Quad-mesh generation and processing: A survey

Computer Graphics Forum

Volumn 32, Issue 6, 2013, Pages 51-76

  Bommes, David ^a   Lévy, Bruno ^b   Pietroni, Nico ^c   Puppo, Enrico ^d   Silva, Claudio ^e,f   Tarini, Marco ^g   Zorin, Denis ^f  

^a INRIA   (France)

^b ALICE/INRIA   (France)

^c CNR   (Italy)

^d UNIVERSITY OF GENOA   (Italy)

^e POLYTECHNIC UNIVERSITY   (United States)

^f NEW YORK UNIVERSITY   (United States)

^g UNIVERSITY OF INSUBRIA   (Italy)

Author keywords

geometry processing; mesh parametrization; quad mesh generation; quad mesh processing

Indexed keywords

DATA STRUCTURES; GEOMETRY; GRAPHIC METHODS; MESH GENERATION; QUALITY CONTROL; SURFACE ANALYSIS; SURVEYS;

ADAPTIVE REFINEMENT; GEOMETRY PROCESSING; MESH PARAMETRIZATION; MESH PROCESSING; PARAMETRISATION; PARAMETRIZATIONS; QUAD MESH GENERATIONS; QUADRILATERAL MESHES;

COMPUTER GRAPHICS;

EID: 84884285537     PISSN: 01677055     EISSN: 14678659     Source Type: Journal    
DOI: 10.1111/cgf.12014     Document Type: Review

References (111)

1. Amenta N., Bern M. W.,: Surface reconstruction by voronoi filtering. Discrete & Computational Geometry 22, 4 (1999), 481-504.
2. Alliez P., Cohen-Steiner D., Devillers O., Lévy B., Desbrun M.,: Anisotropic polygonal remeshing. In Proceedings of the ACM SIGGRAPH 2003 Papers (New York, NY, USA, 2003), SIGGRAPH '03, ACM, pp. 485-493.
3. Alliez P., de Verdière É. C., Devillers O., Isenburg M.,: Centroidal Voronoi diagrams for isotropic surface remeshing. Graphical models 67, 3 (May 2005), 204-231.
4. ALICE: Graphite: an experimental 3d modeler, 2000-2012. http://alice.loria.fr/software/graphite. Accessed January 2013.
5. Alliez P., Ucelli G., Gotsman C., Attene M.,: Recent advances in remeshing of surfaces. In Shape Analysis and Structuring, Mathematics and Visualization (2008), Springer, Berlin, Germany.
6. Borden M., Benzley S., Shepherd J.,: Hexahedral sheet extraction. In Proceedings of the 11th International Meshing Roundtable (Ithaca, New York, USA, September 2002), Springer-Verlag, pp. 147-152.
7. Ben-Chen M., Gotsman C., Bunin G.,: Conformal flattening by curvature prescription and metric scaling. In Computer Graphics Forum (2008), Blackwell Synergy, Hoboken, NJ, USA, vol. 27, pp. 449-458. 9, 18.
8. Bertram M., Duchaineau M., Hamann B., Joy K.,: Generalized b-spline subdivision-surface wavelets for geometry compression. Visualization and Computer Graphics, IEEE Transactions 10, 3 (2004), 326-338.
9. Bush J., Ferguson M., Mason T., McGrouther G.,: The dynamic rotation of langer's lines on facial expression. Journal of Plastic, Reconstructive & Aesthetic Surgery 60, 4 (2007), 393-399.
10. Botsch M., Kobbelt L., Pauly M., Alliez P., Lévy B.,: Polygon Mesh Processing. AK Peters, London, 2010.
11. Bommes D., Lempfer T., Kobbelt L.,: Global structure optimization of quadrilateral meshes. Computer Graphics Forum 30, 2 (2011), 375-384.
12. Boier-Martin I., Rushmeier H., Jin J.,: Parameterization of triangle meshes over quadrilateral domains. In Proceedings of the Eurographics Symposium on Geometry Processing (Nice, France, 2004), R. Scopigno, and, D. Zorin, (Eds.), Eurographics Association, Geneve, Switzerland, pp. 197-208.
13. Bommes D., Vossemer T., Kobbelt L.,: Quadrangular parameterization for reverse engineering. In Proceedings of the Mathematical Methods for Curves and Surfaces (Oslo, Norway, 2008), Springer-Verlag, pp. 55-69.
14. Bommes D., Zimmer H., Kobbelt L.,: Mixed-integer quadrangulation. ACM Transactions on Graphics 28 (July 2009), 77:1-77:10.
15. Bommes D., Zimmer H., Kobbelt L.,: Practical mixed-integer optimization for geometry processing. In Proceedings of the 7th International Conference on Curves and Surfaces (Berlin/Heidelberg, Germany, 2012), Springer-Verlag, pp. 193-206.
16. Campen M., Bommes D., Kobbelt L.,: Dual loops meshing: quality quad layouts on manifolds. ACM Transactions on Graphics 31, 4 (July 2012), 110:1-110:11.
17. Catmull E., Clark J.,: Recursively generated b-spline surfaces on arbitrary topological meshes. Computer-aided Design 10, 6 (1978), 350-355.
18. Cignoni P., Corsini M., Ranzuglia G.,: Meshlab: An open-source 3D mesh processing system. ERCIM News, 73 (April 2008), 45-46.
19. Crane K., Desbrun M., Schröder P.,: Trivial connections on discrete surfaces. Computer Graphics Forum (SGP) 29, 5 (2010), 1525-1533.
20. Cignoni P., Ganovelli F., Gobbetti E., Marton F., Ponchio F., Scopigno R.,: Batched multi triangulation. In Proceedings of the IEEE Visualization (Minneapolis, MI, USA, October 2005), IEEE Computer Society Press, pp. 207-214.
21. Carr N. A., Hoberock J., Crane K., Hart J. C.,: Rectangular multi-chart geometry images. In Symposium on Geometry Processing Conference Proceedings (Sardinia, Italy, June 2006), ACM, pp. 181-190.
22. Ceccato C., Hesselgren P., Pauly M., Pottmann H., Wallner J.,: Advances in Architectural Geometry 2010. Springer, 2010.
23. Chi-Han Peng Eugene Zhang Y. K., Wonka P.,: Connectivity editing for quadrilateral meshes. ACM Transactions on Graphics (Proceedings of ACM SIGGRAPH ASIA) 30, 6 (December 2011), 141:1-141:12. doi: 10.1145/2070781.2024175.
24. Cignoni P., Montani C., Scopigno R.,: A comparison of mesh simplification algorithms. Computers & Graphics 22 (1997), 37-54.
25. Cazals F., Pouget M.,: Estimating differential quantities using polynomial fitting of osculating jets. Computer Aided Geometric Design 22, 2 (2005), 121-146.
26. Cignoni P., Rocchini C., Scopigno R.,: Metro: Measuring error on simplified surfaces. Computer Graphics Forum 17, 2 (1998), 167-174.
27. Cohen-Steiner D., Morvan J.-M.,: Restricted delaunay triangulations and normal cycle. In SCG '03: Proceedings of the 19th Annual Symposium on Computational Geometry (San Diego, CA, USA, June 2003), pp. 312-321.
28. D'Azevedo E. F.,: Are bilinear quadrilaterals better than linear triangles? SIAM Journal on Scientific Computing 22, 1 (January 2000), 198-217.
29. Dong S., Bremer P.-T., Garland M., Pascucci V., Hart J. C.,: Spectral surface quadrangulation. ACM Transactions on Graphics 25, 3 (July 2006), 1057-1066.
30. Du Q., Emelianenko M., Ju L.,: Convergence of the Lloyd algorithm for computing centroidal Voronoi tessellations. SIAM Journal on Numerical Analysis 44, 1 (2006), 102-119.
31. Du Q., Faber V., Gunzburger M.,: Centroidal voronoi tessellations: Applications and algorithms. SIREV: SIAM Review 41, 4 (1999), 637-676.
32. Du Q., Gunzburger M. D., Ju L.,: Voronoi-based finite volume methods, optimal voronoi meshes, and pdes on the sphere. Computer Methods in Applied Mechanics and Engineering 192, 35-36 (2003), 3933-3957.
33. Daniels II J., Silva C. T., Cohen E.,: Localized quadrilateral coarsening. In Proceedings of the Symposium on Geometry Processing (Aire-la Ville, Switzerland, 2009), SGP '09, Eurographics Association, pp. 1437-1444.
34. Daniels II J., Silva C. T., Cohen E.,: Semi-regular quadrilateral-only remeshing from simplified base domains. Computer Graphics on Forum 28, 5 (2009), 1427-1435.
35. Daniels II J., Silva C. T., Shepherd J., Cohen E.,: Quadrilateral mesh simplification. ACM Transactions on Graphics 27 (December 2008), 148:1-148:9.
36. Eck M., DeRose T., Duchamp T., Hoppe H., Lounsbery M., Stuetzle W.,: Multiresolution analysis of arbitrary meshes. In Proceedings of the 22nd International ACM Conference on Computer Graphics and Interactive Techniques (New York, NY, USA, 1995), SIGGRAPH '95, ACM, pp. 173-182.
37. Eppstein D., Goodrich M. T., Kim E., Tamstorf R.,: Motorcycle graphs: Canonical quad mesh partitioning. In Proceedings of the Symposium on Geometry Processing (Aire-la Ville, Switzerland, Switzerland, 2008), SGP '08, Eurographics Association, pp. 1477-1486.
38. Eigensatz M., Kilian M., Schiftner A., Mitra N. J., Pottmann H., Pauly M.,: Paneling architectural freeform surfaces. ACM Transactions on Graphics 29 (July 2010), 45:1-45:10.
39. Fu C.-W., Lai C.-F., He Y., Cohen-Or D.,: K-set tilable surfaces. ACM Transactions on Graphics 29 (July 2010), 44:1-44:6.
40. Floater M. S.,: Parametrization and smooth approximation of surface triangulations. Computer Aided Geometric Design 14, 3 (1997), 231-250.
41. Floater M. S.,: Mean value coordinates. Computer Aided Geometry Design 20 (March 2003), 19-27.
42. Fratarcangeli M.,: A Computational Musco-Skeletal Model for Animating Virtual Faces. PhD thesis, Sapienza University of Rome, 2009.
43. Fisher M., Schröder P., Desbrun M., Hoppe H.,: Design of tangent vector fields. ACM Transactions on Graphics 26, 3 (2007), 56. doi: 10.1145/1276377.1276447.
44. Gu X., Gortler S. J., Hoppe H.,: Geometry images. In Proceedings of the SIGGRAPH Conference Proceedings (San Antonio, TX, 21/07/2002 2002), vol. 21 (3), Association for Computing Machinery, pp. 355-361.
45. Garland M., Heckbert P. S.,: Surface simplification using quadric error metrics. In Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques (New York, NY, USA, 1997), SIGGRAPH '97, ACM Press/Addison-Wesley Publishing Co., pp. 209-216.
46. Gu X., He Y., Qin H.,: Manifold splines. Graphical Models 68, 3 (2006), 237-254.
47. Gurung T., Laney D., Lindstrom P., Rossignac J.,: Squad: Compact representation for triangle meshes. Computer Graphics Forum 30, 2 (2011), 355-364.
48. Glymph J., Shelden D., Ceccato C., Mussel J., Schober H.,: A parametric strategy for free-form glass structures using quadrilateral planar facets. Automation in Construction 13, 2 (2004), 187-202.
49. Guskov I., Vidimče K., Sweldens W., Schröder P.,: Normal meshes. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (New York, NY, USA, 2000), SIGGRAPH '00, ACM Press/Addison-Wesley Publishing Co., pp. 95-102.
50. Gu X., Yau S.-T.,: Global conformal surface parameterization. In Proceedings of the 2003 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing (Aire-la Ville, Switzerland, Switzerland, 2003), SGP '03, Eurographics Association, pp. 127-137.
51. Hausner A.,: Simulating decorative mosaics. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (New York, NY, USA, 2001), SIGGRAPH '01, ACM, pp. 573-580.
52. Hormann K., Tarini M.,: A quadrilateral rendering primitive. In Proceedings of the ACM SIGGRAPH/EUROGRAPHICS Conference on Graphics Hardware (New York, NY, USA, 2004), HWWS ′04, ACM, pp. 7-14.
53. He Y., Wang H., Fu C., Qin H.,: A divide and-conquer approach for automatic polycube map construction. Computers & Graphics 33, 3 (2009), 369-380.
54. He Y., Wang K., Wang H., Gu X., Qin H.,: Manifold t-spline. Geometric Modeling and Processing-GMP 2006 (2006), 409-422.
55. Hertzmann A., Zorin D.,: Illustrating smooth surfaces. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (New York, NY, USA, 2000), SIGGRAPH '00, ACM Press/Addison-Wesley Publishing Co., pp. 517-526.
56. Huang J., Zhang M., Ma J., Liu X., Kobbelt L., Bao H.,: Spectral quadrangulation with orientation and alignment control. ACM Transactions on Graphics 27 (December 2008), 147:1-147:9.
57. Isenburg M., Lindstrom P., Gumhold S., Snoeyink J.,: Large mesh simplification using processing sequences. In Proceedings of the 14th IEEE Visualization 2003 (VIS'03) (Washington, DC, USA, 2003), VIS '03, IEEE Computer Society, pp. 61.
58. Itoh T., Shimada K.,: Automatic conversion of triangular meshes into quadrilateral meshes with directionality. International Journal of CAD/CAM (2001).
59. Khodakovsky A., Litke N., Schröder P.,: Globally smooth parameterizations with low distortion. In Proceedings of the ACM SIGGRAPH 2003 Papers (New York, NY, USA, 2003), SIGGRAPH '03, ACM, pp. 350-357.
60. Kovacs D., Myles A., Zorin D.,: Anisotropic quadrangulation. In Proceedings of the 14th ACM Symposium on Solid and Physical Modeling (New York, NY, USA, 2010), SPM '10, ACM, pp. 137-146.
61. Kälberer F., Nieser M., Polthier K.,: Quadcover-surface parameterization using branched coverings. Computer Graphics Forum 26, 3 (2007), 375-384.
62. Khodakovsky A., Schröder P., Sweldens W.,: Progressive geometry compression. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (New York, NY, USA, 2000), SIGGRAPH '00, ACM Press/Addison-Wesley Publishing Co., pp. 271-278.
63. Lipman Y.,: Bounded distortion mapping spaces for triangular meshes. ACM Transactions on Graphics (SIGGRAPH 2012) 31, 4 (2012), 108:1-108:13. doi: 10.1145/2185520.2185604.
64. Lin J., Jin X., Fan Z., Wang C.,: Automatic polycube-maps. In Proceedings of the 5th International Conference on Advances in Geometric Modeling and Processing (2008), pp. 3-16.
65. Lai Y.-K., Jin M., Xie X., He Y., Palacios J., Zhang E., Hu S.-M., Gu X.,: Metric-driven rosy field design and remeshing. IEEE Transactions on Visualization and Computer Graphics 16, 1 (2010), 95-108.
66. Lai Y.-K., Kobbelt L., Hu S.-M.,: An incremental approach to feature aligned quad dominant remeshing. In SPM '08: Proceedings of the 2008 ACM Symposium on Solid and Physical Modeling (2008), pp. 137-145.
67. Lévy B., Liu Y.,: Lp Centroidal Voronoi Tesselation and its applications. ACM Transactions on Graphics 29, 4 (2010), 119:1-119:11. doi: 10.1145/1778765.1778856.
68. Lloyd S. P.,: Least squares quantization in PCM. IEEE Transactions on Information Theory 28, 2 (1982), 129-137.
69. Li E., Lvy B., Zhang X., Che W., Dong W., Paul J.-C.,: Meshless quadrangulation by global parametrization. Computer and Graphics (2011).
70. Liu D. C., Nocedal J.,: On the limited memory BFGS method for large scale optimization. Mathematical Programming: Series A and B 45, 3 (1989), 503-528.
71. Li W.-C., Ray N., Lévy B.,: Automatic and interactive mesh to t-spline conversion. In Proceedings of the EG/ACM Symposium on Geometry Processing (2006).
72. Lee A., Sweldens W., Schroder P., Cowsar L., Dobkin D.,: Maps: Multiresolution adaptive parameterization of surfaces. In Proceedings of the 25th Annual Conference on Computer Graphics (1998), pp. 95-104.
73. Luebke D. P.,: A developer's survey of polygonal simplification algorithms. IEEE Computer Graphics and Applications 21 (2001), 24-35.
74. Liu Y., Wang W., Lévy B., Sun F., Yan D.-M., Lu L., Yang C.,: On centroidal Voronoi tessellation-energy smoothness and fast computation. ACM Transactions on Graphics 28, 4 (2009), 1-17.
75. Maréchal L.,: Advances in octree-based all-hexahedral mesh generation: Handling sharp features. In Proceedings of the 18th International Meshing Roundtable conference proceedings (Salt Lake City, UT, USA, October 2009), Springer, pp. 65-84.
76. Murdoch P., Benzley S., Blacker T., Mitchell S.,: The spatial twist continuum: A connectivity based method for representing all-hexahedral finite element meshes. Finite Element in Analysis and Design 28, 2 (December 1997), 137-149.
77. Mirebeau J.-M.,: Optimally Adapted Meshes for Finite elements of Arbitrary order and W1,p norms. August 2011.
78. Marinov M., Kobbelt L.,: Direct anisotropic quad-dominant remeshing. In Computer Graphics and Applications, 2004. PG'04 Proceedings of the 12th Pacific Conference (Washington, DC, USA, October 2004), IEEE Computer Society, pp. 207-216.
79. Meyer M., Lee H., Barr A., Desbrun M.,: Generalized barycentric coordinates on irregular polygons. Computer 7, 1 (2005), 0-4.
80. Myles A., Pietroni N., Kovacs D., Zorin D.,: Feature-aligned t-meshes. ACM Transactions on Graphics 29, 4 (July 2010), 117:1-117:11.
81. Nivoliers V., Yan D., LÃvy B.,: Fitting polynomial surfaces to triangular meshes with voronoi squared distance minimization. In International Meshing Roundtable Conference Proceedings (Paris, France, 2011).
82. Panozzo D., Lipman Y., Puppo E., Zorin D.,: Fields on symmetric surfaces. ACM Transactions on Graphics (SIGGRAPH 2012) 31, 4 (2012), 111. doi: 10.1145/2185520.2185607.
83. Panozzo D., Puppo E., Tarini M., Pietroni N., Cignoni P.,: Automatic construction of adaptive quad-based subdivision surfaces using fitmaps. IEEE Transaction on Visualization and Computer Graphics 17, 10 (october 2011), 1510-1520. http://doi.ieeecomputersociety.org/10.1109/TVCG.2011.28.
84. Pietroni N., Tarini M., Cignoni P.,: Almost isometric mesh parameterization through abstract domains. IEEE Transaction on Visualization and Computer Graphics 16, 4 (July/August 2010), 621-635.
85. Pietroni N., Tarini M., Sorkine O., Zorin D.,: Global parametrization of range image sets. ACM Transactions on Graphics, Proceedings of SIGGRAPH Asia 2011 30, 6 (2011), 149. doi: 10.1145/2070781.2024183.
86. Palacios J., Zhang E.,: Rotational symmetry field design on surfaces. ACM Transactions on Graphics 26, 3 (2007), 55 doi: 10.1145/1276377.1276446.
87. Ray N., Li W. C., Lévy B., Sheffer A., Alliez P.,: Periodic global parameterization. ACM Transactions on Graphics 25 (October 2006), 1460-1485.
88. Remacle J.-F., Lambrechts J., Seny B., Marchandise E., Johnen A., Geuzaine C.,: Blossom-quad: A non-uniform quadrilateral mesh generator using a minimum cost perfect matching algorithm. International Journal for Numerical Methods in Engineering 89 (2012), 1102-1119.
89. Ray N., Vallet B., Alonso L., Levy B.,: Geometry-aware direction field processing. ACM Transactions on Graphics 29 (December 2009), 1:1-1:11.
90. Ray N., Vallet B., Li W. C., Lévy B.,: N-symmetry direction field design. ACM Transactions on Graphics 27, 2 (2008), 1-13.
91. Shepherd J. F., Dewey M. W., Woodbury A. C., Benzley S. E., Staten M. L., Owen S. J.,: Adaptive mesh coarsening for quadrilateral and hexahedral meshes. Finite Elements in Analysis and Design 46, 1-2 (2010), 17-32.
92. Steiner D., Fischer A.,: Planar parameterization for closed manifold genus-g meshes using any type of positive weights. Journal of Computing and Information Science in Engineering 5, 2 (2005), 118-125.
93. Shepherd J. F., Johnson C. R.,: Hexahedral mesh generation constraints. Engineering with Computers 24, 3 (2008), 195-213.
94. Shepherd J., Mitchell S. A., Knupp P., White D.,: Methods for multisweep automation. In Proceedings of the 9th International Meshing Roundtable Conference Proceedings (2000), pp. 77-87.
95. Staten M. L., Owen S. J., Blacker T. D.,: Unconstrained paving and plastering: A new idea for all hexahedral mesh generation. In Proceedings of the 14th International Meshing Roundtable Conference Proceedings (2005), pp. 399-416.
96. Springborn B., Schröder P., Pinkall U.,: Conformal equivalence of triangle meshes. ACM Transactions on Graphics 27 (August 2008), 77:1-77:11.
97. Tong Y., Alliez P., Cohen-Steiner D., Desbrun M.,: Designing quadrangulations with discrete harmonic forms. In Proceedings of the fourth Eurographics symposium on Geometry processing (Aire-la Ville, Switzerland, Switzerland, 2006), SGP '06, Eurographics Association, pp. 201-210.
98. Tarini M., Hormann K., Cignoni P., Montani C.,: Polycube-maps. ACM Transactions on Graphics 23 (August 2004), 853-860.
99. Tierny J., II J. D., Nonato L. G., Pascucci V., Silva C.,: Interactive quadrangulation with reeb atlases and connectivity textures, IEEE Transactions on Visualization and Computer Graphics 18, 10 (2012), 1650-1663.
100. Tarini M., Pietroni N., Cignoni P., Panozzo D., Puppo E.,: Practical quad mesh simplification. Computer Graphics Forum 29, 2 (2010), 407-418.
101. Tarini M., Puppo E., Panozzo D., Pietroni N., Cignoni P.,: Simple quad domains for field aligned mesh parametrization. ACM Transactions on Graphics, Proceedings of SIGGRAPH Asia 2011 30, 6 (2011).
102. Velho L., Zorin D.,: 4-8 subdivision. Computer Aided Geometric Design 18, 5 (2001), 397-427 (Subdivision Algorithms).
103. Wang H., He Y., Li X., Gu X., Qin H.,: Polycube splines. Computer-Aided Design 40, 6 (2008), 721-733.
104. Wang H., Jin M., He Y., Gu X., Qin H.,: User-controllable polycube map for manifold spline construction. In Proceedings of the 2008 ACM Symposium on Solid and Physical Modeling (New York, NY, USA, 2008), SPM '08, ACM, pp. 397-404.
105. Weber O., Myles A., Zorin D.,: Computing extremal quasiconformal maps. Computer Graphics Forum 31 (2012), 1679-1689.
106. Xia J., Garcia I., He Y., Xin S.-Q., Patow G.,: Editable polycube map for gpu-based subdivision surfaces. In Symposium on Interactive 3D Graphics and Games (New York, NY, USA, 2011), I3D '11, ACM, pp. 151-158.
107. Yau S.-T.,: The Founders of Index Theory: Reminiscences of Atiyah, Bott, Hirzebruch, and Singer. International Press, 2005.
108. Yeh I.-C., Lin C.-H., Sorkine O., Lee T.-Y.,: Template-based 3D model fitting using dual-domain relaxation. IEEE Transactions on Visualization and Computer Graphics 17, 8 (2011), 1178-1190.
109. Yang Y.-L., Yang Y.-J., Pottmann H., Mitra N. J.,: Shape space exploration of constrained meshes. ACM Transactions on Graphics 30, 6 (December 2011), 124:1-124:12.
110. Zhang M., Huang J., Liu X., Bao H.,: A wave-based anisotropic quadrangulation method. ACM Transactions on Graphics 29 (July 2010), 118:1-118:8.
111. Zhang E., Mischaikow K., Turk G.,: Vector field design on surfaces. ACM Transactions on Graphics 25, 4 (2006), 1294-1326.