Corotational FEM cloth

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Corotational FEM cloth using triangle membrane elements^[1], with the same implicit Euler + CG loop as the mass-spring demo.

50×50 grid, two corners pinned, 4802 triangles. $\mu = 400000$, $\lambda = 100000$, thickness $= 0.01$. Edit the scene above -- changes auto-apply. Click and drag vertices to interact.

Each triangle gets a deformation gradient $F = D_s D_m^{-1}$, then SVD extracts the rotation ($F = U\Sigma V^T,\; R = UV^T$ with reflection fix) for the energy:

$$\Psi = \mu\,\lVert F - R \rVert_F^2 + \tfrac{\lambda}{2}\bigl(\mathrm{tr}(R^T F) - 2\bigr)^2$$

The Hessian uses the Gauss-Newton approximation (drops $\partial R / \partial F$), which stays SPD so CG would converge. Kugelstadt 2018^[2] recovers those terms via operator splitting for better convergence on stiff materials.

Color shows per-triangle area strain (green = rest, red = stretched, blue = compressed). Compared to mass-spring, shear behavior comes from $\mu, \lambda$ directly -- no diagonal springs needed, and refining the mesh doesn't change effective stiffness.

References

1. Müller & Gross 2004 -- Interactive Virtual Materials
2. Kugelstadt et al. 2018 -- Fast Corotated FEM