Discrete elastic rods

SIGGRAPH'08: International Conference on Computer Graphics and Interactive Techniques, ACM SIGGRAPH 2008 Papers 2008

Volumn , Issue , 2008, Pages

  Bergou, Miklós ^a   Wardetzky, Max ^b   Robinson, Stephen ^a   Audoly, Basile ^c   Grinspun, Eitan ^a  

^a Och Spine at New York Presbyterian Hospitals

^b FREIE UNIVERSITÄT BERLIN   (Germany)

^c CNRS   (France)

Author keywords

Discrete differential geometry; Discrete holonomy; Rods; Strands

Indexed keywords

ANGULAR DEVIATIONS; ARBITRARY CROSS SECTIONS; CENTERLINE; DISCRETE DIFFERENTIAL GEOMETRY; DISCRETE HOLONOMY; EFFICIENT TREATMENTS; ELASTIC RODS; FLEXIBLE RODS; GEOMETRIC MODELS; HOLONOMY; PARALLEL TRANSPORTS; PROJECTION METHODS; QUASI STATICS; ROD MODELS; RODS; SIMULATION TECHNIQUES; STRANDS; STRETCHING MODES;

INTERACTIVE COMPUTER GRAPHICS;

COMPUTER GRAPHICS;

EID: 57649088608     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (44)

1. AUDOLY, B., AND POMEAU, Y. 2008. Elasticity and geometry: from hair curls to the nonlinear response of shells, Oxford University Press. To appear.
2. AUDOLY, B., CLAUVELIN, N., AND NEUKIRCH, S. 2007. Elastic knots. Physical Review Letters 99, 16, 164301.
3. AUDOLY, B., CLAUVELIN, N., AND NEUKIRCH, S. 2008. Instabilities of elastic knots under twist. In preparation.
4. BERTAILS, F., AUDOLY, B., CANI, M.-P., QUERLEUX, B., LEROY, F., AND LÉVÊQUE, J.-L. 2006. Super-helices for predicting the dynamics of natural hair. In ACM TOG, 1180-1187.
5. BOBENKO, A. I., AND SURIS, Y. B. 1999. Discrete time lagrangian mechanics on lie groups, with an application to the lagrange top. Comm. in Mathematical Physics 204, 1, 147-188.
6. BROWN, J., LATOMBE, J.-C, AND MONTGOMERY, K. 2004. Real-time knot-tying simulation. Vis. Comp. V20,2, 165-179.
7. CHANG, J., SHEPHERD, D. X., AND ZHANG, J. J. 2007. Cosserat-beam-based dynamic response modelling. Computer Animation and Virtual Worlds 18, 4-5, 429-436.
8. CHOE, B., CHOI, M. G., AND KO, H.-S. 2005. Simulating complex hair with robust collision handling. In SCA '05, 153-160.
9. DE VRIES, R. 2005. Evaluating changes of writhe in computer simulations of supercoiled DNA. J. Chem. Phys. 122, 064905.
10. FALK, R. S., AND XU, J.-M. 1995. Convergence of a second-order scheme for the nonlinear dynamical equations of elastic rods. SJNA 32, 4, 1185-1209.
11. FULLER, F. B. 1971. The writhing number of a space curve. PNAS 68, 4, 815-819.
12. FULLER, F. B. 1978. Decomposition of the linking number of a closed ribbon: a problem from molecular biology. PNAS 75, 8, 3557-3561.
13. GOLDENTHAL, R., HARMON, D., FATTAL, R., BERCOVIER, M., AND GRINSPUN, E. 2007. Efficient simulation of inextensible cloth. In ACM TOG, 49.
14. GOLDSTEIN, R. E., AND LANGER, S. A. 1995. Nonlinear dynamics of stiff polymers. Phys. Rev. Lett. 75, 6 (Aug), 1094-1097.
15. GORIELY, A., AND TABOR, M. 1998. Spontaneous helix hand reversal and tendril perversion in climbing plants. Physical Review Letters 80,7 (Feb), 1564-1567.
16. GORIELY, A. 2006. Twisted elastic rings and the rediscoveries of Michell's instability. Journal of Elasticity 84, 281-299.
17. GOYAL, S., PERKINS, N. C, AND LEE, C. L. 2007. Non-linear dynamic intertwining of rods with self-contact. International Journal of Non-Linear Mechanics In Press, Corrected Proof.
18. GRÉGOIRE, M., AND SCHÖMER, E. 2007. Interactive simulation of one-dimensional flexible parts. CAD 39, 8, 694-707.
19. GRINSPUN, E., ED. 2006. Discrete differential geometry: an applied introduction. ACM SIGGRAPH 2006 Courses.
20. HADAP, S., CANI, M.-P, LIN, M., KIM, T.-Y, BERTAILS, F., MARSCHNER, S., WARD, K., AND KAČIĆ-ALESIĆ, Z. 2007. Strands and hair: modeling, animation, and rendering. ACM SIGGRAPH 2007 Courses, 1-150.
21. HADAP, S. 2006. Oriented strands: dynamics of stiff multi-body system. In SCA '06, 91-100.
22. HAIRER, E., LUBICH, C, AND WANNER, G. 2006. Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations. Series in Comp. Math. Springer.
23. HANSON, A. J. 2006. Visualizing Quaternions. MK/Elsevier.
24. KLAPPER, I. 1996. Biological applications of the dynamics of twisted elastic rods. J. Comp. Phys. 125, 2, 325-337.
25. LANCZOS, C. 1986. The Variational Principles of Mechanics, 4th ed. Dover. langer, J., and singer, D. A. 1996. Lagrangian aspects of the Kirchhoff elastic rod. SIAM Review 38, 4, 605-618.
26. LENOIR, J., COTIN, S., DURIEZ, C., AND NEUMANN, P. 2006. Interactive physically-based simulation of catheter and guidewire. Computer & Graphics 30, 3, 417-423.
27. LIN, C.-C., AND SCHWETLICK, H. R. 2004. On the geometric flow of Kirchhoff elastic rods. SJAM 65, 2, 720-736.
28. MADDOCKS, J. H., AND DICHMANN, D. J. 1994. Conservation laws in the dynamics of rods. Journal of elasticity 34, 83-96.
29. MADDOCKS, J. H. 1984. Stability of nonlinearly elastic rods. Archive for Rational Mechanics and Analysis 85, 4, 311-354.
30. PAI, D. K. 2002. STRANDS: interactive simulation of thin solids using Cosserat models. CGF 21, 3.
31. PHILLIPS, J., LADD, A., AND KAVRAKI, L. 2002. Simulated knot tying. In Proceedings of ICRA 2002, vol. 1, 841-846.
32. PRESS, W. H., VETTERLING, W. T., TEUKOLSKY, S. A., AND FLANNERY, B. P. 2002. Numerical Recipes in C++: the art of scientific computing. Cambridge University Press.
33. RUBIN, M. B. 2000. Cosserat Theories: Shells, Rods and Points. Kluwer Academic Publishers.
34. SHABANA, A. 2001. Computational Dynamics, 2nd ed. John Wiley & Sons, New York.
35. SMITH, R., 2008. Open dynamics engine, http://www.ode.org/.
36. SOMMERFELD, A. 1964. Mechanics of deformable bodies, vol. 2 of Lectures on theoretical physics. Academic Press.
37. SPILLMANN, J., AND TESCHNER, M. 2007. Corde: Cosserat rod elements for the dynamic simulation of one-dimensional elastic objects. In SCA '07, 63-72.
38. SPILLMANN, J., AND TESCHNER, M. 2008. An adaptative contact model for the robust simulation of knots. CGF 27.
39. TERZOPOULOS, D., PLATT, J., BARR, A., AND FLEISCHER, K. 1987. Elastically deformable models. In Proceedings of SIGGRAPH '87, 205-214.
40. THEETTEN, A., GRISONI, L., ANDRIOT, C, AND BARSKY, B. 2006. Geometrically exact dynamic splines. Tech. rep., INRIA.
41. VAN DER HEIJDEN, G. H. M., AND THOMPSON, J. M. T. 2000. Helical and localised buckling in twisted rods: A unified analysis of the symmetric case. Nonlinear Dynamics 21, 1, 71-99.
42. VAN DER HEIJDEN, G. H. M., NEUKIRCH, S., GOSS, V. G. A., AND THOMPSON, J. M. T. 2003. Instability and self-contact phenomena in the writhing of clamped rods. Int. J. Mech. Sci. 45, 161-196.
43. WARD, K., BERTAILS, F., KIM, T.-Y., MARSCHNER, S. R., CANI, M.-P., AND LIN, M. C. 2007. A survey on hair modeling: Styling, simulation, and rendering. IEEE TVCG 13, 2 (Mar./ Apr.), 213-234.
44. YANG, Y, TOBIAS, I., AND OLSON, W. K. 1993. Finite element analysis of DNA supercoiling. J. Chem. Phys. 98, 2, 1673-1686.