Super space clothoids

ACM Transactions on Graphics

Volumn 32, Issue 4, 2013, Pages

  Casati, Romain ^a   Bertails Descoubes, Florence ^a  

^a UNIV GRENOBLE ALPES   (France)

Author keywords

3D Euler spiral; Power series; Thin elastic rod

Indexed keywords

3D EULER SPIRAL; CLOSED FORM SOLUTIONS; DIFFERENTIAL OPERATION; KINEMATICS AND DYNAMICS; POWER SERIES; POWER SERIES EXPANSIONS; THIN ELASTIC RODS; TIME-STEPPING SCHEMES;

ANIMATION; THREE DIMENSIONAL;

KINEMATICS;

EID: 84880842730     PISSN: 07300301     EISSN: 15577368     Source Type: Journal    
DOI: 10.1145/2461912.2461962     Document Type: Article

References (32)

1. ANTMAN, S. 1995. Nonlinear Problems of Elasticity. Springer Verlag.
2. AUDOLY, B., AND POMEAU, Y. 2010. Elasticity and Geometry: from hair curls to the nonlinear response of shells. Oxford University Press.
3. BARAFF, D., AND WITKIN, A. 1998. Large steps in cloth simulation. In Computer Graphics Proceedings (Proc. ACM SIGGRAPH' 98 ), 43-54.
4. BENHAM, C., AND MIELKE, S. 2005. DNA mechanics. Annual Review of Biomedical Engineering 7, 21-53.
5. BERGOU, M., WARDETZKY, M., ROBINSON, S., AUDOLY, B., AND GRINSPUN, E. 2008. Discrete elastic rods. ACM Transactions on Graphics (Proc. ACM SIGGRAPH'08 ) 27, 3, 1-12.
6. BERGOU, M., AUDOLY, B., VOUGA, E., WARDETZKY, M., AND GRINSPUN, E. 2010. Discrete viscous threads. ACM Transactions on Graphics (Proc. ACM SIGGRAPH'10 ) 29, 4.
7. BERTAILS-DESCOUBES, F. 2012. Super-clothoids. Computer Graphics Forum (Proc. Eurographics'12) 31, 2pt2, 509-518.
8. 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. ACM Transactions on Graphics (Proc. ACM SIGGRAPH'06 ) 25, 1180-1187.
9. CGSOCIETY, 2008. SIGGRAPH's Animation Mother. http://www.cgsociety.org/ index.php/CGSFeatures/CGSFeatureSpecial/siggraph animation mother.
10. CHENTANEZ, N., ALTEROVITZ, R., RITCHIE, D., CHO, L., HAUSER, K., GOLDBERG, K., SHEWCHUK, J., AND O'BRIEN, J. 2009. Interactive simulation of surgical needle insertion and steering. ACM Transactions on Graphics (Proc. ACM SIGGRAPH'09 ), 88:1-10.
11. COSSERAT, E., AND COSSERAT, F. 1909. Théorie des corps déformables. Hermann.
12. CRISFIELD, M. A., AND JELENIĆ , G. 1998. Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation. Proc. Royal Society of London, Series A 455, 1983, 1125-1147.
13. DAVIET, G., BERTAILS-DESCOUBES, F., AND BOISSIEUX, L. 2011. A hybrid iterative solver for robustly capturing Coulomb friction in hair dynamics. ACM Transactions on Graphics (Proc. ACM SIGGRAPH Asia'11) 30, 139:1-139:12.
14. DILL, E. 1992. Kirchhoff's theory of rods. Archive for History of Exact Sciences 44, 1, 1-23.
15. GOLDBERG, D. 1991. What every computer scientist should know about floating-point arithmetic. ACM Comp. Surveys 23, 5-48.
16. GORIELY, A., AND NEUKIRCH, S. 2006. Mechanics of climbing and attachment in twining plants. Physical Review Letters 97 (Nov), 184302.
17. GOYAL, S., PERKINS, N., AND LEE, C. 2008. Non-linear dynamic intertwining of rods with self-contact. International Journal of Non-Linear Mechanics 43, 1, 65-73.
18. GRANLUND, T., AND THE GMP DEVELOPMENT TEAM. 2012. GNU MP: The GNU Multiple Precision Arithmetic Library, 5.0.5 ed. http://gmplib.org/.
19. HADAP, S., AND MAGNENAT-THALMANN, N. 2001. Modeling dynamic hair as a continuum. Computer Graphics Forum (Proc. Eurographics'01) 20, 3, 329-338.
20. HADAP, S. 2006. Oriented strands - dynamics of stiff multi-body system. In ACM SIGGRAPH - EG Symposium on Computer Animation (SCA'06), ACM-EG SCA, 91-100.
21. HAIRER, E., LUBICH, C., AND WANNER, G. 2006. Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, vol. 31. Springer Series in Comput. Mathematics.
22. HARARY, G., AND TAL, A. 2012. 3D Euler spirals for 3d shape completion. Computational Geometry 45, 3 (April), 115-126.
23. IVANOVA, E. 2000. On one approach to solving the Darboux problem. Mechanics of Solids 35, 36-43.
24. MEZZAROBBA, M. 2010. NumGfun: a package for numerical and analytic computation with D-finite functions. In ISSAC '10.
25. NEHER, M. 1999. An enclosure method for the solution of linear ODEs with polynomial coefficients. Numerical Functional Analysis and Optimization 20, 779-803.
26. PAI, D. 2002. Strands: Interactive simulation of thin solids using cosserat models. Computer Graphics Forum (Proc. Eurographics' 02) 21, 3, 347-352.
27. POOLE, E. 1936. Introduction to the theory of linear differential equations. Clarendon Press.
28. PRESS, W., TEUKOLSKY, S., VETTERLING, W., AND FLANNERY, B. 2007. Numerical Recipes: The Art of Scientific Computing (Third Edition). Cambridge University Press.
29. REISSNER, E. 1973. One one-dimensional large-displacement finite-strain beam theory. Studies in App. Math. 52, 2, 87-95.
30. SIMO, J., AND VU-QUOC, L. 1986. A three-dimensional finitestrain rod model. part ii: Computational aspects. Computer Methods in Applied Mechanics and Engineering 58, 1, 79-116.
31. SPILLMANN, J., AND TESCHNER, M. 2007. CoRdE: Cosserat rod elements for the dynamic simulation of one-dimensional elastic objects. In ACM SIGGRAPH - EG Symposium on Computer Animation (SCA'07), ACM-EG SCA, 63-72.
32. WARD, K., BERTAILS, F., KIM, T.-Y., MARSCHNER, S., CANI, M.-P., AND LIN, M. 2007. A survey on hair modeling: Styling, simulation, and rendering. IEEE Transactions on Visualization and Computer Graphics (TVCG) 13, 2 (Mar-Apr), 213-34.