Topological mesh operators

Computer Aided Geometric Design

Volumn 27, Issue 1, 2010, Pages 1-22

  Lewiner, Thomas ^a   Lopes, Hélio ^a   Medeiros, Esdras ^b   Tavares, Geovan ^a   Velho, Luiz ^b  

^a PONTIFICAL CATHOLIC UNIVERSITY OF RIO DE JANEIRO   (Brazil)

^b IMPA   (Brazil)

Author keywords

Geometric modeling; Handle operators; Stellar operators

Indexed keywords

COMBINATORIAL STRUCTURES; ELEMENTARY OPERATIONS; GEOMETRIC MODELING; HANDLE OPERATORS; MESH CONSTRUCTION; PRIMITIVE OPERATOR; STELLAR OPERATORS; UNIFIED FRAMEWORK;

GEOMETRY;

EID: 70449529319     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cagd.2009.08.004     Document Type: Article

References (51)

1. Alexander J. The combinatorial theory of complexes. Ann. Math. 31 (1930) 294-322
2. Baumgart B.G. A polyhedron representation for computer vision. AFIPS National Computer Conference 44 (1975) 589-596
3. Bernardini F., Mittleman J., Rushmeier H., Silva C., and Taubin G. The ball-pivoting algorithm for surface reconstruction. IEEE Transactions on Visualization and Computer Graphics 5 4 (1999) 349-359
4. Boissonnat J., Devillers O., Pion S., Teillaud M., and Yvinec M. Triangulations in CGAL. Comput. Geom. Theory Appl. 22 (2002) 5-19. http://www.cgal.org
5. Botsch M., Steinberg S., Bischoff S., and Kobbelt L. OpenMesh - a generic and efficient polygon mesh data structure. In: OpenSG Symposium (2002). http://www.openmesh.org
6. Braid I.C., Hillyard R.C., and Stroud I.A. Stepwise construction of polyhedra in geometric modeling. In: Brodlie K.W. (Ed). Mathematical Methods in Computer Graphics and Design (1980), Academic Press 123-141
7. Castelo, A., Lopes, H., Tavares, G., 1992. Handlebody representation for surfaces and Morse operators. In: Curves and Surfaces in Computer Vision Graphics III, pp. 270-283
8. Catmull E., and Clark J. Recursively generated B-spline surfaces on arbitrary topological meshes. Comput. Aided Design 10 (1978) 350-365
9. de Floriani, L., Hui, A., 2003. A scalable data structure for three-dimensional non-manifold objects. In: Symposium on Geometry Processing, pp. 72-82
10. de Floriani, L., Hui, A., 2007. Shape representations based on simplicial and cell complexes. In: Eurographics State-of-The-Art Report
11. de Goes F., Bergo F., Falcao A., Goldenstein S., and Velho L. Adapted dynamic meshes for deformable surfaces. Proceedings of SIBGRAPI. October 2006 (2006), IEEE Press
12. Desbrun, M., Meyer, M., Schroder, P., Barr, A., 2000. Discrete differential-geometry operators in nd
13. Doo D., and Sabin M. Behaviour of recursive division surfaces near extraordinary points. Comput. Aided Design 10 (1978) 356-360
14. Edelsbrunner, H., 2002. Geometry and topology for mesh generation. Cambridge
15. Enright D., Losasso F., and Fedkiw R. A fast and accurate semi-Lagrangian particle level-set method. Computers and Structures 83 (2005) 479-490
16. Garland M., and Heckbert P.S. Surface simplification using quadric error metrics. Annual Conference Series Computer Graphics 31 (1997) 209-216
17. Goldenstein, S., Vogler, C., Velho, L., 2005. Adaptive deformable models for graphics and vision. In: Computer Graphics Forum
18. Guibas L.J., and Stolfi J. Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. ACM Trans. Graph. 4 (1985) 74-123
19. Higashi M., Torihara F., Takeuchi N., Sata T., Saitoh T., and Hosaka M. Face-based data structure and its application to robust geometric modeling. Solid Modeling and Applications (1995), ACM Press 235-246
20. Hoppe, H., 1996. Progressive meshes. In: SIGGRAPH. New Orleans, August 1996, pp. 99-108
21. Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W., 1993. Mesh optimization. Technical report, University of Washington, TR UW CSE 1993-01-01
22. Isenburg M., and Snoeyink J. Spirale reversi: reverse decoding of the edgebreaker encoding. Comput. Geom. Theory Appl. 20 1-2 (2001) 39-52
23. Kobbelt, L., 2000. sqrt(3) subdivision. In: SIGGRAPH, pp. 103-112
24. Lage M., Lewiner T., Lopes H., and Velho L. CHF: A scalable topological data structure for tetrahedral meshes. SIBGRAPI (2005), IEEE 3349-3356
25. Lickorish, W.B.R., 1999. Simplicial moves on complexes and manifolds. In: Proceedings of the Kirbyfest, vol. 2, pp. 299-320
26. Loop, C., 1987. Smooth subdivision for surfaces based on triangles. Master's thesis, University of Utah
27. Lopes, H., Rossignac, J., Safonova, A., Szymczak, A., Tavares, G., 2002. Edgebreaker: A simple compression for surfaces with handles. In: 7th ACM Siggraph Symposium on Solid Modeling and Application, pp. 289-296
28. Mäntylä M. An Introduction to Solid Modeling (1988), Computer Science Press, Rockville, Maryland
29. Medeiros E., Velho L., and Lopes H. A topological framework for advancing front triangulations. SIBGRAPI. October 2003 (2003), IEEE Press 372-379
30. Mehlhorn, K., Naher, S., Uhrig, C., 1997. The LEDA platform of combinatorial and geometric computing. In: Automata, Languages and Programming, pp. 7-16
31. Mello V., Velho L., Roma Cavalcanti P., and Silva C. A generic programming approach to multiresolution spatial decompositions. Visualization and Mathematics III (2002), Springer Verlag
32. Milnor J. Morse Theory. Annals of Mathematics Study vol. 51 (1963), Princeton University Press
33. Montagner, A., Stolfi, J., 2006. Gems: A general data structure for d-dimensional triangulations. UNICAMP Technical Report IC-06-16
34. Newman M.H.A. On the foundations of combinatorial analysis situs. Proc. Royal Acad. 29 (1926) 610-641
35. Pachner U. PL homeomorphic manifolds are equivalent by elementary shellings. Europ. J. Combinatorics 12 (1991) 129-145
36. Pesco S., Lopes H., and Tavares G. A stratification approach for modeling 2-cell complexes. Computers & Graphics 28 2 (2004) 235-247
37. Poincaré H. Sur la géneralisation d'un théoréme d'euler relatif aux polihédres. C. R. Acad. Sci. Paris 117 (1893) 437-464
38. Rossignac J. Edgebreaker: Connectivity compression for triangle meshes. IEEE Transactions on Visualization and Computer Graphics 5 1 (1999) 47-61
39. Rossignac, J., Safonova, A., Szymczak, A., 2001. 3D compression made simple: Edgebreaker with wrap & zip on a corner-table. In: Proceedings of the 2001 Shape Modeling International Conference, pp. 278-283
40. Scheidegger, C., Fleishman, S., Silva, C., 2005. Triangulating point set surfaces with bounded error. In: Symposium on Geometry Processing
41. Schreiner, J., Scheidegger, C., Silva, C., 2006. High-quality extraction of isosurfaces from regular and irregular grids. In: IEEE Transactions on Visualization and Computer Graphics
42. Taubin, G., 1995. A signal processing approach to fair surface design. In: SIGGRAPH. August 1995, pp. 351-358
43. Taubin G., and Rossignac J. Geometric compression through topological surgery. ACM Transactions on Graphics 17 2 (1998) 84-115
44. Velho L. Mesh simplification using four-face clusters. International Conference on Shape Modeling and Applications. May 2001 (2001), Instituto per la Matematica Applicata - CNR, IEEE Computer Society
45. Velho L. Using semi-regular 4-8 meshes for subdivision surfaces. Journal of Graphics Tools 5 3 (2001) 35-47
46. Velho L. A dynamic adaptive mesh library based on stellar operators. Journal of Graphics Tools 9 2 (2004) 1-29
47. Velho L., and Gomes J. Variable resolution 4 - k meshes: Concepts and applications. Computer Graphics Forum 19 (2000) 195-212
48. Velho L., Medeiros E., and Lopes H. C++ topological operators for mesh manipulation (2005). http://w3.impa.br/~esdras/tops
49. Velho L., and Zorin D. 4-8 subdivision. Computer-Aided Geometric Design 18 5 (2001) 397-427 (special issue on subdivision techniques)
50. Vieira A.W., Velho L., Lopes H., Tavares G., and Lewiner T. Fast stellar mesh simplification. SIBGRAPI. October 2003 (2003), IEEE Press 27-34
51. Weiler K. Edge-based data structures for solid modeling in curved-surface environments. IEEE Computer Graphics and Applications 5 1 (1985) 21-40