<H1>6 Discussion</H1>
        Our experiments focus on measuring the performance of enforcing inextensibility using CLM compared to strain limiting and stiff springs. In addition to the direct benefit of fast projection on computation times, further benefits can be reaped from the resulting inextensibility. For example, the work of 
Bergou et al. [2006] assumes inextensibility in order to accelerate bending computation. In adopting the velocity-filtering viewpoint, we gain speed, simplicity, and software modularity—all key to a practical and maintainable implementation. However, this comes at a theoretical cost: there is no longer an efficient way to perfectly enforce both ideal inextensibility and ideal collision handling, since one filter must execute before the other, and both ideals correspond to sharp constraints. To enforce both perfectly would require combining them in a single pass, an elegant and exciting prospect from the standpoint of theory, but one which is likely to introduce considerable complexity and convergence challenges. Practically, we observe that this drawback does not cause artifacts in our simulation, for several reasons: first, we execute collision-handling last, to avoid glaring collision artifacts, yet we assert that empirically our strain remains negligible, as required. Second, unlike constraint-enforcement approaches such as 
[Witkin et al. 1990], the inextensibility filter does not assume that the constraint is maintained at the beginning of the timestep and errors are not accumulated during the simulation. Conclusion Despite the fact that the most common fabrics do not visibly stretch when draped over the body, the trend in our community is to favor stretching formulations based on penalty-springs. The consequent numerical difficulties are then addressed by a combination of (a) relaxing realism by allowing 10% strain, and (b) adopting simple iterative strain and strain-rate algorithms that have poor convergence behavior. With Constrained Lagrangian Mechanics as our alternative point of departure, we demonstrate a straightforward filter, with good convergence behavior, for enforcing inextensibility. We provide one immediate and pragmatic approach to fast and realistic fabric simulation using CLM, and we hope that it will spur a renaissance of activity along this direction. Acknowledgments We are grateful for the valuable feedback from our reviewers, and in particular for the keen eyes and diligent guidance of the primary reviewer. We thank OptiTex for providing the 3D garment geometry as well as the animated figurines. We are grateful to David Ismailov for setting up the cloth models, and Ruzz Oved and Yaniv Gorali for lighting and shading our scenes. Our work benefited from the valuable insights of Jerrold E. Marsden, Ari Stern, and Max Wardetzky, and from the generous support of the NSF (MSPA 0528402, CSR 0614770, CAREER 0643268), Autodesk, mental images, NVIDIA, and Elsevier.
      
      
        