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Proceedings of the 20th International Meshing Roundtable pp 387–403Cite as

Hybrid Approach for Repair of Geometry with Complex Topology

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Summary

A discrete geometry can have artifacts such as holes, intersections, non-manifold edges, mesh fragment among other defects depending upon its origin. These kinds of defects sometime cause the geometry to be unsuitable for any further use in computational simulation in absence of a satisfactory geometry repair technique. There are two main approaches to geometry repair, surface based and volume based. Surface based approaches, in general, provide better quality results when they work but require that the input model already satisfies certain quality requirements to be able to guarantee a valid output. Many of these requirements cannot even be met or checked automatically. Volume based approaches, in general, can guarantee watertightness but they usually significantly change the underlying model in this process and are computationally more expensive.

A hybrid approach for mesh repair, combining surface based approach and a two step volume based approach is being presented in this paper. The two steps in the volume based approach are heat diffusion solution as the first step and Poisson surface reconstruction from oriented points in 3D space as the second step. This approach presents a reliable method for the repair of those defective discrete surface geometries which otherwise could not be completely repaired using existing surface-based techniques due to geometric and topological complexities presented as holes, isles, intersections and small overlaps.

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References

  1. Botsch, M., Pauly, M., Kobbelt, L., Alliez, P., Lévy, B., Bischoff, S., Rössl, C.: Geometric modeling based on polygonal meshes. In: ACM SIGGRAPH 2007 Courses - International Conference on Computer Graphics and Interactive Techniques (2007)

    Google Scholar 

  2. Turk, G., Levoy, M.: Zippered polygon meshes from range images. In: Proceedings of ACM SIGGRAPH 1994, pp. 311–318 (1994)

    Google Scholar 

  3. Barequet, G., Sharir, M.: Filling gaps in the boundary of a polyhedron. Computer Aided Geometric Design 12, 207–229 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  4. Barequet, G., Kumar, S.: Repairing CAD Models. Proceedings of IEEE Visualization, 363–370 (1997)

    Google Scholar 

  5. Guéziec, A., Taubin, G., Lazarus, F., Horn, B.: Cutting and Stitching: Converting Computer sets of Polygons to Manifold Surfaces. IEEE Transactions on Visualization and Graphics 7(2), 136–151 (2001)

    Article  Google Scholar 

  6. Borodin, P., Novotni, M., Klein, R.: Progressive Gap Closing for mesh repairing. In: Vince, J., Earnshaw, R. (eds.) Advances in Modelling, Animation and Rendering, pp. 201–213. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  7. Liepa, P.: Filling Holes in Meshes. In: Proceedings of the 2003 Eurographics/ACM SIGGRAPH Symposium on Geometry processing, Eurographics Association, pp. 200–205 (2003)

    Google Scholar 

  8. Jun, Y.: A Piecewise Hole Filling Algorithm in Reverse Engineering. Computer-Aided Design 37, 263–270 (2005)

    Article  Google Scholar 

  9. Branch, J., Prieto, F., Boulanger, P.: A Hole-Filling Algorithm for Triangular Meshes using Local Radial Basis Function. In: Proceedings of the 15th International Meshing Roundtable, pp. 411–431. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Pernot, J.P., Moraru, G., Vernon, P.: Filling holes in meshes using a mechanical model to simulate the curvature variation minimization. Computer and Graphics 30(6), 892–902 (2006)

    Article  Google Scholar 

  11. Kumar, A., Shih, M.A., Ito, Y., Ross, H.D., Soni, K.B.: A Hole-Filling Algorithm Using Non-Uniform Rational B-Splines. In: Proceedings of 16th International Meshing Roundtable, pp. 169–182. Springer, Heidelberg (2007), ISBN: 978-3-540-75102-1

    Google Scholar 

  12. Kumar, A., Ito, Y., Yu, T., Ross, H.D., Shih, M.A.: A novel hole patching algorithm for discrete geometry using non-uniform rational B-spline. International Journal for Numerical Methods in Engineering (2011), http://onlinelibrary.wiley.com/doi/10.1002/nme.3157/abstract

  13. Lorenson, E.W., Cline, E.H.: Marching Cubes: A high resolution 3D surface construction algorithm. ACM Computer Graphics 21(4) (1987)

    Google Scholar 

  14. Curless, B., Levoy, M.: A volumetric method for building complex models from range images. Computer Graphics 30, 303–312 (1996)

    Google Scholar 

  15. Murali, M.T., Funkhouser, A.T.: Consistent solid and boundary representations from arbitrary polygonal data. In: Proceedings of Symposium on Interactive 3D Graphics, pp. 155–162 (1997)

    Google Scholar 

  16. Davis, J., Marschner, S.R., Garr, M., Levoy, M.: Filling holes in complex surfaces using volumetric diffusion. In: Proceedings of First International Symposium on 3D Data Processing, Visualization, Transmission, pp. 428–861 (2002)

    Google Scholar 

  17. Nooruddin, F.S., Turk, G.: Simplification and repair of polygonal models using volumetric techniques. IEEE Transactions on Visualization and Computer Graphics 9(2), 191–205 (2003)

    Article  Google Scholar 

  18. Ju, T.: Robust repair of polygonal models. In: Proceedings of ACM SIGGRAPH 2004; ACM Transactions on Graphics 23, 888–895 (2004)

    Google Scholar 

  19. Bischoff, S., Pavic, D., Kobbelt, L.: Automatic restoration of polygon models. Transactions on Graphics 24(4), 1332–1352 (2005)

    Article  Google Scholar 

  20. Podolak, J., Rusinkiewicz, S.: Atomic volumes for mesh completion. In: Symposium on Geometry Processing (2005)

    Google Scholar 

  21. Hoppe, H., DeRose, T., DuChamp, T., HalStead, M., Jin, H., McDonald, J., Schweitzer, J., Stuetzle, W.: Piecewise Smooth Surface Reconstruction. In: Proceedings of ACM SIGGRAPH 1994, New York, NY, pp. 295–302 (1994)

    Google Scholar 

  22. Amenta, N., Bern, M.: Surface Reconstruction by Vornoi Filtering. Discrete & Computational Geometry 22(4), 481–504 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  23. Amenta, N., Hoi, S.C., Kolluri, R.: The power crust, unions of balls, and the medial axis transform. Computational Geometry: Theory and Applications 19, 127–153 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  24. Carr, C.J., Beatson, K.R., Cherrie, B.J., Mitchell, J.T., Evans, R.T., Fright, R.W., McCallum, C.B.: Reconstruction and representation of 3D objects with Radial Basis functions. In: Proceedings of ACM SIGGRAPH 2001, pp. 67–76 (2001)

    Google Scholar 

  25. Dey, K.T., Goswami, S.: Tight Cocone: A Water-tight Surface Reconstructor. Journal of Computing and Information Science in Engineering 3(4), 302–307 (2003)

    Article  Google Scholar 

  26. Dey, K.T., Goswami, S.: Provable surface reconstruction from noisy samples. Computational Geometry 35(1-2), 124–141 (2004)

    Article  MathSciNet  Google Scholar 

  27. Shen, C., O’Brien, F.J., Shewchuk, R.J.: Interpolating and approximating implicit surfaces from polygon soup. In: Proceedings of ACM SIGGRAPH 2004, pp. 896–904 (2004)

    Google Scholar 

  28. Casciola, G., Lazzaro, D., Montefusco, B.L., Morigi, S.: Fast surface reconstruction and hole filling using positive definite radial basis functions. Journal of Numerical Algorithms 39, 289–305 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  29. Kazhdan, M., Bolitho, M., Hoppe, H.: Poisson Surface Reconstruction. In: Proceedings of the fourth Eurographics Symposium on Geometry processing (SGP 2006), Switzerland, pp. 61–70 (2006)

    Google Scholar 

  30. Mullen, P., Goes, D.F., Desbrun, M., Cohen-Steiner, D., Alliez, P.: Signing the Unsigned: Robust Surface Reconstruction from Raw Pointsets. In: Eurographics Symposium on Geometry Processing 2010, vol. 29(5), pp. 1733–1741 (2010)

    Google Scholar 

  31. Doria, D., Gelas, A.: Poisson Surface Reconstruction for VTK. The VTK Journal (2010), http://www.insight-journal.org/download/viewpdf/718/2/download

  32. Akenine-Möller, T.: Fast 3D triangle-box overlap testing. In: Fujii, J. (ed.) ACM SIGGRAPH 2005 Courses, SIGGRAPH 2005. ACM, New York (2005)

    Google Scholar 

  33. Akenine-Möller, T.: AABB-triangle overlap test code (2010), Source code is located at, http://jgt.akpeters.com/papers/AkenineMoller01/tribox.html

  34. See Diffusion Equation on Wikipedia (2011), http://en.wikipedia.org/wiki/Diffusion_equation

  35. Stanford Bunny at The Stanford 3D Scanning Repository(2011), http://graphics.stanford.edu/data/3Dscanrep/

  36. Saboret, L., Attene, M., Alliez, P.: Laurent Hand at AIM@SHAPE Shape Repository (2011), http://shapes.aim-at-shape.net/viewgroup.php?id=785

  37. Saboret, L., Attene, M., Alliez, P.: Chinese Lion at AIM@SHAPE Shape Repository (2011), http://shapes.aim-at-shape.net/viewgroup.php?id=783

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Authors and Affiliations

  1. University of Alabama, Birmingham, AL, USA

    Amitesh Kumar & Alan M. Shih

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  1. Amitesh Kumar
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  2. Alan M. Shih
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Editors and Affiliations

  1. Sandia National Laboratories, P.O. Box 5800, 87185, Albuquerque, NM, USA

    William Roshan Quadros

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© 2011 Springer-Verlag Berlin Heidelberg

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Kumar, A., Shih, A.M. (2011). Hybrid Approach for Repair of Geometry with Complex Topology. In: Quadros, W.R. (eds) Proceedings of the 20th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24734-7_21

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  • DOI: https://doi.org/10.1007/978-3-642-24734-7_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24733-0

  • Online ISBN: 978-3-642-24734-7

  • eBook Packages: EngineeringEngineering (R0)

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