1. Fundamentals of Computer Animation Flexible Objects (2)

2. Hair and strand-like deformable models

3. Strand-like deformable models Hair, sutures, cables, and other 1D structures Flexible chains –geometrically large deformation Twist DOF makes things more interesting Application determines utility of physically based models

4. Faking Dynamics of Ropes and Springs Ronen Barzel. IEEE Computer Graphics & Applications. 17(3), pp. 31-39, 1997. Animator key frames amplitudes of shape functions

15. Recall...

21. Some other approaches Could add torsional springs –[Rosenblum et al. 91] –[Daldegan et al. 93] Simulated Knot Tying. J.M. Phillips, A.M. Ladd, L.E. Kavraki. IEEE International Conference on Robotics and Automation 2002.Simulated Knot Tying See webpage for more examples. From [Hadap and Magnenat-Thalmann 01]

22. Open Kinematic Chains Hair is basically inextensible  numerical stiffness Multibody open chain approx. is now common for hair Can be solved efficiently Articulated-Body Method –Reduced coordinate formulation –O(n) forward dynamics –Featherstone, R., Robot Dynamics Algorithms, Kluwer, Boston, 1987. Could (of course) use fast O(n) Lagrange multiplier methods

23. Interactive Multiresolution Hair Modeling and Editing Tae-Yong Kim, Ulrich Neumann. ACM Transactions on Graphics. 21(3), pp. 620-629, 2002. Sometimes physics just gets in the way Hairstyling doesn’t require physically accurate hair Good survey: –N.Magnenat-Thalmann, S.Hadap, P.Kalra, State of the Art in Hair Simulation, International Workshop on Human Modeling and Animation, Seoul, Korea, Korea Computer Graphics Society, pp. 3-9, June, 2002.State of the Art in Hair Simulation

24. Interactive Multiresolution Hair Modeling and Editing Tae-Yong Kim, Ulrich Neumann. ACM Transactions on Graphics. 21(3), pp. 620-629, 2002.

25. A Practical Model for Hair Mutual Interactions Johnny T. Chang, Jingyi Jin, Yizhou Yu. ACM SIGGRAPH Symp. on Computer Animation. pp. 73-80, 2002. Recent example “Static links” Hair-hair interactions Hair interpolated using guide hairs Use Featherstone’s algorithm

26. A Practical Model for Hair Mutual Interactions Johnny T. Chang, Jingyi Jin, Yizhou Yu. ACM SIGGRAPH Symp. on Computer Animation. pp. 73-80, 2002.

27. Eric Plante, Marie-Paule Cani, Pierre Poulin, Capturing the Complexity of Hair Motion, GMOD number 1 volume 64, january 2002. Capturing the Complexity of Hair Motion