Real-time fluid effects on surfaces using the closest point method

Computer Graphics Forum

Volumn 31, Issue 6, 2012, Pages 1909-1923

  Auer, S ^a   MacDonald, C B ^b   Treib, M ^a   Schneider, J ^c   Westermann, R ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b UNIVERSITY OF OXFORD   (United Kingdom)

^c KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Saudi Arabia)

Author keywords

animation; fluid modelling; ray tracing; real time rendering

Indexed keywords

ANIMATION; NUMERICAL METHODS; RAY TRACING; RENDERING (COMPUTER GRAPHICS); THREE DIMENSIONAL COMPUTER GRAPHICS;

FLUID MODELLING; INCOMPRESSIBLE NAVIER STOKES EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS (PDES); POINT REPRESENTATIONS; REAL TIME PERFORMANCE; REAL-TIME RENDERING; SURFACE PARAMETRIZATION; TRIANGULATED SURFACES;

NAVIER STOKES EQUATIONS;

EID: 84874943510     PISSN: 01677055     EISSN: 14678659     Source Type: Journal    
DOI: 10.1111/j.1467-8659.2012.03071.x     Document Type: Article

References (37)

1. Angst R., Thürey N., Botsch M., Gross M.,: Robust and efficient wave simulations on deforming meshes. Computer Graphics Forum (Proc. Pacific Graphics) 27 (2008), 1895-1900.
2. Amanatides J., Woo A.,: A fast voxel traversal algorithm for ray tracing. In Proceedings of Eurographics' 87 (Amsterdam, 1987), pp. 3-10.
3. Bertalmío M., Cheng L.-T., Osher S., Sapiro G.,: Variational problems and partial differential equations on implicit surfaces. Journal of Computational Physics 174, 2 (2001), 759-780.
4. Bürger K., Krüger J., Westermann R.,: Sample-based surface coloring. IEEE Transactions on Visualization and Computer Graphics 16, 5 (2010), 763-776.
5. Chuang M., Luo L., Brown B. J., Rusinkiewicz S., Kazhdan M.,: Estimating the Laplace-Beltrami operator by restricting 3D functions. In Proceedings of the Eurographics Symposium on Geometry Processing (Berlin, 2009), pp. 1475-1484.
6. Chorin A., Marsden J.,: A Mathematical Introduction to Fluid Mechanics, 4th edition. Springer Verlag (Heidelberg, 2000), chapter 1.3, pp. 36-44.
7. Clarenz U., Rumpf M., Telea A.,: Surface processing methods for point sets using finite elements. Computers and Graphics 28, 6 (2004), 851-868.
8. Dong Z., Chen W., Bao H., Zhang H., Peng Q.,: Real-time voxelization for complex polygonal models. In Proceedings of the Computer Graphics and Applications, 12th Pacific Conference (Seoul, 2004), PG '04, pp. 43-50.
9. Dziuk G., Elliott C.,: Surface finite elements for parabolic equations. J. Comput. Math. 25 (2007), 385-407.
10. Dick C., Georgii J., Westermann R.,: A hexahedral multigrid approach for simulating cuts in deformable objects. IEEE Transactions on Visualization and Computer Graphics 17 (2011), 1663-1675.
11. Eisemann E., Décoret X.,: Fast scene voxelization and applications. In Proceedings of the ACM SIGGRAPH 2006 Sketches, ACM, New York (Boston, MA, USA, 2006).
12. Fan Z., Zhao Y., Kaufman A., He Y.,: Adapted unstructured LBM for flow simulation on curved surfaces. In Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation, ACM, NY (Los Angles, CA, USA, 2005), SCA '05, pp. 245-254.
13. Greer J. B.,: An improvement of a recent Eulerian method for solving PDEs on general geometries. Journal of Scientific Computing 29 (December 2006), 321-352.
14. Harris M.,: Parallel prefix sum (scan) with CUDA. NVIDIA Whitepaper, April 2007.
15. Hong Y., Zhu D., Qiu X., Wang Z.,: Geometry-based control of fire simulation. The Visual Computer 26 (September 2010), 1217-1228.
16. Jones M. W., BÃrentzen J. A., Sramek M.,: 3D distance fields: A survey of techniques and applications. IEEE Transactions on Visualization and Computer Graphics 12 (2006), 581-599.
17. Krüger J., Westermann R.,: Linear algebra operators for GPU implementation of numerical algorithms. ACM Transactions on Graphics (TOG) 22, 3 (2003), 908-916.
18. Lo K.-Y., Fu C.-W., Wong T.-T.,: Interactive reaction-diffusion on surface tiles. In Proceedings of Pacific Graphics (Mani, Hawai, USA 2007), pp. 65-74.
19. Liehr F., Preusser T., Rumpf M., Sauter S., Schwen L. O.,: Composite finite elements for 3D image based computing. Computing and Visualization in Science 12 (March 2009), 171-188.
20. Lui L. M., Wang Y., Chan T. F.,: Solving PDEs on manifolds with global conformal parametrization. In VLSM, Springer Verlag, Heidelberg (Beijing, 2005), pp. 307-319.
21. Macdonald C. B., Ruuth S. J.,: Level set equations on surfaces via the Closest Point Method. Journal of Scientific Computing 35 (2-3), (June 2008), 219-240.
22. Macdonald C. B., Ruuth S. J.,: The implicit Closest Point Method for the numerical solution of partial differential equations on surfaces. SIAM Journal of Scientific Computing 31, 6 (2009), 4330-4350.
23. Neill P., Metoyer R., Zhang E.,: Fluid flow on interacting deformable surfaces. In ACM SIGGRAPH 2007 posters (2007), SIGGRAPH '07.
24. Nemitz O., Nielsen M. B., Rumpf M., Whitaker R.,: Finite element methods on very large, dynamic tubular grid encoded implicit surfaces. SIAM Journal of Scientific Computing 31, 3 (San Diego, CA, USA, 2009), 2258-2281.
25. Pantaleoni J.,: VoxelPipe: A programmable pipeline for 3D voxelization. In Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics (Vancouver, Canada, 2011), HPG '11, pp. 99-106.
26. Ruuth S. J., Merriman B.,: A simple embedding method for solving partial differential equations on surfaces. Journal of Computational Physics 227 (January 2008), 1943-1961.
27. Reuter M., Wolter F.-E., Peinecke N.,: Laplace-Beltrami spectra as "Shape-DNA" of surfaces and solids. Computer-Aided Design 38, 4 (2006), 342-366.
28. Schwarz M., Seidel H.-P.,: Fast parallel surface and solid voxelization on GPUs. ACM Transactions on Graphics (Proc. SIGGRAPH Asia) 29 (2010), 179:1-179:9.
29. Stam J.,: Stable fluids. In Proceedings of the 26th annual conference on Computer graphics and interactive techniques (Los Angeles, CA, USA, 1999), SIGGRAPH ' 99, pp. 121-128.
30. Stam J.,: Flows on surfaces of arbitrary topology. ACM Transactions on Graphics 22 (July 2003), 724-731.
31. Shi L., Yu Y.,: Inviscid and incompressible fluid simulation on triangle meshes: Research articles. Computer Animation and Virtual Worlds 15 (July 2004), 173-181.
32. Taubin G.,: A signal processing approach to fair surface design. In Proceedings of the 22nd annual conference on Computer graphics and interactive techniques (Los Angeles, CA, USA 1995), SIGGRAPH ' 95, pp. 351-358.
33. Tian L., Macdonald C. B., Ruuth S. J.,: Segmentation on surfaces with the Closest Point Method. In Proceedings of the ICIP09, 16th IEEE International Conference on Image Processing, Cairo, Egypt (2009), pp. 3009-3012.
34. Turk G.,: Generating textures on arbitrary surfaces using reaction-diffusion. In Proceedings of the 18th annual conference on Computer graphics and interactive techniques, ACM, NY (Los Angeles, NY, USA 1991), SIGGRAPH ' 91, pp. 289-298.
35. Verlet L.,: Computer "experiments" on classical fluids. I. thermodynamical properties of Lennard-Jones molecules. Physical Review 159, 1 (July 1967), pp. 98-103.
36. Wang H., Miller G., Turk G.,: Solving general shallow wave equations on surfaces. In Proceedings of the 2007 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (2007), SCA' 07, pp. 229-238.
37. Zhang L., Chen W., Ebert D. S., Peng Q.,: Conservative voxelization. Vis. Comput. 23, Springer Verlag, NY (August Secaucus, NJ, August 2007), pp. 783-792.