[16] H. Edelsbrunner, D. Morozov, and V. Pascucci, "Persistence-Sensitive Simplification Functions on 2-Manifolds," Proc. ACM Symp. Computational Geometry, pp. 127-134, 2006.
[17] H. Edelsbrunner and E.P. Mucke, "Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms," ACM Trans. Graphics, vol. 9, pp. 66-104, 1990.
[18] A. Hatcher, Algebraic Topology. Cambridge Univ. Press, 2002.
[19] M. Hilaga, Y. Shinagawa, T. Kohmura, and T.L. Kunii, "Topology Matching for Fully Automatic Similarity Estimation of 3D shapes," Proc. SIGGRAPH, pp. 203-212, 2001.
[20] K. Hormann, K. Polthier, and A. Sheffer, "Mesh Parameterization: Theory and Practice," Proc. ACM SIGGRAPH ASIA, pp. 1-87, 2008.
[21] J. Huang, M. Zhang, J. Ma, X. Liu, L. Kobbelt, and H. Bao, "Spectral Quadrangulation with Orientation and Alignment Control," ACM Trans. Graphics, vol. 27, no. 5, pp. 1-9, 2008.
[22] F. Kalberer, M. Nieser, and K. Polthier, "Quadcover: Surface Parameterization Using Branched Coverings," Computer Graphics Forum, vol. 26, pp. 375-384, 2007.
[23] P. Kinney, "Cleanup: Improving Quadrilateral Finite Element Meshes," Proc. Sixth Int'l Meshing Roundtable, pp. 437-447, 1997.
[24] V. Krishnamurthy and M. Levoy, "Fitting Smooth Surfaces to Dense Polygon Meshes," Proc. ACM SIGGRAPH, pp. 313-324, 1996.
[25] Y.-K. Lai, L. Kobbelt, and S.-M. Hu, "An Incremental Approach to Feature Aligned Quad Dominant Remeshing," Proc. ACM Symp. Solid and Physical Modeling, pp. 137-145, 2008.
[26] J. Lin, X. Jin, Z. Fan, and C. Wang, "Automatic Polycube Maps," Proc. Int'l Conf. Advances in Geometric Modeling and Processing, pp. 3-16, 2008.
[27] F. Losasso and H. Hoppe, "Geometry Clipmaps: Terrain Rendering Using Nested Regular Grids," ACM Trans. Graphics, vol. 23, pp. 769-776, 2004.
[28] J. Milnor, Morse Theory. Princeton Univ. Press, 1963.
[29] S. Owen, M. Staten, S. Canann, and S. Saigal, "Q-morph: An Indirect Approach to Advancing Front Quad Meshing," Int'l J. Numerical Methods in Eng., vol. 44, pp. 1317-1340, 1999.
[30] V. Pascucci, G. Scorzelli, P.T. Bremer, and A. Mascarenhas, "Robust On-Line Computation of Reeb Graphs: Simplicity and Speed," ACM Trans. Graphics, vol. 26, pp. 58.1-58.9, 2007.
[31] G. Patanè, M. Spagnuolo, and B. Falcidieno, "Para-Graph: Graph-Based Parameterization of Triangle Meshes with Arbitrary Genus," Computer Graphics Forum, vol. 23, pp. 789-797, 2004.
[32] G. Patanè, M. Spagnuolo, and B. Falcidieno, "A Minimal Contouring Approach to the Computation of the Reeb Graph," IEEE Trans. Visualization and Computer Graphics, vol. 15, no. 4, pp. 583-595, July-Aug. 2009.
[33] U. Pinkall and K. Polthier, "Computing Discrete Minimal Surfaces and Their Conjugates," Experimental Math., vol. 2, pp. 15-36, 1993.
[34] D. Pinskiy, "Sliding Deformation: Shape Preserving Per-Vertex Displacement," Proc. Eurographics Conf., 2010.
[35] N. Ray, W.C. Li, B. Lévy, A. Sheffer, and P. Alliez, "Periodic Global Parameterization," ACM Trans. Graphics, vol. 25, no. 4, pp. 1460-1485, 2006.
[36] N. Ray, B. Vallet, L. Alonso, and B. Lévy, "Geometry Aware Direction Field Processing," ACM Trans. Graphics, vol. 29, no. 1, 2009.
[37] G. Reeb, "Sur Les Points Singuliers D'une Forme de Pfaff complètement intégrable ou d'une Fonction numérique," Comptes-rend. de l'Acad. des Scien., vol. 222, pp. 847-849, 1946.
[38] O. Schall, R. Zayer, and H.-P. Seidel, "Controlled Field Generation for Quad-Remeshing," Proc. ACM Symp. Solid and Physical Modeling, pp. 295-300, 2008.
[39] M. Staten and S. Canann, "Post Refinement Element Shape Improvement for Quadrilateral Meshes," ASME AMD: Trends in Unstructured Mesh Generation, pp. 9-16, Am. Soc. of Mechanical Eng., 1997.
[40] M. Tarini, K. Hormann, P. Cignoni, and C. Montani, "Polycube-Maps," ACM Trans. Graphics, vol. 23, pp. 853-860, 2004.
[41] M. Tarini, N. Pietroni, P. Cignoni, D. Panozzo, and E. Puppo, "Practical Quad Mesh Simplification," Computer Graphics Forum, vol. 29, pp. 407-418, 2010.
[42] J. Tierny, A. Gyulassy, E. Simon, and V. Pascucci, "Loop Surgery for Volumetric Meshes: Reeb Graphs Reduced to Contour Trees," IEEE Trans. Visualization and Computer Graphics, vol. 15, no. 6, pp. 1177-1184, Nov.-Dec. 2009.
[43] J. Tierny, J.-P. Vandeborre, and M. Daoudi, "Partial 3D Shape Retrieval by Reeb Pattern Unfolding," Computer Graphics Forum, vol. 28, pp. 41-55, 2009.
[44] Y. Tong, P. Alliez, D. Cohen-Steiner, and M. Desbrun, "Designing Quadrangulations with Discrete Harmonic Forms," Proc. Fourth Eurographics Symp. Geometry Processing, pp. 201-210, 2006.
[45] N. Viswanath, K. Shimada, and T. Itoh, "Quadrilateral Meshing with Anisotropy and Directionality Control Via Close Packing of Rectangular Cells," Proc. Ninth Int'l Meshing Roundtable, pp. 227-238, 2000.
[46] K. Xu, H. Zhang, D. Cohen-Or, and Y. Xiong, "Dynamic Harmonic Fields for Surface Processing," Computer and Graphics, vol. 33, no. 3, pp. 391-398, 2009.
[47] M. Zhang, J. Huang, X. Liu, and H. Bao, "A Wave-Based Anisotropic Quadrangulation Method," ACM Trans. Graphics, vol. 29, 2010.
33 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool