“Multimaterial mesh-based surface tracking” by Da, Batty and Grinspun
Conference:
Type(s):
Title:
- Multimaterial mesh-based surface tracking
Session/Category Title: Mesh-Based Simulation
Presenter(s)/Author(s):
Moderator(s):
Abstract:
We present a triangle mesh-based technique for tracking the evolution of three-dimensional multimaterial interfaces undergoing complex deformations. It is the first non-manifold triangle mesh tracking method to simultaneously maintain intersection-free meshes and support the proposed broad set of multimaterial remeshing and topological operations. We represent the interface as a non-manifold triangle mesh with material labels assigned to each half-face to distinguish volumetric regions. Starting from proposed application-dependent vertex velocities, we deform the mesh, seeking a non-intersecting, watertight solution. This goal necessitates development of various collision-safe, label-aware non-manifold mesh operations: multimaterial mesh improvement; T1 and T2 processes, topological transitions arising in foam dynamics and multiphase flows; and multimaterial merging, in which a new interface is created between colliding materials. We demonstrate the robustness and effectiveness of our approach on a range of scenarios including geometric flows and multiphase fluid animation.
References:
1. Alexa, M. 2002. Recent advances in mesh morphing. Computer Graphics Forum 21, 2, 173–198.Google ScholarCross Ref
2. Anderson, J. C., Garth, C., Duchaineau, M. A., and Joy, K. I. 2010. Smooth, volume-accurate material interface reconstruction. IEEE TVCG 16, 5, 802–814. Google ScholarDigital Library
3. Bargteil, A. W., O’Brien, J. F., Goktekin, T. G., and Strain, J. A. 2006. A semi-Lagrangian contouring method for fluid simulation. ACM Trans. Graph. 25, 1 (Jan.), 19–38. Google ScholarDigital Library
4. Batty, C., and Bridson, R. 2008. Accurate viscous free surfaces for buckling, coiling, and rotating liquids. In Symposium on Computer Animation, 219–228. Google ScholarDigital Library
5. Bernstein, G., and Wojtan, C. 2013. Putting holes in holey geometry: Topology change for arbitrary surfaces. ACM Trans. Graph. (SIGGRAPH) 32, 4, 34. Google ScholarDigital Library
6. Bojsen-Hansen, M., and Wojtan, C. 2013. Liquid surface tracking with error compensation. ACM Trans. Graph. (SIGGRAPH) 32, 4, 79:1–79:10. Google ScholarDigital Library
7. Brakke, K. 1992. The surface evolver. Experimental Mathematics 1, 2, 141–165.Google ScholarCross Ref
8. Bridson, R., Fedkiw, R., and Anderson, J. 2002. Robust treatment of collisions, contact and friction for cloth animation. ACM Trans. Graph. (SIGGRAPH) 21, 3, 594–603. Google ScholarDigital Library
9. Brochu, T., and Bridson, R. 2009. Robust topological operations for dynamic explicit surfaces. SIAM J. Sci. Comput. 31, 4, 2472–2493. Google ScholarDigital Library
10. Brochu, T., Batty, C., and Bridson, R. 2010. Matching fluid simulation elements to surface geometry and topology. ACM Trans. Graph. (SIGGRAPH) 29, 4, 47. Google ScholarDigital Library
11. Brochu, T., Edwards, E., and Bridson, R. 2012. Efficient geometrically exact continuous collision detection. ACM Trans. Graph. (SIGGRAPH) 31, 4, 96. Google ScholarDigital Library
12. Campen, M., and Kobbelt, L. 2010. Exact and robust (self-)intersections for polygonal meshes. Computer Graphics Forum (Eurographics) 29, 2 (June), 397–406.Google ScholarCross Ref
13. Clark, B., Ray, N., and Jiao, X. 2012. Surface mesh optimization, adaption, and untangling with high-order accuracy. In International Meshing Roundtable, Springer, Berlin, X. Jiao and J.-C. Weill, Eds., 385–402.Google Scholar
14. Clausen, P., Wicke, M., Shewchuk, J. R., and O’Brien, J. F. 2013. Simulating liquids and solid-liquid interactions with Lagrangian meshes. ACM Trans. Graph. 32, 2, 17. Google ScholarDigital Library
15. Crane, K., Pinkall, U., and Schröder, P. 2013. Robust fairing via conformal curvature flow. ACM Trans. Graph. (SIGGRAPH) 32, 4, 61. Google ScholarDigital Library
16. Da, F., Batty, C., and Grinspun, E. 2014. A convergence study of multimaterial mesh-based surface tracking. Tech. rep., Columbia University.Google Scholar
17. de Sousa, F. S., Mangiavacchi, N., Nonato, L. G., Castelo, A., Tomé, M. F., and McKee, S. 2004. A front-tracking/front-capturing method for the simulation of 3D multi-fluid flows with free surfaces. J. Comp. Phys. 198, 2, 469–499. Google ScholarDigital Library
18. Du, J., Fix, B., Glimm, J., Jia, X., Li, X., Li, Y., and Wu, L. 2006. A simple package for front tracking. J. Comp. Phys. 213, 2, 613–628. Google ScholarDigital Library
19. Dyadechko, V., and Shashkov, M. 2008. Reconstruction of multi-material interfaces from moment data. J. Comp. Phys. 227, 11, 5361–5384. Google ScholarDigital Library
20. Eckstein, I., Pons, J.-P., Tong, Y., Kuo, C.-C. J., and Desbrun, M. 2007. Generalized surface flows for mesh processing. In Symposium on Geometry Processing, 183–192. Google ScholarDigital Library
21. Enright, D., Fedkiw, R., Ferziger, J., and Mitchell, I. 2002. A hybrid particle level set method for improved interface capturing. J. Comp. Phys. 183, 1, 83–116. Google ScholarDigital Library
22. Glimm, J., Grove, J. W., Li, X., Shyue, K.-m., Zeng, Y., and Zhang, Q. 1998. Three-dimensional front tracking. SIAM J. Sci. Comput. 19, 3, 703–727. Google ScholarDigital Library
23. Glimm, J., Grove, J. W., Li, X. L., and Tan, D. C. 2000. Robust computational algorithms for dynamic interface tracking in three dimensions. SIAM J. Sci. Comput. 21, 6, 2240–2256. Google ScholarDigital Library
24. Harmon, D., Vouga, E., Tamstorf, R., and Grinspun, E. 2008. Robust treatment of simultaneous collisions. ACM Trans. Graph. (SIGGRAPH) 27, 3, 23. Google ScholarDigital Library
25. Hirt, C. W., and Nichols, B. D. 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comp. Phys. 39, 1, 201–225.Google ScholarCross Ref
26. Jiao, X., Colombi, A., Ni, X., and Hart, J. 2010. Anisotropic mesh adaptation for evolving triangulated surfaces. Engineering with Computers 26, 4, 363–376. Google ScholarDigital Library
27. Jiao, X. 2007. Face offsetting: A unified approach for explicit moving interfaces. J. Comp. Phys. 220, 2, 612–625. Google ScholarDigital Library
28. Kim, B. 2010. Multiphase fluid simulation using regional level sets. ACM Trans. Graph. (SIGGRAPH Asia) 29, 6, 175. Google ScholarDigital Library
29. Kuprat, A., George, D., Straub, G., and Demirel, M. C. 2003. Modeling microstructure evolution in three dimensions with Grain3D and LaGriT. Computational Materials Science 28, 1, 199–208.Google ScholarCross Ref
30. Lazar, E. 2011. The evolution of cellular structures via curvature flow. PhD thesis, Columbia University.Google Scholar
31. Losasso, F., Shinar, T., Selle, A., and Fedkiw, R. 2006. Multiple interacting liquids. ACM Trans. Graph. (SIGGRAPH) 25, 3, 812–819. Google ScholarDigital Library
32. McKee, S., Tomé, M. F., Ferreira, V. G., Cuminato, J. A., Castelo, A., de Sousa, F. S., and Mangiavacchi, N. 2008. The MAC method. Computers & Fluids 37, 8 (Sept.), 907–930.Google ScholarCross Ref
33. Meyer, M., Desbrun, M., Schröder, P., and Barr, A. 2002. Discrete differential-geometry operators for triangulated 2-manifolds. In VisMath, Springer-Verlag, Berlin, Germany, 35–54.Google Scholar
34. Meyer, M., Whitaker, R. T., Kirby, R. M., Ledergerber, C., and Pfister, H. 2008. Particle-based sampling and meshing of surfaces in multimaterial volumes. IEEE TVCG 14, 6, 1539–1546. Google ScholarDigital Library
35. Misztal, M., Erleben, K., Bargteil, A. W., Christensen, B. B., Baerentzen, A., and Bridson, R. 2012. Multiphase flow of immiscible fluids on unstructured moving meshes. In Symposium on Computer Animation, Eurographics Association, Lausanne, Switzerland, 97–106. Google ScholarDigital Library
36. Mora, L. B., Gottstein, G., and Schvindlerman, L. S. 2008. Three-dimensional grain growth: Analytical approaches and computer simulations. Acta Materialia 56, 1, 5915–5926.Google ScholarCross Ref
37. Müller, M., Solenthaler, B., Keiser, R., and Gross, M. 2005. Particle-based fluid-fluid interaction. In Symposium on Computer Animation, ACM, Los Angeles, CA, USA, 237–244. Google ScholarDigital Library
38. Müller, M. 2009. Fast and robust tracking of fluid surfaces. In Symposium on Computer Animation, ACM, New York, NY, USA, 237–245. Google ScholarDigital Library
39. Narain, R., Samii, A., and O’Brien, J. F. 2012. Adaptive anisotropic remeshing for cloth simulation. ACM Trans. Graph. (SIGGRAPH Asia) 31, 6, 147. Google ScholarDigital Library
40. Osher, S., and Fedkiw, R. 2002. Level Set Methods and Dynamic Implicit Surfaces. Springer, New York.Google Scholar
41. Pan, H., Choi, Y.-K., Liu, Y., Hu, W., Du, Q., Polthier, K., Zhang, C., and Wang, W. 2012. Robust modeling of constant mean curvature surfaces. ACM Trans. Graph. (SIGGRAPH) 31, 4, 85. Google ScholarDigital Library
42. Pons, J.-P., and Boissonnat, J.-D. 2007. A Lagrangian approach to dynamic interfaces through kinetic triangulation of the ambient space. Computer Graphics Forum 26, 2, 227–239.Google ScholarCross Ref
43. Pons, J.-P., and Boissonnat, J.-D. 2007. Delaunay deformable models: Topology-adaptive meshes based on the restricted delaunay triangulation. In CVPR, IEEE, Minneapolis, Minnesota, USA, 1–8.Google Scholar
44. Quan, S., and Schmidt, D. P. 2007. A moving mesh interface tracking method for 3D incompressible two-phase flows. Journal of Computational Physics 221, 2, 761–780. Google ScholarDigital Library
45. Quan, S., Lou, J., and Schmidt, D. P. 2009. Modeling merging and breakup in the moving mesh interface tracking method for multiphase flow simulations. Journal of Computational Physics 228, 7, 2660–2675. Google ScholarDigital Library
46. Saye, R., and Sethian, J. 2012. Analysis and applications of the Voronoi Implicit Interface Method. J. Comp. Phys. 231, 18, 6051–6085. Google ScholarDigital Library
47. Sethian, J. 1999. Level set methods and fast marching methods. Cambridge University Press.Google Scholar
48. Solenthaler, B., and Pajarola, R. 2008. Density contrast SPH interfaces. In Symposium on Computer Animation, Eurographics Association, Dublin, 211–218. Google ScholarDigital Library
49. Stanculescu, L., Chaine, R., and Cani, M.-P. 2011. Freestyle: Sculpting meshes with self-adaptive topology. Computers and Graphics 35, 3, 614–622. Google ScholarDigital Library
50. Starinshak, D. P., Karni, S., and Roe, P. L. 2014. A new level set model for multimaterial flows. J. Comp. Phys. In press. Google ScholarDigital Library
51. Syha, M., and Weygand, D. 2010. A generalized vertex dynamics model for grain growth in three dimensions. Modelling Simul. Mater. Sci. Eng. 18, 1, 015010.Google ScholarCross Ref
52. Thuerey, N., Wojtan, C., Gross, M., and Turk, G. 2010. A multiscale approach to mesh-based surface tension flows. ACM Trans. Graph. (SIGGRAPH) 29, 3. Google ScholarDigital Library
53. Toutant, A., Mathieu, B., and Lebaigue, O. 2012. Volume-conserving smoothing for front tracking methods. Computers & Fluids 67, 16–25.Google ScholarCross Ref
54. Wakai, F., Enomoto, N., and Ogawa, H. 2000. Three-dimensional microstructural evolution in ideal grain growth – general statistics. Acta Materialia 48, 1, 1297–1311.Google ScholarCross Ref
55. Weaire, D., and Hutzler, S. 2001. Physics of Foams. Oxford University Press, New York.Google Scholar
56. Weygand, D., and Brechet, Y. 1999. Three-dimensional grain growth: a vertex dynamics simulation. Philosophical Magazine B 79, 5, 703–716.Google ScholarCross Ref
57. Wicke, M., Ritchie, D., Klingner, B. M., Burke, S., Shewchuk, J. R., and O’Brien, J. F. 2010. Dynamic local remeshing for elastoplastic simulation. ACM Trans. Graph. (SIGGRAPH) 29, 4, 49. Google ScholarDigital Library
58. Wojtan, C., Thuerey, N., Gross, M., and Turk, G. 2009. Deforming meshes that split and merge. ACM Trans. Graph. (SIGGRAPH) 28, 3, 76. Google ScholarDigital Library
59. Wojtan, C., Thuerey, N., Gross, M., and Turk, G. 2010. Physically-inspired topology changes for thin fluid features. ACM Trans. Graph. (SIGGRAPH) 29, 3, 50. Google ScholarDigital Library
60. Wojtan, C., Muller-Fischer, M., and Brochu, T. 2011. Liquid simulation with mesh-based surface tracking. In SIGGRAPH Courses, ACM, Vancouver, 8. Google ScholarDigital Library
61. Yu, J., Wojtan, C., Turk, G., and Yap, C. 2012. Explicit mesh surfaces for particle based fluids. Computer Graphics Forum (Eurographics) 31, 2, 815–824. Google ScholarDigital Library
62. Yuan, Z., Yu, Y., and Wang, W. 2012. Object-space multiphase implicit functions. ACM Trans. Graph. (SIGGRAPH) 31, 4, 114. Google ScholarDigital Library
63. Zaharescu, A., Boyer, E., and Horaud, R. 2011. Topology-adaptive mesh deformation for surface evolution, morphing, and multiview reconstruction. IEEE TPAMI 33, 4, 823–837. Google ScholarDigital Library
64. Zhao, H.-K., Chan, T., Merriman, B., and Osher, S. 1996. A variational level set approach to multiphase motion. J. Comp. Phys. 127, 1, 179–195. Google ScholarDigital Library
65. Zheng, W., Yong, J.-H., and Paul, J.-C. 2006. Simulation of bubbles. In Symposium on Computer Animation, Eurographics Association, Vienna, 325–333. Google ScholarDigital Library
