CHARMS: A simple framework for adaptive simulation

ACM Transactions on Graphics

Volumn 21, Issue 3, 2002, Pages 281-290

  Grinspun, Eitan ^b   Krysl, Petr ^a   Schröder, Peter ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b NONE

Author keywords

Adaptive computation; Basis function; Multiresolution; Refinement relation; Subdivision

Indexed keywords

ANIMATION; APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; FINITE ELEMENT METHOD; PARTIAL DIFFERENTIAL EQUATIONS; TWO DIMENSIONAL;

ADAPTIVE SIMULATION; CONFORMING HIERARCHICAL ADAPTIVE REFINEMENT METHOD;

THREE DIMENSIONAL COMPUTER GRAPHICS;

EID: 0036995449     PISSN: 07300301     EISSN: None     Source Type: Journal    
DOI: 10.1145/566654.566578     Document Type: Conference Paper

References (54)

1. 2 for the Sparse Representation of Integral Operators. SIAM Journal on Mathematical Analysis 24, 246-262.
2. Arnold, D. N., Mukherjee, A., and Pouly, L. 2001. Locally Adapted Tetrahedra Meshes using Bisection. SIAM Journal on Scientific Computing 22 2, 431-448.
3. Azar, F. S., Metaxas, D. N., and Schnall, M. D. 2001. A Deformable Finite Element Model of the Breast for Predicting Mechanical Deformations under External Perturbations. Academic Radiology 8, 10, 965-975.
4. Bajaj, C., Warren, J., and Xu, G. 2002. A Smooth Subdivision Scheme for Hexahedral Meshes. The Visual Computer, to appear.
5. Bank, R., and Xu, J. 1996. An Algorithm for Coarsening Unstructured Meshes. Numerische Mathematik 73, 1, 1-36.
6. Bey, J. 2000. Simiplicial Grid Refinement: On Freudenthal's Algorithm and the Optimal Number of Congruence Classes. Numerische Mathematik 85, 1-29.
7. Catmull, E., and Clark, J. 1978. Recursively generated B-spline surfaces on arbitrary topological meshes. CAD 10, 6, 350-355.
8. Celniker, G., and Gossard, D. 1991. Deformable Curve and Surface Finite Elements for Free-Form Shape Design. Computer Graphics (Proceedings of SIGGRAPH 91) 25, 4, 257-266.
9. 1-conforming subdivision elements for finite deformation thin-shell analysis. IJNME 51, 7, 813-833.
10. Cirak, F., Ortiz, M., and Schröder, P. 2000. Subdivision surfaces: A new paradigm for thin-shell finite-element analysis. IJNME 47, 12, 2039-2072.
11. Cohen, A., DeVore, R., and Dahmen, W. 2001. Adaptive Wavelet Methods for Elliptic Operator Equations: Convergence Rates. Mathematics of Computation 70, 233, 27-75.
12. Debunne, G., Desbrun, M., Cani, M.-P., and Barr, A. H. 2001. Dynamic Real-Time Deformations Using Space & Time Adaptive Sampling. Proceedings of SIGGRAPH 2001, 31-36.
13. Deslauriers, G., and Dubuc, S. 1989. Symmetric iterative interpolation processes. Constructive Approximation 5, 1, 49-68.
14. Doo, D., and Sabin, M. 1978. Analysis of the behaviour of recursive division surfaces near extraordinary points. CAD 10, 6, 356-360.
15. Dyn, N., Levin, D., and Gregory, J. A. 1990. A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control. ACM TOG 9, 2 (April), 160-169.
16. Forsey, D. R., and Bartels, R. H. 1988. Hierarchical B-Spline Refinement. Computer Graphics (Proceedings of SIGGRAPH 88) 22, 4, 205-212.
17. Foster, N., and Fedkiw, R. 2001. Practical Animation of Liquids. Proceedings of SIGGRAPH 2001, 23-30.
18. Gortler, S. J., and Cohen, M. F. 1995. Hierarchical and Variational Geometric Modeling with Wavelets. 1995 Symposium on Interactive 3D Graphics, 35-42.
19. Gortler, S. J., Schröder, P., Cohen, M. F., and Hanrahan, P. 1993. Wavelet Radiosity. Proceedings of SIGGRAPH 93, 221-230.
20. Gourret, J.-P., Thalmann, N. M., and Thalmann, D. 1989. Simulation of Object and Human Skin Deformations in a Grasping Task. Computer Graphics (Proceedings of SIGGRAPH 89) 23, 3, 21-30.
21. Halstead, M., Kass, M., and DeRose, T. 1993. Efficient, Fair Interpolation Using Catmull-Clark Surfaces. Proceedings of SIGGRAPH 93, 35-44.
22. Hoppe, H. 1996. Progressive Meshes. Proceedings of SIGGRAPH 96, 99-108.
23. House, D. H., and Breen, D. E., Eds. 2000. Coth Modeling and Animation. A.K. Peters.
24. Johnson, C. 2001. Adaptive finite element and local regularization methods for the inverse ECG problem. In Inverse Problems in Electrocardiology, WIT Press, P. Johnston, Ed.
25. Kagan, P., and Fischer, A. 2000. Integrated mechanically based CAE system using B-Spline finite elements CAD 32, 8-9, 539-552.
26. Kobbelt, L. 2000. √3 Subdivision. Proceedings of SIGGRAPH 2000, 103-112.
27. Kober, C., and Muller-Hannemann, M. 2000. Hexahedral Mesh Generation for the Simulation of the Human Mandible. In Proceedings of the 9th International Meshing Roundtable, Sandia National Laboratories, 423-434.
28. Kraft, R. 1997. Adaptive and linearly independent multilevel B-splines. In Surface Fitting and Multiresolution Methods, A. L. Méhauté, C. Rabut, and L. L. Schumaker, Eds., vol. 2. Vanderbilt University Press, 209-218.
29. Krysl, P., Grinspun, E., and Schröder, P. 2002. Natural hierarchical refinement for finite element methods. To appear: IJNME, http://hogwarts.ucsd.edu/~pkrysl/pubs/adref.pdf.
30. Langtangen, H. P. 1999. Computational Partial Differential Equations. Springer Verlag.
31. Lee, S., Wolberg, G., and Shin, S. Y. 1997. Scattered Data Interpolation with Multilevel B-Splines. IEEE TVCG 3, 3, 228-244.
32. Loop, C. 1987. Smooth Subdivision Surfaces Based on Triangles. Master's thesis, University of Utah, Department of Mathematics.
33. Lounsbery, M., DeRose, T. D., and Warren, J. 1997. Multiresolution analysis for surfaces of arbitrary topological type. ACM TOG 16, 1, 34-73.
34. Mandal, C., Qin, H., and Vemuri, B. C. 1997. Dynamic Smooth Subdivision Surfaces for Data Visualization. In IEEE Visualization '97, 371-378.
35. Metaxas, D., and Terzopoulos, D. 1992. Dynamic deformation of solid primitives with constraints. Computer Graphics (Proceedings of SIGGRAPH 92) 26, 2, 309-312.
36. O'Brien, J. F., and Hodgins, J. K. 1999. Graphical Modeling and Animation of Brittle Fracture. In Proceedings of SIGGRAPH 99, 137-146.
37. Rivara, M., and Inostroza, P. 1997. Using Longest-side Bisection Techniques for the Automatic Refinement of Delaunay Triangulations IJNME 40, 4, 581-597.
38. Stam, J. 2001. On Subdivision Schemes Generalizing Uniform B-Spline Surfaces of Arbitrary Degree. CAGD 18, 5 (June), 383-396.
39. Strang, G., and Fix, G. 1973. An Analysis of the Finite Element Method. Wellesley-Cambridge Press.
40. Strang, G., and Nguyen, T. 1996. Wavelets and Filter Banks. Wellesley-Cambridge Press.
41. Strela, V., Heller, P. N., Strang, G., Topiwala, P., and Heil, C. 1999. The Application of Multiwavelet Filterbanks to Image Processing. IEEE TIP 8, 4, 548-563.
42. Terzopoulos, D., and Qin, H. 1994. Dynamic NURBS with Geometric Constraints for Interactive Sculpting. ACM TOG 13, 2, 103-136.
43. Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K. 1987. Elastically Deformable Models. Computer Graphics (Proceedings of SIGGRAPH 87) 21, 4, 205-214.
44. Timoshenko, S., and Woinowsky-Krieger, S. 1959. Theory of Plates and Shells. McGraw-Hill Book Company Inc.
45. Velho, L., and Zorin, D. 2001. 4-8 Subdivision. CAGD 18, 5 (June), 397-427.
46. Warfield, S. K., Ferrant, M., Gallez, X., Nabavi, A., Jolesz, F. A., and Kikinis, R. 2000. Real-time biomechanical simulation of volumetric brain deformation for image guided neurosurgery. In SC 2000: High performance networking and computing conference, vol. 230, 1-16.
47. Welch, W., and Witkin, A. 1992. Variational Surface Modeling. Computer Graphics (Proceedings of SIGGRAPH 92) 26, 2, 157-166.
48. Wu, X., Downes, M. S., Goktekin, T., and Tendick, F. 2001. Adaptive Nonlinear Finite Elements for Deformable Body Simulation Using Dynamic Progressive Meshes. Computer Graphics Forum 20, 3, 349-358.
49. Yserentant, H. 1986. On the multilevel splitting of finite-element spaces. Numerische Mathematik 49, 4, 379-412.
50. Zienkiewicz, O. C., and Taylor, R. L. 2000. The finite element method: The basis, 5 ed., vol. 1. Butterworth and Heinemann.
51. Zorin, D., and Schröder, P., Eds. 2000. Subdivision for Modeling and Animation. Course Notes. ACM Siggraph.
52. Zorin, D., and Schröder, P. 2001. A Unified Framework for Primal/Dual Quadrilateral Subdivision Schemes. CAGD 18, 5, 429-454.
53. Zorin, D., Schröder, P., and Sweldens, W. 1996. Interpolating Subdivision for Meshes with Arbitrary Topology. Proceedings of SIGGRAPH 96, 189-192.
54. Zorin, D. 2000. Smoothness of Subdivision on Irregular Meshes. Constructive Approximation 16, 3, 359-397.