Dynamic tubular grid: An efficient data structure and algorithms for high resolution level sets

Journal of Scientific Computing

Volumn 26, Issue 3, 2006, Pages 261-299

  Nielsen, Michael B ^a   Museth, Ken ^b  

^a AARHUS UNIVERSITY   (Denmark)

^b LINKÖPING INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Compact model representations; Deformable surfaces; Interface tracking; Level sets; Partial differential equations

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DATA REDUCTION; HAMILTONIANS; NUMERICAL METHODS; SET THEORY;

COMPACT MODEL REPRESENTATIONS; DEFORMABLE SURFACES; INTERFACE TRACKING; LEVEL SETS;

COMPUTATION THEORY;

EID: 33646239133     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-005-9062-8     Document Type: Article

References (41)

1. Adalsteinsson, D., and Sethian, J. A. (1995). A fast level set method for propagating interlaces. J. Comput. Phys. 118(2), 269-277.
2. Adalsteinsson, D., and Sethian, J. A. (1999). The fast construction of extension velocities in level set methods. J. Comput. Phys. 148, 2-22.
3. Breen, D., Fedkiw, R., Museth, K., Osher, S., Sapiro, G., and Whitaker, R. (2004). Level Sets and PDE Methods for Computer Graphics. ACM SIGGRAPH '04 COURSE #27. ACM SIGGRAPH, Los Angeles, CA. August 2004. ISBN 1-58113-950-X.
4. Bridson, R. (2003). Compuational Aspects of Dynamic Surfaces. Ph.D., thesis, Stanford University, Stanford, California.
5. Chan, T., and Vese, L. (2001). Active contours without edges. IEEE Trans. Image Process. 10, 266-277.
6. Droske, M., Meyer, B., Rumpf, M., and Schaller, C. (2001). An adaptive level set method for medical image segmentation. Lect. Notes Comput. Sci. pp. 412-422.
7. Enright, D., Fedkiw, R., Ferziger, J., and Mitchell, I. (2002). A hybrid particle level set method for improved interface capturing. J. Comput. Phys. 183(1), 83-116.
8. Enright, D., Losasso, F., and Fedkiw, R. (2005). A fast and accurate semi-lagrangian particle level set method. Comput. Struct. 83(6-7), 479-490.
9. Fedkiw, R.. Aslam, T., and Xu, S. (1999). The ghost fluid method for deflagration and detonation discontinuities. J. Comput. Phys. 154, 393-427.
10. Foster, N., and Fedkiw, R. (2001). Practical animation of liquids. In ACM SIGGRAPH '01, ACM Press, pp. 23-30.
11. Osher, S., Losasso, F., and Fedkiw, R. Spatially adaptive techniques for level set methods and incompressible flow. Comput. Fluids (in review).
12. Frisken, S., and Perry, R. (2003). Simple and efficient traversal methods for quadtrees and octrees. J. Graphics Tools 7(3), 1-11.
13. Gibou, F. Fedkiw, R., Caflisch, R., and Osher, S. (2003). A level set approach for the numerical simulation of dendritic growth. J. Sci. Comput. 19(1-3), 183-199.
14. Houston, B., Wiebe, M., and Batty, C. (2004). Rle sparse level sets. In Proceedings of the SIGGRAPH 2004 Conference on Sketches & Applications. ACM Press.
15. Leveque, R. J. (1996). High-resolution conservative algorithms for advection in incompressible flow. SIAM 33(2), 627-665.
16. Losasso, F., Gibou, F., and Fedkiw, R. (2004). Simulating water and smoke with an octree data structure. In ACM SIGGRAPH '04. ACM Press, pp. 457-462.
17. Liu, X. D., Osher, S. J., and Chan, T. (1994). Weighted essentially nonoscillatory schemes. J. Comput. Phys. 115, 200-212.
18. Museth, K., Breen, D., Whitaker, R., and Barr, A. (2002). Level set surface editing operators. ACM Trans. on Graphics (Proc. SIGGRAPH) 21(3), 330-338.
19. Meyers, S. (1997). Effective C++ (2nd ed.): 50 Specific Ways to Improve Your Programs and Designs. Addison-Wesley Longman Publishing Co., Inc.
20. Milne, R. B. (2003). An Adaptive Level Set Method. Ph.D., thesis, Berkeley National Laboratory, Physics Division, Mathematics Department.
21. Min, C. (2004). Local level set method in high dimension and codimension. J. Comput. Phys. 200, 368-382.
22. Nguyen, D., Fedkiw, R., and Jensen, H. W. (2002). Physically based modeling and animation of fire. In ACM SIGGRAPH '02, ACM Press, pp. 721-728.
23. Osher, S. J., and Fedkiw, R. P. (2002). Level Set Methods and Dynamic Implicit Surfaces. Springer, Berlin.
24. Osher, S., and Paragios, N. (eds). (2003). Geometric Level Set Methods in Imaging, Vision and Graphics. Springer-Verlag.
25. Osher, S., and Sethian, J. (1988). Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jaeobi formulations. J. Comput. Phys. 79, 12-19.
26. Osher, S., and Shu, C. W. (1991). High-order essentially nonoscillatory schemes for hamilton-jacobi equations. SIAM J. Num. Anal 28, 907-922.
27. Peng, D., Merriman, B., Osher, S., Zhao, H., and Kang, M. (1999). A pde-based fast local level set method. J. Comput. Phys. 155(2). 410-438.
28. Rudin, L., Osher, S., and Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms. Physica D 60, 259-268.
29. Sussman, M., Almgren, A. S., Bell, J. B., Colella, P., Howell, L. H., and Welcome, M. L. (1999). An adaptive level set approach for incompressible two-phase flows. J. Comput. Phys. 148, 81-124.
30. Samet, H. (1990). Applications of Spatial Data Structures: Computer Graphics, Image Processing, GIS. Addison-Wesley, Reading, MA.
31. Sethian, J. A. (1996). A fast marching level set method for monotonically advancing fronts. Proc. Nat. Acad. Sci. USA 93(4), 1591-1595.
32. Sethian, J. A. (1999). Level Set Methods and Fast Marching Methods, Second edition Cambridge University Press, Cambridge, UK.
33. Stolte, N., and Kaufman, A. (1998). Parallel spatial enumeration of implicit surfaces using interval arithmetic for octree generation and its direct visualization. In Implicit Surfaces '98, pp. 81-87.
34. Shu, C. W., and Osher, S. (1988). Efficient implementation of essentially non-oscillatory shock capturing schemes. J. Comput. Phys. 77, 439-471.
35. Sussman, M., Smereka, P., and Osher, S. (1994). A level set approach to computing solutions to incompressible two-flow. J. Comput. Phys. 114, 146-159.
36. Strain, J. A. (1999). Tree methods for moving interfaces. J. Comput. Phys. 151(2). 616-648.
37. Tsitsiklis, J. N. (1994). Efficient algorithms for globally optimal trajectories. Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista, LF, pp. 1368-1373.
38. Tsitsiklis, J. N. (1995). Efficient algorithms for globally optimal trajectories. IEEE Trans. Automat. Contr. 40, 1528-1538.
39. Whitaker, R. T. (1998). A level-set approach to 3d reconstruction from range data. Int. J. Comput. Vision 29(3), 203-231.
40. Westermann, R., Kobbelt, L., and Ertl, T. (1999). Real-time exploration of regular volume data by adaptive reconstruction of isosurfaces. Visual Comput. 15(2), 100-111.
41. Zhao, H., Osher, S., Merrian, B., and Kang, M. (2000). Implicit and nonparametric shape reconstruction from unorganized data using a variational level set method. Comput. Vision Image understand. 80, 294-314.